Download Minnesota State Standards Alignment Grades One through Eleven

Minnesota State Standards Alignment
Grades One through Eleven
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Minnesota State Standards Alignment
Standards List with Aligned Product Skills
The Standards List with Aligned Product Skills Report is a standardsoriented document showing the entire list of standards for the subject
and grade on the left side of the report with the aligning product
objectives on the right side. This alignment report shows the breadth
of standards coverage for the purpose and focus of this product.
Note to Educator
.....................................................iii
Grade 1
..................................................... 1
Grade 2
..................................................... 7
Grade 3
....................................................14
Grade 4
....................................................22
Grade 5
....................................................32
Grade 6
....................................................46
Grade 7
....................................................61
Grade 8
....................................................93
Grades 9 - 11
.................................................. 123
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written consent of Renaissance Learning, Inc.
ii
P.O. Box 8036
Wisconsin Rapids, WI 54495-8036
Phone: (800) 338-4204
Fax: (715) 424-4242
www.renlearn.com
Note to Educator:
Thank you for your interest in Renaissance Learning technology. The attached document
contains the alignment between the software and/or instructional materials and the skills
described in the state standards documentation.
At Renaissance Learning, we recognize the impact that the standards-based reform
movement and high-stakes standardized testing have on schools, and we share the
concerns of educators and administrators that students perform well on high-stakes
assessments.
We hope this report answers your questions regarding the alignment of Renaissance
Learning technology and materials to your state standards. If you have any questions
about the attached document, please feel free to call us at (800) 338-4204.
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iii
Accelerated Math
Grade 1
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 1.1 - Number & Operation
MN 1.1.1 - Count, compare and
represent whole numbers up to 120,
with an emphasis on groups of tens
and ones.
MN 1.1.1.1 - Use place value to
Topic 1 - Numbers and
Obj. 19 - Count objects grouped in
describe whole numbers between 10 Operations
tens and ones
and 100 in terms of groups of tens
and ones. Example: Recognize the
numbers 11 to 19 as one group of ten
and a particular number of ones.
Obj. 20 - Model a number to 100
using tens and ones
Obj. 21 - Recognize a number from a
model of tens and ones to 100
MN 1.1.1.2 - Read, write and
represent whole numbers up to 120.
Representations may include
numerals, addition and subtraction,
pictures, tally marks, number lines
and manipulatives, such as bundles
of sticks and base 10 blocks.
Topic 1 - Numbers and
Operations
Obj. 22 - Represent a 2-digit number
as tens and ones
Obj. 23 - Determine the 2-digit
number represented as tens and
ones
Obj. 1 - Read a whole number to 30
Obj. 2 - Read a whole number from
31 to 100
Obj. 3 - Determine the word form of a
whole number to 30
Obj. 4 - Determine the word form of a
whole number from 31 to 100
Obj. 9 - Identify a number to 20
represented by a point on a number
line
Obj. 10 - Locate a number to 20 on a
number line
Obj. 19 - Count objects grouped in
tens and ones
Obj. 20 - Model a number to 100
using tens and ones
Obj. 21 - Recognize a number from a
model of tens and ones to 100
Obj. 30 - Determine equivalent forms
of a number, up to 10
Page 1 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 1.1.1.3 - Count, with and without Topic 1 - Numbers and
Obj. 5 - Count objects to 20
objects, forward and backward from Operations
any given number up to 120.
MN 1.1.1.4 - Find a number that is 10 Topic 1 - Numbers and
more or 10 less than a given number. Operations
Example: Using a hundred grid, find
the number that is 10 more than 27.
Grade 1
Obj. 6 - Count on by ones from a
number less than 100
Obj. 7 - Count back by ones from a
number less than 20
Obj. 8 - Count back by ones from a
number between 20 and 100
Obj. 12 - Determine ten more than or
ten less than a given number
MN 1.1.1.5 - Compare and order
whole numbers up to 100.
Topic 1 - Numbers and
Operations
MN 1.1.1.6 - Use words to describe
the relative size of numbers.
Example: Use the words equal to, not
equal to, more than, less than, fewer
than, is about, and is nearly to
describe numbers.
MN 1.1.1.7 - Use counting and
comparison skills to create and
analyze bar graphs and tally charts.
Example: Make a bar graph of
students' birthday months and count
to compare the number in each
month.
Topic 1 - Numbers and
Operations
Obj. 11 - Determine one more than
or one less than a given number
Obj. 28 - Order whole numbers to
100 in ascending order
Obj. 29 - Order whole numbers to
100 in descending order
Obj. 27 - Compare whole numbers to
100 using words
Topic 4 - Data Analysis and
Statistics
Obj. 88 - Read a 2-category tally
chart
MN 1.1.2 - Use a variety of models
and strategies to solve addition and
subtraction problems in real-world
and mathematical contexts.
MN 1.1.2.1 - Use words, pictures,
Topic 1 - Numbers and
objects, length-based models
Operations
(connecting cubes), numerals and
number lines to model and solve
addition and subtraction problems in
part-part-total, adding to, taking away
from and comparing situations.
Page 2 of 198
Obj. 89 - Use a 2-category tally chart
to represent groups of objects (1
symbol = 1 object)
Obj. 97 - Read a bar graph
Obj. 98 - Use a bar graph to
represent groups of objects
Obj. 26 - Compare sets of objects
using words
081309
Accelerated Math
Grade 1
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 31 - Determine the missing
portion in a partially screened
(hidden) collection of up to 10 objects
MN 1.1.2.2 - Compose and
decompose numbers up to 12 with an
emphasis on making ten. Example:
Given 3 blocks, 7 more blocks are
needed to make 10.
MN 1.1.2.3 - Recognize the
Topic 1 - Numbers and
relationship between counting and
Operations
addition and subtraction. Skip count
by 2s, 5s, and 10s.
MN 1.2 - Algebra
MN 1.2.1 - Recognize and create
patterns; use rules to describe
patterns.
Page 3 of 198
Obj. 32 - Relate a picture model to a
basic addition fact
Obj. 33 - Determine the basic
addition fact shown by a picture
model
Obj. 34 - Relate a number-line model
to a basic addition fact
Obj. 35 - Determine the basic
addition fact shown by a number-line
model
Obj. 36 - Relate a picture model to a
basic subtraction fact
Obj. 37 - Determine the basic
subtraction fact shown by a picture
model
Obj. 38 - Determine the basic
subtraction fact shown by a numberline model
Obj. 39 - Relate a number-line model
to a basic subtraction fact
Obj. 13 - Count by 2s to 50 starting
from a multiple of 2
Obj. 14 - Count by 5s or 10s to 100
starting from a multiple of 5 or 10,
respectively
Obj. 40 - Apply the relationship
between addition and counting on
Obj. 41 - Apply the relationship
between subtraction and counting
back
081309
Accelerated Math
Grade 1
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 1.2.1.1 - Create simple patterns Topic 2 - Algebraic Thinking
Obj. 66 - Extend a repeating picture
using objects, pictures, numbers and
pattern
rules. Identify possible rules to
complete or extend patterns. Patterns
may be repeating, growing or
shrinking. Calculators can be used to
create and explore patterns.
Example: Describe rules that can be
used to extend the pattern 2, 4, 6, 8,
__, __, __ and complete the pattern
33, 43, __, 63, __, 83 or 20, __, __,
17.
MN 1.2.2 - Use number sentences
involving addition and subtraction
basic facts to represent and solve
real-world and mathematical
problems; create real-world situations
corresponding to number sentences.
Obj. 67 - Extend a pictorial growth
pattern
MN 1.2.2.1 - Represent real-world
situations involving addition and
subtraction basic facts, using objects
and number sentences. Example:
One way to represent the number of
toys that a child has left after giving
away 4 of 6 toys is to begin with a
stack of 6 connecting cubes and then
break off 4 cubes.
MN 1.2.2.2 - Determine if equations
involving addition and subtraction are
true. Example: Determine if the
following number sentences are true
or false 7 = 7; 7 = 8 - 1; 5 + 2 = 2 + 5;
4 + 1 = 5 + 2.
MN 1.2.2.3 - Use number sense and
models of addition and subtraction,
such as objects and number lines, to
identify the missing number in an
equation such as: 2 + 4 = __; 3 + __
= 7; 5 = __ - 3.
Page 4 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 1.2.2.4 - Use addition or
subtraction basic facts to represent a
given problem situation using a
number sentence. Example: 5 + 3 = 8
could be used to represent a situation
in which 5 red balloons are combined
with 3 blue balloons to make 8 total
balloons.
Grade 1
MN 1.3 - Geometry & Measurement
MN 1.3.1 - Describe characteristics of
basic shapes. Use basic shapes to
compose and decompose other
objects in various contexts.
MN 1.3.1.1 - Describe characteristics Topic 3 - Geometry and
of two- and three-dimensional
Measurement
objects, such as triangles, squares,
rectangles, circles, rectangular
prisms, cylinders, cones and
spheres. Example: Triangles have
three sides and cubes have eight
vertices (corners).
MN 1.3.1.2 - Compose (combine)
and decompose (take apart) two- and
three-dimensional figures such as
triangles, squares, rectangles,
circles, rectangular prisms and
cylinders. Example 1: Decompose a
regular hexagon into 6 equilateral
triangles; build prisms by stacking
layers of cubes; model an ice cream
cone by composing a cone and half
of a sphere. Example 2: Use a
drawing program to find shapes that
can be made with a rectangle and a
triangle.
MN 1.3.2 - Use basic concepts of
measurement in real-world and
mathematical situations involving
length, time and money.
MN 1.3.2.1 - Measure the length of
an object in terms of multiple copies
of another object. Example: Measure
a table by placing paper clips end-toend and counting.
MN 1.3.2.2 - Tell time to the hour and Topic 3 - Geometry and
half-hour.
Measurement
Page 5 of 198
Obj. 82 - Determine the common
attributes in a set of geometric
shapes
Obj. 76 - Tell time to the hour
Obj. 77 - Tell time to the half hour
081309
Accelerated Math
Grade 1
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 1,
Accelerated Math Second Edition Grade 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 1.3.2.3 - Identify pennies, nickels Topic 1 - Numbers and
Obj. 17 - Determine the value of a
and dimes and find the value of a
Operations
collection of like coins
group of these coins, up to one dollar.
Obj. 18 - Determine the value of a
collection of mixed coins
Page 6 of 198
081309
Accelerated Math
Grade 2
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.1 - Number & Operation
MN 2.1.1 - Compare and represent
whole numbers up to 1000, with an
emphasis on place value.
MN 2.1.1.1 - Read, write and
Topic 1 - Number Sense and
Obj. 1 - Read a whole number to
represent whole numbers up to 1000. Operations
1,000
Representations may include
numerals, addition, subtraction,
multiplication, words, pictures, tally
marks, number lines and
manipulatives, such as bundles of
sticks and base 10 blocks.
MN 2.1.1.2 - Use place value to
Topic 1 - Number Sense and
describe whole numbers between 10 Operations
and 1000 in terms of groups of
hundreds, tens and ones. Know that
100 is ten groups of 10, and 1000 is
ten groups of 100. Example: Writing
853 is a shorter way of writing 8
hundreds + 5 tens + 3 ones.
Obj. 2 - Determine the word form of a
whole number to 1,000
Obj. 12 - Model a number using
hundreds, tens, and ones to 1,000
Obj. 13 - Recognize a number from a
model of hundreds, tens, and ones to
1,000
Obj. 9 - Determine the value of a digit
in a 3-digit number
Obj. 10 - Determine which digit is in a
specified place in a 3-digit whole
number
Obj. 14 - Represent a 3-digit number
as hundreds, tens, and ones
MN 2.1.1.3 - Find 10 more or 10 less
than any given three-digit number.
Find 100 more or 100 less than any
given three-digit number. Example:
Find the number that is 10 less than
382 and the number that is 100 more
than 382.
Page 7 of 198
Obj. 15 - Determine the 3-digit
number represented as hundreds,
tens, and ones
Obj. 16 - Recognize equivalent forms
of a 3-digit number using hundreds,
tens, and ones
081309
Accelerated Math
Grade 2
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.1.1.4 - Round numbers up to
the nearest 10 and 100 and round
numbers down to the nearest 10 and
100. Example: If there are 17
students in the class and granola
bars come 10 to a box, you need to
buy 20 bars (2 boxes) in order to
have enough bars for everyone.
MN 2.1.1.5 - Compare and order
Topic 1 - Number Sense and
Obj. 20 - Compare whole numbers to
whole numbers up to 1000.
Operations
1,000 using words
Obj. 21 - Compare whole numbers to
1,000 using the symbols <, >, and =
MN 2.1.1.6 - Use addition and
subtraction to create and obtain
information from tables, bar graphs
and tally charts.
Topic 4 - Data Analysis and
Statistics
Obj. 98 - Answer a question using
information from a bar graph with a yaxis scale by 2s
MN 2.1.2 - Demonstrate mastery of
addition and subtraction basic facts;
add and subtract one- and two-digit
numbers in real-world and
mathematical problems.
MN 2.1.2.1 - Use strategies to
generate addition and subtraction
facts including making tens, fact
families, doubles plus or minus one,
counting on, counting back, and the
commutative and associative
properties. Use the relationship
between addition and subtraction to
generate basic facts. Example: Use
the associative property to make ten
when adding 5 + 8 = (3 + 2) + 8 = 3 +
(2 + 8) = 3 + 10 = 13.
MN 2.1.2.2 - Demonstrate fluency
with basic addition facts and related
subtraction facts.
MN 2.1.2.3 - Estimate sums and
differences up to 100. Example:
Know that 23 + 48 is about 70.
Page 8 of 198
Obj. 22 - Order whole numbers to
1,000 in ascending order
Obj. 23 - Order whole numbers to
1,000 in descending order
Obj. 92 - Answer a question using
information from a tally chart
Topic 1 - Number Sense and
Operations
Obj. 45 - Estimate the difference of
two 2-digit numbers
081309
Accelerated Math
Grade 2
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.1.2.4 - Use mental strategies
Topic 1 - Number Sense and
Obj. 24 - Determine a number pair
and algorithms based on knowledge Operations
that totals 100
of place value to add and subtract
two-digit numbers. Strategies may
include decomposition, expanded
notation, and partial sums and
differences. Example: Using
decomposition, 78 + 42, can be
thought of as: 78 + 2 + 20 + 20 = 80 +
20 + 20 = 100 + 20 = 120 and using
expanded notation, 34 - 21 can be
thought of as: 30 + 4 - 20 - 1 = 30 20 + 4 - 1 = 10 + 3 = 13.
Obj. 30 - Add money values using
cents or dollars with regrouping
Obj. 31 - Add a 2-digit number to a 1digit number with regrouping
Obj. 32 - Add two 2-digit numbers
with regrouping
Obj. 33 - Add three 2-digit numbers
with one regrouping, sum less than
100
Obj. 37 - Subtract money values
using cents or dollars with one
regrouping
Obj. 38 - Subtract a 1- or 2-digit
number from a 2-digit number with
one regrouping
Obj. 42 - WP: Add or subtract up to 2digit numbers with one regrouping
MN 2.1.2.5 - Solve real-world and
Topic 1 - Number Sense and
mathematical addition and
Operations
subtraction problems involving whole
numbers with up to 2 digits.
Page 9 of 198
Obj. 24 - Determine a number pair
that totals 100
Obj. 29 - Add two 2-digit numbers
with regrouping, given a model
Obj. 30 - Add money values using
cents or dollars with regrouping
Obj. 31 - Add a 2-digit number to a 1digit number with regrouping
Obj. 32 - Add two 2-digit numbers
with regrouping
Obj. 33 - Add three 2-digit numbers
with one regrouping, sum less than
100
Obj. 37 - Subtract money values
using cents or dollars with one
regrouping
081309
Accelerated Math
Grade 2
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 38 - Subtract a 1- or 2-digit
number from a 2-digit number with
one regrouping
Obj. 42 - WP: Add or subtract up to 2digit numbers with one regrouping
MN 2.2 - Algebra
MN 2.2.1 - Recognize, create,
describe, and use patterns and rules
to solve real-world and mathematical
problems.
MN 2.2.1.1 - Identify, create and
Topic 1 - Number Sense and
describe simple number patterns
Operations
involving repeated addition or
subtraction, skip counting and arrays
of objects such as counters or tiles.
Use patterns to solve problems in
various contexts. Example 1: Skip
count by 5 beginning at 3 to create
the pattern 3, 8, 13, 18, __. Example
2: Collecting 7 empty milk cartons
each day for 5 days will generate the
pattern 7, 14, 21, 28, 35, resulting in
a total of 35 milk cartons.
Obj. 3 - Complete a skip pattern
starting from a multiple of 2, 5, or 10
Obj. 4 - Complete a skip pattern of 2,
5, or 10 starting from any number
Topic 2 - Algebraic Thinking
MN 2.2.2 - Use number sentences
involving addition, subtraction and
unknowns to represent and solve realworld and mathematical problems;
create real-world situations
corresponding to number sentences.
Page 10 of 198
Obj. 5 - Count on by 100s from any
number
Obj. 70 - Determine an addition or
subtraction number pattern given a
rule
Obj. 71 - Determine the rule for an
addition or subtraction number
pattern
Obj. 72 - Extend a number pattern
involving addition
Obj. 73 - Extend a number pattern
involving subtraction
081309
Accelerated Math
Grade 2
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.2.2.1 - Understand how to
interpret number sentences involving
addition, subtraction and unknowns
represented by letters. Use objects
and number lines and create realworld situations to represent number
sentences. Example: One way to
represent n + 16 = 19 is by
comparing a stack of 16 connecting
cubes to a stack of 19 connecting
cubes; 24 = a + b can be represented
by a situation involving a birthday
party attended by a total of 24 boys
and girls.
MN 2.2.2.2 - Use number sentences Topic 2 - Algebraic Thinking
Obj. 65 - Determine a missing
involving addition, subtraction, and
addend in a number sentence
unknowns to represent given problem
involving 2-digit numbers
situations. Use number sense and
properties of addition and subtraction
to find values for the unknowns that
make the number sentences true.
Example: How many more players
are needed if a soccer team requires
11 players and so far only 6 players
have arrived? This situation can be
represented by the number sentence
11 - 6 = p or by the number sentence
6 + p = 11.
Obj. 66 - Determine a missing
subtrahend in a number sentence
involving 2-digit numbers
Obj. 67 - Determine equivalent
addition expressions involving 2-digit
numbers
Obj. 68 - WP: Determine a missing
addend or a missing subtrahend
involving 2-digit numbers
Obj. 69 - WP: Use an open sentence
to represent a given situation
MN 2.3 - Geometry & Measurement
MN 2.3.1 - Identify, describe and
compare basic shapes according to
their geometric attributes.
Page 11 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.3.1.1 - Describe, compare, and
classify two- and three-dimensional
figures according to number and
shape of faces, and the number of
sides, edges and vertices (corners).
MN 2.3.1.2 - Identify and name basic Topic 3 - Geometry and
two- and three-dimensional shapes, Measurement
such as squares, circles, and
triangles, rectangles, trapezoids,
hexagons, cubes, rectangular prisms,
cones, cylinders and spheres.
Example: Use a drawing program to
show several ways that a rectangle
can be decomposed into exactly
three triangles.
MN 2.3.2 - Understand length as a
measurable attribute; use tools to
measure length.
MN 2.3.2.1 - Understand the
relationship between the size of the
unit of measurement and the number
of units needed to measure the
length of an object. Example: It will
take more paper clips than
whiteboard markers to measure the
length of a table.
MN 2.3.2.2 - Demonstrate an
Topic 3 - Geometry and
understanding of the relationship
Measurement
between length and the numbers on
a ruler by using a ruler to measure
lengths to the nearest centimeter or
inch. Example: Draw a line segment
that is 3 inches long.
MN 2.3.3 - Use time and money in
real-world and mathematical
situations.
MN 2.3.3.1 - Tell time to the quarter- Topic 3 - Geometry and
hour and distinguish between a.m.
Measurement
and p.m.
Page 12 of 198
Grade 2
Obj. 85 - Identify a parallelogram, a
trapezoid, a pentagon, a hexagon, or
an octagon
Obj. 86 - Decompose a plane shape
composed of three or more simpler
shapes
Obj. 87 - Name a 3-dimensional
geometric shape
Obj. 76 - Measure length in inches
Obj. 77 - Measure length in
centimeters
Obj. 78 - Tell time to the quarter hour
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 2,
Accelerated Math Second Edition Grade 2
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 2.3.3.2 - Identify pennies, nickels,
dimes and quarters. Find the value of
a group of coins and determine
combinations of coins that equal a
given amount. Example: 50 cents can
be made up of 2 quarters, or 4 dimes
and 2 nickels, or many other
combinations.
Grade 2
Page 13 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.1 - Number & Operation
MN 3.1.1 - Compare and represent
whole numbers up to 10,000, with an
emphasis on place value.
MN 3.1.1.1 - Read, write and
Topic 1 - Number Sense and
Obj. 1 - Read a 4- or 5-digit whole
represent whole numbers up to
Operations
number
10,000. Representations may include
numerals, expressions with
operations, words, pictures, number
lines, and manipulatives such as
bundles of sticks and base 10 blocks.
MN 3.1.1.2 - Use place value to
Topic 1 - Number Sense and
describe whole numbers between
Operations
1000 and 10,000 in terms of groups
of thousands, hundreds, tens and
ones. Example: Writing 4,873 is a
shorter way of writing the following
sums: 4 thousands + 8 hundreds + 7
tens + 3 ones; 48 hundreds + 7 tens
+ 3 ones; 487 tens + 3 ones.
Obj. 2 - Determine the word form of a
4- or 5-digit whole number
Obj. 3 - Determine the value of a digit
in a 4- or 5-digit whole number
Obj. 4 - Determine which digit is in a
specified place in a 4- or 5-digit whole
number
Obj. 5 - Represent a 4-digit whole
number as thousands, hundreds,
tens, and ones
Obj. 6 - Determine the 4-digit whole
number represented in thousands,
hundreds, tens, and ones
Obj. 7 - Represent a 4- or 5-digit
whole number in expanded form
Obj. 8 - Determine the 4- or 5-digit
whole number represented in
expanded form
Obj. 9 - Determine an equivalent
form of a 4-digit whole number using
thousands, hundreds, tens, and ones
MN 3.1.1.3 - Find 1000 more or 1000
less than any given four-digit number.
Find 100 more or 100 less than a
given four-digit number.
Page 14 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.1.1.4 - Round numbers to the Topic 1 - Number Sense and
Obj. 27 - Round a 2- to 4-digit whole
nearest 1000, 100 and 10. Round up Operations
number to its greatest place
and round down to estimate sums
and differences. Example 1: 8726
rounded to the nearest 1000 is 9000,
rounded to the nearest 100 is 8700,
and rounded to the nearest 10 is
8730. Example 2: 473 - 291 is
between 400 - 300 and 500 - 200, or
between 100 and 300.
Obj. 28 - Estimate a sum or
difference of whole numbers to
10,000 by rounding
Obj. 30 - Estimate a sum or
difference of 2- to 4-digit whole
numbers using any method
Obj. 31 - Estimate a sum of three 2to 4-digit numbers using any method
MN 3.1.1.5 - Compare and order
whole numbers up to 10,000.
Topic 1 - Number Sense and
Operations
MN 3.1.2 - Add and subtract multidigit whole numbers; represent
multiplication and division in various
ways; solve real-world and
mathematical problems using
arithmetic.
MN 3.1.2.1 - Add and subtract multi- Topic 1 - Number Sense and
digit numbers, using efficient and
Operations
generalizable procedures based on
knowledge of place value, including
standard algorithms.
Obj. 32 - WP: Estimate a sum or
difference of two 3- or 4-digit whole
numbers using any method
Obj. 11 - Compare 4- or 5-digit whole
numbers using the symbols <, >, and
=
Obj. 12 - Order 4- or 5-digit whole
numbers in ascending or descending
order
Obj. 13 - Add 3- and 4-digit numbers
with regrouping
Obj. 14 - Add three 2- to 3-digit whole
numbers
Obj. 15 - Subtract 3- and 4-digit
numbers with regrouping
Obj. 16 - WP: Add or subtract 3- and
4-digit whole numbers with
regrouping
Page 15 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.1.2.2 - Use addition and
Topic 1 - Number Sense and
Obj. 10 - Determine the result of
subtraction to solve real-world and
Operations
changing a digit in a 4- or 5-digit
mathematical problems involving
whole number
whole numbers. Assess the
reasonableness of results based on
the context. Use various strategies,
including the use of a calculator and
the relationship between addition and
subtraction, to check for accuracy.
Example: The calculation 117 - 83 =
34 can be checked by adding 83 and
34.
Obj. 16 - WP: Add or subtract 3- and
4-digit whole numbers with
regrouping
Topic 2 - Algebraic Thinking
Obj. 56 - Determine the missing
addend in a number sentence
involving 3-digit numbers
Obj. 57 - Determine the missing
subtrahend in a number sentence
involving 3-digit numbers
MN 3.1.2.3 - Represent multiplication Topic 1 - Number Sense and
Obj. 33 - Use a multiplication
facts by using a variety of
Operations
sentence to represent an area or an
approaches, such as repeated
array model
addition, equal-sized groups, arrays,
area models, equal jumps on a
number line and skip counting.
Represent division facts by using a
variety of approaches, such as
repeated subtraction, equal sharing
and forming equal groups. Recognize
the relationship between
multiplication and division.
Obj. 34 - Use a division sentence to
represent objects divided into equal
groups
MN 3.1.2.4 - Solve real-world and
Topic 1 - Number Sense and
Obj. 35 - Know basic multiplication
mathematical problems involving
Operations
facts to 10 x 10
multiplication and division, including
both "how many in each group" and
"how many groups" division
problems. Example 1: You have 27
people and 9 tables. If each table
seats the same number of people,
how many people will you put at each
table? Example 2: If you have 27
people and tables that will hold 9
people, how many tables will you
need?
Obj. 36 - Know basic multiplication
facts for 11 and 12
Page 16 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 37 - Know basic division facts to
100 ÷ 10
Obj. 38 - Know basic division facts
for 11 and 12
Obj. 39 - WP: Multiply using basic
facts to 10 x 10
Obj. 40 - WP: Divide using basic
facts to 100 ÷ 10
Obj. 41 - Complete a multiplication
and division fact family
MN 3.1.2.5 - Use strategies and
Topic 1 - Number Sense and
Obj. 42 - Multiply a 1-digit whole
algorithms based on knowledge of
Operations
number by a multiple of 10 to 100
place value and properties of addition
and multiplication to multiply a two- or
three-digit number by a one-digit
number. Strategies may include
mental strategies, partial products,
the standard algorithm, and the
commutative, associative, and
distributive properties. Example: 9 ×
26 = 9 × (20 + 6) = 9 × 20 + 9 × 6 =
180 + 54 = 234.
MN 3.1.3 - Understand meanings and
uses of fractions in real-world and
mathematical situations.
MN 3.1.3.1 - Read and write fractions Topic 1 - Number Sense and
with words and symbols. Recognize Operations
that fractions can be used to
represent parts of a whole, parts of a
set, points on a number line, or
distances on a number line. Example:
Parts of a shape (3/4 of a pie), parts
of a set (3 out of 4 people), and
measurements (3/4 of an inch).
Obj. 43 - Multiply a 2-digit whole
number by a 1-digit number
Obj. 44 - Determine a pictorial model
of a fraction of a whole
Obj. 45 - Determine a pictorial model
of a fraction of a set of objects
Obj. 46 - Identify a fraction
represented by a point on a number
line
Obj. 47 - Locate a fraction on a
number line
Obj. 55 - Estimate fractions of a
whole
Page 17 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.1.3.2 - Understand that the size Topic 1 - Number Sense and
Obj. 53 - WP: Compare equal unit
of a fractional part is relative to the
Operations
fractions of different-sized wholes
size of the whole. Example: One-half
of a small pizza is smaller than onehalf of a large pizza, but both
represent one-half.
MN 3.1.3.3 - Order and compare unit Topic 1 - Number Sense and
Obj. 48 - Compare fractions using
fractions and fractions with like
Operations
models
denominators by using models and
an understanding of the concept of
numerator and denominator.
MN 3.2 - Algebra
MN 3.2.1 - Use single-operation inputoutput rules to represent patterns and
relationships and to solve real-world
and mathematical problems.
MN 3.2.1.1 - Create, describe, and
Topic 2 - Algebraic Thinking
apply single-operation input-output
rules involving addition, subtraction
and multiplication to solve problems
in various contexts. Example:
Describe the relationship between
number of chairs and number of legs
by the rule that the number of legs is
four times the number of chairs.
MN 3.2.2 - Use number sentences
involving multiplication and division
basic facts and unknowns to
represent and solve real-world and
mathematical problems; create realworld situations corresponding to
number sentences.
MN 3.2.2.1 - Understand how to
interpret number sentences involving
multiplication and division basic facts
and unknowns. Create real-world
situations to represent number
sentences. Example: The number
sentence 8 × m = 24 could be
represented by the question "How
much did each ticket to a play cost if
8 tickets totaled $24?".
Page 18 of 198
Obj. 65 - Determine a rule for a table
of related number pairs
Obj. 66 - WP: Find the missing
number in a table of paired values
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.2.2.2 - Use multiplication and Topic 2 - Algebraic Thinking
Obj. 58 - Determine the missing
division basic facts to represent a
multiplicand in a number sentence
given problem situation using a
involving basic facts
number sentence. Use number sense
and multiplication and division basic
facts to find values for the unknowns
that make the number sentences
true. Example 1: Find values of the
unknowns that make each number
sentence true 6 = p ÷ 9; 24 = a × b; 5
× 8 = 4 × t. Example 2: How many
math teams are competing if there is
a total of 45 students with 5 students
on each team? This situation can be
represented by 5 × n = 45 or 45/5 = n
or 45/n = 5.
Obj. 59 - Determine the missing
dividend or divisor in a number
sentence involving basic facts
Obj. 60 - Recognize equivalent
multiplication or division expressions
involving basic facts
Obj. 63 - WP: Determine a
multiplication or division sentence for
a given situation
MN 3.3 - Geometry & Measurement
MN 3.3.1 - Use geometric attributes
to describe and create shapes in
various contexts.
MN 3.3.1.1 - Identify parallel and
perpendicular lines in various
contexts, and use them to describe
and create geometric shapes, such
as right triangles, rectangles,
parallelograms and trapezoids.
Topic 3 - Geometry and
Measurement
Obj. 92 - Identify parallel,
perpendicular, and intersecting lines
MN 3.3.1.2 - Sketch polygons with a
given number of sides or vertices
(corners), such as pentagons,
hexagons and octagons.
MN 3.3.2 - Understand perimeter as
a measurable attribute of real-world
and mathematical objects. Use
various tools to measure perimeter.
MN 3.3.2.1 - Use half units when
measuring distances. Example:
Measure a person's height to the
nearest half inch.
Page 19 of 198
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.3.2.2 - Find the perimeter of a Topic 3 - Geometry and
Obj. 86 - Determine a method for
polygon by adding the lengths of the Measurement
finding the perimeter of a shape given
sides.
the side lengths
Obj. 88 - WP: Determine the
perimeter of a shape given a model
showing all side lengths
MN 3.3.2.3 - Measure distances
around objects. Example: Measure
the distance around a classroom, or
measure a person's wrist size.
MN 3.3.3 - Use time, money and
temperature to solve real-world and
mathematical problems.
MN 3.3.3.1 - Tell time to the minute, Topic 3 - Geometry and
Obj. 74 - Tell time to the minute
using digital and analog clocks.
Measurement
Determine elapsed time to the
minute. Example: Your trip began at
9:50 a.m. and ended at 3:10 p.m.
How long were you traveling?
Obj. 76 - Calculate elapsed time
within an hour, given two clocks,
without regrouping
Obj. 77 - Calculate elapsed time
within an hour, given two clocks, with
regrouping
Obj. 78 - WP: Calculate elapsed time
within an hour given two clocks
Obj. 79 - WP: Calculate elapsed time
within an hour
Obj. 80 - WP: Determine the end
time given the start time and the
elapsed time within an hour
Obj. 81 - WP: Determine the start
time given the end time on a clock
and the elapsed time within an hour
MN 3.3.3.2 - Know relationships
Topic 3 - Geometry and
among units of time. Example: Know Measurement
the number of minutes in an hour,
days in a week and months in a year.
Page 20 of 198
Obj. 82 - WP: Determine the start
time given the end time and the
elapsed time within an hour
Obj. 75 - Convert hours to minutes or
minutes to seconds
081309
Accelerated Math
Grade 3
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 3,
Accelerated Math Second Edition Grade 3
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 3.3.3.3 - Make change up to one
dollar in several different ways,
including with as few coins as
possible. Example: A chocolate bar
costs $1.84. You pay for it with $2.
Give two possible ways to make
change.
MN 3.3.3.4 - Use an analog
Topic 3 - Geometry and
Obj. 84 - Read a thermometer in
thermometer to determine
Measurement
degrees Fahrenheit or Celsius
temperature to the nearest degree in
Fahrenheit and Celsius. Example:
Read the temperature in a room with
a thermometer that has both
Fahrenheit and Celsius scales. Use
the thermometer to compare Celsius
and Fahrenheit readings.
MN 3.4 - Data Analysis
MN 3.4.1 - Collect, organize, display,
and interpret data. Use labels and a
variety of scales and units in displays.
MN 3.4.1.1 - Collect, display and
Topic 4 - Data Analysis,
interpret data using frequency tables, Statistics, and Probability
bar graphs, picture graphs and
number line plots having a variety of
scales. Use appropriate titles, labels
and units.
Page 21 of 198
Obj. 105 - Use a bar graph with a
scale interval of 5 or 10 to represent
data
Obj. 106 - Answer a question using
information from a bar graph with a
scale interval of 5 or 10
Obj. 107 - Read a line plot
Obj. 108 - Use a line plot to represent
data
Obj. 109 - Answer a question using
information from a line plot
Obj. 110 - Use a frequency table to
represent data
Obj. 111 - Answer a question using
information from a frequency table
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.1 - Number & Operation
MN 4.1.1 - Compare and represent
whole numbers up to 100,000, with
an emphasis on place value.
MN 4.1.1.1 - Read, write and
Topic 1 - Number Sense and
Obj. 2 - Determine the word form of a
represent whole numbers up to
Operations
6-digit whole number
100,000. Representations include
numerals, words and expressions
with operations.
Obj. 5 - Determine the whole number
represented in expanded form written
in powers of ten
Obj. 6 - Represent a 6-digit whole
number in expanded form using
powers of ten
Obj. 7 - Convert between proper
expanded form and improper
expanded form up to a 5-digit whole
number
Obj. 8 - Convert between standard
form and improper expanded form up
to a 5-digit whole number
MN 4.1.1.2 - Find 10,000 more and
10,000 less than a given five-digit
number. Find 1,000 more and 1,000
less than a given five-digit number.
MN 4.1.1.3 - Use an understanding of
place value to multiply a number by
10, 100 and 1000.
MN 4.1.2 - Demonstrate mastery of
multiplication and division basic facts;
multiply multi-digit numbers; solve
real-world and mathematical
problems using arithmetic.
MN 4.1.2.1 - Demonstrate fluency
with multiplication and division facts.
MN 4.1.2.2 - Multiply multi-digit
numbers, using efficient and
generalizable procedures, based on
knowledge of place value, including
standard algorithms.
Topic 1 - Number Sense and
Operations
Obj. 20 - Multiply a 1- or 2-digit whole
number by a multiple of 10, 100, or
1,000
Obj. 21 - Apply the distributive
property to the multiplication of a 2digit number by a 1- or 2-digit number
Obj. 22 - Apply the distributive
property to multiply a multi-digit
number by a 1-digit number
Page 22 of 198
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 23 - Multiply a 3- or 4-digit whole
number by a 1-digit whole number
Obj. 24 - Multiply a 2-digit whole
number by a 2-digit whole number
Obj. 25 - Multiply a 3-digit whole
number by a 2-digit whole number
Obj. 26 - Multiply three 1- and 2-digit
whole numbers
Obj. 27 - WP: Multiply a multi-digit
whole number by a 1-digit whole
number
Obj. 28 - WP: Multiply a 2-digit whole
number by a 2-digit whole number
Obj. 29 - WP: Multiply a 3-digit whole
number by a 2-digit whole number
MN 4.1.2.3 - Estimate products and Topic 1 - Number Sense and
quotients of multi-digit whole
Operations
numbers by using rounding,
benchmarks and place value to
assess the reasonableness of results
in calculations. Example: 53 × 38 is
between 50 × 30 and 60 × 40, or
between 1500 and 2400, and 411/73
is between 400/80 and 500/70, or
between 5 and 7.
