Download This curriculum is designed with the Common Core Instructional

Grade 7 Curriculum Outline 2016-17
This curriculum is designed with the Common Core Instructional Shifts in Mathematics in mind:
1: Focus: Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They
do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep
conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.
2: Coherence: Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across
grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual
understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.
3: Fluency: Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to
memorize, through repetition, core functions (found in the attached list of fluencies) such as multiplication tables so that they are more able to understand
and manipulate more complex concepts.
4: Deep Understanding: Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of
perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual
understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.
5: Application: Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers
provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math,
particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content.
6: Dual Intensity: Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring
with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math
concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and
therefore, varies throughout the given school year.
Grade level fluencies:
Solve multi-step problems with positive and negative rational numbers
Solve one variable equations of the form px + q = r and p(x + q) = r fluently.
CCLS Major Emphasis Clusters
Ratios and Proportional Relationships
 Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations
 Use properties of operations to generate equivalent expressions.
 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Standards in bold are identified as major standards. Standards with checkmarks are standards recommended for greater emphasis
Unit 1: Accentuate the Negative
Vocabulary: absolute value, additive inverse, common denominator, integer, least common denominator, like fractions, opposites, rational numbers,
repeating decimal, terminating decimal
Standard
Subskills
Materials
7.NS.1. Apply and extend previous understandings  Generalize rules for adding rational numbers with the
of addition and subtraction to add and subtract
same sign.
rational numbers; represent addition and subtraction  Generalize rules for adding rational numbers with the
on a horizontal or vertical number line diagram.
opposite sign.
a. Describe situations in which opposite quantities
 Explain the additive inverse relationship between a
combine to make 0.
rational number and its opposite..
 Interpret sums of rational numbers by describing realb. Understand p + q as the number located a
world contexts.
distance |q| from p, in the positive or negative
 Understand p + q as the number located a distance
direction depending on whether q is positive or
|q| from p, in the positive or negative direction
negative. Show that a number and its opposite have
depending on whether q is positive or negative.
a sum of 0 (are additive inverses). Interpret sums of
Show that a number and its opposite have a sum of 0
rational numbers by describing real-world contexts.
(are additive inverses).
 Illustrate subtraction of rational numbers using
c. Understand subtraction of rational numbers as
models and manipulatives.
adding the additive inverse, p – q = p + (–q). Show  Calculate subtraction of rational numbers on a
that the distance between two rational numbers on
number line either horizontal or vertical..
the number line is the absolute value of their
 Understand subtraction of rational numbers as adding
difference, and apply this principle in real-world
the additive inverse, p – q = p + (– q). Show that the
contexts.
distance between two rational numbers on the
number line is the absolute value of their difference,
d. Apply properties of operations as strategies to add
and apply this principle in real-world contexts.
and subtract rational numbers.
CMP: Accentuate the Negative Inv 1,
2, 4
 Fluently multiply and divide rational numbers.
 Apply the associative property of multiplication to
multiplying rational numbers.
 Apply the commutative property of multiplication to
multiplying rational numbers.
 Apply multiplicative inverse property to multiplying
rational numbers.
 Apply properties of operations as strategies to multiply
and divide rational numbers.
 Convert rational numbers to decimals through the
process of long division dividing the numerator by the
denominator.
b. Understand that integers can be divided, provided
 Differentiate between rational and irrational number.
that the divisor is not zero, and every quotient of
CMP: Accentuate the Negative Inv 3,
4
7.NS.2. Apply and extend previous understandings
of multiplication and division and of fractions to
multiply and divide rational numbers.
a. Understand that multiplication is extended from
fractions to rational numbers by requiring that
operations continue to satisfy the properties of
operations, particularly the distributive property,
leading to products such as (–1)(–1) = 1 and the
rules for multiplying signed numbers. Interpret
products of rational numbers by describing real-world
contexts.
