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Milwaukee Public Schools Curriculum Guide - Grade 5
Houghton Mifflin Math Expressions
1st Quarter
Houghton Mifflin Expressions
Grade 5
2007–2008 Mathematics Curriculum Guides
Wisconsin
Mathematics
Standard
Throughout The Year
A.
Mathematical
Processes
MPS
Learning Target
Note: Mathematical processes
need to be embedded in all
mathematical strands
throughout the school year.
Math processes are assessed on
the WKCE-CRT and reported
as a separate proficiency area.
For example, students are
asked to provide written
justifications and explanations,
pose problems, and represent
concepts.
Wisconsin Assessment
Descriptors for Mathematics
(For Beginning Grade 1)
Curriculum
1) Reasoning: Use reasoning and logic to:
• Perceive patterns
• Identify relationships
• Formulate questions
• Pose problems
• Make conjectures
• Justify strategies
• Test reasonableness of results
2) Communication: Communicate mathematical ideas and reasoning using
the vocabulary of mathematics in a variety of ways (e.g., using words,
numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
3) Connections: Connect mathematics to the real world as well as within
mathematics.
4) Representations: Create and use representations to organize, record, and
communicate mathematical ideas.
5) Problem Solving: Solve and analyze routine and non-routine problems.
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
1
Milwaukee Public Schools Curriculum Guide - Grade 5
Time
September
19 teaching
days
Curricular
Connections
Units/Lessons
Unit 1 Basic
Multiplication and
Division
1.1 Multiplication as
Equal Groups (NO&R)
1.2 Arrays and Area
(NO&R)
1.3 Explore the
Multiplication Tables
(NO&R, AR)
1.4 Make Combinations
(NO&R, AR,
Stats/Prob)
1.5 Understand
Comparisons (NO&R,
AR)
1.6 Practice with
Multiplication Problems
(NO&R, AR)
1.7 Discover
Multiplication Patterns
(NO&R)
1.8 Functions (AR)
1.9 Multiplication
Strategies (NO&R)
1.10 Multiplication and
Division Practice
(NO&R)
1.11 Write Word
Problems (NO&R)
1.12 Equations with
Parentheses (NO&R,
AR)
1.13 Combinations and
MPS Learning Targets
Numbers Operations and
Relationships #1
Pose real-world problems, and use
strategies, including number theory
concepts and place value, to compare
numbers, make estimates, and solve
single and multi-step word problems.
(1.1, 1.2, 1.3,1.4, 1.5, 1.6, 1.7, 1.9,
1.10, 1.11, 1.12, 1.13, 1.14, 1.15,
1.16)
Algebraic Relationships #8
Represent, extend, and describe
patterns and functional relationships
using words, symbolic rules, tables,
and graphs. (1.5, 1.7, 1.8, 1.9, 1.14,
1.15)
1st Quarter
Wisconsin State Framework Assessment Descriptors
Number Operations and Relationships
B.a:4 Identify and use number theory concepts:
 Prime and composite numbers
 Divisibility potential of numbers (divisors of 110, 25, and multiples of 10).
 Least common multiples
 Greatest common factor of two numbers (1.4)
B.b:16 Solve problems using basic multiplication and
division facts. (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9,
1.10, 1.11, 1.13, 1.14, 1.15, 1.16)
B.b:13 Use all operations in everyday situations to
solve single or multi-step word problems. (1.1, 1.2, 1.3,
1.4, 1.5, 1.6, 1.7, 1.12, 1.13, 1.15, 1.16)
Connections
District Model
CABS
MPS Number
Operations and
Relationships
CABS
# 5, # 6
MPS Algebraic
Relationships
CABS
#1
MPS Statistics
and Probability
CABS #5
Measurement
Algebraic Relationships #9
Apply and justify use of equations,
inequalities, properties (e.g.,
distributive, 4x27=4x25+4x2), and
order of operations to represent and
solve one-step and two-step problems
with and without context.
(1.3, 1.4, 1.5, 1.6, 1.12, 1.13, 1.15,
1.16)
Statistics and Probability #7
Describe the difference between
theoretical and experimental
probabilities, determine the likelihood
and fairness of events, and explain
why probabilities are represented as
fractions and percents from 0 to 1.