MN 4.1.2.4 - Solve multi-step realTopic 1 - Number Sense and
world and mathematical problems
Operations
requiring the use of addition,
subtraction and multiplication of multidigit whole numbers. Use various
strategies including the relationships
between the operations and a
calculator to check for accuracy.
Obj. 30 - Estimate a product of whole
numbers by rounding
Obj. 31 - Estimate a product of whole
numbers using any method
Obj. 32 - WP: Estimate a product of
two whole numbers using any
method
Obj. 9 - Add up to 4-digit whole
numbers in expanded form
Obj. 10 - Add a 5-digit or greater
whole number and a 3-digit or greater
whole number
Obj. 11 - Add three multi-digit whole
numbers
Obj. 12 - Subtract a smaller number
from a 3- or 4-digit whole number in
expanded form
Page 23 of 198
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 13 - Subtract a 3-digit or greater
whole number from a 5-digit or
greater whole number
Obj. 14 - WP: Add a 5-digit or greater
whole number and a 3-digit or greater
whole number
Obj. 15 - WP: Add three multi-digit
whole numbers
Obj. 16 - WP: Subtract a 3-digit or
greater whole number from a 5-digit
or greater whole number
Obj. 19 - WP: Solve a 2-step problem
involving addition and/or subtraction
of multi-digit whole numbers
Obj. 20 - Multiply a 1- or 2-digit whole
number by a multiple of 10, 100, or
1,000
Obj. 21 - Apply the distributive
property to the multiplication of a 2digit number by a 1- or 2-digit number
Obj. 24 - Multiply a 2-digit whole
number by a 2-digit whole number
Obj. 25 - Multiply a 3-digit whole
number by a 2-digit whole number
Obj. 28 - WP: Multiply a 2-digit whole
number by a 2-digit whole number
Obj. 29 - WP: Multiply a 3-digit whole
number by a 2-digit whole number
MN 4.1.2.5 - Use strategies and
Topic 1 - Number Sense and
algorithms based on knowledge of
Operations
place value and properties of
operations to divide multi-digit whole
numbers by one- or two-digit
numbers. Strategies may include
mental strategies, partial quotients,
the commutative, associative, and
distributive properties and repeated
subtraction. Example: A group of 324
students are going to a museum in 6
buses. If each bus has the same
number of students, how many
students will be on each bus?
Page 24 of 198
Obj. 42 - WP: Solve a 2-step whole
number problem using more than 1
operation
Obj. 33 - Divide a multi-digit whole
number by 10 or 100 with no
remainder
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 34 - Divide a 2-digit whole
number by a 1-digit whole number
with no remainder in the quotient
Obj. 35 - Divide a 3-digit whole
number by a 1-digit whole number
with no remainder in the quotient
Obj. 36 - Divide a 2-digit whole
number by a 1-digit whole number
with a remainder in the quotient
Obj. 37 - Divide a 3-digit whole
number by a 1-digit whole number
with a remainder in the quotient
Obj. 38 - WP: Divide a 2-digit whole
number by a 1-digit whole number
with no remainder in the quotient
Obj. 39 - WP: Divide a 3-digit whole
number by a 1-digit whole number
with no remainder in the quotient
Obj. 40 - WP: Divide a 2-digit whole
number by a 1-digit whole number
with a remainder in the quotient
Obj. 41 - WP: Divide a 3-digit whole
number by a 1-digit whole number
with a remainder in the quotient
MN 4.1.3 - Represent and compare
fractions and decimals in real-world
and mathematical situations; use
place value to understand how
decimals represent quantities.
MN 4.1.3.1 - Represent equivalent
fractions using fraction models such
as parts of a set, fraction circles,
fraction strips, number lines and
other manipulatives. Use the models
to determine equivalent fractions.
MN 4.1.3.2 - Locate fractions on a
Topic 1 - Number Sense and
number line. Use models to order
Operations
and compare whole numbers and
fractions, including mixed numbers
and improper fractions. Example:
Locate 5/3 and 1 3/4 on a number
line and give a comparison statement
about these two fractions, such as
5/3 " is less than 1 3/4.".
Page 25 of 198
Obj. 43 - Identify a mixed number
represented by a model
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 44 - Identify a mixed number
represented by a point on a number
line
Obj. 45 - Locate a mixed number on
a number line
Obj. 47 - Identify an improper fraction
represented by a model of a mixed
number
Obj. 48 - Identify an improper fraction
represented by a point on a number
line
Obj. 49 - Locate an improper fraction
on a number line
Obj. 52 - Compare fractions on a
number line
Obj. 53 - Order fractions on a
number line
MN 4.1.3.3 - Use fraction models to Topic 1 - Number Sense and
Obj. 54 - Add fractions with like
add and subtract fractions with like
Operations
denominators no greater than 10
denominators in real-world and
using models
mathematical situations. Develop a
rule for addition and subtraction of
fractions with like denominators.
Obj. 58 - Subtract fractions with like
denominators no greater than 10
using models
MN 4.1.3.4 - Read and write
Topic 1 - Number Sense and
Obj. 62 - Read a decimal number
decimals with words and symbols;
Operations
through the hundredths place
use place value to describe decimals
in terms of groups of thousands,
hundreds, tens, ones, tenths,
hundredths and thousandths.
Example: Writing 362.45 is a shorter
way of writing the sum: 3 hundreds +
6 tens + 2 ones + 4 tenths + 5
hundredths, which can also be written
as: three hundred sixty-two and fortyfive hundredths.
Obj. 63 - Determine the word form of
a decimal number through the
hundredths place
Obj. 64 - Determine the decimal
number from a pictorial model of
tenths or hundredths
Obj. 65 - Identify a pictorial model of
tenths or hundredths of a decimal
number
Page 26 of 198
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.1.3.5 - Compare and order
decimals and whole numbers using
place value, a number line and
models such as grids and base 10
blocks.
MN 4.1.3.6 - Locate the relative
Topic 1 - Number Sense and
Obj. 44 - Identify a mixed number
position of fractions, mixed numbers Operations
represented by a point on a number
and decimals on a number line.
line
MN 4.1.3.7 - Read and write tenths
and hundredths in decimal and
fraction notations using words and
symbols; know the fraction and
decimal equivalents for halves and
fourths. Example: 1/2 = 0.5 = 0.50
and 7/4 = 1 3/4 = 1.75, which can
also be written as one and threefourths or one and seventy-five
hundredths.
Topic 1 - Number Sense and
Operations
MN 4.1.3.8 - Round decimal values
to the nearest tenth. Example: The
number 0.36 rounded to the nearest
tenth is 0.4.
MN 4.2 - Algebra
MN 4.2.1 - Use input-output rules,
tables and charts to represent
patterns and relationships and to
solve real-world and mathematical
problems.
Topic 1 - Number Sense and
Operations
Page 27 of 198
Obj. 45 - Locate a mixed number on
a number line
Obj. 48 - Identify an improper fraction
represented by a point on a number
line
Obj. 49 - Locate an improper fraction
on a number line
Obj. 66 - Identify a decimal number
to tenths represented by a point on a
number line
Obj. 67 - Locate a decimal number to
tenths on a number line
Obj. 68 - Determine the decimal
number equivalent to a fraction with a
denominator of 10 or 100
Obj. 69 - Determine a fraction
equivalent to a decimal, using a
denominator of 10 or 100
Obj. 70 - Determine the decimal
number equivalent to a fraction
model
Obj. 71 - Determine the fraction
equivalent to a decimal number
model
Obj. 80 - Round a decimal number to
a specified place through hundredths
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.2.1.1 - Create and use inputTopic 2 - Algebra
Obj. 90 - Generate a table of paired
output rules involving addition,
numbers based on a rule
subtraction, multiplication and
division to solve problems in various
contexts. Record the inputs and
outputs in a chart or table. Example
1: If the rule is "multiply by 3 and add
4," record the outputs for given inputs
in a table. Example 2: A student is
given these three arrangements of
dots: Identify a pattern that is
consistent with these figures, create
an input-output rule that describes
the pattern, and use the rule to find
the number of dots in the 10th figure.
MN 4.2.2 - Use number sentences
involving multiplication, division and
unknowns to represent and solve realworld and mathematical problems;
create real-world situations
corresponding to number sentences.
Obj. 91 - Determine a rule that
relates two variables
Obj. 92 - Extend a number pattern in
a table of related pairs
MN 4.2.2.1 - Understand how to
interpret number sentences involving
multiplication, division and unknowns.
Use real-world situations involving
division to represent number
sentences. Example: The number
sentence a × b = 60 can be
represented by the situation in which
chairs are being arranged in equal
rows and the total number of chairs is
60.
Page 28 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.2.2.2 - Use multiplication,
division and unknowns to represent a
given problem situation using a
number sentence. Use number
sense, properties of multiplication,
and the relationship between
multiplication and division to find
values for the unknowns that make
the number sentences true. Example
1: If $84 is to be shared equally
among a group of children, the
amount of money each child receives
can be determined using the number
sentence 84 ÷ n = d. Example 2: Find
values of the unknowns or variables
that make each number sentence
true: 12 × m = 36; s = 256 ÷ t.
Grade 4
MN 4.3 - Geometry & Measurement
MN 4.3.1 - Name, describe, classify
and sketch polygons.
MN 4.3.1.1 - Describe, classify and
sketch triangles, including equilateral,
right, obtuse and acute triangles.
Recognize triangles in various
contexts.
MN 4.3.1.2 - Describe, classify and
draw quadrilaterals, including
squares, rectangles, trapezoids,
rhombuses, parallelograms and kites.
Recognize quadrilaterals in various
contexts.
MN 4.3.2 - Understand angle and
area as measurable attributes of realworld and mathematical objects. Use
various tools to measure angles and
areas.
MN 4.3.2.1 - Measure angles in
geometric figures and real-world
objects with a protractor or angle
ruler.
MN 4.3.2.2 - Compare angles
according to size. Classify angles as
acute, right and obtuse. Example:
Compare different hockey sticks
according to the angle between the
blade and the shaft.
Topic 3 - Geometry and
Measurement
Obj. 125 - Classify a triangle by its
sides
Topic 3 - Geometry and
Measurement
Obj. 126 - Classify a quadrilateral
Topic 3 - Geometry and
Measurement
Obj. 121 - Classify an angle given a
picture
Obj. 122 - Classify an angle given its
measure
Page 29 of 198
081309
Accelerated Math
Grade 4
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.3.2.3 - Understand that the
Topic 3 - Geometry and
Obj. 114 - Determine the area of a
area of a two-dimensional figure can Measurement
polygon on a grid
be found by counting the total
number of same size square units
that cover a shape without gaps or
overlaps. Justify why length and width
are multiplied to find the area of a
rectangle by breaking the rectangle
into one unit by one unit squares and
viewing these as grouped into rows
and columns. Example: How many
copies of a square sheet of paper are
needed to cover the classroom door?
Measure the length and width of the
door to the nearest inch and compute
the area of the door.
MN 4.3.2.4 - Find the areas of
Topic 3 - Geometry and
geometric figures and real-world
Measurement
objects that can be divided into
rectangular shapes. Use square units
to label area measurements.
MN 4.3.3 - Use translations,
reflections and rotations to establish
congruency and understand
symmetries.
MN 4.3.3.1 - Apply translations
(slides) to figures.
MN 4.3.3.2 - Apply reflections (flips)
to figures by reflecting over vertical or
horizontal lines and relate reflections
to lines of symmetry.
Obj. 119 - Estimate the area of an
irregular polygon on a grid
Obj. 115 - Determine the area of a
rectangle given a picture showing the
length and width
Obj. 116 - Determine the area of a
rectangle given the length and width
Obj. 117 - WP: Determine the area of
a rectangle
Topic 3 - Geometry and
Measurement
Topic 3 - Geometry and
Measurement
Obj. 130 - Determine the result of a
flip, a turn, or a slide
Obj. 130 - Determine the result of a
flip, a turn, or a slide
MN 4.3.3.3 - Apply rotations (turns) of Topic 3 - Geometry and
90° clockwise or counterclockwise.
Measurement
Obj. 131 - Determine the result of a
quarter or a half turn
MN 4.3.3.4 - Recognize that
translations, reflections and rotations
preserve congruency and use them
to show that two figures are
congruent.
MN 4.4 - Data Analysis
Page 30 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 4,
Accelerated Math Second Edition Grade 4
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 4.4.1 - Collect, organize, display
and interpret data, including data
collected over a period of time and
data represented by fractions and
decimals.
Grade 4
MN 4.4.1.1 - Use tables, bar graphs,
timelines and Venn diagrams to
display data sets. The data may
include fractions or decimals.
Understand that spreadsheet tables
and graphs can be used to display
data.
Page 31 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 5.1 - Number & Operation
MN 5.1.1 - Divide multi-digit
numbers; solve real-world and
mathematical problems using
arithmetic.
MN 5.1.1.1 - Divide multi-digit
Topic 1 - Number Sense and
Obj. 13 - Divide a multi-digit whole
numbers, using efficient and
Operations
number by multiples of 100 or 1,000
generalizable procedures, based on
knowledge of place value, including
standard algorithms. Recognize that
quotients can be represented in a
variety of ways, including a whole
number with a remainder, a fraction
or mixed number, or a decimal.
Example: Dividing 153 by 7 can be
used to convert the improper fraction
153/7 to the mixed number 21 6/7.
Obj. 14 - Divide a multi-digit whole
number by a 1-digit number with no
remainder and at least one zero in
the quotient
Obj. 15 - Divide a multi-digit whole
number by a 1-digit number with a
remainder and at least one zero in
the quotient
Obj. 17 - Divide a multi-digit whole
number by a 1-digit number and
express the quotient as a decimal
Obj. 18 - Divide a multi-digit whole
number by a 2-digit whole number,
with no remainder and no zeros in the
quotient
Obj. 19 - Divide a multi-digit whole
number by a 2-digit whole number,
with a remainder and no zeros in the
quotient
Obj. 20 - Divide a multi-digit whole
number by a 2-digit whole number,
with no remainder and at least one
zero in the quotient
Obj. 21 - Divide a multi-digit whole
number by a 2-digit whole number,
with a remainder and at least one
zero in the quotient
Obj. 22 - Divide a multi-digit whole
number by a 2-digit whole number
and express the quotient as a mixed
number
Obj. 23 - WP: Divide a whole
number, with no remainder
Page 32 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 24 - WP: Divide a whole number
and interpret the remainder
MN 5.1.1.2 - Consider the context in Topic 1 - Number Sense and
Obj. 16 - Divide a multi-digit whole
which a problem is situated to select Operations
number by a 1-digit number and
the most useful form of the quotient
express the quotient as a mixed
for the solution and use the context to
number
interpret the quotient appropriately.
Example: If 77 amusement ride
tickets are to be distributed evenly
among 4 children, each child will
receive 19 tickets, and there will be
one left over. If $77 is to be
distributed evenly among 4 children,
each will receive $19.25, with nothing
left over.
MN 5.1.1.3 - Estimate solutions to
Topic 1 - Number Sense and
arithmetic problems in order to
Operations
assess the reasonableness of results
of calculations.
Page 33 of 198
Obj. 27 - Estimate a quotient using
compatible numbers
Obj. 28 - Estimate a quotient using
any method
Obj. 29 - WP: Estimate a quotient
using any method
Obj. 56 - Estimate a fraction sum
using benchmark numbers 0, 1/2,
and 1
Obj. 57 - Estimate a fraction
difference using benchmark numbers
0, 1/2, and 1
Obj. 58 - WP: Estimate a fraction
sum or difference using benchmark
numbers 0, 1/2, and 1
Obj. 83 - Estimate the sum of two
decimal numbers through
thousandths and less than 1 by
rounding to a specified place
Obj. 84 - Estimate the difference of
two decimal numbers through
thousandths and less than 1 by
rounding to a specified place
Obj. 85 - WP: Estimate the sum or
difference of two decimal numbers
through thousandths using any
method
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 5.1.1.4 - Solve real-world and
Topic 1 - Number Sense and
Obj. 11 - Multiply a 3- or 4-digit whole
mathematical problems requiring
Operations
number by a 3-digit whole number
addition, subtraction, multiplication
and division of multi-digit whole
numbers. Use various strategies,
including the use of a calculator and
the inverse relationships between
operations, to check for accuracy.
Example: The calculation 117 ÷ 9 =
13 can be checked by multiplying 9
and 13.
Obj. 12 - WP: Multiply a 3- or 4-digit
whole number by a 3-digit whole
number
Obj. 13 - Divide a multi-digit whole
number by multiples of 100 or 1,000
Page 34 of 198
Obj. 14 - Divide a multi-digit whole
number by a 1-digit number with no
remainder and at least one zero in
the quotient
Obj. 15 - Divide a multi-digit whole
number by a 1-digit number with a
remainder and at least one zero in
the quotient
Obj. 16 - Divide a multi-digit whole
number by a 1-digit number and
express the quotient as a mixed
number
Obj. 17 - Divide a multi-digit whole
number by a 1-digit number and
express the quotient as a decimal
Obj. 18 - Divide a multi-digit whole
number by a 2-digit whole number,
with no remainder and no zeros in the
quotient
Obj. 19 - Divide a multi-digit whole
number by a 2-digit whole number,
with a remainder and no zeros in the
quotient
Obj. 20 - Divide a multi-digit whole
number by a 2-digit whole number,
with no remainder and at least one
zero in the quotient
Obj. 21 - Divide a multi-digit whole
number by a 2-digit whole number,
with a remainder and at least one
zero in the quotient
Obj. 22 - Divide a multi-digit whole
number by a 2-digit whole number
and express the quotient as a mixed
number
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 23 - WP: Divide a whole
number, with no remainder
Obj. 24 - WP: Divide a whole number
and interpret the remainder
Obj. 25 - WP: Solve a 2-step problem
involving whole numbers
MN 5.1.2 - Read, write, represent and
compare fractions and decimals;
recognize and write equivalent
fractions; convert between fractions
and decimals; use fractions and
decimals in real-world and
mathematical situations.
MN 5.1.2.1 - Read and write
Topic 1 - Number Sense and
Obj. 69 - Determine the value of a
decimals using place value to
Operations
digit in a decimal number to
describe decimals in terms of groups
thousandths
from millionths to millions. Example:
Possible names for the number 0.37
are: 37 hundredths; 3 tenths + 7
hundredths; possible names for the
number 1.5 are: one and five tenths;
15 tenths.
Obj. 70 - Determine a decimal
number represented in expanded
form
Obj. 71 - Represent a decimal
number in expanded form
MN 5.1.2.2 - Find 0.1 more than a
number and 0.1 less than a number.
Find 0.01 more than a number and
0.01 less than a number. Find 0.001
more than a number and 0.001 less
than a number.
MN 5.1.2.3 - Order fractions and
Topic 1 - Number Sense and
decimals, including mixed numbers Operations
and improper fractions, and locate on
a number line. Example 1: Which is
larger 1.25 or 6/5 ? Example 2: In
order to work properly, a part must fit
through a 0.24 inch wide space. If a
part is 1/4 inch wide, will it fit?
Obj. 33 - Compare fractions with
unlike denominators
Obj. 34 - Order fractions with unlike
denominators in ascending or
descending order
Page 35 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 5.1.2.4 - Recognize and generate Topic 1 - Number Sense and
Obj. 31 - Determine equivalent
equivalent decimals, fractions, mixed Operations
fractions not in simplest form
numbers and improper fractions in
various contexts. Example: When
comparing 1.5 and 19/12 , note that
1.5 = 1 1/2 = 1 6/12 = 18/12, so 1.5 <
19/12.
MN 5.1.2.5 - Round numbers to the
nearest 0.1, 0.01 and 0.001.
Example: Fifth grade students used a
calculator to find the mean of the
monthly allowance in their class. The
calculator display shows
25.80645161. Round this number to
the nearest cent.
MN 5.1.3 - Add and subtract
fractions, mixed numbers and
decimals to solve real-world and
mathematical problems.
MN 5.1.3.1 - Add and subtract
decimals and fractions, using efficient
and generalizable procedures,
including standard algorithms.
Page 36 of 198
Topic 1 - Number Sense and
Operations
Topic 1 - Number Sense and
Operations
Obj. 32 - Determine the simplest
form of a fraction
Obj. 47 - Convert a mixed number to
an improper fraction
Obj. 48 - Convert an improper
fraction to a mixed number
Obj. 90 - Convert a decimal number
through thousandths to a simplified
fraction
Obj. 91 - Convert a fraction with a
denominator that is a factor of 10,
100, or 1,000 to decimal notation
Obj. 82 - Round a decimal number to
a specified decimal place to
thousandths
Obj. 35 - Add fractions with like
denominators greater than 10 and
simplify the sum
Obj. 37 - Add fractions with unlike
denominators and do not simplify the
sum
Obj. 38 - Add fractions with unlike
denominators that have factors in
common and simplify the sum
Obj. 39 - Add fractions with unlike
denominators that have no factors in
common
Obj. 40 - Subtract fractions with like
denominators greater than 10 and
simplify the difference
Obj. 42 - Subtract fractions with
unlike denominators and do not
simplify the difference
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 43 - Subtract fractions with
unlike denominators that have factors
in common and simplify the
difference
Obj. 44 - Subtract fractions with
unlike denominators that have no
factors in common
Obj. 45 - WP: Add or subtract
fractions with like denominators and
simplify the sum or difference
Obj. 46 - WP: Add or subtract
fractions with unlike denominators
that have no factors in common
Obj. 49 - Add mixed numbers with
like denominators and simplify the
sum
Obj. 50 - Add mixed numbers with
unlike denominators and simplify the
sum
Obj. 51 - Subtract mixed numbers
with like denominators and simplify
the difference
Obj. 52 - Subtract mixed numbers
with unlike denominators and simplify
the difference
Obj. 53 - WP: Add or subtract mixed
numbers with like denominators and
simplify the sum or difference
Obj. 54 - WP: Add or subtract mixed
numbers with unlike denominators
that have no factors in common
Obj. 75 - Add two decimal numbers
of differing places to thousandths
Obj. 76 - Add three or more decimal
numbers
Obj. 77 - Add decimal numbers and
whole numbers
Obj. 78 - Subtract two decimal
numbers of differing places to
thousandths
Obj. 79 - Subtract a decimal number
from a whole number or a whole
number from a decimal number
Obj. 80 - WP: Add or subtract
decimal numbers through
thousandths
Page 37 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 81 - WP: Add or subtract a
decimal number through thousandths
and a whole number
MN 5.1.3.2 - Model addition and
Topic 1 - Number Sense and
Obj. 36 - Add fractions with unlike
subtraction of fractions and decimals Operations
denominators using a model and do
using a variety of representations.
not simplify the sum
Example: Represent 2/3 + 1/4 and
2/3 - 1/4 by drawing a rectangle
divided into 4 columns and 3 rows
and shading the appropriate parts or
by using fraction circles or bars.
MN 5.1.3.3 - Estimate sums and
Topic 1 - Number Sense and
differences of decimals and fractions Operations
to assess the reasonableness of
results in calculations. Example:
Recognize that 12 2/3 - 3 3/4 is
between 8 and 9 (since 2/5 < 3/4).
MN 5.1.3.4 - Solve real-world and
Topic 1 - Number Sense and
mathematical problems requiring
Operations
addition and subtraction of decimals,
fractions and mixed numbers,
including those involving
measurement, geometry and data.
Example: Calculate the perimeter of
the soccer field when the length is
109.7 meters and the width is 73.1
meters.
Page 38 of 198
Obj. 41 - Subtract fractions with
unlike denominators using a model
and do not simplify the difference
Obj. 56 - Estimate a fraction sum
using benchmark numbers 0, 1/2,
and 1
Obj. 57 - Estimate a fraction
difference using benchmark numbers
0, 1/2, and 1
Obj. 58 - WP: Estimate a fraction
sum or difference using benchmark
numbers 0, 1/2, and 1
Obj. 83 - Estimate the sum of two
decimal numbers through
thousandths and less than 1 by
rounding to a specified place
Obj. 84 - Estimate the difference of
two decimal numbers through
thousandths and less than 1 by
rounding to a specified place
Obj. 85 - WP: Estimate the sum or
difference of two decimal numbers
through thousandths using any
method
Obj. 35 - Add fractions with like
denominators greater than 10 and
simplify the sum
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 37 - Add fractions with unlike
denominators and do not simplify the
sum
Obj. 38 - Add fractions with unlike
denominators that have factors in
common and simplify the sum
Obj. 39 - Add fractions with unlike
denominators that have no factors in
common
Obj. 40 - Subtract fractions with like
denominators greater than 10 and
simplify the difference
Obj. 42 - Subtract fractions with
unlike denominators and do not
simplify the difference
Obj. 43 - Subtract fractions with
unlike denominators that have factors
in common and simplify the
difference
Obj. 44 - Subtract fractions with
unlike denominators that have no
factors in common
Obj. 45 - WP: Add or subtract
fractions with like denominators and
simplify the sum or difference
Obj. 46 - WP: Add or subtract
fractions with unlike denominators
that have no factors in common
Obj. 49 - Add mixed numbers with
like denominators and simplify the
sum
Obj. 50 - Add mixed numbers with
unlike denominators and simplify the
sum
Obj. 51 - Subtract mixed numbers
with like denominators and simplify
the difference
Obj. 52 - Subtract mixed numbers
with unlike denominators and simplify
the difference
Obj. 53 - WP: Add or subtract mixed
numbers with like denominators and
simplify the sum or difference
Obj. 54 - WP: Add or subtract mixed
numbers with unlike denominators
that have no factors in common
Obj. 75 - Add two decimal numbers
of differing places to thousandths
Page 39 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 76 - Add three or more decimal
numbers
Obj. 77 - Add decimal numbers and
whole numbers
Obj. 78 - Subtract two decimal
numbers of differing places to
thousandths
Obj. 79 - Subtract a decimal number
from a whole number or a whole
number from a decimal number
MN 5.2 - Algebra
MN 5.2.1 - Recognize and represent
patterns of change; use patterns,
tables, graphs and rules to solve realworld and mathematical problems.
MN 5.2.1.1 - Create and use rules,
Topic 2 - Algebra
tables, spreadsheets and graphs to
describe patterns of change and
solve problems. Example: An end-ofthe-year party for 5th grade costs
$100 to rent the room and $4.50 for
each student. Know how to use a
spreadsheet to create an input-output
table that records the total cost of the
party for any number of students
between 90 and 150.
Obj. 80 - WP: Add or subtract
decimal numbers through
thousandths
Obj. 81 - WP: Add or subtract a
decimal number through thousandths
and a whole number
Obj. 105 - WP: Extend a pattern to
solve a problem
Obj. 106 - Generate a table of paired
numbers based on a variable
expression with one operation
Obj. 107 - Generate a table of paired
numbers based on a variable
expression with two operations
Obj. 108 - Determine the variable
expression with one operation for a
table of paired numbers
Obj. 109 - WP: Generate a table of
paired numbers based on a variable
expression with one operation
Page 40 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 110 - WP: Determine the
variable expression with one
operation for a table of paired
numbers
Obj. 111 - Use a first quadrant graph
to represent the values from a table
generated in context
MN 5.2.1.2 - Use a rule or table to
Topic 2 - Algebra
Obj. 111 - Use a first quadrant graph
represent ordered pairs of positive
to represent the values from a table
integers and graph these ordered
generated in context
pairs on a coordinate system.
Topic 3 - Geometry and
Obj. 151 - Determine the ordered
Measurement
pair of a point in the first quadrant
MN 5.2.2 - Use properties of
arithmetic to generate equivalent
numerical expressions and evaluate
expressions involving whole
numbers.
MN 5.2.2.1 - Apply the commutative,
associative and distributive properties
and order of operations to generate
equivalent numerical expressions and
to solve problems involving whole
numbers. Example: Purchase 5
pencils at 19 cents and 7 erasers at
19 cents. The numerical expression
is 5 × 19 + 7 × 19 which is the same
as (5 + 7) × 19.
MN 5.2.3 - Understand and interpret
equations and inequalities involving
variables and whole numbers, and
use them to represent and solve realworld and mathematical problems.
MN 5.2.3.1 - Determine whether an
equation or inequality involving a
variable is true or false for a given
value of the variable. Example:
Determine whether the inequality 1.5
+ x < 10 is true for x = 2.8, x = 8.1, or
x = 9.2.
Page 41 of 198
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 5.2.3.2 - Represent real-world
Topic 2 - Algebra
Obj. 98 - Use a variable expression
situations using equations and
with one operation to represent a
inequalities involving variables.
verbal expression
Create real-world situations
corresponding to equations and
inequalities. Example: 250 - 27 × a =
b can be used to represent the
number of sheets of paper remaining
from a packet of 250 when each
student in a class of 27 is given a
certain number of sheets.
MN 5.2.3.3 - Evaluate expressions
Topic 2 - Algebra
and solve equations involving
variables when values for the
variables are given. Example: Using
the formula, A= lw, determine the
area when the length is 5, and the
width 6, and find the length when the
area is 24 and the width is 4.
Obj. 99 - Use a verbal expression to
represent a variable expression with
one operation
Obj. 100 - WP: Use a variable
expression with one operation to
represent a situation
Obj. 101 - Evaluate a 1-variable
expression, involving one operation,
using whole number substitution
Obj. 102 - Evaluate a 2-variable
expression, involving one operation,
using whole number substitution
Obj. 103 - WP: Evaluate a 1-variable
expression with one operation using
a whole number value
Obj. 104 - WP: Evaluate a 2-variable
expression with one operation using
whole number values
MN 5.3 - Geometry & Measurement
MN 5.3.1 - Describe, classify, and
draw representations of threedimensional figures.
MN 5.3.1.1 - Describe and classify
Topic 3 - Geometry and
three-dimensional figures including
Measurement
cubes, prisms and pyramids by the
number of edges, faces or vertices as
well as the types of faces.
Page 42 of 198
Obj. 144 - Determine the number of
faces, edges, and vertices in a 3dimensional shape
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 5.3.1.2 - Recognize and draw a Topic 3 - Geometry and
Obj. 142 - Determine the 3net for a three-dimensional figure.
Measurement
dimensional shape that can be
formed from a net
Obj. 143 - Determine a net of a 3dimensional shape
MN 5.3.2 - Determine the area of
triangles and quadrilaterals;
determine the surface area and
volume of rectangular prisms in
various contexts.
MN 5.3.2.1 - Develop and use
Topic 3 - Geometry and
Obj. 126 - Use a formula to
formulas to determine the area of
Measurement
determine the area of a triangle
triangles, parallelograms and figures
that can be decomposed into
triangles.
Obj. 127 - Determine the area of a
complex figure divided into basic
shapes
Obj. 128 - Use a formula to
determine the area of a parallelogram
MN 5.3.2.2 - Determine the surface Topic 3 - Geometry and
area of a rectangular prism by
Measurement
applying various strategies. Example:
Use a net or decompose the surface
into rectangles.
MN 5.3.2.3 - Understand that the
volume of a three-dimensional figure
can be found by counting the total
number of same-size cubic units that
fill a shape without gaps or overlaps.
Use cubic units to label volume
measurements. Example: Use cubes
to find the volume of a small fish
tank.
MN 5.3.2.4 - Develop and use the
formulas V = lwh and V = Bh to
determine the volume of rectangular
prisms. Justify why base area B and
height h are multiplied to find the
volume of a rectangular prism by
breaking the prism into layers of unit
cubes.
Page 43 of 198
Topic 3 - Geometry and
Measurement
Topic 3 - Geometry and
Measurement
Obj. 129 - WP: Determine the area of
a triangle
Obj. 130 - WP: Determine the area of
a square or rectangle
Obj. 138 - Determine the surface
area of a cube or a rectangular prism
given a net
Obj. 139 - Determine the surface
area of a rectangular prism
Obj. 140 - WP: Find the surface area
of a rectangular prism
Obj. 136 - Determine the volume of
an object composed of rectangular
prisms by counting units
Obj. 132 - Determine the volume of a
rectangular prism given a diagram
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 133 - WP: Determine the
volume of a rectangular prism given a
diagram
Obj. 134 - Determine the volume of a
rectangular prism
Obj. 135 - WP: Determine the
volume of a rectangular prism
MN 5.3.2.5 - Use various tools to
measure the volume and surface
area of various objects that are
shaped like rectangular prisms.
Example 1: Measure the surface area
of a cereal box by cutting it into
rectangles. Example 2: Measure the
volume of a cereal box by using a
ruler to measure its height, width and
length, or by filling it with cereal and
then emptying the cereal into
containers of known volume.
MN 5.4 - Data Analysis
MN 5.4.1 - Display and interpret data;
determine mean, median and range.
MN 5.4.1.1 - Know and use the
Topic 4 - Data Analysis,
definitions of the mean, median and Statistics, and Probability
range of a set of data. Know how to
use a spreadsheet to find the mean,
median and range of a data set.
Understand that the mean is a
"leveling out" of data. Example: The
set of numbers 1, 1, 4, 6 has mean 3.
It can be leveled by taking one unit
from the 4 and three units from the 6
and adding them to the 1s, making
four 3s.
MN 5.4.1.2 - Create and analyze
Topic 4 - Data Analysis,
double-bar graphs and line graphs by Statistics, and Probability
applying understanding of whole
numbers, fractions and decimals.
Know how to create spreadsheet
tables and graphs to display data.
Page 44 of 198
Obj. 160 - Determine the range from
a graph
Obj. 161 - Determine the mean of a
set of whole number data, whole
number results
Obj. 162 - Determine the median of
an odd number of data values
Obj. 164 - Determine the range of a
set of whole number data
Obj. 152 - Answer a question using
information from a line graph that
does not start at zero or has a broken
vertical scale
Obj. 154 - Read a double- or stackedbar graph
081309
Accelerated Math
Grade 5
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 5,
Accelerated Math Second Edition Grade 5
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 155 - Use a double- or stackedbar graph to represent data
Obj. 156 - Answer a question using
information from a double- or stackedbar graph
Page 45 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.1 - Number & Operation
MN 6.1.1 - Read, write, represent and
compare positive rational numbers
expressed as fractions, decimals,
percents and ratios; write positive
integers as products of factors; use
these representations in real-world
and mathematical situations.
MN 6.1.1.1 - Locate positive rational
numbers on a number line and plot
pairs of positive rational numbers on
a coordinate grid.
MN 6.1.1.2 - Compare positive
rational numbers represented in
various forms. Use the symbols <
and >. Example: 1/2 > 0.36.
MN 6.1.1.3 - Understand that percent
represents parts out of 100 and ratios
to 100. Example: 75% is equivalent to
the ratio 75 to 100, which is
equivalent to the ratio 3 to 4.
Grade 6
Topic 1 - Number Sense and
Operations
Obj. 76 - Compare numbers in
decimal and fractional forms
Topic 1 - Number Sense and
Operations
Obj. 78 - Determine a percent where
a ratio, not in 100ths, is given in
words
MN 6.1.1.4 - Determine equivalences Topic 1 - Number Sense and
among fractions, decimals and
Operations
percents; select among these
representations to solve problems.
Example: Since 1/10 is equivalent to
10%, if a woman making $25 an hour
gets a 10% raise, she will make an
additional $2.50 an hour, because
$2.50 is 1/10 of $25.
Obj. 83 - WP: Determine a part given
a ratio and the whole where the
whole is less than 50
Obj. 68 - Convert a mixed number to
a decimal number
Obj. 69 - Convert a decimal number
to a mixed number
Obj. 70 - Convert a fraction to a
repeating decimal number
Obj. 72 - Convert a decimal number
to a percentage
Obj. 73 - Convert a percentage to a
decimal number
Obj. 74 - Convert a fraction to a
percentage
Obj. 75 - Convert a percentage to a
fraction
Obj. 79 - Calculate a percent of a
whole number where the answer is a
whole number
Page 46 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 80 - WP: Calculate the percent
of a whole number where the answer
is a whole number
MN 6.1.1.5 - Factor whole numbers; Topic 1 - Number Sense and
Obj. 1 - Determine the prime
express a whole number as a product Operations
factorization of a number between 50
of prime factors with exponents.
and 200
Example: 24= 2³ x 3.