Glencoe: Chapter 3: Lesson 2, 3
Chapter 4: Lesson 3, 4, 5
Common Core Mathematics: 1.6,
1.7, 3.2, 3.3, CC.1
Big Ideas Math: 1.1, 1.2, 1.3, 2.2,
2.3
Glencoe: Chapter 3: Lesson 4, 5
Chapter 4: Lesson 1, 2, 6, 7, 8
Common Core Mathematics: 1.3,
1.4, 1.8, 2.6, 2.7, 3.4, 3.5, CC.2,
CC.3
Big Ideas Math: 1.1, 1.4, 1.5, 2.1,
2.4
integers (with non-zero divisor) is a rational number.  Calculate the remainder of each division as
If p and q are integers, then –(p/q) = (–p)/q =
terminating or repeating using correct form.
p/(–q). Interpret quotients of rational numbers by
 Convert a rational number to a decimal using long
describing real world contexts.
division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
c. Apply properties of operations as strategies to
multiply and divide rational numbers.
d. Convert a rational number to a decimal using long
division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
7.NS.3( ). Solve real-world and mathematical
problems involving the four operations with rational
numbers.
 Fluently add, subtract, multiply, and divide rational
numbers.
 Construct and explain situations involving multiple
operations involving rational numbers.
 Solve real world and mathematical problems involving
rational numbers, including multi-step.
Benchmark 1: Unit 1 Assessment
CMP: Accentuate the Negative: Inv.
1, 2, 3, 4; Stretching and Shrinking:
Inv. 4
Filling and Wrapping: Inv 2, 3, 4
Glencoe: Chapter 1: Lesson 2
Chapter 3: Lesson 1, 2, 3, 4, 5
Chapter 4: Lesson 3, 4, 5, 6, 7, 8
Common Core Mathematics: 1.3,
1.4, 1.8, 3.4, 3.5,
Big Ideas Math: 1.1, 1.2, 1.3, 1.4,
1.5, 2.2, 2.3, 2.4
Unit 2: Stretching & Shrinking / Unit 3: Comparing & Scaling
Vocabulary: Ratios, proportional relationships, rate, scaling, equivalent ratios, unit rate, commission, constant of proportionality, rate table, part to
part ratio, markup, percent, adjacent sides; corresponding angles; corresponding sides; equivalent ratios; image; midpoint; nested triangles;
proportion; ratio; scale drawing; scale factor; similar
Standard
7.RP.1. Compute unit rates associated with ratios
of fractions, including ratios of lengths, areas and
other quantities measured in like or different units.
7.RP.2. Recognize and represent proportional
relationships between quantities.
a. Decide whether two quantities are in a
proportional relationship, e.g., by testing for
equivalent ratios in a table or graphing on a
coordinate plane and observing whether the graph
is a straight line through the origin.
b. Identify the constant of proportionality (unit rate)
in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
c. Represent proportional relationships by
equatons.
Subskills
 Identify ratios that compare two quantities.
 Show ways for expressing ratios.
 Solve problems using part to part and part to whole
relationships.
 Compare part to part and part to whole relationships
with and without models and pictures.
 Compute unit rates from given comparisons of
quantities measured in like or different units (i.e.
length, area, miles per hours, better purchase).
 Solve unit rates involving real world applications.
 Apply unit rate understanding to convert ratios.
 Apply unit rate understanding to compute equivalent
measurements (i.e. area, length).
 Compute unit rates associated with ratios of fractions,
including ratios of lengths, areas and other quantities
measured in like or different units.
 Define ratio and proportion.
 Compare two ratios to determine if they are
proportional.
 Create a table of unit/rate values for a proportional
relationship.
 Graph a set of unit/rate values for a proportional
relationship on a coordinate grid.
 Use tables and graphs to identify ordered pairs of
proportional values.
 Compare proportional and non-proportional
relationships on a graph.
 Decide whether two quantities are in a proportional
relationship, e.g., by testing for equivalent ratios in a
table or graphing on a coordinate plane and
observing whether the graph is a straight line through
the origin
 Define scale factor.
 Scale unit rates to correspond with given criteria (i.e.
double, triple, half, etc.).
 Identify the constant rate of proportionality (unit rate)
when given data in a table.
Materials
CMP: Comparing and Scaling: Inv.
2
Glencoe: Chapter 1: Lesson 2
Common Core Mathematics: 5.1,
5.2,5.4, 5.5, CC.7
Big Ideas Math: 5.1
CMP: Stretching and Shrinking: Inv.