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Houghton Mifflin Math Expressions
D.a:1 Identify appropriate units to measure length,
liquid capacity, volume, time, weight/mass,
temperature, including measures. Units include: inches,
feet, yards, (i.e. 1 foot 3 inches) miles, centimeters,
millimeters, meters, kilometers, ounces, cups, quarts,
gallons, liters, hours, minutes, seconds (i.e. 1 hour 15
minutes), days, months, years, ounces, pounds, grams,
kilograms, and degrees Fahrenheit/Celsius. (A.1)
D.a:2 Compare attributes of length, volume, and weight
by observation or when given actual measurements
(A.1)
D.a:3 Make measurement conversions within a system
between units (e.g., feet and yards; inches and yards;
quarts and gallons; meters and centimeters; seconds and
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
2
Milwaukee Public Schools Curriculum Guide - Grade 5
Comparisons (NO&R,
(1.4, 1.13)
AR, Stats/Prob)
September
19 teaching
days
1.14 Practice with
Factors (NO&R)
1.15 Multiple Step
Problem (NO&R, AR)
1.16 Properties of
Multiplication (NO&R,
AR)
Measurement
Mini Unit A Perimeter
and Area
Measurement # 5
Compare measurement attributes and
elapsed time, explain estimates,
selection of unit, and conversions of
measures, and determine
measurements (e.g., area, size of
angles, elapsed time) with tools and
scales to specified degrees of
accuracy (A.1)
A.1 Square Units and
Area (M)
Houghton Mifflin Math Expressions
hours (A.1)
1st Quarter
D.c:9 Determine the area of regular shapes including
right triangles. (A.1)
Statistics and Probability
E.b:10 Describe and determine the number of
combinations of selecting three items from four or more
items.(1.4,1.13)
Algebraic Relationships
F.a:1 Recognize, extend, describe, create and replicate
a variety of patterns including attribute, numeric, and
geometric patterns (1.7)
F.a:2 Represent patterns and relationships with
pictures, tables, and charts (1.5)
F.a:3 Describe a rule that explains a functional
relationship or pattern using addition, subtraction, or
multiplication rules (1.8, 1.9, 1.14)
F.b:7 Solve one-step equations with “box” variable and
whole number coefficients in problems with and
without context using whole number coefficients (1.4,
1.5, 1.6)
F.b:8 Solve two-step multi-operation equations with
“box” or letter variable and whole number coefficients
with and without context. Ex: 3 * “box” + 1 = 7 (1.15)
F.b:9 Represent problem situations with one or twostep equations or expressions. Solve simple two-step,
two-operation patterns (1.3, 1.4, 1.5, 1.6, 1.12 ,1.13,
1.15)
F.b:11 Solve equations involving any two
operations. (1.12)
F.c:12 Use the commutative property of multiplication
with positive single digits (1.3)
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
3
Milwaukee Public Schools Curriculum Guide - Grade 5
October
20 teaching
days
Measurement
Mini Unit A Perimeter
and Area
A.2 Perimeter and Area
of Rectangles (M)
A.3 Area of Right
Triangles and
Parallelograms (M,G)
A.4 The Area of Any
Triangle (M,G)
A.5 Consolidate
Perimeter and Area (M)
A.6 Customary Units of
Length (M)
Unit 2
Addition and
Subtraction with
Whole Numbers and
Decimals
2.1 Thousands to
Thousandths (NO&R)
2.2 Equate and Compare
(NO&R)
2.3 Use Decimal
Numbers (NO&R)
2.4 Billions to Billionths
(NO&R)
2.5 Use Place Value
(NO&R)
2.6 Add Whole
Numbers and Decimals
(NO&R)
2.7 Addition to the
Millions (NO&R)
2.8 Subtract Whole and
Decimal Numbers
Numbers Operations and
Relationships #1
Pose real-world problems, and use
strategies, including number theory
concepts and place value, to compare
numbers, make estimates, and solve
single and multi-step word problems.