MN 6.1.1.6 - Determine greatest
Topic 1 - Number Sense and
Obj. 2 - Determine the greatest
common factors and least common Operations
common factor of three numbers to
multiples. Use common factors and
100
common multiples to do arithmetic
with fractions and find equivalent
fractions. Example: Factor the
numerator and denominator of a
fraction to determine an equivalent
fraction.
Obj. 3 - Determine the least common
multiple of three numbers
Obj. 4 - WP: Determine the least
common multiple of two or more
numbers
Obj. 13 - Add fractions with unlike
denominators and simplify the sum
Obj. 14 - Subtract fractions with
unlike denominators and simplify the
difference
Obj. 15 - Subtract a fraction from a
whole number
Obj. 16 - WP: Add or subtract
fractions with unlike denominators
and simplify the sum or difference
Obj. 17 - Add mixed numbers with
unlike denominators or a mixed
number and a fraction with unlike
denominators and simplify the sum
Obj. 18 - Subtract a mixed number
from a whole number
Obj. 19 - Subtract mixed numbers
with unlike denominators or a mixed
number and a fraction and simplify
the difference
Obj. 20 - Add and subtract three
unlike-denominator fractions, mixed
numbers, or fractions and mixed
numbers, and simplify the answer
Obj. 21 - WP: Add or subtract mixed
numbers with unlike denominators or
a mixed number and a fraction with
unlike denominators and simplify the
sum or difference
Page 47 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.1.1.7 - Convert between
equivalent representations of positive
rational numbers. Example: Express
10/7 as (7+3)/7 = 7/7 + 3/7 = 1 3/7.
MN 6.1.2 - Understand the concept of
ratio and its relationship to fractions
and to the multiplication and division
of whole numbers. Use ratios to solve
real-world and mathematical
problems.
MN 6.1.2.1 - Identify and use ratios to Topic 1 - Number Sense and
compare quantities; understand that Operations
comparing quantities using ratios is
not the same as comparing quantities
using subtraction. Example: In a
classroom with 15 boys and 10 girls,
compare the numbers by subtracting
(there are 5 more boys than girls) or
by dividing (there are 1.5 times as
many boys as girls). The comparison
using division may be expressed as a
ratio of boys to girls (3 to 2 or 3:2 or
1.5 to 1).
MN 6.1.2.2 - Apply the relationship
Topic 1 - Number Sense and
between ratios, equivalent fractions Operations
and percents to solve problems in
various contexts, including those
involving mixtures and
concentrations. Example: If 5 cups of
trail mix contains 2 cups of raisins,
the ratio of raisins to trail mix is 2 to
5. This ratio corresponds to the fact
that the raisins are 2/5 of the total, or
40% of the total. And if one trail mix
consists of 2 parts peanuts to 3 parts
raisins, and another consists of 4
parts peanuts to 8 parts raisins, then
the first mixture has a higher
concentration of peanuts.
Grade 6
Obj. 81 - WP: Determine a ratio
using whole numbers less than 50
Obj. 83 - WP: Determine a part given
a ratio and the whole where the
whole is less than 50
Obj. 84 - WP: Determine a part given
a ratio and another part where the
whole is less than 50
Obj. 85 - WP: Determine the whole
given a ratio and a part where the
whole is less than 50
Page 48 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.1.2.3 - Determine the rate for Topic 1 - Number Sense and
Obj. 86 - WP: Determine a unit rate
ratios of quantities with different units. Operations
with a whole number value
Example: 60 miles in 3 hours is
equivalent to 20 miles in one hour (20
mph).
MN 6.1.2.4 - Use reasoning about
Topic 1 - Number Sense and
Obj. 81 - WP: Determine a ratio
multiplication and division to solve
Operations
using whole numbers less than 50
ratio and rate problems. Example: If 5
items cost $3.75, and all items are
the same price, then 1 item costs 75
cents, so 12 items cost $9.00.
MN 6.1.3 - Multiply and divide
decimals, fractions and mixed
numbers; solve real-world and
mathematical problems using
arithmetic with positive rational
numbers.
MN 6.1.3.1 - Multiply and divide
Topic 1 - Number Sense and
decimals and fractions, using efficient Operations
and generalizable procedures,
including standard algorithms.
Obj. 83 - WP: Determine a part given
a ratio and the whole where the
whole is less than 50
Obj. 84 - WP: Determine a part given
a ratio and another part where the
whole is less than 50
Obj. 85 - WP: Determine the whole
given a ratio and a part where the
whole is less than 50
Obj. 86 - WP: Determine a unit rate
with a whole number value
Obj. 87 - WP: Use a unit rate, with a
whole number or whole cent value, to
solve a problem
Obj. 22 - Multiply a fraction by a
fraction
Obj. 28 - Divide a fraction by a whole
number resulting in a fractional
quotient
Obj. 29 - Divide a fraction by a
fraction
Obj. 30 - Divide a whole number by a
fraction resulting in a fractional
quotient
Obj. 33 - WP: Multiply or divide a
fraction by a fraction
Obj. 43 - Multiply a decimal number
through thousandths by a whole
number
Page 49 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 44 - WP: Multiply a decimal
number through thousandths by a
whole number
Obj. 45 - WP: Multiply a money
expression by a decimal number
Obj. 46 - Multiply a decimal number
greater than one, in tenths, by a
decimal number in tenths
Obj. 47 - Multiply decimal numbers to
thousandths using basic facts
Obj. 48 - Multiply decimal numbers
less than one in hundredths or
thousandths
Obj. 49 - Multiply a decimal number
greater than one by a decimal
number to thousandths that has only
1 nonzero digit
Obj. 50 - Multiply decimal numbers
greater than one where the product
has 2 or 3 decimal places
Obj. 51 - WP: Multiply two decimal
numbers to thousandths
Obj. 53 - Divide a decimal number by
10, 100, or 1,000
Obj. 55 - Divide a decimal number
through thousandths by a 1- or 2-digit
whole number where the quotient has
2-5 decimal places
Obj. 56 - WP: Divide a decimal
number through thousandths by a 1or 2-digit whole number
Obj. 57 - Divide a whole number or a
decimal number by 0.1, 0.01, or
0.001
Obj. 60 - Divide a 1- to 3-digit whole
number by a decimal number to
tenths where the quotient is a whole
number
Obj. 61 - Divide a 1- to 3-digit whole
number by a decimal number to
tenths where the quotient is a
decimal number to thousandths
Obj. 62 - Divide a 2- or 3-digit whole
number by a decimal number to
hundredths or thousandths, rounded
quotient if needed
Page 50 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 63 - Divide a decimal number by
a decimal number through
thousandths, rounded quotient if
needed
Obj. 64 - WP: Divide a whole number
by a decimal number through
thousandths, rounded quotient if
needed
Obj. 65 - WP: Divide a decimal
through thousandths by a decimal
through thousandths, rounded
quotient if needed
MN 6.1.3.2 - Use the meanings of
Topic 1 - Number Sense and
Obj. 54 - Relate division by a whole
fractions, multiplication, division and Operations
number power of ten to multiplication
the inverse relationship between
by the related decimal fraction power
multiplication and division to make
of ten
sense of procedures for multiplying
and dividing fractions. Example: Just
as 12/4 = 3 means 12 = 3x4, 2/3 ÷
4/5 = 5/6 means 5/6 x 4/5 = 2/3.
MN 6.1.3.3 - Calculate the percent of Topic 1 - Number Sense and
a number and determine what
Operations
percent one number is of another
number to solve problems in various
contexts. Example: If John has $45
and spends $15, what percent of his
money did he keep?
MN 6.1.3.4 - Solve real-world and
mathematical problems requiring
arithmetic with decimals, fractions
and mixed numbers.
Page 51 of 198
Topic 1 - Number Sense and
Operations
Obj. 58 - Relate division by a decimal
fraction power of ten to multiplication
by the related whole number power of
ten
Obj. 79 - Calculate a percent of a
whole number where the answer is a
whole number
Obj. 80 - WP: Calculate the percent
of a whole number where the answer
is a whole number
Obj. 13 - Add fractions with unlike
denominators and simplify the sum
Obj. 14 - Subtract fractions with
unlike denominators and simplify the
difference
Obj. 15 - Subtract a fraction from a
whole number
Obj. 16 - WP: Add or subtract
fractions with unlike denominators
and simplify the sum or difference
Obj. 17 - Add mixed numbers with
unlike denominators or a mixed
number and a fraction with unlike
denominators and simplify the sum
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 18 - Subtract a mixed number
from a whole number
Obj. 19 - Subtract mixed numbers
with unlike denominators or a mixed
number and a fraction and simplify
the difference
Obj. 20 - Add and subtract three
unlike-denominator fractions, mixed
numbers, or fractions and mixed
numbers, and simplify the answer
Obj. 21 - WP: Add or subtract mixed
numbers with unlike denominators or
a mixed number and a fraction with
unlike denominators and simplify the
sum or difference
Obj. 22 - Multiply a fraction by a
fraction
Obj. 23 - Multiply a mixed number by
a whole number
Obj. 24 - Multiply a mixed number by
a fraction
Obj. 25 - Multiply a mixed number by
a mixed number
Obj. 28 - Divide a fraction by a whole
number resulting in a fractional
quotient
Obj. 29 - Divide a fraction by a
fraction
Obj. 30 - Divide a whole number by a
fraction resulting in a fractional
quotient
Obj. 31 - Divide a mixed number by a
fraction
Obj. 32 - Divide a mixed number by a
mixed number
Obj. 33 - WP: Multiply or divide a
fraction by a fraction
Obj. 34 - WP: Multiply or divide two
mixed numbers or a mixed number
and a fraction
Obj. 35 - WP: Solve a 2-step problem
involving fractions
Obj. 40 - Add three decimal numbers
Obj. 41 - Add and subtract three
decimal numbers
Obj. 42 - WP: Add and subtract three
decimal numbers
Page 52 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 43 - Multiply a decimal number
through thousandths by a whole
number
Obj. 44 - WP: Multiply a decimal
number through thousandths by a
whole number
Obj. 45 - WP: Multiply a money
expression by a decimal number
Obj. 46 - Multiply a decimal number
greater than one, in tenths, by a
decimal number in tenths
Obj. 47 - Multiply decimal numbers to
thousandths using basic facts
Obj. 48 - Multiply decimal numbers
less than one in hundredths or
thousandths
Obj. 49 - Multiply a decimal number
greater than one by a decimal
number to thousandths that has only
1 nonzero digit
Obj. 50 - Multiply decimal numbers
greater than one where the product
has 2 or 3 decimal places
Obj. 51 - WP: Multiply two decimal
numbers to thousandths
Obj. 53 - Divide a decimal number by
10, 100, or 1,000
Obj. 55 - Divide a decimal number
through thousandths by a 1- or 2-digit
whole number where the quotient has
2-5 decimal places
Obj. 56 - WP: Divide a decimal
number through thousandths by a 1or 2-digit whole number
Obj. 57 - Divide a whole number or a
decimal number by 0.1, 0.01, or
0.001
Obj. 60 - Divide a 1- to 3-digit whole
number by a decimal number to
tenths where the quotient is a whole
number
Obj. 61 - Divide a 1- to 3-digit whole
number by a decimal number to
tenths where the quotient is a
decimal number to thousandths
Page 53 of 198
Obj. 63 - Divide a decimal number by
a decimal number through
thousandths, rounded quotient if
needed
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 64 - WP: Divide a whole number
by a decimal number through
thousandths, rounded quotient if
needed
Obj. 65 - WP: Divide a decimal
through thousandths by a decimal
through thousandths, rounded
quotient if needed
Obj. 67 - WP: Solve a 2-step problem
involving decimals
MN 6.1.3.5 - Estimate solutions to
Topic 1 - Number Sense and
Obj. 52 - WP: Estimate the product
problems with whole numbers,
Operations
of two decimals
fractions and decimals and use the
estimations to assess the
reasonableness of computations and
of results in the context of the
problem. Example: The sum 1/3 +
0.25 can be estimated to be between
1/2 and 1, and this estimate can be
used as a check on the result of a
more detailed calculation.
MN 6.2 - Algebra
MN 6.2.1 - Recognize and represent
relationships between varying
quantities; translate from one
representation to another; use
patterns, tables, graphs and rules to
solve real-world and mathematical
problems.
MN 6.2.1.1 - Understand that a
variable can be used to represent a
quantity that can change, often in
relationship to another changing
quantity. Use variables in various
contexts. Example: If a student earns
$7 an hour in a job, the amount of
money earned can be represented by
a variable and is related to the
number of hours worked, which also
can be represented by a variable.
Page 54 of 198
Obj. 66 - WP: Estimate the quotient
of two decimals
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.2.1.2 - Represent the
Topic 2 - Algebra
Obj. 103 - WP: Generate a table of
relationship between two varying
paired numbers based on a variable
quantities with function rules, graphs
expression with two operations
and tables; translate between any two
of these representations. Example:
Describe the terms in the sequence
of perfect squares t = 1, 4, 9, 16, ...
by using the rule t-n² for n = 1, 2, 3, 4,
....
Obj. 104 - Use a 2-variable equation
to construct an input-output table
Obj. 105 - Use a 2-variable equation
to represent a relationship expressed
in a table
Obj. 106 - Use a first quadrant graph
to represent the values in an inputoutput table
Obj. 107 - Use a graph to determine
the entries in an input-output table
MN 6.2.2 - Use properties of
arithmetic to generate equivalent
numerical expressions and evaluate
expressions involving positive rational
numbers.
MN 6.2.2.1 - Apply the associative,
Topic 2 - Algebra
commutative and distributive
properties and order of operations to
generate equivalent expressions and
to solve problems involving positive
rational numbers. Example 1: 30/15 x
5/6 = (32x5)/(15x6) =
(2x16x5)/(3x5x3x2) = 16/9 x 2/2 x 5/5
= 16/9. Example 2: Use the
distributive law to write: 1/2 + 1/3 (9/2
- 15/8) = 1/2 + 1/3 x 9/2 - 1/3 x 15/8 =
1/2 + 3/2 - 5/8 = 2 - 5/8 = 1 3/8.
Obj. 92 - Determine which property of
addition or multiplication justifies a
step in the simplification of an
expression
MN 6.2.3 - Understand and interpret
equations and inequalities involving
variables and positive rational
numbers. Use equations and
inequalities to represent real-world
and mathematical problems; use the
idea of maintaining equality to solve
equations. Interpret solutions in the
original context.
Page 55 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.2.3.1 - Represent real-world or Topic 2 - Algebra
Obj. 96 - WP: Use a 2-variable
mathematical situations using
equation to represent a situation
equations and inequalities involving
involving a direct proportion
variables and positive rational
numbers. Example: The number of
miles m in a k kilometer race is
represented by the equation m = 0.62
k.
Obj. 97 - WP: Use a 2-variable linear
equation to represent a situation
MN 6.2.3.2 - Solve equations
Topic 2 - Algebra
involving positive rational numbers
using number sense, properties of
arithmetic and the idea of maintaining
equality on both sides of the
equation. Interpret a solution in the
original context and assess the
reasonableness of results. Example:
A cellular phone company charges
$0.12 per minute. If the bill was
$11.40 in April, how many minutes
were used?
Obj. 101 - Solve a 1-step equation
involving whole numbers
MN 6.3 - Geometry & Measurement
MN 6.3.1 - Calculate perimeter, area,
surface area and volume of two- and
three-dimensional figures to solve
real-world and mathematical
problems.
MN 6.3.1.1 - Calculate the surface
Topic 3 - Geometry and
area and volume of prisms and use Measurement
appropriate units, such as cm² and
cm³. Justify the formulas used.
Justification may involve
decomposition, nets or other models.
Example: The surface area of a
triangular prism can be derived by
decomposing the surface into two
triangles and three rectangles.
Obj. 127 - Determine the volume of a
prism with a right triangle base
Obj. 128 - Determine the surface
area of a 3-dimensional shape made
from cubes
Page 56 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.3.1.2 - Calculate the area of
quadrilaterals. Quadrilaterals include
squares, rectangles, rhombuses,
parallelograms, trapezoids and kites.
When formulas are used, be able to
explain why they are valid. Example:
The area of a kite is one-half the
product of the lengths of the
diagonals, and this can be justified by
decomposing the kite into two
triangles.
Grade 6
MN 6.3.1.3 - Estimate the perimeter
and area of irregular figures on a grid
when they cannot be decomposed
into common figures and use correct
units, such as cm and cm².
MN 6.3.2 - Understand and use
relationships between angles in
geometric figures.
MN 6.3.2.1 - Solve problems using
Topic 3 - Geometry and
the relationships between the angles Measurement
formed by intersecting lines. Example
1: If two streets cross, forming four
corners such that one of the corners
forms an angle of 120°, determine
the measures of the remaining three
angles. Example 2: Recognize that
pairs of interior and exterior angles in
polygons have measures that sum to
180°.
Obj. 129 - Determine the measure of
a missing angle using straight and
right angle relationships
MN 6.3.2.2 - Determine missing
angle measures in a triangle using
the fact that the sum of the interior
angles of a triangle is 180°. Use
models of triangles to illustrate this
fact. Example 1: Cut a triangle out of
paper, tear off the corners and
rearrange these corners to form a
straight line. Example 2: Recognize
that the measures of the two acute
angles in a right triangle sum to 90°.
MN 6.3.2.3 - Develop and use
formulas for the sums of the interior
angles of polygons by decomposing
them into triangles.
Page 57 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.3.3 - Choose appropriate units
of measurement and use ratios to
convert within measurement systems
to solve real-world and mathematical
problems.
MN 6.3.3.1 - Solve problems in
Topic 3 - Geometry and
various contexts involving conversion Measurement
of weights, capacities, geometric
measurements and times within
measurement systems using
appropriate units.
MN 6.3.3.2 - Estimate weights,
capacities and geometric
measurements using benchmarks in
measurement systems with
appropriate units. Example: Estimate
the height of a house by comparing to
a 6-foot man standing nearby.
Grade 6
Obj. 108 - WP: Add or subtract
customary measures of capacity
requiring unit conversion
Obj. 109 - WP: Add or subtract
metric measures of capacity requiring
unit conversion
Obj. 110 - WP: Add or subtract
customary measures of weight
requiring unit conversion
Obj. 111 - WP: Add or subtract
metric measures of mass requiring
unit conversion
Obj. 113 - WP: Multiply or divide
metric measures of capacity requiring
unit conversion
Obj. 114 - WP: Multiply or divide
customary measures of weight
requiring unit conversion
Obj. 115 - WP: Multiply or divide
metric measures of mass requiring
unit conversion
MN 6.4 - Data Analysis & Probability
MN 6.4.1 - Use probabilities to solve
real-world and mathematical
problems; represent probabilities
using fractions, decimals and
percents.
Page 58 of 198
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.4.1.1 - Determine the sample Topic 4 - Data Analysis,
Obj. 157 - Determine the number of
space (set of possible outcomes) for Statistics, and Probability
possible combinations of a set of
a given experiment and determine
objects
which members of the sample space
are related to certain events. Sample
space may be determined by the use
of tree diagrams, tables or pictorial
representations. Example: A 6 x 6
table with entries such as (1,1), (1,2),
(1,3), ..., (6,6) can be used to
represent the sample space for the
experiment of simultaneously rolling
two number cubes.
MN 6.4.1.2 - Determine the
probability of an event using the ratio
between the size of the event and the
size of the sample space; represent
probabilities as percents, fractions
and decimals between 0 and 1
inclusive. Understand that
probabilities measure likelihood.
Example: Each outcome for a
balanced number cube has
probability 1/6 , and the probability of
rolling an even number is 1/2.
MN 6.4.1.3 - Perform experiments for
situations in which the probabilities
are known, compare the resulting
relative frequencies with the known
probabilities; know that there may be
differences. Example: Heads and
tails are equally likely when flipping a
fair coin, but if several different
students flipped fair coins 10 times, it
is likely that they will find a variety of
relative frequencies of heads and
tails.
Page 59 of 198
Topic 4 - Data Analysis,
Statistics, and Probability
Obj. 152 - Determine the probability
of a single event
Topic 4 - Data Analysis,
Statistics, and Probability
Obj. 156 - Compare predictions from
experimental and theoretical
probability
081309
Accelerated Math
Grade 6
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 6,
Accelerated Math Second Edition Grade 6
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 6.4.1.4 - Calculate experimental Topic 4 - Data Analysis,
Obj. 151 - Determine an
probabilities from experiments;
Statistics, and Probability
experimental probability given a list of
represent them as percents, fractions
results
and decimals between 0 and 1
inclusive. Use experimental
probabilities to make predictions
when actual probabilities are
unknown. Example: Repeatedly draw
colored chips with replacement from
a bag with an unknown mixture of
chips, record relative frequencies,
and use the results to make
predictions about the contents of the
bag.
Obj. 154 - Make a prediction based
on an experimental probability
Obj. 155 - Make a prediction based
on a theoretical probability
Page 60 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.1 - Number & Operation
MN 7.1.1 - Read, write, represent and
compare positive and negative
rational numbers, expressed as
integers, fractions and decimals.
MN 7.1.1.1 - Know that every rational
number can be written as the ratio of
two integers or as a terminating or
repeating decimal. Recognize that pi
is not rational, but that it can be
approximated by rational numbers
such as 22/7 and 3.14.
Grade 7
MN 7.1.1.2 - Understand that division
of two integers will always result in a
rational number. Use this information
to interpret the decimal result of a
division problem when using a
calculator. Example: 125/30 gives
4.16666667 on a calculator. This
answer is not exact. The exact
answer can be expressed as 4 1/6 ,
which is the same as 4.16 repeating.
The calculator expression does not
guarantee that the 6 is repeated, but
that possibility should be anticipated.
MN 7.1.1.3 - Locate positive and
Topic 1 - Number Sense and
negative rational numbers on the
Operations
number line, understand the concept
of opposites, and plot pairs of positive
and negative rational numbers on a
coordinate grid.
Obj. 34 - Determine the opposite of
an integer
Obj. 57 - Identify a positive or
negative rational number represented
by a point on a number line
MN 7.1.1.4 - Compare positive and
Topic 1 - Number Sense and
negative rational numbers expressed Operations
in various forms using the symbols <,
>, "less than or equal to", "greater
than or equal to". Example: -1/2 < 36.
Page 61 of 198
Obj. 58 - Locate a positive or
negative rational number on a
number line
Obj. 59 - Compare rational numbers
(positive and negative)
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.1.1.5 - Recognize and generate
equivalent representations of positive
and negative rational numbers,
including equivalent fractions.
Example: -40/12 = -120/36 = -10/3 = 3.3 repeating.
MN 7.1.2 - Calculate with positive
and negative rational numbers, and
rational numbers with whole number
exponents, to solve real-world and
mathematical problems.
MN 7.1.2.1 - Add, subtract, multiply Topic 1 - Number Sense and
and divide positive and negative
Operations
rational numbers that are integers,
fractions and terminating decimals;
use efficient and generalizable
procedures, including standard
algorithms; raise positive rational
numbers to whole-number
exponents. Example: 3 to the 4th
power x (1/2)² = 81/4.
MN 7.1.2.2 - Use real-world contexts
and the inverse relationship between
addition and subtraction to explain
why the procedures of arithmetic with
negative rational numbers make
sense. Example: Multiplying a
distance by -1 can be thought of as
representing that same distance in
the opposite direction. Multiplying by 1 a second time reverses directions
again, giving the distance in the
original direction.
Page 62 of 198
Grade 7
Obj. 30 - WP: Answer a question
involving a fraction and a decimal
Obj. 31 - WP: Solve a multi-step
problem involving decimal numbers
Obj. 32 - WP: Solve a multi-step
problem involving fractions or mixed
numbers
Obj. 37 - Add integers
Obj. 39 - Subtract integers
Obj. 40 - WP: Add and subtract using
integers
Obj. 41 - Multiply integers
Obj. 42 - Divide integers
Obj. 43 - WP: Multiply or divide
integers
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.1.2.3 - Understand that
calculators and other computing
technologies often truncate or round
numbers. Example: A decimal that
repeats or terminates after a large
number of digits is truncated or
rounded.
MN 7.1.2.4 - Solve problems in
Topic 1 - Number Sense and
Obj. 30 - WP: Answer a question
various contexts involving
Operations
involving a fraction and a decimal
calculations with positive and
negative rational numbers and
positive integer exponents, including
computing simple and compound
interest.
Obj. 31 - WP: Solve a multi-step
problem involving decimal numbers
Obj. 32 - WP: Solve a multi-step
problem involving fractions or mixed
numbers
Obj. 40 - WP: Add and subtract using
integers
Obj. 43 - WP: Multiply or divide
integers
Obj. 50 - WP: Determine the whole,
given part to whole ratio and a part,
where the whole is greater than 50
Obj. 51 - WP: Determine the whole,
given part to part ratio and a part,
where the whole is greater than 50
Obj. 52 - WP: Determine a unit rate
MN 7.1.2.5 - Use proportional
Topic 1 - Number Sense and
reasoning to solve problems involving Operations
ratios in various contexts. Example: A
recipe calls for milk, flour and sugar
in a ratio of 4:6:3 (this is how recipes
are often given in large institutions,
such as hospitals). How much flour
and milk would be needed with 1 cup
of sugar?
Obj. 53 - WP: Use a unit rate to solve
a problem
Obj. 46 - WP: Determine a part,
given part to whole ratio and the
whole, where the whole is greater
than 50
Obj. 47 - WP: Determine a part,
given part to part ratio and the whole,
where the whole is greater than 50
Page 63 of 198
Obj. 48 - WP: Determine a part,
given part to whole ratio and a part,
where the whole is greater than 50
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 49 - WP: Determine a part,
given part to part ratio and a part,
where the whole is greater than 50
Topic 2 - Algebra
Obj. 71 - WP: Solve a proportion
Obj. 72 - WP: Use direct variation to
solve a problem
MN 7.1.2.6 - Demonstrate an
understanding of the relationship
between the absolute value of a
rational number and distance on a
number line. Use the symbol for
absolute value. Example: |- 3|
represents the distance from - 3 to 0
on a number line or 3 units; the
distance between 3 and 9/2 on the
number line is |3 - 9/2| or 3/2.
MN 7.2 - Algebra
MN 7.2.1 - Understand the concept of
proportionality in real-world and
mathematical situations, and
distinguish between proportional and
other relationships.
MN 7.2.1.1 - Understand that a
relationship between two variables, x
and y, is proportional if it can be
expressed in the form y/x = k or y =
kx. Distinguish proportional
relationships from other relationships,
including inversely proportional
relationships (xy=k or y= k/x).
Example: The radius and
circumference of a circle are
proportional, whereas the length x
and the width y of a rectangle with
area 12 are inversely proportional,
since xy = 12 or equivalently, y =
12/x.
MN 7.2.1.2 - Understand that the
Topic 2 - Algebra
Obj. 82 - Use a graph to represent
graph of a proportional relationship is
the ordered pairs in a function table
a line through the origin whose slope
is the unit rate (constant of
proportionality). Know how to use
graphing technology to examine what
happens to a line when the unit rate
is changed.
Obj. 83 - Determine the graph of a 1operation linear function
Page 64 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.2 - Recognize proportional
relationships in real-world and
mathematical situations; represent
these and other relationships with
tables, verbal descriptions, symbols
and graphs; solve problems involving
proportional relationships and explain
results in the original context.
MN 7.2.2.1 - Represent proportional Topic 2 - Algebra
relationships with tables, verbal
descriptions, symbols, equations and
graphs; translate from one
representation to another. Determine
the unit rate (constant of
proportionality or slope) given any of
these representations. Example:
Larry drives 114 miles and uses 5
gallons of gasoline. Sue drives 300
miles and uses 11.5 gallons of
gasoline. Use equations and graphs
to compare fuel efficiency and to
determine the costs of various trips.
MN 7.2.2.2 - Solve multi-step
Topic 1 - Number Sense and
problems involving proportional
Operations
relationships in numerous contexts.
Example 1: Distance-time, percent
increase or decrease, discounts, tips,
unit pricing, lengths in similar
geometric figures, and unit
conversion when a conversion factor
is given, including conversion
between different measurement
systems. Example 2: How many
kilometers are there in 26.2 miles?
Grade 7
Obj. 68 - Use a variable expression
with two operations to represent a
table of paired numbers
Obj. 69 - WP: Use a 2-variable
expression to represent a situation
Obj. 81 - Use a table to represent a
linear function
Obj. 82 - Use a graph to represent
the ordered pairs in a function table
Obj. 22 - WP: Determine a percent of
a whole number using less than
100%
Obj. 23 - WP: Determine the percent
a whole number is of another whole
number, with a result less than 100%
Obj. 24 - WP: Determine a whole
number given a part and a
percentage
Page 65 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 25 - WP: Determine the percent
of decrease applied to a number
Obj. 26 - WP: Determine the percent
of increase applied to a number
Obj. 27 - WP: Determine the result of
applying a percent of decrease to a
value
Obj. 28 - WP: Determine the result of
applying a percent of increase to a
value
Obj. 46 - WP: Determine a part,
given part to whole ratio and the
whole, where the whole is greater
than 50
Obj. 47 - WP: Determine a part,
given part to part ratio and the whole,
where the whole is greater than 50
Obj. 48 - WP: Determine a part,
given part to whole ratio and a part,
where the whole is greater than 50
Obj. 49 - WP: Determine a part,
given part to part ratio and a part,
where the whole is greater than 50
Obj. 50 - WP: Determine the whole,
given part to whole ratio and a part,
where the whole is greater than 50
Obj. 51 - WP: Determine the whole,
given part to part ratio and a part,
where the whole is greater than 50
Obj. 52 - WP: Determine a unit rate
Topic 2 - Algebra
MN 7.2.2.3 - Use knowledge of
proportions to assess the
reasonableness of solutions.
Example: Recognize that it would be
unreasonable for a cashier to request
$200 if you purchase a $225 item at
25% off.
Page 66 of 198
Obj. 53 - WP: Use a unit rate to solve
a problem
Obj. 71 - WP: Solve a proportion
Obj. 72 - WP: Use direct variation to
solve a problem
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.2.4 - Represent real-world or Topic 2 - Algebra
Obj. 75 - WP: Use a 1-variable 1mathematical situations using
step equation to represent a situation
equations and inequalities involving
variables and positive and negative
rational numbers. Example 1: "Fourfifths is three greater than the
opposite of a number" can be
represented as 4/5 = -n + 3, and
"height no bigger than half the radius"
can be represented as h is less than
or equal to r/2. Example 2: "x is at
least -3 and less than 5" can be
represented as -3 is less than or
equal to x < 5, and also on a number
line.
Obj. 76 - Determine the graph of an
inequality on a number line
Obj. 79 - Determine the graph of the
solution set of a 1-step linear
inequality
Obj. 80 - WP: Use a 1-variable linear
inequality to represent a situation
MN 7.2.3 - Apply understanding of
order of operations and algebraic
properties to generate equivalent
numerical and algebraic expressions
containing positive and negative
rational numbers and grouping
symbols; evaluate such expressions.
MN 7.2.3.1 - Generate equivalent
numerical and algebraic expressions
containing rational numbers and
whole number exponents. Properties
of algebra include associative,
commutative and distributive laws.
Example: Combine like terms (use
the distributive law) to write 3x - 7x +
1 = (3-7)x + 1 = -4x + 1.
MN 7.2.3.2 - Evaluate algebraic
Topic 2 - Algebra
expressions containing rational
numbers and whole number
exponents at specified values of their
variables. Example: Evaluate the
expression 1/3 (2x - 5)² at x = 5.
Obj. 62 - Evaluate a 1-variable
expression, with two or three
operations, using integer substitution
Obj. 64 - Evaluate an algebraic
expression involving whole number
exponents
Page 67 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 65 - WP: Evaluate a variable
expression
Obj. 66 - WP: Evaluate a variable
expression involving exponents
MN 7.2.3.3 - Apply understanding of Topic 1 - Number Sense and
Obj. 10 - Evaluate an expression
order of operations and grouping
Operations
containing the fraction bar as the
symbols when using calculators and
division sign
other technologies. Example:
Recognize the conventions of using a
carat (^ raise to a power), asterisk (*
multiply), and also pay careful
attention to the use of nested
parentheses.
Obj. 11 - Evaluate a numerical
expression, with parentheses and
exponents, using order of operations
Topic 2 - Algebra
Obj. 63 - Evaluate a 2-variable
expression, with two or three
operations, using integer substitution
MN 7.2.4 - Represent real-world and
mathematical situations using
equations with variables. Solve
equations symbolically, using the
properties of equality. Also solve
equations graphically and
numerically. Interpret solutions in the
original context.
MN 7.2.4.1 - Represent relationships
in various contexts with equations
involving variables and positive and
negative rational numbers. Use the
properties of equality to solve for the
value of a variable. Interpret the
solution in the original context.
Example 1: Solve for w in the
equation P = 2w + 2l when P = 3.5
and l = 0.4. Example 2: To post an
Internet website, Mary must pay $300
for initial set up and a monthly fee of
$12. She has $842 in savings, how
long can she sustain her website?
Page 68 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.4.2 - Solve equations
Topic 2 - Algebra
Obj. 71 - WP: Solve a proportion
resulting from proportional
relationships in various contexts.
Example 1: Given the side lengths of
one triangle and one side length of a
second triangle that is similar to the
first, find the remaining side lengths
of the second triangle. Example 2:
Determine the price of 12 yards of
ribbon if 5 yards of ribbon cost $1.85.
Obj. 72 - WP: Use direct variation to
solve a problem
MN 7.3 - Geometry & Measurement
MN 7.3.1 - Use reasoning with
proportions and ratios to determine
measurements, justify formulas and
solve real-world and mathematical
problems involving circles and related
geometric figures.
MN 7.3.1.1 - Demonstrate an
Topic 3 - Geometry and
understanding of the proportional
Measurement
relationship between the diameter
and circumference of a circle and that
the unit rate (constant of
proportionality) is pi. Calculate the
circumference and area of circles and
sectors of circles to solve problems in
various contexts.
MN 7.3.1.2 - Calculate the volume
and surface area of cylinders and
justify the formulas used. Example:
Justify the formula for the surface
area of a cylinder by decomposing
the surface into two circles and a
rectangle.
Page 69 of 198
Topic 3 - Geometry and
Measurement
Obj. 84 - Determine the
circumference of a circle in terms of
pi
Obj. 88 - Determine the area of a
circle in terms of pi
Obj. 89 - Determine the area of a
circle using 3.14 for pi
Obj. 90 - Determine the area of a
circle using 22/7 for pi
Obj. 91 - WP: Determine the area of
a circle using 3.14 for pi
Obj. 94 - Determine the volume of a
cylinder
Obj. 95 - WP: Determine the volume
of a cylinder
Obj. 99 - Determine the surface area
of a cylinder
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.3.2 - Analyze the effect of
change of scale, translations and
reflections on the attributes of twodimensional figures.
MN 7.3.2.1 - Describe the properties Topic 3 - Geometry and
Obj. 106 - Determine the scale for a
of similarity, compare geometric
Measurement
drawing or map question
figures for similarity, and determine
scale factors. Example:
Corresponding angles in similar
geometric figures have the same
measure.
MN 7.3.2.2 - Apply scale factors,
Topic 3 - Geometry and
Obj. 104 - Determine a missing
length ratios and area ratios to
Measurement
dimension given two similar shapes
determine side lengths and areas of
similar geometric figures. Example: If
two similar rectangles have heights of
3 and 5, and the first rectangle has a
base of length 7, the base of the
second rectangle has length 35/3.
MN 7.3.2.3 - Use proportions and
ratios to solve problems involving
scale drawings and conversions of
measurement units. Example 1: 1
square foot equals 144 square
inches. Example 2: In a map where 1
inch represents 50 miles, 1/2 inch
represents 25 miles.
MN 7.3.2.4 - Graph and describe
translations and reflections of figures
on a coordinate grid and determine
the coordinates of the vertices of the
figure after the transformation.