1, 2, 3,4
Comparing and Scaling: Inv. 1, 2, 3
Moving Straight Ahead: Inv. 1, 2
Glencoe: Chapter 1: Lesson 1, 3,
4, 5, 6, 7, 8, 9
Chapter 2: Lessons4,
Common Core Mathematics: 5.2,
5.4, 5.5
Big Ideas Math: 5.2, 5.3, 5.4, 5.5,
5.6
7.RP.3( ). Use proportional relationships to solve
multistep ratio and percent problems
7.G.1. Solve problems involving scale drawings of
geometric figures, including computing actual
lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale
 Identify the constant rate of proportionality (unit rate)
when given a verbal description.
 Identify the constant rate of proportionality (unit rate)
when given a diagram.
 Create algebraic equations that illustrates constant
rate of proportionality.
 Predict outcomes from given proportional
relationships, using tables, graphs, and equations.
 Identify the constant of proportionality to solve
problems.
 Write equations given a proportional relationship from
tables and graphs.
 Graph proportional relationship using (x,y) values
from function table.
 Explain the relationship between the x values and the
y values in a table or on a graph.
 Explain what a point (x, y) on the graph of a
proportional relationship means in terms of the
situation.
 Convert between fractions, decimals, and percent
equivalents.
 Solve percent problems:
o Find part of a number when given whole and
percent.
o Find percent when given part and whole.
o Find whole when given part and percent.
 Define tax, commission, and gratuity
 Calculate
o Discount on purchased items.
o Percentage of discount.
o Tax/gratuities added to a purchase.
o Commission on transactions.
o Percent of increase or decrease.
o Simple interest.
 Percent of error Use the formula (difference/original
x 100 = percent) to calculate the percent of change
in a number.
 Use real world situations to show application a
variety of proportional relationships.
 Calculate scale factor between corresponding
lengths in similar objects.
 Calculate actual lengths of corresponding sides
when given a scale factor.
CMP: Stretching and Shrinking: Inv.
3
Comparing and Scaling: Inv. 1, 2, 3
What Do You Expect?: Inv. 1, 2, 3,
4, 5
Glencoe: Chapter 1: Lesson 3, 6
Chapter 2: Lesson 1, 2, 3, 4, 5, 6, 7,
8
Chapter 4: Lesson 7
Common Core Mathematics: 6.7,
6.8, 9.7
Big Ideas Math: 5.1, 5.3, 6.3, 6.4,
6.5, 6.6, 6.7
CMP: Stretching and Shrinking, Inv.
1, 2, 3, 4
Glencoe: Chapter 7: Lesson
 Create a similar drawing through enlarging or
shrinking by incorporating the scale factor.
 Calculate area of actual shape when given scale
drawing..
 Solve problems involving scale drawings of
geometric figures, including computing actual
lengths and areas from a scale drawing and
reproducing a scale drawing at a different scale.
7.SP.1. Understand that statistics can be used to
 Identify correct population sector for taking a given
gain information about a population by examining a
sample population
sample of the population; generalizations about a
 Demonstrate examples of representative bias and
population from a sample are valid only if the
insufficient samples.
sample is representative of that population.
 Infer valid statistics about a population based on
Understand that random sampling tends to produce
random sampling.
representative samples and support valid
 Draw conclusions about a population.
inferences.
 Understand that statistics can be used to gain
information about a population by examining a
sample of the population; generalizations about a
population from a sample are valid only if the
sample is representative of that population.
7.SP.2. Use data from a random sample to draw
 .Explain variation in random samples.
inferences about a population with an unknown
 Make predictions based on possible outcomes and
characteristic of interest. Generate multiple
from compiled data..
samples (or simulated samples) of the same size to  Apply the principles of probability to solve problems
gauge the variation in estimates or predictions.
in real world contexts.
 Use data from a random sample to draw inferences
about a population with an unknown characteristic of
interest. Generate multiple samples (or simulated
samples) of the same size to gauge the variation in
estimates or predictions. For example, estimate the
mean word length in a book by randomly sampling
words from the book; predict the winner of a school
election based on randomly sampled survey data.
Gauge how far off the estimate or prediction might
be.