Example: The point (1, 2) moves to (1, 2) after reflection about the y-axis.
Topic 3 - Geometry and
Measurement
Topic 3 - Geometry and
Measurement
Obj. 105 - WP: Solve a problem
involving similar shapes
Obj. 107 - WP: Solve a problem
involving a map or scale drawing
Obj. 107 - WP: Solve a problem
involving a map or scale drawing
Obj. 121 - Determine the coordinates
of a translated, a rotated, or a
reflected shape on the Cartesian
plane
MN 7.4 - Data Analysis & Probability
MN 7.4.1 - Use mean, median and
range to draw conclusions about data
and make predictions.
Page 70 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.4.1.1 - Determine mean,
Topic 4 - Data Analysis,
Obj. 132 - Determine the mean of a
median and range for quantitative
Statistics, and Probability
set of data
data and from data represented in a
display. Use these quantities to draw
conclusions about the data, compare
different data sets, and make
predictions. Example: By looking at
data from the past, Sandy calculated
that the mean gas mileage for her car
was 28 miles per gallon. She expects
to travel 400 miles during the next
week. Predict the approximate
number of gallons that she will use.
MN 7.4.1.2 - Describe the impact that
inserting or deleting a data point has
on the mean and the median of a
data set. Know how to create data
displays using a spreadsheet to
examine this impact. Example: How
does dropping the lowest test score
affect a student's mean test score?
MN 7.4.2 - Display and interpret data
in a variety of ways, including circle
graphs and histograms.
MN 7.4.2.1 - Use reasoning with
Topic 4 - Data Analysis,
proportions to display and interpret
Statistics, and Probability
data in circle graphs (pie charts) and
histograms. Choose the appropriate
data display and know how to create
the display using a spreadsheet or
other graphing technology.
MN 7.4.3 - Calculate probabilities and
reason about probabilities using
proportions to solve real-world and
mathematical problems.
Page 71 of 198
Obj. 134 - Determine the median of a
set of data
Obj. 135 - WP: Use the mean of a
data set to solve a problem
Obj. 125 - Answer a question using
information from a circle graph using
percentage calculations
Obj. 126 - Use a circle graph to
represent percentage data
Obj. 127 - Use a histogram to
represent data
Obj. 128 - Answer a question using
information from a histogram
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 7
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.4.3.1 - Use random numbers
generated by a calculator or a
spreadsheet or taken from a table to
simulate situations involving
randomness, make a histogram to
display the results, and compare the
results to known probabilities.
Example: Use a spreadsheet function
such as RANDBETWEEN(1, 10) to
generate random whole numbers
from 1 to 10, and display the results
in a histogram.
MN 7.4.3.2 - Calculate probability as
a fraction of sample space or as a
fraction of area. Express probabilities
as percents, decimals and fractions.
Example: Determine probabilities for
different outcomes in game spinners
by finding fractions of the area of the
spinner.
MN 7.4.3.3 - Use proportional
reasoning to draw conclusions about
and predict relative frequencies of
outcomes based on probabilities.
Example: When rolling a number
cube 600 times, one would predict
that a 3 or 6 would be rolled roughly
200 times, but probably not exactly
200 times.
Page 72 of 198
Grade 7
Topic 4 - Data Analysis,
Statistics, and Probability
Obj. 137 - Determine the probability
for independent events
Topic 4 - Data Analysis,
Statistics, and Probability
Obj. 138 - Determine the probability
for dependent events
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.1 - Number & Operation
MN 7.1.1 - Read, write, represent and
compare positive and negative
rational numbers, expressed as
integers, fractions and decimals.
MN 7.1.1.1 - Know that every rational
number can be written as the ratio of
two integers or as a terminating or
repeating decimal. Recognize that pi
is not rational, but that it can be
approximated by rational numbers
such as 22/7 and 3.14.
Grade 7
MN 7.1.1.2 - Understand that division
of two integers will always result in a
rational number. Use this information
to interpret the decimal result of a
division problem when using a
calculator. Example: 125/30 gives
4.16666667 on a calculator. This
answer is not exact. The exact
answer can be expressed as 4 1/6 ,
which is the same as 4.16 repeating.
The calculator expression does not
guarantee that the 6 is repeated, but
that possibility should be anticipated.
MN 7.1.1.3 - Locate positive and
negative rational numbers on the
number line, understand the concept
of opposites, and plot pairs of positive
and negative rational numbers on a
coordinate grid.
MN 7.1.1.4 - Compare positive and
negative rational numbers expressed
in various forms using the symbols <,
>, "less than or equal to", "greater
than or equal to". Example: -1/2 < 36.
MN 7.1.1.5 - Recognize and generate
equivalent representations of positive
and negative rational numbers,
including equivalent fractions.
Example: -40/12 = -120/36 = -10/3 = 3.3 repeating.
Page 73 of 198
Topic 1 - Number Sense and
Operations
Obj. 19 - Compare rational numbers
and/or irrational numbers in various
forms
Topic 1 - Number Sense and
Operations
Obj. 17 - Convert a repeating decimal
to a fraction or a mixed number
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.1.2 - Calculate with positive
and negative rational numbers, and
rational numbers with whole number
exponents, to solve real-world and
mathematical problems.
MN 7.1.2.1 - Add, subtract, multiply Topic 1 - Number Sense and
Obj. 6 - Add or subtract signed
and divide positive and negative
Operations
fractions or mixed numbers
rational numbers that are integers,
fractions and terminating decimals;
use efficient and generalizable
procedures, including standard
algorithms; raise positive rational
numbers to whole-number
exponents. Example: 3 to the 4th
power x (1/2)² = 81/4.
Obj. 7 - Multiply or divide signed
fractions or mixed numbers
Obj. 8 - Add or subtract signed
decimals
Obj. 9 - Multiply or divide signed
decimals
Obj. 11 - Determine the square of a
fraction or a decimal
MN 7.1.2.2 - Use real-world contexts
and the inverse relationship between
addition and subtraction to explain
why the procedures of arithmetic with
negative rational numbers make
sense. Example: Multiplying a
distance by -1 can be thought of as
representing that same distance in
the opposite direction. Multiplying by 1 a second time reverses directions
again, giving the distance in the
original direction.
MN 7.1.2.3 - Understand that
calculators and other computing
technologies often truncate or round
numbers. Example: A decimal that
repeats or terminates after a large
number of digits is truncated or
rounded.
MN 7.1.2.4 - Solve problems in
Topic 1 - Number Sense and
various contexts involving
Operations
calculations with positive and
negative rational numbers and
positive integer exponents, including
computing simple and compound
interest.
Page 74 of 198
Obj. 21 - Determine a percent of a
number given a percent that is not a
whole percent
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 22 - Determine the percent one
number is of another number
Obj. 23 - Determine a number given
a part and a decimal percentage or a
percentage more than 100%
Obj. 24 - WP: Determine a given
percent of a number
Obj. 25 - WP: Determine the percent
one number is of another number
MN 7.1.2.5 - Use proportional
reasoning to solve problems involving
ratios in various contexts. Example: A
recipe calls for milk, flour and sugar
in a ratio of 4:6:3 (this is how recipes
are often given in large institutions,
such as hospitals). How much flour
and milk would be needed with 1 cup
of sugar?
Obj. 26 - WP: Determine a number
given a part and a decimal
percentage or a percentage more
than 100%
Obj. 27 - Solve a problem involving
simple interest
Obj. 28 - Solve a problem involving
annually compounded interest
Obj. 29 - WP: Find the result of two
consecutive percentage changes
applied to a given number
MN 7.1.2.6 - Demonstrate an
understanding of the relationship
between the absolute value of a
rational number and distance on a
number line. Use the symbol for
absolute value. Example: |- 3|
represents the distance from - 3 to 0
on a number line or 3 units; the
distance between 3 and 9/2 on the
number line is |3 - 9/2| or 3/2.
MN 7.2 - Algebra
MN 7.2.1 - Understand the concept of
proportionality in real-world and
mathematical situations, and
distinguish between proportional and
other relationships.
Page 75 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.1.1 - Understand that a
relationship between two variables, x
and y, is proportional if it can be
expressed in the form y/x = k or y =
kx. Distinguish proportional
relationships from other relationships,
including inversely proportional
relationships (xy=k or y= k/x).
Example: The radius and
circumference of a circle are
proportional, whereas the length x
and the width y of a rectangle with
area 12 are inversely proportional,
since xy = 12 or equivalently, y =
12/x.
MN 7.2.1.2 - Understand that the
graph of a proportional relationship is
a line through the origin whose slope
is the unit rate (constant of
proportionality). Know how to use
graphing technology to examine what
happens to a line when the unit rate
is changed.
MN 7.2.2 - Recognize proportional
relationships in real-world and
mathematical situations; represent
these and other relationships with
tables, verbal descriptions, symbols
and graphs; solve problems involving
proportional relationships and explain
results in the original context.
MN 7.2.2.1 - Represent proportional Topic 2 - Algebra
relationships with tables, verbal
descriptions, symbols, equations and
graphs; translate from one
representation to another. Determine
the unit rate (constant of
proportionality or slope) given any of
these representations. Example:
Larry drives 114 miles and uses 5
gallons of gasoline. Sue drives 300
miles and uses 11.5 gallons of
gasoline. Use equations and graphs
to compare fuel efficiency and to
determine the costs of various trips.
Grade 7
Obj. 46 - Determine the slope of a
line given its graph or a graph of a
line with a given slope
Obj. 50 - WP: Determine a linear
graph that can represent a situation
Page 76 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.2.2 - Solve multi-step
Topic 1 - Number Sense and
Obj. 29 - WP: Find the result of two
problems involving proportional
Operations
consecutive percentage changes
relationships in numerous contexts.
applied to a given number
Example 1: Distance-time, percent
increase or decrease, discounts, tips,
unit pricing, lengths in similar
geometric figures, and unit
conversion when a conversion factor
is given, including conversion
between different measurement
systems. Example 2: How many
kilometers are there in 26.2 miles?
Topic 3 - Geometry and
Measurement
MN 7.2.2.3 - Use knowledge of
proportions to assess the
reasonableness of solutions.
Example: Recognize that it would be
unreasonable for a cashier to request
$200 if you purchase a $225 item at
25% off.
MN 7.2.2.4 - Represent real-world or Topic 2 - Algebra
mathematical situations using
equations and inequalities involving
variables and positive and negative
rational numbers. Example 1: "Fourfifths is three greater than the
opposite of a number" can be
represented as 4/5 = -n + 3, and
"height no bigger than half the radius"
can be represented as h is less than
or equal to r/2. Example 2: "x is at
least -3 and less than 5" can be
represented as -3 is less than or
equal to x < 5, and also on a number
line.
MN 7.2.3 - Apply understanding of
order of operations and algebraic
properties to generate equivalent
numerical and algebraic expressions
containing positive and negative
rational numbers and grouping
symbols; evaluate such expressions.
Page 77 of 198
Obj. 57 - WP: Solve a distance-ratetime problem that involves unit
conversions
Obj. 39 - WP: Use a 1-variable
equation with rational coefficients to
represent a situation involving two
operations
Obj. 40 - WP: Use a 2-variable
equation with rational coefficients to
represent a situation
Obj. 53 - WP: Use a 2-step linear
inequality in one variable to represent
a situation
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.3.1 - Generate equivalent
Topic 1 - Number Sense and
Obj. 1 - Evaluate an integer raised to
numerical and algebraic expressions Operations
a whole number power
containing rational numbers and
whole number exponents. Properties
of algebra include associative,
commutative and distributive laws.
Example: Combine like terms (use
the distributive law) to write 3x - 7x +
1 = (3-7)x + 1 = -4x + 1.
Topic 2 - Algebra
Obj. 10 - Evaluate a numerical
expression involving nested
parentheses
Obj. 33 - Simplify an algebraic
expression by combining like terms
Obj. 36 - Use the distributive property
to simplify an algebraic expression
MN 7.2.3.2 - Evaluate algebraic
Topic 2 - Algebra
expressions containing rational
numbers and whole number
exponents at specified values of their
variables. Example: Evaluate the
expression 1/3 (2x - 5)² at x = 5.
Obj. 31 - Evaluate a 2-variable
expression with two or three
operations substituting fractions or
decimals
MN 7.2.3.3 - Apply understanding of
order of operations and grouping
symbols when using calculators and
other technologies. Example:
Recognize the conventions of using a
carat (^ raise to a power), asterisk (*
multiply), and also pay careful
attention to the use of nested
parentheses.
MN 7.2.4 - Represent real-world and
mathematical situations using
equations with variables. Solve
equations symbolically, using the
properties of equality. Also solve
equations graphically and
numerically. Interpret solutions in the
original context.
Page 78 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.2.4.1 - Represent relationships Topic 2 - Algebra
Obj. 37 - Solve a 1-step equation
in various contexts with equations
involving rational numbers
involving variables and positive and
negative rational numbers. Use the
properties of equality to solve for the
value of a variable. Interpret the
solution in the original context.
Example 1: Solve for w in the
equation P = 2w + 2l when P = 3.5
and l = 0.4. Example 2: To post an
Internet website, Mary must pay $300
for initial set up and a monthly fee of
$12. She has $842 in savings, how
long can she sustain her website?
MN 7.2.4.2 - Solve equations
resulting from proportional
relationships in various contexts.
Example 1: Given the side lengths of
one triangle and one side length of a
second triangle that is similar to the
first, find the remaining side lengths
of the second triangle. Example 2:
Determine the price of 12 yards of
ribbon if 5 yards of ribbon cost $1.85.
Obj. 38 - Solve a 2-step equation
involving rational numbers
Obj. 39 - WP: Use a 1-variable
equation with rational coefficients to
represent a situation involving two
operations
Obj. 40 - WP: Use a 2-variable
equation with rational coefficients to
represent a situation
Obj. 41 - WP: Solve a problem
involving a 1-variable, 2-step
equation
MN 7.3 - Geometry & Measurement
MN 7.3.1 - Use reasoning with
proportions and ratios to determine
measurements, justify formulas and
solve real-world and mathematical
problems involving circles and related
geometric figures.
Page 79 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.3.1.1 - Demonstrate an
understanding of the proportional
relationship between the diameter
and circumference of a circle and that
the unit rate (constant of
proportionality) is pi. Calculate the
circumference and area of circles and
sectors of circles to solve problems in
various contexts.
MN 7.3.1.2 - Calculate the volume
and surface area of cylinders and
justify the formulas used. Example:
Justify the formula for the surface
area of a cylinder by decomposing
the surface into two circles and a
rectangle.
MN 7.3.2 - Analyze the effect of
change of scale, translations and
reflections on the attributes of twodimensional figures.
MN 7.3.2.1 - Describe the properties
of similarity, compare geometric
figures for similarity, and determine
scale factors. Example:
Corresponding angles in similar
geometric figures have the same
measure.
MN 7.3.2.2 - Apply scale factors,
Topic 3 - Geometry and
Obj. 59 - Determine the ratio of the
length ratios and area ratios to
Measurement
perimeters or areas of similar shapes
determine side lengths and areas of
similar geometric figures. Example: If
two similar rectangles have heights of
3 and 5, and the first rectangle has a
base of length 7, the base of the
second rectangle has length 35/3.
MN 7.3.2.3 - Use proportions and
Topic 3 - Geometry and
ratios to solve problems involving
Measurement
scale drawings and conversions of
measurement units. Example 1: 1
square foot equals 144 square
inches. Example 2: In a map where 1
inch represents 50 miles, 1/2 inch
represents 25 miles.
Page 80 of 198
Obj. 70 - WP: Solve a problem
involving scale
Obj. 70 - WP: Solve a problem
involving scale
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.3.2.4 - Graph and describe
translations and reflections of figures
on a coordinate grid and determine
the coordinates of the vertices of the
figure after the transformation.
Example: The point (1, 2) moves to (1, 2) after reflection about the y-axis.
Grade 7
MN 7.4 - Data Analysis & Probability
MN 7.4.1 - Use mean, median and
range to draw conclusions about data
and make predictions.
MN 7.4.1.1 - Determine mean,
Topic 4 - Data Analysis,
median and range for quantitative
Statistics, and Probability
data and from data represented in a
display. Use these quantities to draw
conclusions about the data, compare
different data sets, and make
predictions. Example: By looking at
data from the past, Sandy calculated
that the mean gas mileage for her car
was 28 miles per gallon. She expects
to travel 400 miles during the next
week. Predict the approximate
number of gallons that she will use.
MN 7.4.1.2 - Describe the impact that Topic 4 - Data Analysis,
inserting or deleting a data point has Statistics, and Probability
on the mean and the median of a
data set. Know how to create data
displays using a spreadsheet to
examine this impact. Example: How
does dropping the lowest test score
affect a student's mean test score?
Obj. 89 - Compare the medians, the
modes, or the ranges of the data in a
double stem-and-leaf plot
Obj. 90 - Determine the median of
the data in a frequency table or a bar
graph
Obj. 91 - Determine the mean of the
data in a frequency table or a bar
graph
Obj. 88 - Analyze the effect that
changing elements in a data set has
on the mean, the median, or the
range
MN 7.4.2 - Display and interpret data
in a variety of ways, including circle
graphs and histograms.
Page 81 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 7,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 7.4.2.1 - Use reasoning with
Topic 4 - Data Analysis,
Obj. 76 - Use a circle graph to
proportions to display and interpret
Statistics, and Probability
organize data
data in circle graphs (pie charts) and
histograms. Choose the appropriate
data display and know how to create
the display using a spreadsheet or
other graphing technology.
MN 7.4.3 - Calculate probabilities and
reason about probabilities using
proportions to solve real-world and
mathematical problems.
MN 7.4.3.1 - Use random numbers
generated by a calculator or a
spreadsheet or taken from a table to
simulate situations involving
randomness, make a histogram to
display the results, and compare the
results to known probabilities.
Example: Use a spreadsheet function
such as RANDBETWEEN(1, 10) to
generate random whole numbers
from 1 to 10, and display the results
in a histogram.
MN 7.4.3.2 - Calculate probability as
a fraction of sample space or as a
fraction of area. Express probabilities
as percents, decimals and fractions.
Example: Determine probabilities for
different outcomes in game spinners
by finding fractions of the area of the
spinner.
MN 7.4.3.3 - Use proportional
reasoning to draw conclusions about
and predict relative frequencies of
outcomes based on probabilities.
Example: When rolling a number
cube 600 times, one would predict
that a 3 or 6 would be rolled roughly
200 times, but probably not exactly
200 times.
Page 82 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.1 - Number & Operation
MN 8.1.1 - Read, write, compare,
classify and represent real numbers,
and use them to solve problems in
various contexts.
MN 8.1.1.1 - Classify real numbers
Topic 1 - Number Sense and
Obj. 18 - Identify rational or irrational
as rational or irrational. Know that
Operations
numbers
when a square root of a positive
integer is not an integer, then it is
irrational. Know that the sum of a
rational number and an irrational
number is irrational, and the product
of a non-zero rational number and an
irrational number is irrational.
Example: Classify the following
numbers as whole numbers, integers,
rational numbers, irrational numbers,
recognizing that some numbers
belong in more than one category:
6/3, 3/6, 3.6 repeating, pi/2, - the
square root of 4, the square root of
10, -6.7.
MN 8.1.1.2 - Compare real numbers; Topic 1 - Number Sense and
locate real numbers on a number
Operations
line. Identify the square root of a
positive integer as an integer, or if it
is not an integer, locate it as a real
number between two consecutive
positive integers. Example 1: Put the
following numbers in order from
smallest to largest: 2, square root of
3, -4, -6.8, - the square root of 37.
Example 2: The square root of 68 is
an irrational number between 8 and
9.
Obj. 14 - Determine the two closest
integers to a given square root
Obj. 15 - Approximate the location of
a square root on a number line
Obj. 19 - Compare rational numbers
and/or irrational numbers in various
forms
Obj. 20 - Order rational numbers and
irrational numbers
Page 83 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.1.1.3 - Determine rational
Topic 1 - Number Sense and
Obj. 16 - Determine the square root
approximations for solutions to
Operations
of a whole number to the nearest
problems involving real numbers.
tenth
Example 1: A calculator can be used
to determine that the square root of 7
is approximately 2.65. Example 2: To
check that 1 5/12 is slightly bigger
than the square root of 2, do the
calculation (1 5/12)² = (17/12)² =
289/144 = 2 1/144. Example 3:
Knowing that the square root of 10 is
between 3 and 4, try squaring
numbers like 3.5, 3.3, 3.1 to
determine that 3.1 is a reasonable
rational approximation of the square
root of 10.
MN 8.1.1.4 - Know and apply the
Topic 1 - Number Sense and
Obj. 1 - Evaluate an integer raised to
properties of positive and negative
Operations
a whole number power
integer exponents to generate
equivalent numerical expressions.
Example: 3² x 3 to the -5 power = 3 to
the -3 power (1/3)³ = 1/27.
Obj. 2 - Evaluate a zero or negative
power of an integer
Obj. 3 - Evaluate a numerical
expression involving integer
exponents and/or integer bases
Obj. 10 - Evaluate a numerical
expression involving nested
parentheses
MN 8.1.1.5 - Express approximations Topic 1 - Number Sense and
Obj. 4 - Convert a number less than
of very large and very small numbers Operations
1 to scientific notation
using scientific notation; understand
how calculators display numbers in
scientific notation. Multiply and divide
numbers expressed in scientific
notation, express the answer in
scientific notation, using the correct
number of significant digits when
physical measurements are involved.
Example: (4.2 x 10 to the 4th power)
x (8.25 x 10³)= 3.465 x 10 to the 8th
power, but if these numbers
represent physical measurements,
the answer should be expressed as
3.5 x 10 to the 8th power because the
first factor, 4.2 x 10 to the 4th power,
only has two significant digits.
Page 84 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 5 - Convert a number less than
1 from scientific notation to standard
form
MN 8.2 - Algebra
MN 8.2.1 - Understand the concept of
function in real-world and
mathematical situations, and
distinguish between linear and nonlinear functions.
MN 8.2.1.1 - Understand that a
function is a relationship between an
independent variable and a
dependent variable in which the value
of the independent variable
determines the value of the
dependent variable. Use functional
notation, such as f(x), to represent
such relationships. Example: The
relationship between the area of a
square and the side length can be
expressed as f(x)=x². In this case,
f(5)=25 , which represents the fact
that a square of side length 5 units
has area 25 units squared.
MN 8.2.1.2 - Use linear functions to
represent relationships in which
changing the input variable by some
amount leads to a change in the
output variable that is a constant
times that amount. Example: Uncle
Jim gave Emily $50 on the day she
was born and $25 on each birthday
after that. The function f(x)=50+25x
represents the amount of money Jim
has given after x years. The rate of
change is $25 per year.
MN 8.2.1.3 - Understand that a
function is linear if it can be
expressed in the form f(x)=mx+b or if
its graph is a straight line. Example:
The function f(x)=x² is not a linear
function because its graph contains
the points (1,1), (-1,1) and (0,0),
which are not on a straight line.
Page 85 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.1.4 - Understand that an
arithmetic sequence is a linear
function that can be expressed in the
form f(x)=mx+b, where x = 0, 1, 2, 3,
.... Example: The arithmetic
sequence 3, 7, 11, 15, ..., can be
expressed as f(x) = 4x + 3.
Grade 7
MN 8.2.1.5 - Understand that a
geometric sequence is a non-linear
function that can be expressed in the
form , fx(x)=ab where x = 0, 1, 2, 3,
.... Example: The geometric
sequence 6, 12, 24, 48, ... , can be
expressed in the form f(x) = 6(2 to
the x power).
MN 8.2.2 - Recognize linear functions
in real-world and mathematical
situations; represent linear functions
and other functions with tables,
verbal descriptions, symbols and
graphs; solve problems involving
these functions and explain results in
the original context.
MN 8.2.2.1 - Represent linear
Topic 2 - Algebra
functions with tables, verbal
descriptions, symbols, equations and
graphs; translate from one
representation to another.
Obj. 42 - Determine the graph of a
line for a given table of values
MN 8.2.2.2 - Identify graphical
Topic 2 - Algebra
properties of linear functions
including slopes and intercepts. Know
that the slope equals the rate of
change, and that the y-intercept is
zero when the function represents a
proportional relationship.
Obj. 46 - Determine the slope of a
line given its graph or a graph of a
line with a given slope
Page 86 of 198
Obj. 43 - Determine the table of
values that represents a linear
equation with rational coefficients in
two variables
Obj. 44 - Determine a linear equation
in two variables that represents a
table of values
Obj. 45 - Determine the graph of a 2operation linear function
Obj. 50 - WP: Determine a linear
graph that can represent a situation
Obj. 47 - Determine the x- or yintercept of a line given its graph
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 48 - WP: Interpret the meaning
of the slope of a graphed line
Obj. 49 - WP: Interpret the meaning
of the y-intercept of a graphed line
MN 8.2.2.3 - Identify how coefficient
changes in the equation f(x) = mx + b
affect the graphs of linear functions.
Know how to use graphing
technology to examine these effects.
MN 8.2.2.4 - Represent arithmetic
sequences using equations, tables,
graphs and verbal descriptions, and
use them to solve problems.
Example: If a girl starts with $100 in
savings and adds $10 at the end of
each month, she will have 100 + 10x
dollars after x months.
MN 8.2.2.5 - Represent geometric
sequences using equations, tables,
graphs and verbal descriptions, and
use them to solve problems.
Example: If a girl invests $100 at 10%
annual interest, she will have 100(1.1
to the x power) dollars after x years.
MN 8.2.3 - Generate equivalent
numerical and algebraic expressions
and use algebraic properties to
evaluate expressions.
MN 8.2.3.1 - Evaluate algebraic
Topic 2 - Algebra
expressions, including expressions
containing radicals and absolute
values, at specified values of their
variables. Example: Evaluate pi r²h
when r = 3 and h = 0.5, and then use
an approximation of pi, to obtain an
approximate answer.
MN 8.2.3.2 - Justify steps in
generating equivalent expressions by
identifying the properties used,
including the properties of algebra.
Properties include the associative,
commutative and distributive laws,
and the order of operations, including
grouping symbols.
Page 87 of 198
Obj. 31 - Evaluate a 2-variable
expression with two or three
operations substituting fractions or
decimals
Obj. 32 - Evaluate an algebraic
expression involving negative integer
exponents
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear expressions. Solve equations
and inequalities symbolically and
graphically. Interpret solutions in the
original context.
MN 8.2.4.1 - Use linear equations to Topic 2 - Algebra
represent situations involving a
constant rate of change, including
proportional and non-proportional
relationships. Example: For a cylinder
with fixed radius of length 5, the
surface area A = 2 pi(5)h + 2 pi(5)² =
10 pi h + 50 pi, is a linear function of
the height h, but it is not proportional
to the height.
MN 8.2.4.2 - Solve multi-step
Topic 2 - Algebra
equations in one variable. Solve for
one variable in a multi-variable
equation in terms of the other
variables. Justify the steps by
identifying the properties of equalities
used. Example 1: The equation 10x +
17 = 3x can be changed to 7x + 17 =
0, and then to 7x = -17 by
adding/subtracting the same
quantities to both sides. These
changes do not change the solution
of the equation. Example 2: Express
the radius of a circle in terms of its
circumference.
MN 8.2.4.3 - Express linear
equations in slope-intercept, pointslope and standard forms, and
convert between these forms. Given
sufficient information, find an
equation of a line. Example:
Determine an equation of the line
through the points (-1,6) and (2/3, 3/4).
Page 88 of 198
Grade 7
Obj. 39 - WP: Use a 1-variable
equation with rational coefficients to
represent a situation involving two
operations
Obj. 40 - WP: Use a 2-variable
equation with rational coefficients to
represent a situation
Obj. 38 - Solve a 2-step equation
involving rational numbers
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.4 - Use linear inequalities to
represent relationships in various
contexts. Example: A gas station
charges $0.10 less per gallon of
gasoline if a customer also gets a car
wash. Without the car wash, gas
costs $2.79 per gallon. The car wash
is $8.95. What are the possible
amounts (in gallons) of gasoline that
you can buy if you also get a car
wash and can spend at most $35?
MN 8.2.4.5 - Solve linear inequalities Topic 2 - Algebra
using properties of inequalities.
Graph the solutions on a number line.
Example: The inequality -3x < 6 is
equivalent to x > -2 , which can be
represented on the number line by
shading in the interval to the right of 2.
MN 8.2.4.6 - Represent relationships
in various contexts with equations
and inequalities involving the
absolute value of a linear expression.
Solve such equations and inequalities
and graph the solutions on a number
line. Example: A cylindrical machine
part is manufactured with a radius of
2.1 cm, with a tolerance of 1/100 cm.
The radius r satisfies the inequality |r 2.1| is less than or equal to .01.
Page 89 of 198
Grade 7
Obj. 52 - Solve a 2-step linear
inequality in one variable
Obj. 54 - WP: Solve a problem
involving a 2-step linear inequality in
one variable
Obj. 55 - Determine the graph of the
solutions to a 2-step linear inequality
in one variable
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.7 - Represent relationships
in various contexts using systems of
linear equations. Solve systems of
linear equations in two variables
symbolically, graphically and
numerically. Example: Marty's cell
phone company charges $15 per
month plus $0.04 per minute for each
call. Jeannine's company charges
$0.25 per minute. Use a system of
equations to determine the
advantages of each plan based on
the number of minutes used.
Grade 7
MN 8.2.4.8 - Understand that a
system of linear equations may have
no solution, one solution, or an
infinite number of solutions. Relate
the number of solutions to pairs of
lines that are intersecting, parallel or
identical. Check whether a pair of
numbers satisfies a system of two
linear equations in two unknowns by
substituting the numbers into both
equations.
MN 8.2.4.9 - Use the relationship
between square roots and squares of
a number to solve problems.
Example: If pi x² = 5, then |x| = the
square root of (5/pi), or equivalently,
x = the square root of (5/pi) or x = the square root of (5/pi). If x is
understood as the radius of a circle in
this example, then the negative
solution should be discarded and x =
the square root of (5/pi).
MN 8.3 - Geometry & Measurement
MN 8.3.1 - Solve problems involving
right triangles using the Pythagorean
Theorem and its converse.
MN 8.3.1.1 - Use the Pythagorean
Topic 3 - Geometry and
Theorem to solve problems involving Measurement
right triangles. Example 1: Determine
the perimeter of a right triangle, given
the lengths of two of its sides.
Example 2: Show that a triangle with
side lengths 4, 5 and 6 is not a right
triangle.
Page 90 of 198
Obj. 71 - Determine the length of the
hypotenuse of a right triangle using
the Pythagorean theorem
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 72 - Determine the length of a
leg of a right triangle using the
Pythagorean theorem
Obj. 73 - WP: Use the Pythagorean
theorem to find a length or a distance
MN 8.3.1.2 - Determine the distance Topic 3 - Geometry and
between two points on a horizontal or Measurement
vertical line in a coordinate system.
Use the Pythagorean Theorem to find
the distance between any two points
in a coordinate system.
Obj. 75 - Determine if a triangle is a
right triangle by using the
Pythagorean theorem
Obj. 74 - Determine a distance on
the Cartesian plane using the
Pythagorean theorem
MN 8.3.1.3 - Informally justify the
Pythagorean Theorem by using
measurements, diagrams and
computer software.
MN 8.3.2 - Solve problems involving
parallel and perpendicular lines on a
coordinate system.
MN 8.3.2.1 - Understand and apply
the relationships between the slopes
of parallel lines and between the
slopes of perpendicular lines.
Dynamic graphing software may be
used to examine the relationships
between lines and their equations.
MN 8.3.2.2 - Analyze polygons on a
coordinate system by determining the
slopes of their sides. Example: Given
the coordinates of four points,
determine whether the corresponding
quadrilateral is a parallelogram.
MN 8.3.2.3 - Given a line on a
coordinate system and the
coordinates of a point not on the line,
find lines through that point that are
parallel and perpendicular to the
given line, symbolically and
graphically.
MN 8.4 - Data Analysis & Probability
MN 8.4.1 - Interpret data using
scatterplots and approximate lines of
best fit. Use lines of best fit to draw
conclusions about data.
Page 91 of 198
081309
Accelerated Math
Grade 7
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Grade 8
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.4.1.1 - Collect, display and
Topic 4 - Data Analysis,
Obj. 77 - Use a scatter plot to
interpret data using scatterplots. Use Statistics, and Probability
organize data
the shape of the scatterplot to
informally estimate a line of best fit
and determine an equation for the
line. Use appropriate titles, labels and
units. Know how to use graphing
technology to display scatterplots and
corresponding lines of best fit.
MN 8.4.1.2 - Use a line of best fit to Topic 4 - Data Analysis,
make statements about approximate Statistics, and Probability
rate of change and to make
predictions about values not in the
original data set. Example: Given a
scatterplot relating student heights to
shoe sizes, predict the shoe size of a
5'4" student, even if the data does not
contain information for a student of
that height.
Obj. 79 - Approximate a trend line for
a scatter plot
Obj. 80 - Answer a question using
information from a scatter plot
Obj. 80 - Answer a question using
information from a scatter plot
MN 8.4.1.3 - Assess the
reasonableness of predictions using
scatterplots by interpreting them in
the original context. Example: A set
of data may show that the number of
women in the U.S. Senate is growing
at a certain rate each election cycle.
Is it reasonable to use this trend to
predict the year in which the Senate
will eventually include 1000 female
Senators?
Page 92 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.1 - Number & Operation
MN 8.1.1 - Read, write, compare,
classify and represent real numbers,
and use them to solve problems in
various contexts.
MN 8.1.1.1 - Classify real numbers
as rational or irrational. Know that
when a square root of a positive
integer is not an integer, then it is
irrational. Know that the sum of a
rational number and an irrational
number is irrational, and the product
of a non-zero rational number and an
irrational number is irrational.
Example: Classify the following
numbers as whole numbers, integers,
rational numbers, irrational numbers,
recognizing that some numbers
belong in more than one category:
6/3, 3/6, 3.6 repeating, pi/2, - the
square root of 4, the square root of
10, -6.7.
Grade 8
MN 8.1.1.2 - Compare real numbers;
locate real numbers on a number
line. Identify the square root of a
positive integer as an integer, or if it
is not an integer, locate it as a real
number between two consecutive
positive integers. Example 1: Put the
following numbers in order from
smallest to largest: 2, square root of
3, -4, -6.8, - the square root of 37.
Example 2: The square root of 68 is
an irrational number between 8 and
9.
Page 93 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.1.1.3 - Determine rational
approximations for solutions to
problems involving real numbers.
Example 1: A calculator can be used
to determine that the square root of 7
is approximately 2.65. Example 2: To
check that 1 5/12 is slightly bigger
than the square root of 2, do the
calculation (1 5/12)² = (17/12)² =
289/144 = 2 1/144. Example 3:
Knowing that the square root of 10 is
between 3 and 4, try squaring
numbers like 3.5, 3.3, 3.1 to
determine that 3.1 is a reasonable
rational approximation of the square
root of 10.
MN 8.1.1.4 - Know and apply the
Topic 1 - Numbers and
Obj. 4 - Evaluate a fraction raised to
properties of positive and negative
Operations
an integer power
integer exponents to generate
equivalent numerical expressions.
Example: 3² x 3 to the -5 power = 3 to
the -3 power (1/3)³ = 1/27.
Topic 5 - Properties of Powers
Obj. 58 - Apply the product of powers
property to a monomial numerical
expression
Obj. 60 - Apply the power of a power
property to a monomial numerical
expression
Obj. 63 - Apply the quotient of
powers property to monomial
numerical expressions
MN 8.1.1.5 - Express approximations
of very large and very small numbers
using scientific notation; understand
how calculators display numbers in
scientific notation. Multiply and divide
numbers expressed in scientific
notation, express the answer in
scientific notation, using the correct
number of significant digits when
physical measurements are involved.
Example: (4.2 x 10 to the 4th power)
x (8.25 x 10³)= 3.465 x 10 to the 8th
power, but if these numbers
represent physical measurements,
the answer should be expressed as
3.5 x 10 to the 8th power because the
first factor, 4.2 x 10 to the 4th power,
only has two significant digits.