Benchmark 2: Stretching & Shrinking Assessment
Benchmark 3: Task 1 (Animals of Rhomar)
Common Core Mathematics: 5.5,
5.6
Big Ideas Math: 7.5
CMP: Samples and Populations:
Inv. 2
Glencoe: Chapter 10: Lesson1, 2,
3
Common Core Mathematics: 11.4
Big Ideas Math: 10.6
CMP: Samples and Populations:
Inv. 2
Glencoe: Chapter 10: Lesson1, 2
Common Core Mathematics:
11.5, CC.13
Big Ideas Math: 10.6
Unit 4: Moving Straight Ahead
Vocabulary: Coefficient, y-intercept, independent variable, dependent variable, linear relationship
Standard
7.EE.1( ). Apply properties of operations as
strategies to add, subtract, factor, and expand
linear expressions with rational coefficients.
7.EE.2. Understand that rewriting an expression in
different forms in a problem context can shed light
on the problem and how the quantities in it are
related.
7.EE.3( ). Solve multi-step real-life and
mathematical problems posed with positive and
negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to
calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies.
Subskills
 Recall mathematical properties of operations as
they apply to rational numbers (integers)
 Recognize terms (like/unlike)
 Use properties of operations to combine like terms
 Explain the application of the commutative property
to solve different types of problems.
 Explain the application of the distributive property to
solve different types of problems.
 Explain the application of the associative property to
solve different types of problems.
 Simplify, expand, and combine like terms of linear
expressions with Rational Coefficients.
 Apply properties of operations as strategies to add,
subtract, factor, and expand linear expressions with
rational coefficients.
 Recall mathematical properties of operations as
they apply to rational numbers (integers)
 Explain that expressions in different forms can be
equivalent, and rewrite an expression to represent a
quantity in a different way.
 Generate equivalent forms of the same expression
given a word problem (a 20% discount = 80% of the
cost).
 Understand that rewriting an expression in different
forms in a problem context can shed light on the
problem and how the quantities in it are related
 Convert among fractions, decimals, and percents.
 Apply properties of operations to solve real-world
problems involving rational numbers in expressions
and equations.
 Apply number sense to understand, perform
operations, and solve problems with rational
numbers of equations and expressions in any form.
 Assess the reasonableness of answers using mental
computation and estimation strategies.
 Solve multi-step real-life and mathematical problems
Materials
CMP: Moving Straight Ahead: Inv. 4
Glencoe: Chapter 5: Lesson1, 2, 3,
4, 5, 6, 7, 8
Common Core Mathematics:
CC.4
Big Ideas Math: 3.1, 3.2
CMP: Shapes and Designs: Inv 2
Moving Straight Ahead: Inv. 3, 4
Glencoe: Chapter 2: Lessons 6
Chapter 5: Lesson1, 2, 3, 4, 5, 6, 7,
8
Common Core Mathematics: 6.4,
6.6, 6.7, 9.8
Big Ideas Math: 3.1, 3.2
CMP: Moving Straight Ahead: Inv.
1, 2
What Do You Expect?: Inv. 1, 2, 3,
4, 5
Glencoe: Chapter 2: Lesson 1, 2,
4, 5, 6, 7, 8
Chapter 3: Lesson 2, 4
Chapter 4: Lesson 1, 2, 3, 4, 5, 6, 8
Chapter 6: Problem solving

7.EE.4. Use variables to represent quantities in a
real-world or mathematical problem, and construct
simple equations and inequalities to solve
problems by reasoning about the quantities.
a( ). Solve word problems leading to equations
of the form px + q = r and p(x + q) = r, where p, q,
and r are specific rational numbers. Solve
equations of these forms fluently. Compare an
algebraic solution to an arithmetic solution,
identifying the sequence of the operations used in
each approach.
For example, the perimeter of a rectangle is 54
cm. Its length is 6 cm. What is its width?

b. Solve word problems leading to inequalities of
the form px + q > r or px + q < r, where p, q, and r
are specific rational numbers. Graph the solution
set of the inequality and interpret it in the context
of the problem.

7.G.4. Know the formulas for the area and
circumference of a circle and use them to solve
problems; give an informal derivation of the
relationship between the circumference and area
of a circle.













Benchmark 4: Unit Assessment
posed with positive and negative rational numbers in
any form (whole numbers, fractions, and decimals),
using tools strategically.
Apply properties of operations to calculate with
numbers in any form; convert between forms as
appropriate; and assess the reasonableness of
answers using mental computation and estimation
strategies.
Select appropriate variables to represent unknown
quantities.
Identify the correct operation used to write and solve
for unknown values.
Identify the correct sequence of the operations used
to solve an algebraic equation.
Evaluate, simplify, and solve equations.
Construct algebraic equations from real-world
problems by reasoning.
Graph solutions of inequalities on a number line.
Interpret solutions of inequalities from graphs.
Model real-world problems using graphs to
demonstrate inequalities including negative
coefficients.
Graph the solution set of the inequality and interpret
it in the context of the problem
Solve word problems leading to equations of the
form px + q = r and p(x + q) = r, where p, q, and r
are specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic solution
to an arithmetic solution, identifying the sequence of
the operations used in each approach
Show the relationship between the circumference
and the diameter expressed as pi
Derive the formula for the area of a circle and the
circumference of circle.
Determine the relationship between the
circumference and area of a circle.
Determine the area of complex or composite figures
Know the formulas for the area and circumference of
a circle and use them to solve problems; give an
informal derivation of the relationship between the
circumference and area of a circle.
Benchmark 5: Performance Task 2 (The Road Trip)
Investigation
Common Core Mathematics: 1.2,
1.3, 1.4, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5,
6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8
Big Ideas Math: 6.1, 6.2, 6.4
CMP: Shapes and Designs: Inv 2, 3
Stretching and Shrinking: Inv. 4
Moving Straight Ahead: Inv. 1, 2, 4
Glencoe: Chapter 6: Lesson1, 2, 3,
4, 5, 6, 7, 8,
Common Core Mathematics: 4.1,
4.2, CC.5, CC.6
Big Ideas Math: 3.3, 3.4, 3.5, 4.1,
4.2, 4.3, 4.4
CMP: Filling and Wrapping: Inv. 3
Glencoe: Chapter 8: Lesson1, 2, 3,
Common Core Mathematics: 8.5
Big Ideas Math: 8.1, 8.2, 8.3, 9.3
Unit 5: What Do You Expect
Vocabulary: Biased sample, box and whisker plots, complementary events, compound events, dependent events, dot plot, experimental
probability, fair, fundamental counting principle, independent events, inter-quartile range, outcome, population, probability, random, sample space,
simple event, standard deviation, statistics, survey, theoretical probability, tree diagram
Standard
7.SP.3. Informally assess the degree of visual
overlap of two numerical data distributions with
similar variabilities, measuring the difference
between the centers by expressing it as a multiple
of a measure of variability.
7.SP.4. Use measures of center and measures of
variability for numerical data from random
samples to draw informal comparative inferences
about two populations.
7.SP.5. Understand that the probability of a
chance event is a number between 0 and 1 that
expresses the likelihood of the event occurring.
Larger numbers indicate greater likelihood. A
probability near 0 indicates an unlikely event, a
probability around ½ indicates an event that is
neither unlikely nor likely, and a probability near 1
indicates a likely event.
7.SP.6. Approximate the probability of a chance
Subskills
 Represent and draw conclusions for 2 data sets
using a table, graph, dot plot, and box plot.
 Calculate, compare, and interpret the mean,
median, upper quartile, lower quartile, and interquartile range for two sets of data.
 Calculate Mean Absolute Deviation
 Analyze and summarize data sets, including initial
analysis of variability.
 Informally assess the degree of visual overlap of two
numerical data distributions with similar variability,
measuring the difference between the centers by
expressing it as a multiple of a measure of
variability.
 Compare two sets of data using measures of center
and variability
 Draw informal comparative inferences about two
populations
 Use measures of center and measures of variability
for numerical data from random samples to draw
informal comparative inferences about two
populations. For example, decide whether the words
in a chapter of a seventh-grade science book are
generally longer than the words in a chapter of a
fourth-grade science book
 Explain how the probability of an event is expressed
as a fraction.
 Represent the probability of events that are
impossible, unlikely, likely and certain using rational
numbers from 0 to 1.