Page 94 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2 - Algebra
MN 8.2.1 - Understand the concept of
function in real-world and
mathematical situations, and
distinguish between linear and nonlinear functions.
MN 8.2.1.1 - Understand that a
Topic 2 - Relations and
Obj. 7 - Determine the independent
function is a relationship between an Functions
or dependent variable in a given
independent variable and a
situation
dependent variable in which the value
of the independent variable
determines the value of the
dependent variable. Use functional
notation, such as f(x), to represent
such relationships. Example: The
relationship between the area of a
square and the side length can be
expressed as f(x)=x². In this case,
f(5)=25 , which represents the fact
that a square of side length 5 units
has area 25 units squared.
MN 8.2.1.2 - Use linear functions to
represent relationships in which
changing the input variable by some
amount leads to a change in the
output variable that is a constant
times that amount. Example: Uncle
Jim gave Emily $50 on the day she
was born and $25 on each birthday
after that. The function f(x)=50+25x
represents the amount of money Jim
has given after x years. The rate of
change is $25 per year.
MN 8.2.1.3 - Understand that a
Topic 2 - Relations and
function is linear if it can be
Functions
expressed in the form f(x)=mx+b or if
its graph is a straight line. Example:
The function f(x)=x² is not a linear
function because its graph contains
the points (1,1), (-1,1) and (0,0),
which are not on a straight line.
Obj. 12 - Determine if a function is
linear or nonlinear
Obj. 13 - Determine whether a graph
or a table represents a linear or
nonlinear function
Page 95 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.1.4 - Understand that an
arithmetic sequence is a linear
function that can be expressed in the
form f(x)=mx+b, where x = 0, 1, 2, 3,
.... Example: The arithmetic
sequence 3, 7, 11, 15, ..., can be
expressed as f(x) = 4x + 3.
Grade 8
MN 8.2.1.5 - Understand that a
geometric sequence is a non-linear
function that can be expressed in the
form , fx(x)=ab where x = 0, 1, 2, 3,
.... Example: The geometric
sequence 6, 12, 24, 48, ... , can be
expressed in the form f(x) = 6(2 to
the x power).
MN 8.2.2 - Recognize linear functions
in real-world and mathematical
situations; represent linear functions
and other functions with tables,
verbal descriptions, symbols and
graphs; solve problems involving
these functions and explain results in
the original context.
MN 8.2.2.1 - Represent linear
functions with tables, verbal
descriptions, symbols, equations and
graphs; translate from one
representation to another.
MN 8.2.2.2 - Identify graphical
properties of linear functions
including slopes and intercepts. Know
that the slope equals the rate of
change, and that the y-intercept is
zero when the function represents a
proportional relationship.
MN 8.2.2.3 - Identify how coefficient
changes in the equation f(x) = mx + b
affect the graphs of linear functions.
Know how to use graphing
technology to examine these effects.
Page 96 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.2.4 - Represent arithmetic
sequences using equations, tables,
graphs and verbal descriptions, and
use them to solve problems.
Example: If a girl starts with $100 in
savings and adds $10 at the end of
each month, she will have 100 + 10x
dollars after x months.
Grade 8
MN 8.2.2.5 - Represent geometric
sequences using equations, tables,
graphs and verbal descriptions, and
use them to solve problems.
Example: If a girl invests $100 at 10%
annual interest, she will have 100(1.1
to the x power) dollars after x years.
MN 8.2.3 - Generate equivalent
numerical and algebraic expressions
and use algebraic properties to
evaluate expressions.
MN 8.2.3.1 - Evaluate algebraic
expressions, including expressions
containing radicals and absolute
values, at specified values of their
variables. Example: Evaluate pi r²h
when r = 3 and h = 0.5, and then use
an approximation of pi, to obtain an
approximate answer.
MN 8.2.3.2 - Justify steps in
generating equivalent expressions by
identifying the properties used,
including the properties of algebra.
Properties include the associative,
commutative and distributive laws,
and the order of operations, including
grouping symbols.
MN 8.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear expressions. Solve equations
and inequalities symbolically and
graphically. Interpret solutions in the
original context.
Page 97 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.1 - Use linear equations to Topic 3 - Linear Equations and
Obj. 16 - WP: Determine a linear
represent situations involving a
Inequalities
equation that can be used to solve a
constant rate of change, including
percent problem
proportional and non-proportional
relationships. Example: For a cylinder
with fixed radius of length 5, the
surface area A = 2 pi(5)h + 2 pi(5)² =
10 pi h + 50 pi, is a linear function of
the height h, but it is not proportional
to the height.
MN 8.2.4.2 - Solve multi-step
Topic 3 - Linear Equations and
Obj. 14 - Solve a 1-variable linear
equations in one variable. Solve for Inequalities
equation that requires simplification
one variable in a multi-variable
and has the variable on one side
equation in terms of the other
variables. Justify the steps by
identifying the properties of equalities
used. Example 1: The equation 10x +
17 = 3x can be changed to 7x + 17 =
0, and then to 7x = -17 by
adding/subtracting the same
quantities to both sides. These
changes do not change the solution
of the equation. Example 2: Express
the radius of a circle in terms of its
circumference.
Obj. 15 - Solve a 1-variable linear
equation with the variable on both
sides
Obj. 24 - Rewrite an equation to
solve for a specified variable
MN 8.2.4.3 - Express linear
Topic 3 - Linear Equations and
Obj. 25 - Determine the slopeequations in slope-intercept, pointInequalities
intercept form or the standard form of
slope and standard forms, and
a linear equation
convert between these forms. Given
sufficient information, find an
equation of a line. Example:
Determine an equation of the line
through the points (-1,6) and (2/3, 3/4).
Obj. 31 - Determine an equation of a
line given the slope and y-intercept of
the line
Obj. 33 - Determine an equation for a
line given the slope of the line and a
point on the line that is not the yintercept
Obj. 34 - Determine an equation of a
line given two points on the line
Page 98 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.4 - Use linear inequalities to
represent relationships in various
contexts. Example: A gas station
charges $0.10 less per gallon of
gasoline if a customer also gets a car
wash. Without the car wash, gas
costs $2.79 per gallon. The car wash
is $8.95. What are the possible
amounts (in gallons) of gasoline that
you can buy if you also get a car
wash and can spend at most $35?
MN 8.2.4.5 - Solve linear inequalities Topic 3 - Linear Equations and
using properties of inequalities.
Inequalities
Graph the solutions on a number line.
Example: The inequality -3x < 6 is
equivalent to x > -2 , which can be
represented on the number line by
shading in the interval to the right of 2.
MN 8.2.4.6 - Represent relationships Topic 3 - Linear Equations and
in various contexts with equations
Inequalities
and inequalities involving the
absolute value of a linear expression.
Solve such equations and inequalities
and graph the solutions on a number
line. Example: A cylindrical machine
part is manufactured with a radius of
2.1 cm, with a tolerance of 1/100 cm.
The radius r satisfies the inequality |r 2.1| is less than or equal to .01.
Grade 8
Obj. 21 - Solve a 1-variable linear
inequality with the variable on one
side
Obj. 22 - Solve a 1-variable linear
inequality with the variable on both
sides
Obj. 23 - Solve a 1-variable
compound inequality
Obj. 20 - Solve a 1-variable absolute
value equation
Obj. 43 - Solve a 1-variable absolute
value inequality
Obj. 44 - Determine the graph of a 1variable absolute value inequality
Page 99 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.7 - Represent relationships Topic 4 - Systems of Linear
Obj. 45 - Solve a system of linear
in various contexts using systems of Equations and Inequalities
equations in two variables by
linear equations. Solve systems of
graphing
linear equations in two variables
symbolically, graphically and
numerically. Example: Marty's cell
phone company charges $15 per
month plus $0.04 per minute for each
call. Jeannine's company charges
$0.25 per minute. Use a system of
equations to determine the
advantages of each plan based on
the number of minutes used.
MN 8.2.4.8 - Understand that a
Topic 4 - Systems of Linear
system of linear equations may have Equations and Inequalities
no solution, one solution, or an
infinite number of solutions. Relate
the number of solutions to pairs of
lines that are intersecting, parallel or
identical. Check whether a pair of
numbers satisfies a system of two
linear equations in two unknowns by
substituting the numbers into both
equations.
Page 100 of 198
Obj. 46 - Solve a system of linear
equations in two variables by
substitution
Obj. 47 - Solve a system of linear
equations in two variables by
elimination
Obj. 49 - Solve a system of linear
equations in two variables using any
method
Obj. 50 - WP: Determine a system of
linear equations that represents a
given situation
Obj. 51 - WP: Solve a mixture
problem that can be represented by a
system of linear equations
Obj. 52 - WP: Solve a motion
problem that can be represented by a
system of linear equations
Obj. 53 - Solve a number problem
that can be represented by a linear
system of equations
Obj. 48 - Determine the number of
solutions to a system of linear
equations
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.2.4.9 - Use the relationship
Topic 8 - Quadratic Equations
Obj. 89 - Solve a quadratic equation
between square roots and squares of and Functions
by taking the square root
a number to solve problems.
Example: If pi x² = 5, then |x| = the
square root of (5/pi), or equivalently,
x = the square root of (5/pi) or x = the square root of (5/pi). If x is
understood as the radius of a circle in
this example, then the negative
solution should be discarded and x =
the square root of (5/pi).
MN 8.3 - Geometry & Measurement
MN 8.3.1 - Solve problems involving
right triangles using the Pythagorean
Theorem and its converse.
MN 8.3.1.1 - Use the Pythagorean
Theorem to solve problems involving
right triangles. Example 1: Determine
the perimeter of a right triangle, given
the lengths of two of its sides.
Example 2: Show that a triangle with
side lengths 4, 5 and 6 is not a right
triangle.
MN 8.3.1.2 - Determine the distance
between two points on a horizontal or
vertical line in a coordinate system.
Use the Pythagorean Theorem to find
the distance between any two points
in a coordinate system.
MN 8.3.1.3 - Informally justify the
Pythagorean Theorem by using
measurements, diagrams and
computer software.
MN 8.3.2 - Solve problems involving
parallel and perpendicular lines on a
coordinate system.
MN 8.3.2.1 - Understand and apply
the relationships between the slopes
of parallel lines and between the
slopes of perpendicular lines.
Dynamic graphing software may be
used to examine the relationships
between lines and their equations.
Page 101 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.3.2.2 - Analyze polygons on a
coordinate system by determining the
slopes of their sides. Example: Given
the coordinates of four points,
determine whether the corresponding
quadrilateral is a parallelogram.
Grade 8
MN 8.3.2.3 - Given a line on a
coordinate system and the
coordinates of a point not on the line,
find lines through that point that are
parallel and perpendicular to the
given line, symbolically and
graphically.
MN 8.4 - Data Analysis & Probability
MN 8.4.1 - Interpret data using
scatterplots and approximate lines of
best fit. Use lines of best fit to draw
conclusions about data.
MN 8.4.1.1 - Collect, display and
interpret data using scatterplots. Use
the shape of the scatterplot to
informally estimate a line of best fit
and determine an equation for the
line. Use appropriate titles, labels and
units. Know how to use graphing
technology to display scatterplots and
corresponding lines of best fit.
MN 8.4.1.2 - Use a line of best fit to
make statements about approximate
rate of change and to make
predictions about values not in the
original data set. Example: Given a
scatterplot relating student heights to
shoe sizes, predict the shoe size of a
5'4" student, even if the data does not
contain information for a student of
that height.
Page 102 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grade 8,
Accelerated Math Second Edition Algebra 1
Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 8.4.1.3 - Assess the
reasonableness of predictions using
scatterplots by interpreting them in
the original context. Example: A set
of data may show that the number of
women in the U.S. Senate is growing
at a certain rate each election cycle.
Is it reasonable to use this trend to
predict the year in which the Senate
will eventually include 1000 female
Senators?
Grade 8
Page 103 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2 - Algebra
MN 9.2.1 - Understand the concept of
function, and identify important
features of functions and other
relations using symbolic and
graphical methods where
appropriate.
MN 9.2.1.1 - Understand the
Topic 2 - Relations and
Obj. 11 - Evaluate a function written
definition of a function. Use functional Functions
in function notation for a given value
notation and evaluate a function at a
given point in its domain. Example: If
f(x) - 1/(x²-3),find f(-4).
MN 9.2.1.2 - Distinguish between
functions and other relations defined
symbolically, graphically or in tabular
form.
MN 9.2.1.3 - Find the domain of a
function defined symbolically,
graphically or in a real-world context.
Example: The formula f(x) = pi x² can
represent a function whose domain is
all real numbers, but in the context of
the area of a circle, the domain would
be restricted to positive x.
MN 9.2.1.4 - Obtain information and
draw conclusions from graphs of
functions and other relations.
Example: If a graph shows the
relationship between the elapsed
flight time of a golf ball at a given
moment and its height at that same
moment, identify the time interval
during which the ball is at least 100
feet above the ground.
MN 9.2.1.5 - Identify the vertex, line
of symmetry and intercepts of the
parabola corresponding to a
quadratic function, using symbolic
and graphical methods, when the
function is expressed in the form f(x)
= ax² + bx + c, in the form f(x) = a(x h)² + k , or in factored form.
MN 9.2.1.6 - Identify intercepts,
zeros, maxima, minima and intervals
of increase and decrease from the
graph of a function.
Page 104 of 198
Topic 2 - Relations and
Functions
Obj. 8 - Determine if a relation is a
function
Topic 2 - Relations and
Functions
Obj. 9 - Determine the domain or
range of a function
Obj. 10 - WP: Determine a
reasonable domain or range for a
function in a given situation
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.1.7 - Understand the concept
of an asymptote and identify
asymptotes for exponential functions
and reciprocals of linear functions,
using symbolic and graphical
methods.
MN 9.2.1.8 - Make qualitative
statements about the rate of change
of a function, based on its graph or
table of values. Example: The
function f(x) = 3 to the x power
increases for all x, but it increases
faster when x > 2 than it does when x
< 2.
MN 9.2.1.9 - Determine how
translations affect the symbolic and
graphical forms of a function. Know
how to use graphing technology to
examine translations. Example:
Determine how the graph of f(x) = |x h| + k changes as h and k change.
Grade 8
MN 9.2.2 - Recognize linear,
quadratic, exponential and other
common functions in real-world and
mathematical situations; represent
these functions with tables, verbal
descriptions, symbols and graphs;
solve problems involving these
functions, and explain results in the
original context.
MN 9.2.2.1 - Represent and solve
Topic 8 - Quadratic Equations
problems in various contexts using
and Functions
linear and quadratic functions.
Example: Write a function that
represents the area of a rectangular
garden that can be surrounded with
32 feet of fencing, and use the
function to determine the possible
dimensions of such a garden if the
area must be at least 50 square feet.
Obj. 87 - WP: Answer a question
using the graph of a quadratic
function
Obj. 94 - WP: Use a given quadratic
equation to solve a problem
MN 9.2.2.2 - Represent and solve
Topic 9 - Exponential Equations
problems in various contexts using
and Functions
exponential functions, such as
investment growth, depreciation and
population growth.
Page 105 of 198
Obj. 96 - WP: Evaluate an
exponential growth or an exponential
decay function
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 97 - Solve a problem involving
exponential growth or exponential
decay
MN 9.2.2.3 - Sketch graphs of linear, Topic 8 - Quadratic Equations
Obj. 86 - Determine the graph of a
quadratic and exponential functions, and Functions
given quadratic function
and translate between graphs, tables
and symbolic representations. Know
how to use graphing technology to
graph these functions.
MN 9.2.2.4 - Express the terms in a
geometric sequence recursively and
by giving an explicit (closed form)
formula, and express the partial sums
of a geometric series recursively.
Example 1: A closed form formula for
the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)
to the (n-1) power, where n = 1, 2, 3,
... , and this sequence can be
expressed recursively by writing t1 =
3 and tn = 2t(n-1), for n is greater
than or equal to 2. Example 2: the
partial sums sn of the series 3 + 6 +
12 + 24 + ... can be expressed
recursively by writing s1 = 3 and sn =
3 + 2s(n-1), for n is greater than or
equal to 2.
Topic 9 - Exponential Equations
and Functions
Obj. 95 - Determine the graph of an
exponential function
MN 9.2.2.5 - Recognize and solve
problems that can be modeled using
finite geometric sequences and
series, such as home mortgage and
other compound interest examples.
Know how to use spreadsheets and
calculators to explore geometric
sequences and series in various
contexts.
MN 9.2.2.6 - Sketch the graphs of
Topic 11 - Radical Equations and Obj. 111 - Determine the graph of a
common non-linear functions such as Functions
radical function
f(x)= the square root of x, f(x) = |x|,
f(x)= 1/x, f(x) = x³, and translations of
these functions, such as f(x) = the
square root of (x-2) + 4. Know how to
use graphing technology to graph
these functions.
Topic 13 - Rational Equations
and Functions
Page 106 of 198
Obj. 126 - Determine the graph of a
rational function
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.3 - Generate equivalent
algebraic expressions involving
polynomials and radicals; use
algebraic properties to evaluate
expressions.
MN 9.2.3.1 - Evaluate polynomial and
rational expressions and expressions
containing radicals and absolute
values at specified points in their
domains.
MN 9.2.3.2 - Add, subtract and
Topic 6 - Polynomial Expressions Obj. 70 - Add polynomial expressions
multiply polynomials; divide a
polynomial by a polynomial of equal
or lower degree.
Obj. 71 - Subtract polynomial
expressions
Obj. 72 - Multiply a polynomial by a
monomial
Obj. 73 - Multiply two binomials of the
form (x +/- a)(x +/- b)
Obj. 74 - Multiply two binomials of the
form (ax +/- b)(cx +/- d)
Obj. 75 - Multiply two binomials of the
form (ax +/- by)(cx +/- dy)
Obj. 76 - Square a binomial
Obj. 77 - Multiply two nonlinear
binomials
Obj. 78 - Multiply a trinomial by a
binomial
Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial
expression by a monomial
Obj. 118 - Divide a polynomial
expression by a binomial
MN 9.2.3.3 - Factor common
Topic 7 - Factor Algebraic
Obj. 79 - Factor the GCF from a
monomial factors from polynomials, Expressions
polynomial expression
factor quadratic polynomials, and
factor the difference of two squares.
Example: 9x to the 6th power - x to
the 4th power = (3x³ - x²)(3x³ + x²).
Obj. 80 - Factor trinomials that result
in factors of the form (x +/- a)(x +/- b)
Page 107 of 198
Obj. 81 - Factor trinomials that result
in factors of the form (ax +/- b)(cx +/d)
Obj. 82 - Factor trinomials that result
in factors of the form (ax +/- by)(cx +/dy)
Obj. 83 - Factor the difference of two
squares
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 84 - Factor a perfect-square
trinomial
Obj. 85 - Factor a polynomial that
has a GCF and two linear binomial
factors
MN 9.2.3.4 - Add, subtract, multiply, Topic 12 - Rational Expressions Obj. 114 - Simplify a rational
divide and simplify algebraic
expression involving polynomial
fractions. Example: 1/(1-x) + x/(1+x)
terms
is equivalent to (1+2x-x²)/(1-x²).
Obj. 115 - Multiply rational
expressions
Obj. 116 - Divide rational expressions
MN 9.2.3.5 - Check whether a given
complex number is a solution of a
quadratic equation by substituting it
for the variable and evaluating the
expression, using arithmetic with
complex numbers. Example: The
complex number (1+i)/2 is a solution
of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.
MN 9.2.3.6 - Apply the properties of Topic 5 - Properties of Powers
positive and negative rational
exponents to generate equivalent
algebraic expressions, including
those involving nth roots. Example:
The square root of 2 x the square
root of 7 = 2 to the 1/2 power x 7 to
the 1/2 power = 14 to the 1/2 power =
the square root of 14. Rules for
computing directly with radicals may
also be used: the square root of 2 x
the square root of x= the square root
of 2x.
Page 108 of 198
Obj. 120 - Add or subtract two
rational expressions with like
denominators
Obj. 121 - Add or subtract two
rational expressions with unlike
monomial denominators
Obj. 122 - Add or subtract two
rational expressions with unlike
polynomial denominators
Obj. 58 - Apply the product of powers
property to a monomial numerical
expression
Obj. 59 - Apply the product of powers
property to a monomial algebraic
expression
Obj. 60 - Apply the power of a power
property to a monomial numerical
expression
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 61 - Apply the power of a power
property to a monomial algebraic
expression
Obj. 62 - Apply the power of a
product property to a monomial
algebraic expression
Obj. 63 - Apply the quotient of
powers property to monomial
numerical expressions
Obj. 64 - Apply the quotient of
powers property to monomial
algebraic expressions
Obj. 65 - Apply the power of a
quotient property to monomial
algebraic expressions
Obj. 67 - Apply properties of
exponents to monomial algebraic
expressions
Topic 10 - Radical Expressions Obj. 98 - Simplify a monomial
numerical expression involving the
square root of a whole number
Obj. 99 - Multiply monomial
numerical expressions involving
radicals
Obj. 100 - Divide monomial
numerical expressions involving
radicals
Obj. 101 - Add and/or subtract
numerical radical expressions
Obj. 102 - Multiply a binomial
numerical radical expression by a
numerical radical expression
Obj. 103 - Rationalize the
denominator of a numerical radical
expression
Obj. 104 - Simplify a monomial
algebraic radical expression
Obj. 105 - Rationalize the
denominator of an algebraic radical
expression
Obj. 106 - Add or subtract algebraic
radical expressions
Obj. 107 - Multiply monomial
algebraic radical expressions
Obj. 108 - Divide monomial algebraic
radical expressions
Page 109 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.3.7 - Justify steps in
generating equivalent expressions by
identifying the properties used. Use
substitution to check the equality of
expressions for some particular
values of the variables; recognize
that checking with substitution does
not guarantee equality of expressions
for all values of the variables.
MN 9.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear, quadratic, exponential, and nth
root functions. Solve equations and
inequalities symbolically and
graphically. Interpret solutions in the
original context.
MN 9.2.4.1 - Represent relationships Topic 8 - Quadratic Equations
in various contexts using quadratic
and Functions
equations and inequalities. Solve
quadratic equations and inequalities
by appropriate methods including
factoring, completing the square,
graphing and the quadratic formula.
Find non-real complex roots when
they exist. Recognize that a particular
solution may not be applicable in the
original context. Know how to use
calculators, graphing utilities or other
technology to solve quadratic
equations and inequalities. Example:
A diver jumps from a 20 meter
platform with an upward velocity of 3
meters per second. In finding the
time at which the diver hits the
surface of the water, the resulting
quadratic equation has a positive and
a negative solution. The negative
solution should be discarded because
of the context.
Grade 8
Obj. 88 - Solve a quadratic equation
by graphing the associated quadratic
function
Obj. 89 - Solve a quadratic equation
by taking the square root
Obj. 90 - Determine the solution(s) of
an equation given in factored form
Obj. 91 - Solve a quadratic equation
by factoring
Page 110 of 198
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 92 - Solve a quadratic equation
using the quadratic formula
MN 9.2.4.2 - Represent relationships
in various contexts using equations
involving exponential functions; solve
these equations graphically or
numerically. Know how to use
calculators, graphing utilities or other
technology to solve these equations.
MN 9.2.4.3 - Recognize that to solve
certain equations, number systems
need to be extended from whole
numbers to integers, from integers to
rational numbers, from rational
numbers to real numbers, and from
real numbers to complex numbers. In
particular, non-real complex numbers
are needed to solve some quadratic
equations with real coefficients.
MN 9.2.4.4 - Represent relationships Topic 4 - Systems of Linear
in various contexts using systems of Equations and Inequalities
linear inequalities; solve them
graphically. Indicate which parts of
the boundary are included in and
excluded from the solution set using
solid and dotted lines.
MN 9.2.4.5 - Solve linear
programming problems in two
variables using graphical methods.
MN 9.2.4.6 - Represent relationships
in various contexts using absolute
value inequalities in two variables;
solve them graphically. Example: If a
pipe is to be cut to a length of 5
meters accurate to within a tenth of
its diameter, the relationship between
the length x of the pipe and its
diameter y satisfies the inequality |x 5| is less than or equal to 0.1y.
Page 111 of 198
Obj. 55 - Determine the graph of the
solution set of a system of linear
inequalities in two variables
Obj. 56 - WP: Determine a system of
linear inequalities that represents a
given situation
Obj. 57 - WP: Determine possible
solutions to a problem that can be
represented by a system of linear
inequalities
081309
Accelerated Math
Grade 8
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.4.7 - Solve equations that
Topic 11 - Radical Equations and Obj. 109 - Solve a radical equation
contain radical expressions.
Functions
that leads to a linear equation
Recognize that extraneous solutions
may arise when using symbolic
methods. Example 1: The equation
the square root of x-9 = 9 the square
root of x may be solved by squaring
both sides to obtain x - 9 = 81x, which
has the solution x = -9/80. However,
this is not a solution of the original
equation, so it is an extraneous
solution that should be discarded.
The original equation has no solution
in this case. Example 2: Solve the
cubed root of (-x+1) = -5.
MN 9.2.4.8 - Assess the
reasonableness of a solution in its
given context and compare the
solution to appropriate graphical or
numerical estimates; interpret a
solution in the original context.
MN 9.3 - Geometry & Measurement
Obj. 110 - Solve a radical equation
that leads to a quadratic equation
MN 9.3.1 - Calculate measurements
of plane and solid geometric figures;
know that physical measurements
depend on the choice of a unit and
that they are approximations.
MN 9.3.1.1 - Determine the surface
area and volume of pyramids, cones
and spheres. Use measuring devices
or formulas as appropriate. Example:
Measure the height and radius of a
cone and then use a formula to find
its volume.
MN 9.3.1.2 - Compose and
decompose two- and threedimensional figures; use
decomposition to determine the
perimeter, area, surface area and
volume of various figures. Example:
Find the volume of a regular
hexagonal prism by decomposing it
into six equal triangular prisms.
Page 112 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.1.3 - Understand that
quantities associated with physical
measurements must be assigned
units; apply such units correctly in
expressions, equations and problem
solutions that involve measurements;
and convert between measurement
systems. Example: 60 miles/hour =
60 miles/hour × 5280 feet/mile × 1
hour/3600 seconds = 88 feet/second.
Grade 8
MN 9.3.1.4 - Understand and apply
the fact that the effect of a scale
factor k on length, area and volume is
to multiply each by k, k² and k³,
respectively.
MN 9.3.1.5 - Make reasonable
estimates and judgments about the
accuracy of values resulting from
calculations involving measurements.
Example: Suppose the sides of a
rectangle are measured to the
nearest tenth of a centimeter at 2.6
cm and 9.8 cm. Because of
measurement errors, the width could
be as small as 2.55 cm or as large as
2.65 cm, with similar errors for the
height. These errors affect
calculations. For instance, the actual
area of the rectangle could be
smaller than 25 cm² or larger than 26
cm², even though 2.6 × 9.8 = 25.48.
MN 9.3.2 - Construct logical
arguments, based on axioms,
definitions and theorems, to prove
theorems and other results in
geometry.
MN 9.3.2.1 - Understand the roles of
axioms, definitions, undefined terms
and theorems in logical arguments.
Page 113 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.2.2 - Accurately interpret and
use words and phrases in geometric
proofs such as "if...then," "if and only
if," "all," and "not." Recognize the
logical relationships between an
"if...then" statement and its inverse,
converse and contrapositive.
Example: The statement "If you don't
do your homework, you can't go to
the dance" is not logically equivalent
to its inverse "If you do your
homework, you can go to the dance.".
Grade 8
MN 9.3.2.3 - Assess the validity of a
logical argument and give
counterexamples to disprove a
statement.
MN 9.3.2.4 - Construct logical
arguments and write proofs of
theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a
form that clearly justifies the
reasoning, such as two-column
proofs, paragraph proofs, flow charts
or illustrations. Example: Prove that
the sum of the interior angles of a
pentagon is 540° using the fact that
the sum of the interior angles of a
triangle is 180°.
MN 9.3.2.5 - Use technology tools to
examine theorems, test conjectures,
perform constructions and develop
mathematical reasoning skills in multistep problems. The tools may include
compass and straight edge, dynamic
geometry software, design software
or Internet applets.
MN 9.3.3 - Know and apply
properties of geometric figures to
solve real-world and mathematical
problems and to logically justify
results in geometry.
Page 114 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.3.1 - Know and apply
properties of parallel and
perpendicular lines, including
properties of angles formed by a
transversal, to solve problems and
logically justify results. Example:
Prove that the perpendicular bisector
of a line segment is the set of all
points equidistant from the two
endpoints, and use this fact to solve
problems and justify other results.
Grade 8
MN 9.3.3.2 - Know and apply
properties of angles, including
corresponding, exterior, interior,
vertical, complementary and
supplementary angles, to solve
problems and logically justify results.
Example: Prove that two triangles
formed by a pair of intersecting lines
and a pair of parallel lines (an "X"
trapped between two parallel lines)
are similar.
MN 9.3.3.3 - Know and apply
properties of equilateral, isosceles
and scalene triangles to solve
problems and logically justify results.
Example: Use the triangle inequality
to prove that the perimeter of a
quadrilateral is larger than the sum of
the lengths of its diagonals.
MN 9.3.3.4 - Apply the Pythagorean
Theorem and its converse to solve
problems and logically justify results.
Example: When building a wooden
frame that is supposed to have a
square corner, ensure that the corner
is square by measuring lengths near
the corner and applying the
Pythagorean Theorem.
Page 115 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.3.5 - Know and apply
properties of right triangles, including
properties of 45-45-90 and 30-60-90
triangles, to solve problems and
logically justify results. Example 1:
Use 30-60-90 triangles to analyze
geometric figures involving equilateral
triangles and hexagons. Example 2:
Determine exact values of the
trigonometric ratios in these special
triangles using relationships among
the side lengths.
Grade 8
MN 9.3.3.6 - Know and apply
properties of congruent and similar
figures to solve problems and
logically justify results. Example 1:
Analyze lengths and areas in a figure
formed by drawing a line segment
from one side of a triangle to a
second side, parallel to the third side.
Example 2: Determine the height of a
pine tree by comparing the length of
its shadow to the length of the
shadow of a person of known height.
Example 3: When attempting to build
two identical 4-sided frames, a
person measured the lengths of
corresponding sides and found that
they matched. Can the person
conclude that the shapes of the
frames are congruent?
MN 9.3.3.7 - Use properties of
polygons-including quadrilaterals and
regular polygons-to define them,
classify them, solve problems and
logically justify results. Example 1:
Recognize that a rectangle is a
special case of a trapezoid. Example
2: Give a concise and clear definition
of a kite.
MN 9.3.3.8 - Know and apply
properties of a circle to solve
problems and logically justify results.
Example: Show that opposite angles
of a quadrilateral inscribed in a circle
are supplementary.
Page 116 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.4 - Solve real-world and
mathematical geometric problems
using algebraic methods.
MN 9.3.4.1 - Understand how the
properties of similar right triangles
allow the trigonometric ratios to be
defined, and determine the sine,
cosine and tangent of an acute angle
in a right triangle.
MN 9.3.4.2 - Apply the trigonometric
ratios sine, cosine and tangent to
solve problems, such as determining
lengths and areas in right triangles
and in figures that can be
decomposed into right triangles.
Know how to use calculators, tables
or other technology to evaluate
trigonometric ratios. Example: Find
the area of a triangle, given the
measure of one of its acute angles
and the lengths of the two sides that
form that angle.
MN 9.3.4.3 - Use calculators, tables
or other technologies in connection
with the trigonometric ratios to find
angle measures in right triangles in
various contexts.
MN 9.3.4.4 - Use coordinate
Topic 3 - Linear Equations and
geometry to represent and analyze
Inequalities
line segments and polygons,
including determining lengths,
midpoints and slopes of line
segments.
MN 9.3.4.5 - Know the equation for
the graph of a circle with radius r and
center (h,k), (x - h)² + (y - k)² = r², and
justify this equation using the
Pythagorean Theorem and properties
of translations.
MN 9.3.4.6 - Use numeric, graphic
and symbolic representations of
transformations in two dimensions,
such as reflections, translations,
scale changes and rotations about
the origin by multiples of 90°, to solve
problems involving figures on a
coordinate grid. Example: If the point
(3,-2) is rotated 90° counterclockwise
about the origin, it becomes the point
(2,3).
Page 117 of 198
Grade 8
Obj. 26 - Determine the slope of a
line given two points on the line
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.4.7 - Use algebra to solve
geometric problems unrelated to
coordinate geometry, such as solving
for an unknown length in a figure
involving similar triangles, or using
the Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
MN 9.4 - Data Analysis & Probability
Grade 8
MN 9.4.1 - Display and analyze data;
use various measures associated
with data to draw conclusions, identify
trends and describe relationships.
MN 9.4.1.1 - Describe a data set
using data displays, such as box-andwhisker plots; describe and compare
data sets using summary statistics,
including measures of center,
location and spread. Measures of
center and location include mean,
median, quartile and percentile.
Measures of spread include standard
deviation, range and inter-quartile
range. Know how to use calculators,
spreadsheets or other technology to
display data and calculate summary
statistics.
MN 9.4.1.2 - Analyze the effects on
summary statistics of changes in data
sets. Example 1: Understand how
inserting or deleting a data point may
affect the mean and standard
deviation. Example 2: Understand
how the median and interquartile
range are affected when the entire
data set is transformed by adding a
constant to each data value or
multiplying each data value by a
constant.
MN 9.4.1.3 - Use scatterplots to
analyze patterns and describe
relationships between two variables.
Using technology, determine
regression lines (line of best fit) and
correlation coefficients; use
regression lines to make predictions
and correlation coefficients to assess
the reliability of those predictions.
Page 118 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.1.4 - Use the mean and
standard deviation of a data set to fit
it to a normal distribution (bell-shaped
curve) and to estimate population
percentages. Recognize that there
are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets and tables
to estimate areas under the normal
curve. Example 1: After performing
several measurements of some
attribute of an irregular physical
object, it is appropriate to fit the data
to a normal distribution and draw
conclusions about measurement
error. Example 2: When data
involving two very different
populations is combined, the resulting
histogram may show two distinct
peaks, and fitting the data to a
normal distribution is not appropriate.
Grade 8
MN 9.4.2 - Explain the uses of data
and statistical thinking to draw
inferences, make predictions and
justify conclusions
MN 9.4.2.1 - Evaluate reports based
on data published in the media by
identifying the source of the data, the
design of the study, and the way the
data are analyzed and displayed.
Show how graphs and data can be
distorted to support different points of
view. Know how to use spreadsheet
tables and graphs or graphing
technology to recognize and analyze
distortions in data displays. Example:
Shifting data on the vertical axis can
make relative changes appear
deceptively large.
MN 9.4.2.2 - Identify and explain
misleading uses of data; recognize
when arguments based on data
confuse correlation and causation.
MN 9.4.2.3 - Explain the impact of
sampling methods, bias and the
phrasing of questions asked during
data collection.
Page 119 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3 - Calculate probabilities and
apply probability concepts to solve
real-world and mathematical
problems.
MN 9.4.3.1 - Select and apply
counting procedures, such as the
multiplication and addition principles
and tree diagrams, to determine the
size of a sample space (the number
of possible outcomes) and to
calculate probabilities. Example: If
one girl and one boy are picked at
random from a class with 20 girls and
15 boys, there are 20 × 15 = 300
different possibilities, so the
probability that a particular girl is
chosen together with a particular boy
is 1/300.
Grade 8
MN 9.4.3.2 - Calculate experimental
probabilities by performing
simulations or experiments involving
a probability model and using relative
frequencies of outcomes.
MN 9.4.3.3 - Understand that the Law
of Large Numbers expresses a
relationship between the probabilities
in a probability model and the
experimental probabilities found by
performing simulations or
experiments involving the model.
MN 9.4.3.4 - Use random numbers
generated by a calculator or a
spreadsheet, or taken from a table, to
perform probability simulations and to
introduce fairness into decision
making. Example: If a group of
students needs to fairly select one of
its members to lead a discussion,
they can use a random number to
determine the selection.
Page 120 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3.5 - Apply probability
concepts such as intersections,
unions and complements of events,
and conditional probability and
independence, to calculate
probabilities and solve problems.