 Understand that the probability of a chance event is
a number between 0 and 1 that expresses the
likelihood of the event occurring. Larger numbers
indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around 1/2
indicates an event that is neither unlikely nor likely,
and a probability near 1 indicates a likely event.
 Define theoretical probability and proportions
Materials
CMP: Samples and Populations:
Inv. 1, 3
Glencoe: Chapter 10: Inquiry Lab
Common Core Mathematics:
CC.12
Big Ideas Math: 10.7
CMP: Samples and Populations:
Inv. 1
Glencoe: Chapter 10: Lesson 4
Common Core Mathematics:
Activity Lab 1.10b
Big Ideas Math: 10.7
CMP: What Do You Expect?: Inv. 2,
4, 5
Glencoe: Chapter : Lesson 1, 5
Common Core Mathematics: 12.1
Big Ideas Math: 10.1, 10.2, 10.3
CMP: What Do You Expect?: Inv. 1,
event by collecting data on the chance process
that produces it and observing its long-run relative
frequency, and predict the approximate relative
frequency given the probability.
7.SP.7. Develop a probability model and use it to
find probabilities of events. Compare probabilities
from a model to observed frequencies; if the
agreement is not good, explain possible sources
of the discrepancy.
a. Develop a uniform probability model by
assigning equal probability to all outcomes, and
use the model to determine probabilities of events.
b. Develop a probability model (which may not be
uniform) by observing frequencies in data
generated from a chance process.
7.SP.8. Find probabilities of compound events
using organized lists, tables, tree diagrams, and
simulation.
 Design, perform, and collect data on a chance event
 Analyze data from tables (frequency), graphs and
plots to determine probabilities of an event
 Use probability to predict outcomes of long-run or
repeated/ larger events
 Organize collected data from experiments
performed in tables, graphs, and plots.
 Compare theoretical and experimental probability
using the “Law of Large Numbers.”
 Use theoretical probability and proportions to make
approximate predictions.
 Approximate the probability of a chance event by
collecting data on the chance process that produces
it and observing its long-run relative frequency, and
predict the approximate relative frequency given the
probability. For example, when rolling a number
cube 600 times, predict that a 3 or 6 would be rolled
roughly 200 times, but probably not exactly 200
times.
 Predict frequencies of outcomes based on
theoretical probability
 Recognize an appropriate design to conduct an
experiment with simple probability events.
 Develop a probability model to predict outcomes
based on a series of random events (experimental
probability).
 Use a variety of experiments to explore the
relationship between experimental and theoretical
probabilities and the affect of sample size on this
relationship.
 Recognize the frequency of outcomes based on
theoretical probability.
 Compare outcomes from theoretical to experimental
probability.
 Develop a uniform probability model by assigning
equal probability to all outcomes, and use the model
to determine probabilities of events. For example, if
a student is selected at random from a class, find
the probability that Jane will be selected and the
probability that a girl will be selected
 Compare frequency of events based on a mode.
 Develop a uniform probability model by assigning
equal probability to all outcomes and use it to
2, 3, 4
Glencoe: Chapter 9: Inquiry Lab
Common Core Mathematics:
12.1, 12.2. Activity Lab 12.2a
Big Ideas Math: 10.3
CMP: What Do You Expect?: Inv.
3,5
Glencoe: Chapter : Lesson 1, 2
Common Core Mathematics:
12.2. Activity Lab 12.2a
Big Ideas Math: 10.2, 10.3
CMP: What Do You Expect?: Inv. 1,
2, 3, 4, 5
a. Understand that, just as with simple events, the
probability of a compound event is the fraction of
outcomes in the sample space for which the
compound event occurs.
b. Represent sample spaces for compound events
using methods such as organized lists, tables and
tree diagrams. For an event described in everyday
language (e.g., “rolling double sixes”), identify the
outcomes in the sample space which compose the
event.
c. Design and use a simulation to generate
frequencies for compound events.
Benchmark 6: Task 3 (M & M Task)
determine probability of events.
 Develop a non-uniform probability model by
assigning unequal probability to all outcomes
 Explain and justify discrepancy of events from
observed frequencies.