Example: The probability of tossing at
least one head when flipping a fair
coin three times can be calculated by
looking at the complement of this
event (flipping three tails in a row).
Grade 8
MN 9.4.3.6 - Describe the concepts
of intersections, unions and
complements using Venn diagrams.
Understand the relationships
between these concepts and the
words AND, OR, NOT, as used in
computerized searches and
spreadsheets.
MN 9.4.3.7 - Understand and use
simple probability formulas involving
intersections, unions and
complements of events. Example 1:
If the probability of an event is p, then
the probability of the complement of
an event is 1 - p; the probability of the
intersection of two independent
events is the product of their
probabilities. Example 2: The
probability of the union of two events
equals the sum of the probabilities of
the two individual events minus the
probability of the intersection of the
events.
MN 9.4.3.8 - Apply probability
concepts to real-world situations to
make informed decisions. Example 1:
Explain why a hockey coach might
decide near the end of the game to
pull the goalie to add another forward
position player if the team is behind.
Example 2: Consider the role that
probabilities play in health care
decisions, such as deciding between
having eye surgery and wearing
glasses.
Page 121 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Algebra 1
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3.9 - Use the relationship
between conditional probabilities and
relative frequencies in contingency
tables. Example: A table that displays
percentages relating gender (male or
female) and handedness (righthanded or left-handed) can be used
to determine the conditional
probability of being left-handed, given
that the gender is male.
Grade 8
Page 122 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2 - Algebra
MN 9.2.1 - Understand the concept of
function, and identify important
features of functions and other
relations using symbolic and
graphical methods where
appropriate.
MN 9.2.1.1 - Understand the
definition of a function. Use functional
notation and evaluate a function at a
given point in its domain. Example: If
f(x) - 1/(x²-3),find f(-4).
MN 9.2.1.2 - Distinguish between
functions and other relations defined
symbolically, graphically or in tabular
form.
MN 9.2.1.3 - Find the domain of a
function defined symbolically,
graphically or in a real-world context.
Example: The formula f(x) = pi x² can
represent a function whose domain is
all real numbers, but in the context of
the area of a circle, the domain would
be restricted to positive x.
MN 9.2.1.4 - Obtain information and
draw conclusions from graphs of
functions and other relations.
Example: If a graph shows the
relationship between the elapsed
flight time of a golf ball at a given
moment and its height at that same
moment, identify the time interval
during which the ball is at least 100
feet above the ground.
MN 9.2.1.5 - Identify the vertex, line
of symmetry and intercepts of the
parabola corresponding to a
quadratic function, using symbolic
and graphical methods, when the
function is expressed in the form f(x)
= ax² + bx + c, in the form f(x) = a(x h)² + k , or in factored form.
MN 9.2.1.6 - Identify intercepts,
zeros, maxima, minima and intervals
of increase and decrease from the
graph of a function.
Page 123 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.1.7 - Understand the concept
of an asymptote and identify
asymptotes for exponential functions
and reciprocals of linear functions,
using symbolic and graphical
methods.
MN 9.2.1.8 - Make qualitative
statements about the rate of change
of a function, based on its graph or
table of values. Example: The
function f(x) = 3 to the x power
increases for all x, but it increases
faster when x > 2 than it does when x
< 2.
MN 9.2.1.9 - Determine how
translations affect the symbolic and
graphical forms of a function. Know
how to use graphing technology to
examine translations. Example:
Determine how the graph of f(x) = |x h| + k changes as h and k change.
MN 9.2.2 - Recognize linear,
quadratic, exponential and other
common functions in real-world and
mathematical situations; represent
these functions with tables, verbal
descriptions, symbols and graphs;
solve problems involving these
functions, and explain results in the
original context.
MN 9.2.2.1 - Represent and solve
problems in various contexts using
linear and quadratic functions.
Example: Write a function that
represents the area of a rectangular
garden that can be surrounded with
32 feet of fencing, and use the
function to determine the possible
dimensions of such a garden if the
area must be at least 50 square feet.
MN 9.2.2.2 - Represent and solve
problems in various contexts using
exponential functions, such as
investment growth, depreciation and
population growth.
Page 124 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.2.3 - Sketch graphs of linear,
quadratic and exponential functions,
and translate between graphs, tables
and symbolic representations. Know
how to use graphing technology to
graph these functions.
MN 9.2.2.4 - Express the terms in a
geometric sequence recursively and
by giving an explicit (closed form)
formula, and express the partial sums
of a geometric series recursively.
Example 1: A closed form formula for
the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)
to the (n-1) power, where n = 1, 2, 3,
... , and this sequence can be
expressed recursively by writing t1 =
3 and tn = 2t(n-1), for n is greater
than or equal to 2. Example 2: the
partial sums sn of the series 3 + 6 +
12 + 24 + ... can be expressed
recursively by writing s1 = 3 and sn =
3 + 2s(n-1), for n is greater than or
equal to 2.
MN 9.2.2.5 - Recognize and solve
problems that can be modeled using
finite geometric sequences and
series, such as home mortgage and
other compound interest examples.
Know how to use spreadsheets and
calculators to explore geometric
sequences and series in various
contexts.
MN 9.2.2.6 - Sketch the graphs of
common non-linear functions such as
f(x)= the square root of x, f(x) = |x|,
f(x)= 1/x, f(x) = x³, and translations of
these functions, such as f(x) = the
square root of (x-2) + 4. Know how to
use graphing technology to graph
these functions.
MN 9.2.3 - Generate equivalent
algebraic expressions involving
polynomials and radicals; use
algebraic properties to evaluate
expressions.
Page 125 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.3.1 - Evaluate polynomial and
rational expressions and expressions
containing radicals and absolute
values at specified points in their
domains.
MN 9.2.3.2 - Add, subtract and
multiply polynomials; divide a
polynomial by a polynomial of equal
or lower degree.
MN 9.2.3.3 - Factor common
monomial factors from polynomials,
factor quadratic polynomials, and
factor the difference of two squares.
Example: 9x to the 6th power - x to
the 4th power = (3x³ - x²)(3x³ + x²).
MN 9.2.3.4 - Add, subtract, multiply,
divide and simplify algebraic
fractions. Example: 1/(1-x) + x/(1+x)
is equivalent to (1+2x-x²)/(1-x²).
MN 9.2.3.5 - Check whether a given
complex number is a solution of a
quadratic equation by substituting it
for the variable and evaluating the
expression, using arithmetic with
complex numbers. Example: The
complex number (1+i)/2 is a solution
of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.
MN 9.2.3.6 - Apply the properties of
positive and negative rational
exponents to generate equivalent
algebraic expressions, including
those involving nth roots. Example:
The square root of 2 x the square
root of 7 = 2 to the 1/2 power x 7 to
the 1/2 power = 14 to the 1/2 power =
the square root of 14. Rules for
computing directly with radicals may
also be used: the square root of 2 x
the square root of x= the square root
of 2x.
Page 126 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.3.7 - Justify steps in
generating equivalent expressions by
identifying the properties used. Use
substitution to check the equality of
expressions for some particular
values of the variables; recognize
that checking with substitution does
not guarantee equality of expressions
for all values of the variables.
MN 9.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear, quadratic, exponential, and nth
root functions. Solve equations and
inequalities symbolically and
graphically. Interpret solutions in the
original context.
MN 9.2.4.1 - Represent relationships
in various contexts using quadratic
equations and inequalities. Solve
quadratic equations and inequalities
by appropriate methods including
factoring, completing the square,
graphing and the quadratic formula.
Find non-real complex roots when
they exist. Recognize that a particular
solution may not be applicable in the
original context. Know how to use
calculators, graphing utilities or other
technology to solve quadratic
equations and inequalities. Example:
A diver jumps from a 20 meter
platform with an upward velocity of 3
meters per second. In finding the
time at which the diver hits the
surface of the water, the resulting
quadratic equation has a positive and
a negative solution. The negative
solution should be discarded because
of the context.
MN 9.2.4.2 - Represent relationships
in various contexts using equations
involving exponential functions; solve
these equations graphically or
numerically. Know how to use
calculators, graphing utilities or other
technology to solve these equations.
Page 127 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.4.3 - Recognize that to solve
certain equations, number systems
need to be extended from whole
numbers to integers, from integers to
rational numbers, from rational
numbers to real numbers, and from
real numbers to complex numbers. In
particular, non-real complex numbers
are needed to solve some quadratic
equations with real coefficients.
MN 9.2.4.4 - Represent relationships
in various contexts using systems of
linear inequalities; solve them
graphically. Indicate which parts of
the boundary are included in and
excluded from the solution set using
solid and dotted lines.
MN 9.2.4.5 - Solve linear
programming problems in two
variables using graphical methods.
MN 9.2.4.6 - Represent relationships
in various contexts using absolute
value inequalities in two variables;
solve them graphically. Example: If a
pipe is to be cut to a length of 5
meters accurate to within a tenth of
its diameter, the relationship between
the length x of the pipe and its
diameter y satisfies the inequality |x 5| is less than or equal to 0.1y.
MN 9.2.4.7 - Solve equations that
contain radical expressions.
Recognize that extraneous solutions
may arise when using symbolic
methods. Example 1: The equation
the square root of x-9 = 9 the square
root of x may be solved by squaring
both sides to obtain x - 9 = 81x, which
has the solution x = -9/80. However,
this is not a solution of the original
equation, so it is an extraneous
solution that should be discarded.
The original equation has no solution
in this case. Example 2: Solve the
cubed root of (-x+1) = -5.
Page 128 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.4.8 - Assess the
reasonableness of a solution in its
given context and compare the
solution to appropriate graphical or
numerical estimates; interpret a
solution in the original context.
MN 9.3 - Geometry & Measurement
MN 9.3.1 - Calculate measurements
of plane and solid geometric figures;
know that physical measurements
depend on the choice of a unit and
that they are approximations.
MN 9.3.1.1 - Determine the surface Topic 10 - Surface Area and
area and volume of pyramids, cones Volume
and spheres. Use measuring devices
or formulas as appropriate. Example:
Measure the height and radius of a
cone and then use a formula to find
its volume.
Obj. 88 - Solve a problem involving
the surface area of a cone or a
pyramid that has a rectangle or right
triangle as a base
Obj. 91 - Determine the volume of a
right pyramid or a right cone
Obj. 92 - Solve a problem involving
the volume of a right pyramid or a
right cone
Obj. 93 - Determine the volume of an
oblique pyramid or an oblique cone
MN 9.3.1.2 - Compose and
decompose two- and threedimensional figures; use
decomposition to determine the
perimeter, area, surface area and
volume of various figures. Example:
Find the volume of a regular
hexagonal prism by decomposing it
into six equal triangular prisms.
Topic 9 - Area
Topic 10 - Surface Area and
Volume
Page 129 of 198
Obj. 94 - Determine the surface area
of a sphere
Obj. 99 - Determine the volume of a
sphere or hemisphere
Obj. 100 - WP: Determine the
volume of a sphere or hemisphere
Obj. 74 - Determine the area of a
regular polygon
Obj. 79 - WP: Solve a problem
involving the area of a complex
shape formed by circles and
polygons
Obj. 97 - Determine the surface area
of a complex solid figure
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 98 - Solve a problem involving
the surface area of a complex solid
figure
Obj. 101 - Determine the volume of a
complex solid figure
Obj. 102 - WP: Solve a problem
involving the volume of a complex
solid figure
MN 9.3.1.3 - Understand that
quantities associated with physical
measurements must be assigned
units; apply such units correctly in
expressions, equations and problem
solutions that involve measurements;
and convert between measurement
systems. Example: 60 miles/hour =
60 miles/hour × 5280 feet/mile × 1
hour/3600 seconds = 88 feet/second.
MN 9.3.1.4 - Understand and apply Topic 10 - Surface Area and
the fact that the effect of a scale
Volume
factor k on length, area and volume is
to multiply each by k, k² and k³,
respectively.
Obj. 103 - Solve a problem involving
the surface areas of similar solid
figures
Obj. 104 - Solve a problem involving
the volumes of similar solid figures
MN 9.3.1.5 - Make reasonable
estimates and judgments about the
accuracy of values resulting from
calculations involving measurements.
Example: Suppose the sides of a
rectangle are measured to the
nearest tenth of a centimeter at 2.6
cm and 9.8 cm. Because of
measurement errors, the width could
be as small as 2.55 cm or as large as
2.65 cm, with similar errors for the
height. These errors affect
calculations. For instance, the actual
area of the rectangle could be
smaller than 25 cm² or larger than 26
cm², even though 2.6 × 9.8 = 25.48.
MN 9.3.2 - Construct logical
arguments, based on axioms,
definitions and theorems, to prove
theorems and other results in
geometry.
Page 130 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.2.1 - Understand the roles of
axioms, definitions, undefined terms
and theorems in logical arguments.
MN 9.3.2.2 - Accurately interpret and
use words and phrases in geometric
proofs such as "if...then," "if and only
if," "all," and "not." Recognize the
logical relationships between an
"if...then" statement and its inverse,
converse and contrapositive.
Example: The statement "If you don't
do your homework, you can't go to
the dance" is not logically equivalent
to its inverse "If you do your
homework, you can go to the dance.".
MN 9.3.2.3 - Assess the validity of a
logical argument and give
counterexamples to disprove a
statement.
MN 9.3.2.4 - Construct logical
arguments and write proofs of
theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a
form that clearly justifies the
reasoning, such as two-column
proofs, paragraph proofs, flow charts
or illustrations. Example: Prove that
the sum of the interior angles of a
pentagon is 540° using the fact that
the sum of the interior angles of a
triangle is 180°.
MN 9.3.2.5 - Use technology tools to
examine theorems, test conjectures,
perform constructions and develop
mathematical reasoning skills in multistep problems. The tools may include
compass and straight edge, dynamic
geometry software, design software
or Internet applets.
MN 9.3.3 - Know and apply
properties of geometric figures to
solve real-world and mathematical
problems and to logically justify
results in geometry.
Page 131 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.3.1 - Know and apply
Topic 2 - Parallel and
Obj. 10 - Determine the measure of
properties of parallel and
Perpendicular lines
an angle formed by parallel lines and
perpendicular lines, including
one or more transversals
properties of angles formed by a
transversal, to solve problems and
logically justify results. Example:
Prove that the perpendicular bisector
of a line segment is the set of all
points equidistant from the two
endpoints, and use this fact to solve
problems and justify other results.
Obj. 11 - Identify parallel lines using
angle relationships
Obj. 12 - Determine the measure of
an angle in a figure involving parallel
and/or perpendicular lines
Obj. 13 - Determine if lines through
points with given coordinates are
parallel or perpendicular
Obj. 14 - Determine the coordinates
of a point through which a line must
pass in order to be parallel or
perpendicular to a given line
MN 9.3.3.2 - Know and apply
Topic 2 - Parallel and
properties of angles, including
Perpendicular lines
corresponding, exterior, interior,
vertical, complementary and
supplementary angles, to solve
problems and logically justify results.
Example: Prove that two triangles
formed by a pair of intersecting lines
and a pair of parallel lines (an "X"
trapped between two parallel lines)
are similar.
Topic 3 - Relationships Within
Triangles
Page 132 of 198
Obj. 9 - Identify angle relationships
formed by multiple lines and
transversals
Obj. 10 - Determine the measure of
an angle formed by parallel lines and
one or more transversals
Obj. 12 - Determine the measure of
an angle in a figure involving parallel
and/or perpendicular lines
Obj. 16 - Determine the measure of
an angle using angle relationships
and the sum of the interior angles in a
triangle
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.3.3 - Know and apply
Topic 3 - Relationships Within
Obj. 19 - Solve a problem using
properties of equilateral, isosceles
Triangles
inequalities in a triangle
and scalene triangles to solve
problems and logically justify results.
Example: Use the triangle inequality
to prove that the perimeter of a
quadrilateral is larger than the sum of
the lengths of its diagonals.
MN 9.3.3.4 - Apply the Pythagorean Topic 3 - Relationships Within
Theorem and its converse to solve
Triangles
problems and logically justify results.
Example: When building a wooden
frame that is supposed to have a
square corner, ensure that the corner
is square by measuring lengths near
the corner and applying the
Pythagorean Theorem.
Topic 7 - Right Triangles and
Trigonometry
MN 9.3.3.5 - Know and apply
Topic 7 - Right Triangles and
properties of right triangles, including Trigonometry
properties of 45-45-90 and 30-60-90
triangles, to solve problems and
logically justify results. Example 1:
Use 30-60-90 triangles to analyze
geometric figures involving equilateral
triangles and hexagons. Example 2:
Determine exact values of the
trigonometric ratios in these special
triangles using relationships among
the side lengths.
Obj. 20 - Solve a problem involving
two triangles by using the hinge
theorem and other triangle inequality
relationships
Obj. 18 - Solve for the length of a
side of a triangle using the
Pythagorean theorem
Obj. 44 - Determine a length in a
complex figure using the
Pythagorean theorem
Obj. 48 - WP: Solve a problem
involving a complex figure using the
Pythagorean theorem
Obj. 45 - Determine a length using
the properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle
Obj. 46 - Solve a problem using
multiple non-trigonometric righttriangle relationships
Obj. 47 - WP: Determine a length
using the properties of a 45-45-90
degree triangle or a 30-60-90 degree
triangle
Page 133 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.3.6 - Know and apply
Topic 4 - Congruent Triangles
Obj. 22 - Determine the length of a
properties of congruent and similar
side or the measure of an angle in
figures to solve problems and
congruent triangles
logically justify results. Example 1:
Analyze lengths and areas in a figure
formed by drawing a line segment
from one side of a triangle to a
second side, parallel to the third side.
Example 2: Determine the height of a
pine tree by comparing the length of
its shadow to the length of the
shadow of a person of known height.
Example 3: When attempting to build
two identical 4-sided frames, a
person measured the lengths of
corresponding sides and found that
they matched. Can the person
conclude that the shapes of the
frames are congruent?
Topic 6 - Similarity
Page 134 of 198
Obj. 23 - Identify a triangle
congruence postulate that justifies a
congruence statement
Obj. 24 - Identify congruent triangles
using triangle congruence postulates
or theorems
Obj. 25 - Solve a problem involving a
point on the bisector of an angle
Obj. 34 - Determine the length of a
side in one of two similar polygons
Obj. 35 - Determine the length of a
side or the measure of an angle in
similar triangles
Obj. 36 - Determine a length given
the perimeters of similar triangles or
the lengths of corresponding interior
line segments
Obj. 37 - Identify a triangle similarity
postulate that justifies a similarity
statement
Obj. 38 - Identify similar triangles
using triangle similarity postulates or
theorems
Obj. 39 - Determine a length in a
triangle using a midsegment
Obj. 40 - Determine a length using
parallel lines and proportional parts
Obj. 42 - Determine a length using
similar triangles formed by the
altitude to the hypotenuse of a right
triangle
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 43 - WP: Determine a length
using similarity
MN 9.3.3.7 - Use properties of
Topic 5 - Quadrilaterals and
Obj. 26 - Determine the measure of
polygons-including quadrilaterals and Other Polygons
an angle or the sum of the angles in a
regular polygons-to define them,
polygon
classify them, solve problems and
logically justify results. Example 1:
Recognize that a rectangle is a
special case of a trapezoid. Example
2: Give a concise and clear definition
of a kite.
Topic 9 - Area
MN 9.3.3.8 - Know and apply
Topic 8 - Circles
properties of a circle to solve
problems and logically justify results.
Example: Show that opposite angles
of a quadrilateral inscribed in a circle
are supplementary.
Obj. 27 - Determine a length or an
angle measure using general
properties of parallelograms
Obj. 28 - Determine a length or an
angle measure using properties of
squares, rectangles, or rhombi
Obj. 29 - Determine a length or an
angle measure using properties of
kites
Obj. 30 - Determine a length or an
angle measure using properties of
trapezoids
Obj. 31 - Determine a length or an
angle measure in a complex figure
using properties of polygons
Obj. 32 - WP: Solve a problem using
the properties of angles and/or sides
of polygons
Obj. 70 - Determine the area of a
quadrilateral
Obj. 71 - Determine a length given
the area of a quadrilateral
Obj. 72 - WP: Solve a problem
involving the area of a quadrilateral
Obj. 75 - Determine a length given
the area of a regular polygon
Obj. 54 - Determine the measure of
an arc or a central angle using the
relationship between the arc and the
central angle
Obj. 55 - Solve a problem involving
the length of an arc
Obj. 56 - Determine the length of a
line segment, the measure of an
angle, or the measure of an arc using
a tangent to a circle
Page 135 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 57 - Determine a length using a
line segment tangent to a circle and
the radius that intersects the tangent
Obj. 58 - Determine a length using
two intersecting tangents to a circle
Obj. 59 - Determine a length or an
arc measure using the properties of
congruent chords
Obj. 60 - Determine a length using a
perpendicular bisector of a chord
Obj. 61 - Determine the measure of
an arc or an angle using the
relationship between an inscribed
angle and its intercepted arc
Obj. 62 - Determine the measure of
an arc or an angle using properties of
an inscribed triangle or quadrilateral
Topic 9 - Area
Obj. 63 - Determine the measure of
an arc or an angle formed by
intersecting chords or a chord that
intersects a tangent to a circle
Obj. 64 - Determine the measure of
an arc or an angle formed by two
tangents, two secants, or a tangent
and a secant that intersect outside a
circle
Obj. 65 - Determine a length using
intersecting chords, two secants that
intersect outside a circle, or a tangent
and a secant that intersect outside a
circle
Obj. 66 - Solve a problem involving
intersecting chords, tangents, and/or
secants of a circle
Obj. 80 - Determine the area of a
sector of a circle
Obj. 81 - Determine the area of a
segment of a circle
Obj. 82 - Determine the length of the
radius or the diameter of a circle
given the area of a sector
Obj. 83 - WP: Determine a length or
an area involving a sector of a circle
MN 9.3.4 - Solve real-world and
mathematical geometric problems
using algebraic methods.
Page 136 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.3.4.1 - Understand how the
Topic 7 - Right Triangles and
Obj. 49 - Determine a sine, cosine, or
properties of similar right triangles
Trigonometry
tangent ratio in a right triangle
allow the trigonometric ratios to be
defined, and determine the sine,
cosine and tangent of an acute angle
in a right triangle.
MN 9.3.4.2 - Apply the trigonometric Topic 7 - Right Triangles and
Obj. 50 - Determine a length using a
ratios sine, cosine and tangent to
Trigonometry
sine, cosine, or tangent ratio in a right
solve problems, such as determining
triangle
lengths and areas in right triangles
and in figures that can be
decomposed into right triangles.
Know how to use calculators, tables
or other technology to evaluate
trigonometric ratios. Example: Find
the area of a triangle, given the
measure of one of its acute angles
and the lengths of the two sides that
form that angle.
Topic 9 - Area
MN 9.3.4.3 - Use calculators, tables
or other technologies in connection
with the trigonometric ratios to find
angle measures in right triangles in
various contexts.
Topic 7 - Right Triangles and
Trigonometry
MN 9.3.4.4 - Use coordinate
geometry to represent and analyze
line segments and polygons,
including determining lengths,
midpoints and slopes of line
segments.
Topic 1 - Basic Concepts of
Geometry
Page 137 of 198
Obj. 52 - WP: Determine a length in
a right triangle using a sine, cosine,
or tangent ratio
Obj. 53 - WP: Determine the
measure of an angle in a right
triangle using a sine, cosine, or
tangent ratio
Obj. 76 - Approximate the area of a
right triangle using trigonometry
Obj. 77 - Approximate the area of a
regular polygon using trigonometry
Obj. 51 - Determine the measure of
an angle using a sine, cosine, or
tangent ratio in a right triangle
Obj. 53 - WP: Determine the
measure of an angle in a right
triangle using a sine, cosine, or
tangent ratio
Obj. 4 - Determine the distance
between two points
Obj. 5 - Solve a problem involving the
distance formula
Obj. 6 - Determine the midpoint of a
line segment given the coordinates of
the endpoints
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 7 - Determine the area of a right
triangle or a rectangle given the
coordinates of the vertices of the
figure
Obj. 8 - Solve a problem involving the
midpoint formula
MN 9.3.4.5 - Know the equation for
Topic 8 - Circles
Obj. 67 - Determine an equation of a
the graph of a circle with radius r and
circle
center (h,k), (x - h)² + (y - k)² = r², and
justify this equation using the
Pythagorean Theorem and properties
of translations.
MN 9.3.4.6 - Use numeric, graphic
Topic 11 - Transformations in the Obj. 107 - Relate the coordinates of a
and symbolic representations of
coordinate plane
preimage or an image to a translation
transformations in two dimensions,
described using mapping notation
such as reflections, translations,
scale changes and rotations about
the origin by multiples of 90°, to solve
problems involving figures on a
coordinate grid. Example: If the point
(3,-2) is rotated 90° counterclockwise
about the origin, it becomes the point
(2,3).
Obj. 108 - Determine the coordinates
of a preimage or an image given a
reflection across a horizontal line, a
vertical line, the line y = x, or the line
y = -x
Obj. 109 - Relate the coordinates of a
preimage or an image to a dilation
centered at the origin
Obj. 110 - Determine the angle of
rotational symmetry of a figure
Obj. 111 - Determine the coordinates
of the image of a figure after two
transformations of the same type
Obj. 112 - Determine the coordinates
of the image of a figure after two
transformations of different types
MN 9.3.4.7 - Use algebra to solve
Topic 3 - Relationships Within
geometric problems unrelated to
Triangles
coordinate geometry, such as solving
for an unknown length in a figure
involving similar triangles, or using
the Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
Page 138 of 198
Obj. 15 - Determine the measure of
an angle using the sum of the interior
angles in a triangle
Obj. 17 - Determine a length in a
triangle using a median
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
Obj. 18 - Solve for the length of a
side of a triangle using the
Pythagorean theorem
Obj. 19 - Solve a problem using
inequalities in a triangle
Obj. 20 - Solve a problem involving
two triangles by using the hinge
theorem and other triangle inequality
relationships
Topic 4 - Congruent Triangles
Obj. 22 - Determine the length of a
side or the measure of an angle in
congruent triangles
Topic 5 - Quadrilaterals and
Obj. 27 - Determine a length or an
Other Polygons
angle measure using general
properties of parallelograms
Obj. 28 - Determine a length or an
angle measure using properties of
squares, rectangles, or rhombi
Obj. 29 - Determine a length or an
angle measure using properties of
kites
Obj. 30 - Determine a length or an
angle measure using properties of
trapezoids
Topic 6 - Similarity
Obj. 35 - Determine the length of a
side or the measure of an angle in
similar triangles
Obj. 39 - Determine a length in a
triangle using a midsegment
Obj. 42 - Determine a length using
similar triangles formed by the
altitude to the hypotenuse of a right
triangle
MN 9.4 - Data Analysis & Probability
MN 9.4.1 - Display and analyze data;
use various measures associated
with data to draw conclusions, identify
trends and describe relationships.
Page 139 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.1.1 - Describe a data set
using data displays, such as box-andwhisker plots; describe and compare
data sets using summary statistics,
including measures of center,
location and spread. Measures of
center and location include mean,
median, quartile and percentile.
Measures of spread include standard
deviation, range and inter-quartile
range. Know how to use calculators,
spreadsheets or other technology to
display data and calculate summary
statistics.
MN 9.4.1.2 - Analyze the effects on
summary statistics of changes in data
sets. Example 1: Understand how
inserting or deleting a data point may
affect the mean and standard
deviation. Example 2: Understand
how the median and interquartile
range are affected when the entire
data set is transformed by adding a
constant to each data value or
multiplying each data value by a
constant.
MN 9.4.1.3 - Use scatterplots to
analyze patterns and describe
relationships between two variables.
Using technology, determine
regression lines (line of best fit) and
correlation coefficients; use
regression lines to make predictions
and correlation coefficients to assess
the reliability of those predictions.
Page 140 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.1.4 - Use the mean and
standard deviation of a data set to fit
it to a normal distribution (bell-shaped
curve) and to estimate population
percentages. Recognize that there
are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets and tables
to estimate areas under the normal
curve. Example 1: After performing
several measurements of some
attribute of an irregular physical
object, it is appropriate to fit the data
to a normal distribution and draw
conclusions about measurement
error. Example 2: When data
involving two very different
populations is combined, the resulting
histogram may show two distinct
peaks, and fitting the data to a
normal distribution is not appropriate.
MN 9.4.2 - Explain the uses of data
and statistical thinking to draw
inferences, make predictions and
justify conclusions
MN 9.4.2.1 - Evaluate reports based
on data published in the media by
identifying the source of the data, the
design of the study, and the way the
data are analyzed and displayed.
Show how graphs and data can be
distorted to support different points of
view. Know how to use spreadsheet
tables and graphs or graphing
technology to recognize and analyze
distortions in data displays. Example:
Shifting data on the vertical axis can
make relative changes appear
deceptively large.
MN 9.4.2.2 - Identify and explain
misleading uses of data; recognize
when arguments based on data
confuse correlation and causation.
MN 9.4.2.3 - Explain the impact of
sampling methods, bias and the
phrasing of questions asked during
data collection.
Page 141 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3 - Calculate probabilities and
apply probability concepts to solve
real-world and mathematical
problems.
MN 9.4.3.1 - Select and apply
counting procedures, such as the
multiplication and addition principles
and tree diagrams, to determine the
size of a sample space (the number
of possible outcomes) and to
calculate probabilities. Example: If
one girl and one boy are picked at
random from a class with 20 girls and
15 boys, there are 20 × 15 = 300
different possibilities, so the
probability that a particular girl is
chosen together with a particular boy
is 1/300.
MN 9.4.3.2 - Calculate experimental
probabilities by performing
simulations or experiments involving
a probability model and using relative
frequencies of outcomes.
MN 9.4.3.3 - Understand that the Law
of Large Numbers expresses a
relationship between the probabilities
in a probability model and the
experimental probabilities found by
performing simulations or
experiments involving the model.
MN 9.4.3.4 - Use random numbers
generated by a calculator or a
spreadsheet, or taken from a table, to
perform probability simulations and to
introduce fairness into decision
making. Example: If a group of
students needs to fairly select one of
its members to lead a discussion,
they can use a random number to
determine the selection.
Page 142 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3.5 - Apply probability
Topic 9 - Area
Obj. 86 - Determine a probability
concepts such as intersections,
using an area model
unions and complements of events,
and conditional probability and
independence, to calculate
probabilities and solve problems.
Example: The probability of tossing at
least one head when flipping a fair
coin three times can be calculated by
looking at the complement of this
event (flipping three tails in a row).
MN 9.4.3.6 - Describe the concepts
of intersections, unions and
complements using Venn diagrams.
Understand the relationships
between these concepts and the
words AND, OR, NOT, as used in
computerized searches and
spreadsheets.
MN 9.4.3.7 - Understand and use
simple probability formulas involving
intersections, unions and
complements of events. Example 1:
If the probability of an event is p, then
the probability of the complement of
an event is 1 - p; the probability of the
intersection of two independent
events is the product of their
probabilities. Example 2: The
probability of the union of two events
equals the sum of the probabilities of
the two individual events minus the
probability of the intersection of the
events.
MN 9.4.3.8 - Apply probability
concepts to real-world situations to
make informed decisions. Example 1:
Explain why a hockey coach might
decide near the end of the game to
pull the goalie to add another forward
position player if the team is behind.
Example 2: Consider the role that
probabilities play in health care
decisions, such as deciding between
having eye surgery and wearing
glasses.
Page 143 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Second Edition Geometry
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.4.3.9 - Use the relationship
between conditional probabilities and
relative frequencies in contingency
tables. Example: A table that displays
percentages relating gender (male or
female) and handedness (righthanded or left-handed) can be used
to determine the conditional
probability of being left-handed, given
that the gender is male.
Page 144 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2 - Algebra
MN 9.2.1 - Understand the concept of
function, and identify important
features of functions and other
relations using symbolic and
graphical methods where
appropriate.
MN 9.2.1.1 - Understand the
Topic 3 - Relations, Functions,
definition of a function. Use functional and Graphs
notation and evaluate a function at a
given point in its domain. Example: If
f(x) - 1/(x²-3),find f(-4).
MN 9.2.1.2 - Distinguish between
functions and other relations defined
symbolically, graphically or in tabular
form.
MN 9.2.1.3 - Find the domain of a
function defined symbolically,
graphically or in a real-world context.
Example: The formula f(x) = pi x² can
represent a function whose domain is
all real numbers, but in the context of
the area of a circle, the domain would
be restricted to positive x.
Objective Description
Obj. 31 - Evaluate functions for given
values
Topic 3 - Relations, Functions,
and Graphs
Obj. 37 - WP: Function problems
Obj. 29 - Determine if relations are
functions
Topic 3 - Relations, Functions,
and Graphs
Obj. 27 - Domain and range,
functions
Topic 10 - Rational Expressions
and Equations
Obj. 143 - Rational expressions,
domains
MN 9.2.1.4 - Obtain information and
draw conclusions from graphs of
functions and other relations.
Example: If a graph shows the
relationship between the elapsed
flight time of a golf ball at a given
moment and its height at that same
moment, identify the time interval
during which the ball is at least 100
feet above the ground.
MN 9.2.1.5 - Identify the vertex, line Topic 11 - Conics and Secondof symmetry and intercepts of the
Degree Equations
parabola corresponding to a
quadratic function, using symbolic
and graphical methods, when the
function is expressed in the form f(x)
= ax² + bx + c, in the form f(x) = a(x h)² + k , or in factored form.
MN 9.2.1.6 - Identify intercepts,
zeros, maxima, minima and intervals
of increase and decrease from the
graph of a function.
Page 145 of 198
Grades 9 - 11
Obj. 170 - Parabolas, find vertex
from equation
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.1.7 - Understand the concept
of an asymptote and identify
asymptotes for exponential functions
and reciprocals of linear functions,
using symbolic and graphical
methods.
MN 9.2.1.8 - Make qualitative
statements about the rate of change
of a function, based on its graph or
table of values. Example: The
function f(x) = 3 to the x power
increases for all x, but it increases
faster when x > 2 than it does when x
< 2.
MN 9.2.1.9 - Determine how
translations affect the symbolic and
graphical forms of a function. Know
how to use graphing technology to
examine translations. Example:
Determine how the graph of f(x) = |x h| + k changes as h and k change.
Grades 9 - 11
Objective Description
MN 9.2.2 - Recognize linear,
quadratic, exponential and other
common functions in real-world and
mathematical situations; represent
these functions with tables, verbal
descriptions, symbols and graphs;
solve problems involving these
functions, and explain results in the
original context.
MN 9.2.2.1 - Represent and solve
Topic 2 - Linear Equations and
problems in various contexts using
Inequalities
linear and quadratic functions.
Example: Write a function that
represents the area of a rectangular
garden that can be surrounded with
32 feet of fencing, and use the
function to determine the possible
dimensions of such a garden if the
area must be at least 50 square feet.
Topic 3 - Relations, Functions,
and Graphs
Topic 7 - Quadratic
Page 146 of 198
Obj. 12 - WP: Solve linear equations
Obj. 40 - WP: Linear equations
Obj. 97 - WP: Graph quadratic
functions
Obj. 99 - WP: Variation problems
Obj. 101 - WP: Number problems
using quadratic equations
Obj. 102 - WP: Area and perimeter
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.2.2 - Represent and solve
problems in various contexts using
exponential functions, such as
investment growth, depreciation and
population growth.
Topic 11 - Conics and SecondDegree Equations
Topic 9 - Exponents and
Logarithms
MN 9.2.2.3 - Sketch graphs of linear, Topic 3 - Relations, Functions,
quadratic and exponential functions, and Graphs
and translate between graphs, tables
and symbolic representations. Know
how to use graphing technology to
graph these functions.
Topic 7 - Quadratic
Grades 9 - 11
Objective Description
Obj. 103 - WP: Other problems using
quadratic equations
Obj. 173 - WP: Production and profit
problems
Obj. 138 - WP: Interest problems
Obj. 139 - WP: Growth and decay
problems
Obj. 34 - Graph linear equations, ax
+ by = c
Obj. 35 - Graph linear equations, y =
ax + b
Obj. 96 - Graph quadratic functions
Obj. 97 - WP: Graph quadratic
functions
Obj. 141 - Graph exponential
functions
Obj. 171 - Graph parabolas (y = x^2)
MN 9.2.2.4 - Express the terms in a
geometric sequence recursively and
by giving an explicit (closed form)
formula, and express the partial sums
of a geometric series recursively.