 Compare probability from models to observed
frequencies
 Develop a probability model (which may not be
uniform) by observing frequencies in data generated
from a chance process. For example, find the
approximate probability that a spinning penny will
land heads up or that a tossed paper cup will land
open-end down. Do the outcomes for the spinning
penny appear to be equally likely based on the
observed frequencies?
Glencoe: Chapter : Lesson 3, 4, 5,
6, 7
Common Core Mathematics:
12.3, 12.4
Big Ideas Math: 10.4, 10.5
Unit 6: Geometry
Vocabulary: Angles: corresponding, vertical, equal, obtuse, right, acute, adjacent, complementary, supplementary; Triangles: isosceles, scalene,
equilateral, obtuse, acute, right; parallel lines; perpendicular lines; line segments; quadrilaterals; polygons; cubes; right prisms; pyramids
Standard
7.G.2. Draw (freehand, with ruler and protractor,
and with technology) geometric shapes with given
conditions. Focus on constructing triangles from
three measures of angles or sides, noticing when
the conditions determine a unique triangle, more
than one triangle, or no triangle.
7.G.3. Describe the two-dimensional figures that
result from slicing three dimensional figures, as in
plane sections of right rectangular prisms and
right rectangular pyramids.
7.G.5. Use facts about supplementary,
complementary, vertical, and adjacent angles in a
multi-step problem to write and solve simple
equations for an unknown angle in a figure.
Subskills
 Recall that the combined angle measures of a
triangle equals 180 degrees.
 Construct shapes, focusing on the drawing of
triangles with given measurements.
 Distinguish between different types of angles.
 Apply knowledge of geometric terms to draw
geometric shapes with given conditions, which should
include:
o Parallel lines, angles, perpendicular lines, line
segments, etc.
 Draw (freehand, with ruler and protractor, and with
technology) geometric shapes with given conditions.
Focus on constructing triangles from three measures
of angles or sides, noticing when the conditions
determine a unique triangle, more than one triangle,
or no triangle
 Examine parallel and perpendicular cross sections of
three-dimensional figures.
 Slice (dissect) 3-dimensional figures into 2dimensional cross sections
 Evaluate the two-dimensional cross sections that
result from the dissecting of the three- dimensional
shape.
 Describe the two-dimensional figures that result from
slicing three-dimensional figures, as in plane sections
of right rectangular prisms and right rectangular
pyramids.
 Interpret facts about angles that are created when a
transversal cuts parallel lines.
 Explain why the sum of the measures of the angles
in a triangle is 180 degrees.
 Apply knowledge about triangles to find unknown
measures of angles.
 Identify and draw complementary angles,
supplementary angles, vertical angles, and adjacent
angles.
 Apply algebraic concepts to solve for unknown
measures.
Materials
CMP: Shapes and Designs: Inv. 1,
2, 3
Stretching and Shrinking: Inv. 3
Glencoe: Chapter 7: Lesson 3
Common Core Mathematics:
CC.8
Big Ideas Math: 7.3, 7.4
CMP: Filling and Wrapping: Inv. 2
Glencoe: Chapter 7: Lesson 5, 6
Common Core Mathematics:
CC.9
Big Ideas Math: Extension 9.5
CMP: Shapes and Designs: Inv. 1,
2, 3
Glencoe: Chapter 7: Lesson 1,2
Common Core Mathematics: 7.2
Big Ideas Math: 7.1, 7.2
7.G.6. Solve real-world and mathematical
problems involving area, volume and surface area
of two- and three-dimensional objects composed
of triangles, quadrilaterals, polygons, cubes, and
right prisms
 Interpret information in a word problem about angles
to write and solve equations
 Use facts about supplementary, complementary,
vertical, and adjacent angles in a multi-step problem
to write and solve simple equations for an unknown
angle in a figure.
 Recall the formulas for area, surface area and
volume of two and three-dimensional figures.
 Apply the understanding of two- and threedimensional figures to solve real-world problems.
 Solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
CMP: Filling and Wrapping: Inv. 1,
2
Glencoe: Chapter 8: Lesson 3, 4,
5, 6, 7, 8
Common Core Mathematics: 8.2,
8.3, 8.4, 8.9, 8.10
Big Ideas Math: 8.4, 9.1, 9.2, 9.4,
9.5
Unit 6 Assessment