Example 1: A closed form formula for
the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)
to the (n-1) power, where n = 1, 2, 3,
... , and this sequence can be
expressed recursively by writing t1 =
3 and tn = 2t(n-1), for n is greater
than or equal to 2. Example 2: the
partial sums sn of the series 3 + 6 +
12 + 24 + ... can be expressed
recursively by writing s1 = 3 and sn =
3 + 2s(n-1), for n is greater than or
equal to 2.
Page 147 of 198
Topic 9 - Exponents and
Logarithms
Topic 11 - Conics and SecondDegree Equations
Topic 12 - Sequences and Series Obj. 189 - Find general terms of geo
seq given first 4 terms
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.2.5 - Recognize and solve
Topic 12 - Sequences and Series Obj. 190 - WP: Geometric
problems that can be modeled using
sequences
finite geometric sequences and
series, such as home mortgage and
other compound interest examples.
Know how to use spreadsheets and
calculators to explore geometric
sequences and series in various
contexts.
Obj. 195 - WP: Geometric series
MN 9.2.2.6 - Sketch the graphs of
Topic 6 - Roots, Radicals, and
Obj. 78 - Graph square roots
common non-linear functions such as Complex Numbers
f(x)= the square root of x, f(x) = |x|,
f(x)= 1/x, f(x) = x³, and translations of
these functions, such as f(x) = the
square root of (x-2) + 4. Know how to
use graphing technology to graph
these functions.
Topic 9 - Exponents and
Logarithms
Topic 10 - Rational Expressions
and Equations
MN 9.2.3 - Generate equivalent
algebraic expressions involving
polynomials and radicals; use
algebraic properties to evaluate
expressions.
MN 9.2.3.1 - Evaluate polynomial and Topic 1 - The Real Numbers
rational expressions and expressions
containing radicals and absolute
values at specified points in their
domains.
Topic 8 - Polynomials
MN 9.2.3.2 - Add, subtract and
multiply polynomials; divide a
polynomial by a polynomial of equal
or lower degree.
Topic 8 - Polynomials
Obj. 142 - Graph logarithmic
functions
Obj. 147 - Graph rational functions
and equations
Obj. 8 - Evaluate expressions for
given values
Obj. 9 - WP: Evaluate expressions
Obj. 109 - Evaluate polynomials for
given values
Obj. 110 - Add polynomials
Obj. 111 - Subtract polynomials
Obj. 112 - Add and subtract
polynomials
Obj. 113 - Square a binomial, ax + by
Obj. 114 - Multiply 2 binomials
Obj. 115 - Multiply monomials by
polynomials
Obj. 116 - Multiply binomials by
trinomials
Obj. 117 - Square trinomials
Page 148 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.3.3 - Factor common
monomial factors from polynomials,
factor quadratic polynomials, and
factor the difference of two squares.
Example: 9x to the 6th power - x to
the 4th power = (3x³ - x²)(3x³ + x²).
MN 9.2.3.4 - Add, subtract, multiply,
divide and simplify algebraic
fractions. Example: 1/(1-x) + x/(1+x)
is equivalent to (1+2x-x²)/(1-x²).
Topic 8 - Polynomials
Topic 10 - Rational Expressions
and Equations
Grades 9 - 11
Objective Description
Obj. 118 - Simplify polynomial expr
using multiplication
Obj. 119 - Divide polynomials by
monomials
Obj. 120 - Divide polynomials
Obj. 122 - Factor trinomials, ax(x +
b)(x - c)
Obj. 123 - Factor difference of
squares
Obj. 145 - Simplify rational
expressions
Obj. 146 - Simplify rational
expressions by factoring
Obj. 148 - Multiply and simplify
rational expressions
Obj. 149 - Divide and simplify rational
expressions
Obj. 150 - Add rational expressions
MN 9.2.3.5 - Check whether a given
complex number is a solution of a
quadratic equation by substituting it
for the variable and evaluating the
expression, using arithmetic with
complex numbers. Example: The
complex number (1+i)/2 is a solution
of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.
Page 149 of 198
Obj. 151 - Subtract rational
expressions
Obj. 152 - Add and subtract rational
expressions
Obj. 154 - Simplify complex rational
expressions
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.3.6 - Apply the properties of Topic 6 - Roots, Radicals, and
positive and negative rational
Complex Numbers
exponents to generate equivalent
algebraic expressions, including
those involving nth roots. Example:
The square root of 2 x the square
root of 7 = 2 to the 1/2 power x 7 to
the 1/2 power = 14 to the 1/2 power =
the square root of 14. Rules for
computing directly with radicals may
also be used: the square root of 2 x
the square root of x= the square root
of 2x.
MN 9.2.3.7 - Justify steps in
generating equivalent expressions by
identifying the properties used. Use
substitution to check the equality of
expressions for some particular
values of the variables; recognize
that checking with substitution does
not guarantee equality of expressions
for all values of the variables.
Grades 9 - 11
Objective Description
Obj. 69 - Write square roots as
exponential expressions
Obj. 70 - Simplify expressions with
fractional exponents
Obj. 71 - Simplify nth roots
Obj. 73 - Simplify expressions with
rational exponents
Obj. 74 - Add and subtract radical
expressions
Obj. 75 - Rationalize denominators
MN 9.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear, quadratic, exponential, and nth
root functions. Solve equations and
inequalities symbolically and
graphically. Interpret solutions in the
original context.
Page 150 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.4.1 - Represent relationships Topic 7 - Quadratic
in various contexts using quadratic
equations and inequalities. Solve
quadratic equations and inequalities
by appropriate methods including
factoring, completing the square,
graphing and the quadratic formula.
Find non-real complex roots when
they exist. Recognize that a particular
solution may not be applicable in the
original context. Know how to use
calculators, graphing utilities or other
technology to solve quadratic
equations and inequalities. Example:
A diver jumps from a 20 meter
platform with an upward velocity of 3
meters per second. In finding the
time at which the diver hits the
surface of the water, the resulting
quadratic equation has a positive and
a negative solution. The negative
solution should be discarded because
of the context.
Grades 9 - 11
Objective Description
Obj. 87 - Solve quad eqns, square
root rule (real roots)
Obj. 88 - Solve quad eqns, square
root rule (complex roots)
Obj. 89 - Factor quadratics, real roots
MN 9.2.4.2 - Represent relationships Topic 9 - Exponents and
in various contexts using equations Logarithms
involving exponential functions; solve
these equations graphically or
numerically. Know how to use
calculators, graphing utilities or other
technology to solve these equations.
Page 151 of 198
Obj. 90 - Factor quadratics, roots
with radicals
Obj. 91 - Quadratic formula, 2 real
roots
Obj. 92 - Quadratic formula, complex
roots
Obj. 101 - WP: Number problems
using quadratic equations
Obj. 102 - WP: Area and perimeter
Obj. 105 - Solve quadratic
inequalities
Obj. 136 - Solve exponential
equations
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.4.3 - Recognize that to solve
certain equations, number systems
need to be extended from whole
numbers to integers, from integers to
rational numbers, from rational
numbers to real numbers, and from
real numbers to complex numbers. In
particular, non-real complex numbers
are needed to solve some quadratic
equations with real coefficients.
MN 9.2.4.4 - Represent relationships Topic 4 - Systems of Equations
in various contexts using systems of and Inequalities
linear inequalities; solve them
graphically. Indicate which parts of
the boundary are included in and
excluded from the solution set using
solid and dotted lines.
Grades 9 - 11
Objective Description
Obj. 56 - Solve systems of linear
inequalities by graphing
MN 9.2.4.5 - Solve linear
programming problems in two
variables using graphical methods.
MN 9.2.4.6 - Represent relationships
in various contexts using absolute
value inequalities in two variables;
solve them graphically. Example: If a
pipe is to be cut to a length of 5
meters accurate to within a tenth of
its diameter, the relationship between
the length x of the pipe and its
diameter y satisfies the inequality |x 5| is less than or equal to 0.1y.
MN 9.2.4.7 - Solve equations that
Topic 6 - Roots, Radicals, and
contain radical expressions.
Complex Numbers
Recognize that extraneous solutions
may arise when using symbolic
methods. Example 1: The equation
the square root of x-9 = 9 the square
root of x may be solved by squaring
both sides to obtain x - 9 = 81x, which
has the solution x = -9/80. However,
this is not a solution of the original
equation, so it is an extraneous
solution that should be discarded.
The original equation has no solution
in this case. Example 2: Solve the
cubed root of (-x+1) = -5.
Topic 7 - Quadratic
Page 152 of 198
Obj. 76 - Solve equations containing
radicals
Obj. 90 - Factor quadratics, roots
with radicals
081309
Accelerated Math
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.4.8 - Assess the
reasonableness of a solution in its
given context and compare the
solution to appropriate graphical or
numerical estimates; interpret a
solution in the original context.
MN 9.3 - Geometry & Measurement
Grades 9 - 11
Objective Description
MN 9.3.1 - Calculate measurements
of plane and solid geometric figures;
know that physical measurements
depend on the choice of a unit and
that they are approximations.
MN 9.3.1.1 - Determine the surface
area and volume of pyramids, cones
and spheres. Use measuring devices
or formulas as appropriate. Example:
Measure the height and radius of a
cone and then use a formula to find
its volume.
MN 9.3.1.2 - Compose and
decompose two- and threedimensional figures; use
decomposition to determine the
perimeter, area, surface area and
volume of various figures. Example:
Find the volume of a regular
hexagonal prism by decomposing it
into six equal triangular prisms.
MN 9.3.1.3 - Understand that
quantities associated with physical
measurements must be assigned
units; apply such units correctly in
expressions, equations and problem
solutions that involve measurements;
and convert between measurement
systems. Example: 60 miles/hour =
60 miles/hour × 5280 feet/mile × 1
hour/3600 seconds = 88 feet/second.
MN 9.3.1.4 - Understand and apply
the fact that the effect of a scale
factor k on length, area and volume is
to multiply each by k, k² and k³,
respectively.
Page 153 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.1.5 - Make reasonable
estimates and judgments about the
accuracy of values resulting from
calculations involving measurements.
Example: Suppose the sides of a
rectangle are measured to the
nearest tenth of a centimeter at 2.6
cm and 9.8 cm. Because of
measurement errors, the width could
be as small as 2.55 cm or as large as
2.65 cm, with similar errors for the
height. These errors affect
calculations. For instance, the actual
area of the rectangle could be
smaller than 25 cm² or larger than 26
cm², even though 2.6 × 9.8 = 25.48.
Grades 9 - 11
Objective Description
MN 9.3.2 - Construct logical
arguments, based on axioms,
definitions and theorems, to prove
theorems and other results in
geometry.
MN 9.3.2.1 - Understand the roles of
axioms, definitions, undefined terms
and theorems in logical arguments.
MN 9.3.2.2 - Accurately interpret and
use words and phrases in geometric
proofs such as "if...then," "if and only
if," "all," and "not." Recognize the
logical relationships between an
"if...then" statement and its inverse,
converse and contrapositive.
Example: The statement "If you don't
do your homework, you can't go to
the dance" is not logically equivalent
to its inverse "If you do your
homework, you can go to the dance.".
MN 9.3.2.3 - Assess the validity of a
logical argument and give
counterexamples to disprove a
statement.
Page 154 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.2.4 - Construct logical
arguments and write proofs of
theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a
form that clearly justifies the
reasoning, such as two-column
proofs, paragraph proofs, flow charts
or illustrations. Example: Prove that
the sum of the interior angles of a
pentagon is 540° using the fact that
the sum of the interior angles of a
triangle is 180°.
MN 9.3.2.5 - Use technology tools to
examine theorems, test conjectures,
perform constructions and develop
mathematical reasoning skills in multistep problems. The tools may include
compass and straight edge, dynamic
geometry software, design software
or Internet applets.
Grades 9 - 11
Objective Description
MN 9.3.3 - Know and apply
properties of geometric figures to
solve real-world and mathematical
problems and to logically justify
results in geometry.
MN 9.3.3.1 - Know and apply
properties of parallel and
perpendicular lines, including
properties of angles formed by a
transversal, to solve problems and
logically justify results. Example:
Prove that the perpendicular bisector
of a line segment is the set of all
points equidistant from the two
endpoints, and use this fact to solve
problems and justify other results.
MN 9.3.3.2 - Know and apply
properties of angles, including
corresponding, exterior, interior,
vertical, complementary and
supplementary angles, to solve
problems and logically justify results.
Example: Prove that two triangles
formed by a pair of intersecting lines
and a pair of parallel lines (an "X"
trapped between two parallel lines)
are similar.
Page 155 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.3.3 - Know and apply
properties of equilateral, isosceles
and scalene triangles to solve
problems and logically justify results.
Example: Use the triangle inequality
to prove that the perimeter of a
quadrilateral is larger than the sum of
the lengths of its diagonals.
MN 9.3.3.4 - Apply the Pythagorean Topic 7 - Quadratic
Theorem and its converse to solve
problems and logically justify results.
Example: When building a wooden
frame that is supposed to have a
square corner, ensure that the corner
is square by measuring lengths near
the corner and applying the
Pythagorean Theorem.
Grades 9 - 11
Objective Description
Obj. 100 - WP: Pythagorean
Theorem
MN 9.3.3.5 - Know and apply
properties of right triangles, including
properties of 45-45-90 and 30-60-90
triangles, to solve problems and
logically justify results. Example 1:
Use 30-60-90 triangles to analyze
geometric figures involving equilateral
triangles and hexagons. Example 2:
Determine exact values of the
trigonometric ratios in these special
triangles using relationships among
the side lengths.
Page 156 of 198
081309
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Agency Tag Set Name
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.3.6 - Know and apply
properties of congruent and similar
figures to solve problems and
logically justify results. Example 1:
Analyze lengths and areas in a figure
formed by drawing a line segment
from one side of a triangle to a
second side, parallel to the third side.
Example 2: Determine the height of a
pine tree by comparing the length of
its shadow to the length of the
shadow of a person of known height.
Example 3: When attempting to build
two identical 4-sided frames, a
person measured the lengths of
corresponding sides and found that
they matched. Can the person
conclude that the shapes of the
frames are congruent?
Grades 9 - 11
Objective Description
MN 9.3.3.7 - Use properties of
polygons-including quadrilaterals and
regular polygons-to define them,
classify them, solve problems and
logically justify results. Example 1:
Recognize that a rectangle is a
special case of a trapezoid. Example
2: Give a concise and clear definition
of a kite.
MN 9.3.3.8 - Know and apply
properties of a circle to solve
problems and logically justify results.
Example: Show that opposite angles
of a quadrilateral inscribed in a circle
are supplementary.
MN 9.3.4 - Solve real-world and
mathematical geometric problems
using algebraic methods.
MN 9.3.4.1 - Understand how the
Topic 15 - Trigonometry
properties of similar right triangles
allow the trigonometric ratios to be
defined, and determine the sine,
cosine and tangent of an acute angle
in a right triangle.
Page 157 of 198
Obj. 223 - Find the sine, cosine, or
tangent
081309
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.4.2 - Apply the trigonometric Topic 15 - Trigonometry
ratios sine, cosine and tangent to
solve problems, such as determining
lengths and areas in right triangles
and in figures that can be
decomposed into right triangles.
Know how to use calculators, tables
or other technology to evaluate
trigonometric ratios. Example: Find
the area of a triangle, given the
measure of one of its acute angles
and the lengths of the two sides that
form that angle.
MN 9.3.4.3 - Use calculators, tables
or other technologies in connection
with the trigonometric ratios to find
angle measures in right triangles in
various contexts.
MN 9.3.4.4 - Use coordinate
geometry to represent and analyze
line segments and polygons,
including determining lengths,
midpoints and slopes of line
segments.
MN 9.3.4.5 - Know the equation for
the graph of a circle with radius r and
center (h,k), (x - h)² + (y - k)² = r², and
justify this equation using the
Pythagorean Theorem and properties
of translations.
MN 9.3.4.6 - Use numeric, graphic
and symbolic representations of
transformations in two dimensions,
such as reflections, translations,
scale changes and rotations about
the origin by multiples of 90°, to solve
problems involving figures on a
coordinate grid. Example: If the point
(3,-2) is rotated 90° counterclockwise
about the origin, it becomes the point
(2,3).
Page 158 of 198
Grades 9 - 11
Objective Description
Obj. 234 - Find a side given side and
angle
Obj. 235 - Find unknown sides of
right triangles
Obj. 236 - WP: Trigonometry
Topic 3 - Relations, Functions,
and Graphs
Obj. 39 - Find slopes from 2 points
Topic 11 - Conics and SecondDegree Equations
Obj. 158 - Graph circles
Obj. 160 - Circles, write equations
given centers and radii
Obj. 162 - WP: Circles
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.4.7 - Use algebra to solve
Topic 7 - Quadratic
geometric problems unrelated to
coordinate geometry, such as solving
for an unknown length in a figure
involving similar triangles, or using
the Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
MN 9.4 - Data Analysis & Probability
Grades 9 - 11
Objective Description
Obj. 100 - WP: Pythagorean
Theorem
MN 9.4.1 - Display and analyze data;
use various measures associated
with data to draw conclusions, identify
trends and describe relationships.
MN 9.4.1.1 - Describe a data set
Topic 14 - Statistics
using data displays, such as box-andwhisker plots; describe and compare
data sets using summary statistics,
including measures of center,
location and spread. Measures of
center and location include mean,
median, quartile and percentile.
Measures of spread include standard
deviation, range and inter-quartile
range. Know how to use calculators,
spreadsheets or other technology to
display data and calculate summary
statistics.
MN 9.4.1.2 - Analyze the effects on
summary statistics of changes in data
sets. Example 1: Understand how
inserting or deleting a data point may
affect the mean and standard
deviation. Example 2: Understand
how the median and interquartile
range are affected when the entire
data set is transformed by adding a
constant to each data value or
multiplying each data value by a
constant.
Page 159 of 198
Obj. 208 - Line and stem-and-leaf
plots
Obj. 209 - Box-and-whisker plots
Obj. 210 - Interquartile ranges of data
sets
Obj. 211 - Means of data sets
Obj. 212 - Medians of data sets
Obj. 213 - Modes of data sets
Obj. 214 - Means, medians, and
modes of data sets
081309
Accelerated Math
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Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.1.3 - Use scatterplots to
analyze patterns and describe
relationships between two variables.
Using technology, determine
regression lines (line of best fit) and
correlation coefficients; use
regression lines to make predictions
and correlation coefficients to assess
the reliability of those predictions.
Grades 9 - 11
Objective Description
MN 9.4.1.4 - Use the mean and
standard deviation of a data set to fit
it to a normal distribution (bell-shaped
curve) and to estimate population
percentages. Recognize that there
are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets and tables
to estimate areas under the normal
curve. Example 1: After performing
several measurements of some
attribute of an irregular physical
object, it is appropriate to fit the data
to a normal distribution and draw
conclusions about measurement
error. Example 2: When data
involving two very different
populations is combined, the resulting
histogram may show two distinct
peaks, and fitting the data to a
normal distribution is not appropriate.
MN 9.4.2 - Explain the uses of data
and statistical thinking to draw
inferences, make predictions and
justify conclusions
Page 160 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.2.1 - Evaluate reports based
on data published in the media by
identifying the source of the data, the
design of the study, and the way the
data are analyzed and displayed.
Show how graphs and data can be
distorted to support different points of
view. Know how to use spreadsheet
tables and graphs or graphing
technology to recognize and analyze
distortions in data displays. Example:
Shifting data on the vertical axis can
make relative changes appear
deceptively large.
MN 9.4.2.2 - Identify and explain
misleading uses of data; recognize
when arguments based on data
confuse correlation and causation.
MN 9.4.2.3 - Explain the impact of
sampling methods, bias and the
phrasing of questions asked during
data collection.
MN 9.4.3 - Calculate probabilities and
apply probability concepts to solve
real-world and mathematical
problems.
MN 9.4.3.1 - Select and apply
Topic 13 - Probability
counting procedures, such as the
multiplication and addition principles
and tree diagrams, to determine the
size of a sample space (the number
of possible outcomes) and to
calculate probabilities. Example: If
one girl and one boy are picked at
random from a class with 20 girls and
15 boys, there are 20 × 15 = 300
different possibilities, so the
probability that a particular girl is
chosen together with a particular boy
is 1/300.
Grades 9 - 11
Objective Description
Obj. 196 - Fundamental Counting
Principle
Obj. 202 - Probability of single events
MN 9.4.3.2 - Calculate experimental
probabilities by performing
simulations or experiments involving
a probability model and using relative
frequencies of outcomes.
Page 161 of 198
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11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.3.3 - Understand that the Law
of Large Numbers expresses a
relationship between the probabilities
in a probability model and the
experimental probabilities found by
performing simulations or
experiments involving the model.
MN 9.4.3.4 - Use random numbers
generated by a calculator or a
spreadsheet, or taken from a table, to
perform probability simulations and to
introduce fairness into decision
making. Example: If a group of
students needs to fairly select one of
its members to lead a discussion,
they can use a random number to
determine the selection.
MN 9.4.3.5 - Apply probability
Topic 13 - Probability
concepts such as intersections,
unions and complements of events,
and conditional probability and
independence, to calculate
probabilities and solve problems.
Example: The probability of tossing at
least one head when flipping a fair
coin three times can be calculated by
looking at the complement of this
event (flipping three tails in a row).
MN 9.4.3.6 - Describe the concepts
of intersections, unions and
complements using Venn diagrams.
Understand the relationships
between these concepts and the
words AND, OR, NOT, as used in
computerized searches and
spreadsheets.
Page 162 of 198
Grades 9 - 11
Objective Description
Obj. 204 - Probability of independent
events
Obj. 205 - Conditional probability
081309
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Minnesota, Math, 2007, Grades: 9Accelerated Math Algebra 2
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.3.7 - Understand and use
simple probability formulas involving
intersections, unions and
complements of events. Example 1:
If the probability of an event is p, then
the probability of the complement of
an event is 1 - p; the probability of the
intersection of two independent
events is the product of their
probabilities. Example 2: The
probability of the union of two events
equals the sum of the probabilities of
the two individual events minus the
probability of the intersection of the
events.
MN 9.4.3.8 - Apply probability
concepts to real-world situations to
make informed decisions. Example 1:
Explain why a hockey coach might
decide near the end of the game to
pull the goalie to add another forward
position player if the team is behind.
Example 2: Consider the role that
probabilities play in health care
decisions, such as deciding between
having eye surgery and wearing
glasses.
MN 9.4.3.9 - Use the relationship
Topic 13 - Probability
between conditional probabilities and
relative frequencies in contingency
tables. Example: A table that displays
percentages relating gender (male or
female) and handedness (righthanded or left-handed) can be used
to determine the conditional
probability of being left-handed, given
that the gender is male.
Page 163 of 198
Grades 9 - 11
Objective Description
Obj. 205 - Conditional probability
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2 - Algebra
MN 9.2.1 - Understand the concept of
function, and identify important
features of functions and other
relations using symbolic and
graphical methods where
appropriate.
MN 9.2.1.1 - Understand the
Topic 1 - Review of Fundamental Obj. 17 - Evaluate functions for given
definition of a function. Use functional Concepts of Algebra
values
notation and evaluate a function at a
given point in its domain. Example: If
f(x) - 1/(x²-3),find f(-4).
MN 9.2.1.2 - Distinguish between
functions and other relations defined
symbolically, graphically or in tabular
form.
MN 9.2.1.3 - Find the domain of a
function defined symbolically,
graphically or in a real-world context.
Example: The formula f(x) = pi x² can
represent a function whose domain is
all real numbers, but in the context of
the area of a circle, the domain would
be restricted to positive x.
MN 9.2.1.4 - Obtain information and
draw conclusions from graphs of
functions and other relations.
Example: If a graph shows the
relationship between the elapsed
flight time of a golf ball at a given
moment and its height at that same
moment, identify the time interval
during which the ball is at least 100
feet above the ground.
MN 9.2.1.5 - Identify the vertex, line Topic 2 - Polynomials
of symmetry and intercepts of the
parabola corresponding to a
quadratic function, using symbolic
and graphical methods, when the
function is expressed in the form f(x)
= ax² + bx + c, in the form f(x) = a(x h)² + k , or in factored form.
MN 9.2.1.6 - Identify intercepts,
zeros, maxima, minima and intervals
of increase and decrease from the
graph of a function.
Page 164 of 198
Obj. 35 - Parabolas, find vertex from
equation
081309
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Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.1.7 - Understand the concept
of an asymptote and identify
asymptotes for exponential functions
and reciprocals of linear functions,
using symbolic and graphical
methods.
MN 9.2.1.8 - Make qualitative
statements about the rate of change
of a function, based on its graph or
table of values. Example: The
function f(x) = 3 to the x power
increases for all x, but it increases
faster when x > 2 than it does when x
< 2.
MN 9.2.1.9 - Determine how
translations affect the symbolic and
graphical forms of a function. Know
how to use graphing technology to
examine translations. Example:
Determine how the graph of f(x) = |x h| + k changes as h and k change.
Grades 9 - 11
Objective Description
MN 9.2.2 - Recognize linear,
quadratic, exponential and other
common functions in real-world and
mathematical situations; represent
these functions with tables, verbal
descriptions, symbols and graphs;
solve problems involving these
functions, and explain results in the
original context.
MN 9.2.2.1 - Represent and solve
Topic 1 - Review of Fundamental Obj. 4 - Solve linear equations
problems in various contexts using
Concepts of Algebra
linear and quadratic functions.
Example: Write a function that
represents the area of a rectangular
garden that can be surrounded with
32 feet of fencing, and use the
function to determine the possible
dimensions of such a garden if the
area must be at least 50 square feet.
Topic 2 - Polynomials
MN 9.2.2.2 - Represent and solve
Topic 3 - Exponential and
problems in various contexts using
Logarithmic Functions
exponential functions, such as
investment growth, depreciation and
population growth.
Page 165 of 198
Obj. 5 - WP: Linear Equations
Obj. 15 - WP: Quadratic equations
Obj. 37 - WP: Quadratic functions
Obj. 57 - WP: Exponential functions
081309
Accelerated Math
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Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
Grades 9 - 11
Objective Description
Obj. 59 - Solve exponential equations
Obj. 60 - WP: Compound interest
Obj. 61 - WP: Radioactive decay
MN 9.2.2.3 - Sketch graphs of linear, Topic 1 - Review of Fundamental Obj. 2 - Graph lines
quadratic and exponential functions, Concepts of Algebra
and translate between graphs, tables
and symbolic representations. Know
how to use graphing technology to
graph these functions.
MN 9.2.2.4 - Express the terms in a
geometric sequence recursively and
by giving an explicit (closed form)
formula, and express the partial sums
of a geometric series recursively.
Example 1: A closed form formula for
the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)
to the (n-1) power, where n = 1, 2, 3,
... , and this sequence can be
expressed recursively by writing t1 =
3 and tn = 2t(n-1), for n is greater
than or equal to 2. Example 2: the
partial sums sn of the series 3 + 6 +
12 + 24 + ... can be expressed
recursively by writing s1 = 3 and sn =
3 + 2s(n-1), for n is greater than or
equal to 2.
Topic 2 - Polynomials
Obj. 36 - Graph quadratic functions
Topic 3 - Exponential and
Logarithmic Functions
Topic 7 - Conic Sections
Obj. 55 - Graph exponential functions
Obj. 91 - Parabolas, graph given
equations
Topic 9 - Sequences and Series Obj. 130 - Find terms of geo seq (1st
term & common ratio)
Obj. 131 - Find terms of geo seq
given first terms
MN 9.2.2.5 - Recognize and solve
Topic 9 - Sequences and Series Obj. 132 - WP: Geometric
problems that can be modeled using
sequences
finite geometric sequences and
series, such as home mortgage and
other compound interest examples.
Know how to use spreadsheets and
calculators to explore geometric
sequences and series in various
contexts.
Obj. 136 - WP: Geometric series
Page 166 of 198
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Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.2.6 - Sketch the graphs of
Topic 1 - Review of Fundamental Obj. 22 - Use rigid & nonrigid
common non-linear functions such as Concepts of Algebra
transformations to graph func
f(x)= the square root of x, f(x) = |x|,
f(x)= 1/x, f(x) = x³, and translations of
these functions, such as f(x) = the
square root of (x-2) + 4. Know how to
use graphing technology to graph
these functions.
Topic 2 - Polynomials
Topic 3 - Exponential and
Logarithmic Functions
MN 9.2.3 - Generate equivalent
algebraic expressions involving
polynomials and radicals; use
algebraic properties to evaluate
expressions.
MN 9.2.3.1 - Evaluate polynomial and
rational expressions and expressions
containing radicals and absolute
values at specified points in their
domains.
MN 9.2.3.2 - Add, subtract and
Topic 2 - Polynomials
multiply polynomials; divide a
polynomial by a polynomial of equal
or lower degree.
MN 9.2.3.3 - Factor common
monomial factors from polynomials,
factor quadratic polynomials, and
factor the difference of two squares.
Example: 9x to the 6th power - x to
the 4th power = (3x³ - x²)(3x³ + x²).
MN 9.2.3.4 - Add, subtract, multiply,
divide and simplify algebraic
fractions. Example: 1/(1-x) + x/(1+x)
is equivalent to (1+2x-x²)/(1-x²).
Obj. 23 - Graph rational functions
Obj. 36 - Graph quadratic functions
Obj. 55 - Graph exponential functions
Obj. 39 - Synthetic division
Topic 1 - Review of Fundamental Obj. 32 - Simplify, multiply, & divide
Concepts of Algebra
rational expressions
MN 9.2.3.5 - Check whether a given
complex number is a solution of a
quadratic equation by substituting it
for the variable and evaluating the
expression, using arithmetic with
complex numbers. Example: The
complex number (1+i)/2 is a solution
of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.
Page 167 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.3.6 - Apply the properties of Topic 1 - Review of Fundamental Obj. 27 - Simplify expressions w/
positive and negative rational
Concepts of Algebra
rational exponents
exponents to generate equivalent
algebraic expressions, including
those involving nth roots. Example:
The square root of 2 x the square
root of 7 = 2 to the 1/2 power x 7 to
the 1/2 power = 14 to the 1/2 power =
the square root of 14. Rules for
computing directly with radicals may
also be used: the square root of 2 x
the square root of x= the square root
of 2x.
Obj. 28 - Factor expressions w/
rational exponents
Obj. 29 - Simplify radical expressions
MN 9.2.3.7 - Justify steps in
generating equivalent expressions by
identifying the properties used. Use
substitution to check the equality of
expressions for some particular
values of the variables; recognize
that checking with substitution does
not guarantee equality of expressions
for all values of the variables.
MN 9.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear, quadratic, exponential, and nth
root functions. Solve equations and
inequalities symbolically and
graphically. Interpret solutions in the
original context.
Page 168 of 198
081309
Accelerated Math
Grades 9 - 11
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
Objective Description
MN 9.2.4.1 - Represent relationships Topic 1 - Review of Fundamental Obj. 11 - Solve quad eqns, square
in various contexts using quadratic
Concepts of Algebra
root rule
equations and inequalities. Solve
quadratic equations and inequalities
by appropriate methods including
factoring, completing the square,
graphing and the quadratic formula.
Find non-real complex roots when
they exist. Recognize that a particular
solution may not be applicable in the
original context. Know how to use
calculators, graphing utilities or other
technology to solve quadratic
equations and inequalities. Example:
A diver jumps from a 20 meter
platform with an upward velocity of 3
meters per second. In finding the
time at which the diver hits the
surface of the water, the resulting
quadratic equation has a positive and
a negative solution. The negative
solution should be discarded because
of the context.
MN 9.2.4.2 - Represent relationships Topic 3 - Exponential and
in various contexts using equations Logarithmic Functions
involving exponential functions; solve
these equations graphically or
numerically. Know how to use
calculators, graphing utilities or other
technology to solve these equations.
Obj. 12 - Solve quad eqns, factor
(real roots)
Obj. 13 - Solve quad eqns, quadratic
formula
Obj. 15 - WP: Quadratic equations
Obj. 57 - WP: Exponential functions
Obj. 59 - Solve exponential equations
Obj. 60 - WP: Compound interest
Obj. 61 - WP: Radioactive decay
Page 169 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.4.3 - Recognize that to solve
certain equations, number systems
need to be extended from whole
numbers to integers, from integers to
rational numbers, from rational
numbers to real numbers, and from
real numbers to complex numbers. In
particular, non-real complex numbers
are needed to solve some quadratic
equations with real coefficients.
MN 9.2.4.4 - Represent relationships Topic 8 - Systems of Linear
in various contexts using systems of Equations and Inequalities
linear inequalities; solve them
graphically. Indicate which parts of
the boundary are included in and
excluded from the solution set using
solid and dotted lines.
Grades 9 - 11
Objective Description
Obj. 119 - Solve systems of linear
inequalities
MN 9.2.4.5 - Solve linear
programming problems in two
variables using graphical methods.
MN 9.2.4.6 - Represent relationships
in various contexts using absolute
value inequalities in two variables;
solve them graphically. Example: If a
pipe is to be cut to a length of 5
meters accurate to within a tenth of
its diameter, the relationship between
the length x of the pipe and its
diameter y satisfies the inequality |x 5| is less than or equal to 0.1y.
MN 9.2.4.7 - Solve equations that
Topic 1 - Review of Fundamental Obj. 30 - Solve radical equations
contain radical expressions.
Concepts of Algebra
Recognize that extraneous solutions
may arise when using symbolic
methods. Example 1: The equation
the square root of x-9 = 9 the square
root of x may be solved by squaring
both sides to obtain x - 9 = 81x, which
has the solution x = -9/80. However,
this is not a solution of the original
equation, so it is an extraneous
solution that should be discarded.
The original equation has no solution
in this case. Example 2: Solve the
cubed root of (-x+1) = -5.
Page 170 of 198
081309
Accelerated Math
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Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.4.8 - Assess the
reasonableness of a solution in its
given context and compare the
solution to appropriate graphical or
numerical estimates; interpret a
solution in the original context.
MN 9.3 - Geometry & Measurement
Grades 9 - 11
Objective Description
MN 9.3.1 - Calculate measurements
of plane and solid geometric figures;
know that physical measurements
depend on the choice of a unit and
that they are approximations.
MN 9.3.1.1 - Determine the surface
area and volume of pyramids, cones
and spheres. Use measuring devices
or formulas as appropriate. Example:
Measure the height and radius of a
cone and then use a formula to find
its volume.
MN 9.3.1.2 - Compose and
decompose two- and threedimensional figures; use
decomposition to determine the
perimeter, area, surface area and
volume of various figures. Example:
Find the volume of a regular
hexagonal prism by decomposing it
into six equal triangular prisms.
MN 9.3.1.3 - Understand that
quantities associated with physical
measurements must be assigned
units; apply such units correctly in
expressions, equations and problem
solutions that involve measurements;
and convert between measurement
systems. Example: 60 miles/hour =
60 miles/hour × 5280 feet/mile × 1
hour/3600 seconds = 88 feet/second.
MN 9.3.1.4 - Understand and apply
the fact that the effect of a scale
factor k on length, area and volume is
to multiply each by k, k² and k³,
respectively.
Page 171 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.1.5 - Make reasonable
estimates and judgments about the
accuracy of values resulting from
calculations involving measurements.
Example: Suppose the sides of a
rectangle are measured to the
nearest tenth of a centimeter at 2.6
cm and 9.8 cm. Because of
measurement errors, the width could
be as small as 2.55 cm or as large as
2.65 cm, with similar errors for the
height. These errors affect
calculations. For instance, the actual
area of the rectangle could be
smaller than 25 cm² or larger than 26
cm², even though 2.6 × 9.8 = 25.48.
Grades 9 - 11
Objective Description
MN 9.3.2 - Construct logical
arguments, based on axioms,
definitions and theorems, to prove
theorems and other results in
geometry.
MN 9.3.2.1 - Understand the roles of
axioms, definitions, undefined terms
and theorems in logical arguments.
MN 9.3.2.2 - Accurately interpret and
use words and phrases in geometric
proofs such as "if...then," "if and only
if," "all," and "not." Recognize the
logical relationships between an
"if...then" statement and its inverse,
converse and contrapositive.
Example: The statement "If you don't
do your homework, you can't go to
the dance" is not logically equivalent
to its inverse "If you do your
homework, you can go to the dance.".
MN 9.3.2.3 - Assess the validity of a
logical argument and give
counterexamples to disprove a
statement.
Page 172 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.2.4 - Construct logical
arguments and write proofs of
theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a
form that clearly justifies the
reasoning, such as two-column
proofs, paragraph proofs, flow charts
or illustrations. Example: Prove that
the sum of the interior angles of a
pentagon is 540° using the fact that
the sum of the interior angles of a
triangle is 180°.
MN 9.3.2.5 - Use technology tools to
examine theorems, test conjectures,
perform constructions and develop
mathematical reasoning skills in multistep problems. The tools may include
compass and straight edge, dynamic
geometry software, design software
or Internet applets.
Grades 9 - 11
Objective Description
MN 9.3.3 - Know and apply
properties of geometric figures to
solve real-world and mathematical
problems and to logically justify
results in geometry.
MN 9.3.3.1 - Know and apply
properties of parallel and
perpendicular lines, including
properties of angles formed by a
transversal, to solve problems and
logically justify results. Example:
Prove that the perpendicular bisector
of a line segment is the set of all
points equidistant from the two
endpoints, and use this fact to solve
problems and justify other results.
MN 9.3.3.2 - Know and apply
properties of angles, including
corresponding, exterior, interior,
vertical, complementary and
supplementary angles, to solve
problems and logically justify results.
Example: Prove that two triangles
formed by a pair of intersecting lines
and a pair of parallel lines (an "X"
trapped between two parallel lines)
are similar.
Page 173 of 198
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.3.3 - Know and apply
properties of equilateral, isosceles
and scalene triangles to solve
problems and logically justify results.
Example: Use the triangle inequality
to prove that the perimeter of a
quadrilateral is larger than the sum of
the lengths of its diagonals.
Grades 9 - 11
Objective Description
MN 9.3.3.4 - Apply the Pythagorean
Theorem and its converse to solve
problems and logically justify results.
Example: When building a wooden
frame that is supposed to have a
square corner, ensure that the corner
is square by measuring lengths near
the corner and applying the
Pythagorean Theorem.
MN 9.3.3.5 - Know and apply
Topic 5 - Applications in
properties of right triangles, including Trigonometry
properties of 45-45-90 and 30-60-90
triangles, to solve problems and
logically justify results. Example 1:
Use 30-60-90 triangles to analyze
geometric figures involving equilateral
triangles and hexagons. Example 2:
Determine exact values of the
trigonometric ratios in these special
triangles using relationships among
the side lengths.
Page 174 of 198
Obj. 73 - WP: Right triangles
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.3.6 - Know and apply
properties of congruent and similar
figures to solve problems and
logically justify results. Example 1:
Analyze lengths and areas in a figure
formed by drawing a line segment
from one side of a triangle to a
second side, parallel to the third side.
Example 2: Determine the height of a
pine tree by comparing the length of
its shadow to the length of the
shadow of a person of known height.
Example 3: When attempting to build
two identical 4-sided frames, a
person measured the lengths of
corresponding sides and found that
they matched. Can the person
conclude that the shapes of the
frames are congruent?
Grades 9 - 11
Objective Description
MN 9.3.3.7 - Use properties of
polygons-including quadrilaterals and
regular polygons-to define them,
classify them, solve problems and
logically justify results. Example 1:
Recognize that a rectangle is a
special case of a trapezoid. Example
2: Give a concise and clear definition
of a kite.
MN 9.3.3.8 - Know and apply
properties of a circle to solve
problems and logically justify results.
Example: Show that opposite angles
of a quadrilateral inscribed in a circle
are supplementary.
MN 9.3.4 - Solve real-world and
mathematical geometric problems
using algebraic methods.
MN 9.3.4.1 - Understand how the
properties of similar right triangles
allow the trigonometric ratios to be
defined, and determine the sine,
cosine and tangent of an acute angle
in a right triangle.
Page 175 of 198
081309
Accelerated Math
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Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.3.4.2 - Apply the trigonometric Topic 5 - Applications in
ratios sine, cosine and tangent to
Trigonometry
solve problems, such as determining
lengths and areas in right triangles
and in figures that can be
decomposed into right triangles.
Know how to use calculators, tables
or other technology to evaluate
trigonometric ratios. Example: Find
the area of a triangle, given the
measure of one of its acute angles
and the lengths of the two sides that
form that angle.
MN 9.3.4.3 - Use calculators, tables Topic 5 - Applications in
or other technologies in connection
Trigonometry
with the trigonometric ratios to find
angle measures in right triangles in
various contexts.
MN 9.3.4.4 - Use coordinate
geometry to represent and analyze
line segments and polygons,
including determining lengths,
midpoints and slopes of line
segments.
MN 9.3.4.5 - Know the equation for
Topic 7 - Conic Sections
the graph of a circle with radius r and
center (h,k), (x - h)² + (y - k)² = r², and
justify this equation using the
Pythagorean Theorem and properties
of translations.
MN 9.3.4.6 - Use numeric, graphic
and symbolic representations of
transformations in two dimensions,
such as reflections, translations,
scale changes and rotations about
the origin by multiples of 90°, to solve
problems involving figures on a
coordinate grid. Example: If the point
(3,-2) is rotated 90° counterclockwise
about the origin, it becomes the point
(2,3).
MN 9.3.4.7 - Use algebra to solve
geometric problems unrelated to
coordinate geometry, such as solving
for an unknown length in a figure
involving similar triangles, or using
the Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
Page 176 of 198
Grades 9 - 11
Objective Description
Obj. 73 - WP: Right triangles
Obj. 78 - Find values of inverse trig
functions
Obj. 95 - Circles, write eqns from
given information
Obj. 96 - Circle, graph given
equations
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4 - Data Analysis & Probability
Grades 9 - 11
Objective Description
MN 9.4.1 - Display and analyze data;
use various measures associated
with data to draw conclusions, identify
trends and describe relationships.
MN 9.4.1.1 - Describe a data set
using data displays, such as box-andwhisker plots; describe and compare
data sets using summary statistics,
including measures of center,
location and spread. Measures of
center and location include mean,
median, quartile and percentile.
Measures of spread include standard
deviation, range and inter-quartile
range. Know how to use calculators,
spreadsheets or other technology to
display data and calculate summary
statistics.
MN 9.4.1.2 - Analyze the effects on
summary statistics of changes in data
sets. Example 1: Understand how
inserting or deleting a data point may
affect the mean and standard
deviation. Example 2: Understand
how the median and interquartile
range are affected when the entire
data set is transformed by adding a
constant to each data value or
multiplying each data value by a
constant.
MN 9.4.1.3 - Use scatterplots to
analyze patterns and describe
relationships between two variables.
Using technology, determine
regression lines (line of best fit) and
correlation coefficients; use
regression lines to make predictions
and correlation coefficients to assess
the reliability of those predictions.
Page 177 of 198
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Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.1.4 - Use the mean and
standard deviation of a data set to fit
it to a normal distribution (bell-shaped
curve) and to estimate population
percentages. Recognize that there
are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets and tables
to estimate areas under the normal
curve. Example 1: After performing
several measurements of some
attribute of an irregular physical
object, it is appropriate to fit the data
to a normal distribution and draw
conclusions about measurement
error. Example 2: When data
involving two very different
populations is combined, the resulting
histogram may show two distinct
peaks, and fitting the data to a
normal distribution is not appropriate.
Grades 9 - 11
Objective Description
MN 9.4.2 - Explain the uses of data
and statistical thinking to draw
inferences, make predictions and
justify conclusions
MN 9.4.2.1 - Evaluate reports based
on data published in the media by
identifying the source of the data, the
design of the study, and the way the
data are analyzed and displayed.
Show how graphs and data can be
distorted to support different points of
view. Know how to use spreadsheet
tables and graphs or graphing
technology to recognize and analyze
distortions in data displays. Example:
Shifting data on the vertical axis can
make relative changes appear
deceptively large.
MN 9.4.2.2 - Identify and explain
misleading uses of data; recognize
when arguments based on data
confuse correlation and causation.
MN 9.4.2.3 - Explain the impact of
sampling methods, bias and the
phrasing of questions asked during
data collection.
Page 178 of 198
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Accelerated Math
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Agency Tag Set Name
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Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.3 - Calculate probabilities and
apply probability concepts to solve
real-world and mathematical
problems.
MN 9.4.3.1 - Select and apply
Topic 10 - Probability
counting procedures, such as the
multiplication and addition principles
and tree diagrams, to determine the
size of a sample space (the number
of possible outcomes) and to
calculate probabilities. Example: If
one girl and one boy are picked at
random from a class with 20 girls and
15 boys, there are 20 × 15 = 300
different possibilities, so the
probability that a particular girl is
chosen together with a particular boy
is 1/300.
Grades 9 - 11
Objective Description
Obj. 137 - Fundamental Counting
Principle
Obj. 140 - WP: Permutations
Obj. 141 - Find number of distinct
arrangements of letters
Obj. 143 - WP: Combinations
Obj. 144 - Probability of single events
MN 9.4.3.2 - Calculate experimental
probabilities by performing
simulations or experiments involving
a probability model and using relative
frequencies of outcomes.
Obj. 145 - Probability of independent
events
Obj. 146 - Conditional probability
Obj. 147 - Probability of dependent
events
Obj. 148 - Probability of mutually
exclusive events
MN 9.4.3.3 - Understand that the Law
of Large Numbers expresses a
relationship between the probabilities
in a probability model and the
experimental probabilities found by
performing simulations or
experiments involving the model.
Page 179 of 198
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Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.3.4 - Use random numbers
generated by a calculator or a
spreadsheet, or taken from a table, to
perform probability simulations and to
introduce fairness into decision
making. Example: If a group of
students needs to fairly select one of
its members to lead a discussion,
they can use a random number to
determine the selection.
MN 9.4.3.5 - Apply probability
Topic 10 - Probability
concepts such as intersections,
unions and complements of events,
and conditional probability and
independence, to calculate
probabilities and solve problems.
Example: The probability of tossing at
least one head when flipping a fair
coin three times can be calculated by
looking at the complement of this
event (flipping three tails in a row).
MN 9.4.3.6 - Describe the concepts
of intersections, unions and
complements using Venn diagrams.
Understand the relationships
between these concepts and the
words AND, OR, NOT, as used in
computerized searches and
spreadsheets.
MN 9.4.3.7 - Understand and use
Topic 10 - Probability
simple probability formulas involving
intersections, unions and
complements of events. Example 1:
If the probability of an event is p, then
the probability of the complement of
an event is 1 - p; the probability of the
intersection of two independent
events is the product of their
probabilities. Example 2: The
probability of the union of two events
equals the sum of the probabilities of
the two individual events minus the
probability of the intersection of the
events.
Page 180 of 198
Grades 9 - 11
Objective Description
Obj. 145 - Probability of independent
events
Obj. 146 - Conditional probability
Obj. 147 - Probability of dependent
events
Obj. 145 - Probability of independent
events
Obj. 147 - Probability of dependent
events
081309
Accelerated Math
Standards List with Aligned Product Skills
Agency Tag Set Name
Product Name
Minnesota, Math, 2007, Grades: 9Accelerated Math Pre-Calculus
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.4.3.8 - Apply probability
concepts to real-world situations to
make informed decisions. Example 1:
Explain why a hockey coach might
decide near the end of the game to
pull the goalie to add another forward
position player if the team is behind.
Example 2: Consider the role that
probabilities play in health care
decisions, such as deciding between
having eye surgery and wearing
glasses.
MN 9.4.3.9 - Use the relationship
Topic 10 - Probability
between conditional probabilities and
relative frequencies in contingency
tables. Example: A table that displays
percentages relating gender (male or
female) and handedness (righthanded or left-handed) can be used
to determine the conditional
probability of being left-handed, given
that the gender is male.
Page 181 of 198
Grades 9 - 11
Objective Description
Obj. 146 - Conditional probability
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Minnesota, Math, 2007, Grades: 9AM Probability & Statistics
11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2 - Algebra
MN 9.2.1 - Understand the concept of
function, and identify important
features of functions and other
relations using symbolic and
graphical methods where
appropriate.
MN 9.2.1.1 - Understand the
definition of a function. Use functional
notation and evaluate a function at a
given point in its domain. Example: If
f(x) - 1/(x²-3),find f(-4).
Grades 9 - 11
Objective Description
MN 9.2.1.2 - Distinguish between
functions and other relations defined
symbolically, graphically or in tabular
form.
MN 9.2.1.3 - Find the domain of a
function defined symbolically,
graphically or in a real-world context.
Example: The formula f(x) = pi x² can
represent a function whose domain is
all real numbers, but in the context of
the area of a circle, the domain would
be restricted to positive x.
MN 9.2.1.4 - Obtain information and
draw conclusions from graphs of
functions and other relations.
Example: If a graph shows the
relationship between the elapsed
flight time of a golf ball at a given
moment and its height at that same
moment, identify the time interval
during which the ball is at least 100
feet above the ground.
MN 9.2.1.5 - Identify the vertex, line
of symmetry and intercepts of the
parabola corresponding to a
quadratic function, using symbolic
and graphical methods, when the
function is expressed in the form f(x)
= ax² + bx + c, in the form f(x) = a(x h)² + k , or in factored form.
MN 9.2.1.6 - Identify intercepts,
zeros, maxima, minima and intervals
of increase and decrease from the
graph of a function.
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Standard
Topic Description
MN 9.2.1.7 - Understand the concept
of an asymptote and identify
asymptotes for exponential functions
and reciprocals of linear functions,
using symbolic and graphical
methods.
MN 9.2.1.8 - Make qualitative
statements about the rate of change
of a function, based on its graph or
table of values. Example: The
function f(x) = 3 to the x power
increases for all x, but it increases
faster when x > 2 than it does when x
< 2.
MN 9.2.1.9 - Determine how
translations affect the symbolic and
graphical forms of a function. Know
how to use graphing technology to
examine translations. Example:
Determine how the graph of f(x) = |x h| + k changes as h and k change.
Grades 9 - 11
Objective Description
MN 9.2.2 - Recognize linear,
quadratic, exponential and other
common functions in real-world and
mathematical situations; represent
these functions with tables, verbal
descriptions, symbols and graphs;
solve problems involving these
functions, and explain results in the
original context.
MN 9.2.2.1 - Represent and solve
problems in various contexts using
linear and quadratic functions.
Example: Write a function that
represents the area of a rectangular
garden that can be surrounded with
32 feet of fencing, and use the
function to determine the possible
dimensions of such a garden if the
area must be at least 50 square feet.
MN 9.2.2.2 - Represent and solve
problems in various contexts using
exponential functions, such as
investment growth, depreciation and
population growth.
Page 183 of 198
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11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.2.3 - Sketch graphs of linear,
quadratic and exponential functions,
and translate between graphs, tables
and symbolic representations. Know
how to use graphing technology to
graph these functions.
Grades 9 - 11
Objective Description
MN 9.2.2.4 - Express the terms in a
geometric sequence recursively and
by giving an explicit (closed form)
formula, and express the partial sums
of a geometric series recursively.
Example 1: A closed form formula for
the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)
to the (n-1) power, where n = 1, 2, 3,
... , and this sequence can be
expressed recursively by writing t1 =
3 and tn = 2t(n-1), for n is greater
than or equal to 2. Example 2: the
partial sums sn of the series 3 + 6 +
12 + 24 + ... can be expressed
recursively by writing s1 = 3 and sn =
3 + 2s(n-1), for n is greater than or
equal to 2.
MN 9.2.2.5 - Recognize and solve
problems that can be modeled using
finite geometric sequences and
series, such as home mortgage and
other compound interest examples.
Know how to use spreadsheets and
calculators to explore geometric
sequences and series in various
contexts.
MN 9.2.2.6 - Sketch the graphs of
common non-linear functions such as
f(x)= the square root of x, f(x) = |x|,
f(x)= 1/x, f(x) = x³, and translations of
these functions, such as f(x) = the
square root of (x-2) + 4. Know how to
use graphing technology to graph
these functions.
MN 9.2.3 - Generate equivalent
algebraic expressions involving
polynomials and radicals; use
algebraic properties to evaluate
expressions.
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Department of Education
Standard
Topic Description
MN 9.2.3.1 - Evaluate polynomial and
rational expressions and expressions
containing radicals and absolute
values at specified points in their
domains.
MN 9.2.3.2 - Add, subtract and
multiply polynomials; divide a
polynomial by a polynomial of equal
or lower degree.
MN 9.2.3.3 - Factor common
monomial factors from polynomials,
factor quadratic polynomials, and
factor the difference of two squares.
Example: 9x to the 6th power - x to
the 4th power = (3x³ - x²)(3x³ + x²).
Grades 9 - 11
Objective Description
MN 9.2.3.4 - Add, subtract, multiply,
divide and simplify algebraic
fractions. Example: 1/(1-x) + x/(1+x)
is equivalent to (1+2x-x²)/(1-x²).
MN 9.2.3.5 - Check whether a given
complex number is a solution of a
quadratic equation by substituting it
for the variable and evaluating the
expression, using arithmetic with
complex numbers. Example: The
complex number (1+i)/2 is a solution
of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.
MN 9.2.3.6 - Apply the properties of
positive and negative rational
exponents to generate equivalent
algebraic expressions, including
those involving nth roots. Example:
The square root of 2 x the square
root of 7 = 2 to the 1/2 power x 7 to
the 1/2 power = 14 to the 1/2 power =
the square root of 14. Rules for
computing directly with radicals may
also be used: the square root of 2 x
the square root of x= the square root
of 2x.
Page 185 of 198
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11, Academic Standards, State
Department of Education
Standard
Topic Description
MN 9.2.3.7 - Justify steps in
generating equivalent expressions by
identifying the properties used. Use
substitution to check the equality of
expressions for some particular
values of the variables; recognize
that checking with substitution does
not guarantee equality of expressions
for all values of the variables.
Grades 9 - 11
Objective Description
MN 9.2.4 - Represent real-world and
mathematical situations using
equations and inequalities involving
linear, quadratic, exponential, and nth
root functions. Solve equations and
inequalities symbolically and
graphically. Interpret solutions in the
original context.
MN 9.2.4.1 - Represent relationships
in various contexts using quadratic
equations and inequalities. Solve
quadratic equations and inequalities
by appropriate methods including
factoring, completing the square,
graphing and the quadratic formula.
Find non-real complex roots when
they exist. Recognize that a particular
solution may not be applicable in the
original context. Know how to use
calculators, graphing utilities or other
technology to solve quadratic
equations and inequalities. Example:
A diver jumps from a 20 meter
platform with an upward velocity of 3
meters per second. In finding the
time at which the diver hits the
surface of the water, the resulting
quadratic equation has a positive and
a negative solution. The negative
solution should be discarded because
of the context.
MN 9.2.4.2 - Represent relationships
in various contexts using equations
involving exponential functions; solve
these equations graphically or
numerically. Know how to use
calculators, graphing utilities or other
technology to solve these equations.
Page 186 of 198
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Standard
Topic Description
MN 9.2.4.3 - Recognize that to solve
certain equations, number systems
need to be extended from whole
numbers to integers, from integers to
rational numbers, from rational
numbers to real numbers, and from
real numbers to complex numbers. In
particular, non-real complex numbers
are needed to solve some quadratic
equations with real coefficients.
Grades 9 - 11
Objective Description
MN 9.2.4.4 - Represent relationships
in various contexts using systems of
linear inequalities; solve them
graphically. Indicate which parts of
the boundary are included in and
excluded from the solution set using
solid and dotted lines.
MN 9.2.4.5 - Solve linear
programming problems in two
variables using graphical methods.
MN 9.2.4.6 - Represent relationships
in various contexts using absolute
value inequalities in two variables;
solve them graphically. Example: If a
pipe is to be cut to a length of 5
meters accurate to within a tenth of
its diameter, the relationship between
the length x of the pipe and its
diameter y satisfies the inequality |x 5| is less than or equal to 0.1y.
MN 9.2.4.7 - Solve equations that
contain radical expressions.
Recognize that extraneous solutions
may arise when using symbolic
methods. Example 1: The equation
the square root of x-9 = 9 the square
root of x may be solved by squaring
both sides to obtain x - 9 = 81x, which
has the solution x = -9/80. However,
this is not a solution of the original
equation, so it is an extraneous
solution that should be discarded.
The original equation has no solution
in this case. Example 2: Solve the
cubed root of (-x+1) = -5.
Page 187 of 198
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Topic Description
MN 9.2.4.8 - Assess the
reasonableness of a solution in its
given context and compare the
solution to appropriate graphical or
numerical estimates; interpret a
solution in the original context.
MN 9.3 - Geometry & Measurement
Grades 9 - 11
Objective Description
MN 9.3.1 - Calculate measurements
of plane and solid geometric figures;
know that physical measurements
depend on the choice of a unit and
that they are approximations.
MN 9.3.1.1 - Determine the surface
area and volume of pyramids, cones
and spheres. Use measuring devices
or formulas as appropriate. Example:
Measure the height and radius of a
cone and then use a formula to find
its volume.
MN 9.3.1.2 - Compose and
decompose two- and threedimensional figures; use
decomposition to determine the
perimeter, area, surface area and
volume of various figures. Example:
Find the volume of a regular
hexagonal prism by decomposing it
into six equal triangular prisms.
MN 9.3.1.3 - Understand that
quantities associated with physical
measurements must be assigned
units; apply such units correctly in
expressions, equations and problem
solutions that involve measurements;
and convert between measurement
systems. Example: 60 miles/hour =
60 miles/hour × 5280 feet/mile × 1
hour/3600 seconds = 88 feet/second.
MN 9.3.1.4 - Understand and apply
the fact that the effect of a scale
factor k on length, area and volume is
to multiply each by k, k² and k³,
respectively.
Page 188 of 198
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Standard
Topic Description
MN 9.3.1.5 - Make reasonable
estimates and judgments about the
accuracy of values resulting from
calculations involving measurements.
Example: Suppose the sides of a
rectangle are measured to the
nearest tenth of a centimeter at 2.6
cm and 9.8 cm. Because of
measurement errors, the width could
be as small as 2.55 cm or as large as
2.65 cm, with similar errors for the
height. These errors affect
calculations. For instance, the actual
area of the rectangle could be
smaller than 25 cm² or larger than 26
cm², even though 2.6 × 9.8 = 25.48.
Grades 9 - 11
Objective Description
MN 9.3.2 - Construct logical
arguments, based on axioms,
definitions and theorems, to prove
theorems and other results in
geometry.
MN 9.3.2.1 - Understand the roles of
axioms, definitions, undefined terms
and theorems in logical arguments.
MN 9.3.2.2 - Accurately interpret and
use words and phrases in geometric
proofs such as "if...then," "if and only
if," "all," and "not." Recognize the
logical relationships between an
"if...then" statement and its inverse,
converse and contrapositive.
Example: The statement "If you don't
do your homework, you can't go to
the dance" is not logically equivalent
to its inverse "If you do your
homework, you can go to the dance.".
MN 9.3.2.3 - Assess the validity of a
logical argument and give
counterexamples to disprove a
statement.
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Standard
Topic Description
MN 9.3.2.4 - Construct logical
arguments and write proofs of
theorems and other results in
geometry, including proofs by
contradiction. Express proofs in a
form that clearly justifies the
reasoning, such as two-column
proofs, paragraph proofs, flow charts
or illustrations. Example: Prove that
the sum of the interior angles of a
pentagon is 540° using the fact that
the sum of the interior angles of a
triangle is 180°.
MN 9.3.2.5 - Use technology tools to
examine theorems, test conjectures,
perform constructions and develop
mathematical reasoning skills in multistep problems. The tools may include
compass and straight edge, dynamic
geometry software, design software
or Internet applets.
Grades 9 - 11
Objective Description
MN 9.3.3 - Know and apply
properties of geometric figures to
solve real-world and mathematical
problems and to logically justify
results in geometry.
MN 9.3.3.1 - Know and apply
properties of parallel and
perpendicular lines, including
properties of angles formed by a
transversal, to solve problems and
logically justify results. Example:
Prove that the perpendicular bisector
of a line segment is the set of all
points equidistant from the two
endpoints, and use this fact to solve
problems and justify other results.
MN 9.3.3.2 - Know and apply
properties of angles, including
corresponding, exterior, interior,
vertical, complementary and
supplementary angles, to solve
problems and logically justify results.
Example: Prove that two triangles
formed by a pair of intersecting lines
and a pair of parallel lines (an "X"
trapped between two parallel lines)
are similar.
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Topic Description
MN 9.3.3.3 - Know and apply
properties of equilateral, isosceles
and scalene triangles to solve
problems and logically justify results.
Example: Use the triangle inequality
to prove that the perimeter of a
quadrilateral is larger than the sum of
the lengths of its diagonals.
Grades 9 - 11
Objective Description
MN 9.3.3.4 - Apply the Pythagorean
Theorem and its converse to solve
problems and logically justify results.
Example: When building a wooden
frame that is supposed to have a
square corner, ensure that the corner
is square by measuring lengths near
the corner and applying the
Pythagorean Theorem.
MN 9.3.3.5 - Know and apply
properties of right triangles, including
properties of 45-45-90 and 30-60-90
triangles, to solve problems and
logically justify results. Example 1:
Use 30-60-90 triangles to analyze
geometric figures involving equilateral
triangles and hexagons. Example 2:
Determine exact values of the
trigonometric ratios in these special
triangles using relationships among
the side lengths.
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Standard
Topic Description
MN 9.3.3.6 - Know and apply
properties of congruent and similar
figures to solve problems and
logically justify results. Example 1:
Analyze lengths and areas in a figure
formed by drawing a line segment
from one side of a triangle to a
second side, parallel to the third side.
Example 2: Determine the height of a
pine tree by comparing the length of
its shadow to the length of the
shadow of a person of known height.
Example 3: When attempting to build
two identical 4-sided frames, a
person measured the lengths of
corresponding sides and found that
they matched. Can the person
conclude that the shapes of the
frames are congruent?
Grades 9 - 11
Objective Description
MN 9.3.3.7 - Use properties of
polygons-including quadrilaterals and
regular polygons-to define them,
classify them, solve problems and
logically justify results. Example 1:
Recognize that a rectangle is a
special case of a trapezoid. Example
2: Give a concise and clear definition
of a kite.
MN 9.3.3.8 - Know and apply
properties of a circle to solve
problems and logically justify results.
Example: Show that opposite angles
of a quadrilateral inscribed in a circle
are supplementary.
MN 9.3.4 - Solve real-world and
mathematical geometric problems
using algebraic methods.
MN 9.3.4.1 - Understand how the
properties of similar right triangles
allow the trigonometric ratios to be
defined, and determine the sine,
cosine and tangent of an acute angle
in a right triangle.
Page 192 of 198
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Topic Description
MN 9.3.4.2 - Apply the trigonometric
ratios sine, cosine and tangent to
solve problems, such as determining
lengths and areas in right triangles
and in figures that can be
decomposed into right triangles.
Know how to use calculators, tables
or other technology to evaluate
trigonometric ratios. Example: Find
the area of a triangle, given the
measure of one of its acute angles
and the lengths of the two sides that
form that angle.
MN 9.3.4.3 - Use calculators, tables
or other technologies in connection
with the trigonometric ratios to find
angle measures in right triangles in
various contexts.
MN 9.3.4.4 - Use coordinate
Topic 1 - Pre-requisites
geometry to represent and analyze
line segments and polygons,
including determining lengths,
midpoints and slopes of line
segments.
MN 9.3.4.5 - Know the equation for
the graph of a circle with radius r and
center (h,k), (x - h)² + (y - k)² = r², and
justify this equation using the
Pythagorean Theorem and properties
of translations.
MN 9.3.4.6 - Use numeric, graphic
and symbolic representations of
transformations in two dimensions,
such as reflections, translations,
scale changes and rotations about
the origin by multiples of 90°, to solve
problems involving figures on a
coordinate grid. Example: If the point
(3,-2) is rotated 90° counterclockwise
about the origin, it becomes the point
(2,3).
MN 9.3.4.7 - Use algebra to solve
geometric problems unrelated to
coordinate geometry, such as solving
for an unknown length in a figure
involving similar triangles, or using
the Pythagorean Theorem to obtain a
quadratic equation for a length in a
geometric figure.
MN 9.4 - Data Analysis & Probability
Page 193 of 198
Grades 9 - 11
Objective Description
Obj. 4 - Slope of a line
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Topic Description
MN 9.4.1 - Display and analyze data;
use various measures associated
with data to draw conclusions, identify
trends and describe relationships.
MN 9.4.1.1 - Describe a data set
Topic 1 - Pre-requisites
using data displays, such as box-andwhisker plots; describe and compare
data sets using summary statistics,
including measures of center,
location and spread. Measures of
center and location include mean,
median, quartile and percentile.
Measures of spread include standard
deviation, range and inter-quartile
range. Know how to use calculators,
spreadsheets or other technology to
display data and calculate summary
statistics.
Topic 3 - Sample spaces
Topic 4 - Descriptive statistics
MN 9.4.1.2 - Analyze the effects on
summary statistics of changes in data
sets. Example 1: Understand how
inserting or deleting a data point may
affect the mean and standard
deviation. Example 2: Understand
how the median and interquartile
range are affected when the entire
data set is transformed by adding a
constant to each data value or
multiplying each data value by a
constant.
Page 194 of 198
Topic 8 - Bivariate data
Grades 9 - 11
Objective Description
Obj. 3 - Scatter plots
Obj. 19 - Circle graphs
Obj. 23 - Frequency histograms
Obj. 24 - Relative frequency
histograms
Obj. 25 - Stem-and-leaf plots
Obj. 27 - Mean
Obj. 28 - Median
Obj. 29 - Mode
Obj. 30 - Choose best measure of
central tendency
Obj. 31 - Range
Obj. 32 - Percentiles
Obj. 35 - Box-and-whisker plots
Obj. 38 - Standard deviation
Obj. 69 - Stacked bar charts
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Topic Description
MN 9.4.1.3 - Use scatterplots to
Topic 1 - Pre-requisites
analyze patterns and describe
relationships between two variables.
Using technology, determine
regression lines (line of best fit) and
correlation coefficients; use
regression lines to make predictions
and correlation coefficients to assess
the reliability of those predictions.
Topic 8 - Bivariate data
Topic 11 - Linear regression
MN 9.4.1.4 - Use the mean and
Topic 6 - Continuous probability
standard deviation of a data set to fit distributions
it to a normal distribution (bell-shaped
curve) and to estimate population
percentages. Recognize that there
are data sets for which such a
procedure is not appropriate. Use
calculators, spreadsheets and tables
to estimate areas under the normal
curve. Example 1: After performing
several measurements of some
attribute of an irregular physical
object, it is appropriate to fit the data
to a normal distribution and draw
conclusions about measurement
error. Example 2: When data
involving two very different
populations is combined, the resulting
histogram may show two distinct
peaks, and fitting the data to a
normal distribution is not appropriate.
Topic 9 - Confidence intervals
MN 9.4.2 - Explain the uses of data
and statistical thinking to draw
inferences, make predictions and
justify conclusions
Page 195 of 198
Grades 9 - 11
Objective Description
Obj. 3 - Scatter plots
Obj. 71 - Calculate correlation
coefficient
Obj. 92 - Interpret scatter plots
Obj. 94 - Calculate Sxx
Obj. 95 - Calculate the slope of
regression line
Obj. 96 - Calculate a
Obj. 97 - Calculate regression line
equation
Obj. 98 - Estimate the predicted
value y-hat
Obj. 99 - Forecasting
Obj. 57 - Normal distribution
Obj. 75 - Areas in tails
Obj. 76 - Areas between tails
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Standard
Topic Description
MN 9.4.2.1 - Evaluate reports based
on data published in the media by
identifying the source of the data, the
design of the study, and the way the
data are analyzed and displayed.
Show how graphs and data can be
distorted to support different points of
view. Know how to use spreadsheet
tables and graphs or graphing
technology to recognize and analyze
distortions in data displays. Example:
Shifting data on the vertical axis can
make relative changes appear
deceptively large.
MN 9.4.2.2 - Identify and explain
misleading uses of data; recognize
when arguments based on data
confuse correlation and causation.
MN 9.4.2.3 - Explain the impact of
sampling methods, bias and the
phrasing of questions asked during
data collection.
Objective Description
Topic 4 - Descriptive statistics
Obj. 26 - Misleading graphs
Topic 7 - Data collection
Obj. 62 - Sampling techniques
MN 9.4.3 - Calculate probabilities and
apply probability concepts to solve
real-world and mathematical
problems.
MN 9.4.3.1 - Select and apply
Topic 2 - Counting
counting procedures, such as the
multiplication and addition principles
and tree diagrams, to determine the
size of a sample space (the number
of possible outcomes) and to
calculate probabilities. Example: If
one girl and one boy are picked at
random from a class with 20 girls and
15 boys, there are 20 × 15 = 300
different possibilities, so the
probability that a particular girl is
chosen together with a particular boy
is 1/300.
Topic 3 - Sample spaces
Page 196 of 198
Grades 9 - 11
Obj. 63 - Identify bias
Obj. 5 - Fundamental counting
principle
Obj. 8 - Permutations
Obj. 9 - Combinations
Obj. 10 - Pascal's triangle
Obj. 13 - Probability of simple events
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MN 9.4.3.2 - Calculate experimental Topic 7 - Data collection
probabilities by performing
simulations or experiments involving
a probability model and using relative
frequencies of outcomes.
MN 9.4.3.3 - Understand that the Law
of Large Numbers expresses a
relationship between the probabilities
in a probability model and the
experimental probabilities found by
performing simulations or
experiments involving the model.
MN 9.4.3.4 - Use random numbers
Topic 2 - Counting
generated by a calculator or a
spreadsheet, or taken from a table, to
perform probability simulations and to
introduce fairness into decision
making. Example: If a group of
students needs to fairly select one of
its members to lead a discussion,
they can use a random number to
determine the selection.
MN 9.4.3.5 - Apply probability
Topic 3 - Sample spaces
concepts such as intersections,
unions and complements of events,
and conditional probability and
independence, to calculate
probabilities and solve problems.
Example: The probability of tossing at
least one head when flipping a fair
coin three times can be calculated by
looking at the complement of this
event (flipping three tails in a row).
MN 9.4.3.6 - Describe the concepts
of intersections, unions and
complements using Venn diagrams.
Understand the relationships
between these concepts and the
words AND, OR, NOT, as used in
computerized searches and
spreadsheets.
Page 197 of 198
Topic 5 - Discrete probability
distributions
Topic 3 - Sample spaces
Grades 9 - 11
Objective Description
Obj. 64 - Experimental probability predict using sample results
Obj. 12 - Random numbers
Obj. 14 - Probability of compound
events
Obj. 15 - Complement of events
Obj. 20 - Bayes' formula for
conditional probability
Obj. 40 - WP: Discrete uniform
distribution
Obj. 17 - Venn diagrams
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Standard
Topic Description
MN 9.4.3.7 - Understand and use
Topic 3 - Sample spaces
simple probability formulas involving
intersections, unions and
complements of events. Example 1:
If the probability of an event is p, then
the probability of the complement of
an event is 1 - p; the probability of the
intersection of two independent
events is the product of their
probabilities. Example 2: The
probability of the union of two events
equals the sum of the probabilities of
the two individual events minus the
probability of the intersection of the
events.
MN 9.4.3.8 - Apply probability
concepts to real-world situations to
make informed decisions. Example 1:
Explain why a hockey coach might
decide near the end of the game to
pull the goalie to add another forward
position player if the team is behind.
Example 2: Consider the role that
probabilities play in health care
decisions, such as deciding between
having eye surgery and wearing
glasses.
MN 9.4.3.9 - Use the relationship
between conditional probabilities and
relative frequencies in contingency
tables. Example: A table that displays
percentages relating gender (male or
female) and handedness (righthanded or left-handed) can be used
to determine the conditional
probability of being left-handed, given
that the gender is male.
Page 198 of 198
Grades 9 - 11
Objective Description
Obj. 14 - Probability of compound
events
Obj. 15 - Complement of events
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