(2.1, 2.2, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9)
Numbers Operations and
Relationships #2
Generate and represent equivalent
forms of commonly used fractions,
decimals, and percents; estimate with
benchmarks; and use strategies to
compare, add, and subtract fractions
and decimals with and without
context.(2.1, 2.2, 2.3, 2.9)
Geometry #3
Describe, construct, and classify
polygons and polyhedrons using
properties (e.g., angles, lines of
symmetry, parallel lines, similarity)
of plane and coordinate geometry.
(A.3, A.4 A.5))
Measurement # 5
Compare measurement attributes and
elapsed time, explain estimates,
selection of unit, and conversions of
measures, and determine
measurements (e.g., area, size of
angles, elapsed time) with tools and
scales to specified degrees of
accuracy.
(A.2, A.3, A.4, A.5, A.6, 2.3, 2.12)
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Houghton Mifflin Math Expressions
1st Quarter
F.c:13 Use the inverse relationship of division and
multiplication with single whole digits. (1.3, 1.4, 1.6,
1.16
F.c:14 Simplify (evaluate) two-step numerical
expressions using correct order of operations (1.12,
1.15)
F.c:15 Demonstrate understanding of distributive
property (1.16)
Numbers Operations and Relationships
MPS Algebraic
Relationships
CABS #2, #3, #4,
#5. #6
MPS
Measurement
CABS #7
MPS Geometry
CABS # 4
B.a:1 Recognize and apply place-value concepts to
whole numbers less than 10,000,000. (2.1, 2.2, 2.3, 2.4,
2.5, 2.6, 2.7, 2.9)
B.a:2 Read, write, and represent numbers using words,
numerals, pictures (base-ten blocks), number lines,
arrays expanded forms
(12,436=10,000+2,000+400+30+6), and symbolic
reasoning e.g., 12,436=12,450-14 (2.1, 2.2, 2.4, 2.5)
B.a:3 Compare and order numbers less than 100,000
represented in numbers, arrays, symbols (<, >, =) and
words.
(2.2, 2.4)
B.a:12 Identify and represent equivalence between
fractions, percents, and decimals.
(2.1, 2.2)
B.b:13 Use all operations in everyday situations to
solve single or multi-step word problems. (2.8, 2.9)
B.b:14: Solve three and four-digit addition and
subtraction with regrouping, multiplication of threedigit by two-digit numbers, division with single-digit
divisors and four-digit dividends with two-step or
mixed operation problems.(2.6, 2.7, 2.8, 2.9)
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
4
Milwaukee Public Schools Curriculum Guide - Grade 5
(NO&R)
2.9 Place Value Word
Problems (NO&R)
Houghton Mifflin Math Expressions
1st Quarter
Number Operations and Relationships
October
20 teaching
days
Unit 2
Addition and
Subtraction with
Whole Numbers and
Decimals
2.10 Properties and
Strategies (AR)
2.11 Pictographs With
Large Numbers
(NO&R, Stats/Prob)
2.12 Round Numbers on
Graphs (NO&R, M)
2.13 Bar Graph and
Rounding (Stats/Prob)
Statistic and Probability # 6
Conduct data investigations, interpret
and summarize (e.g., mean, median,
mode, range) data sets and displays
(e.g., line plots, Venn diagrams), and
make context-based conclusions and
predictions.(2.11, 2.13)
Algebraic Relationships #9
Apply and justify use of equations,
inequalities, properties (e.g.,
distributive, 4x27=4x25+4x2), and
order of operations to represent and
solve one-step and two-step problems
with and without context.
(2.10)
B.b:15 Compute with decimals in the context of money
and make change (2.1, 2.3, 2.6)
B.b 19 Estimate using basic whole number operations,
benchmark fractions, and benchmark decimals. (2.9,
2.12)
Geometry
C.a:1 Recognize and name polygons with 3, 4, 5, 6 or 8
sides. (A.3, A.4, A.5)
C.a:2 Identify lines and line segments in a plane figure.
(A.4)
C.a: 3 Classify plane figures by characteristics of
angles (acute, obtuse, and right) and describe rays
found in open-angle situations. (A.3, A.4)
C.b:5 Identify figures that are congruent and/or similar.
(A.5)
Measurement
D.a:1 Identify appropriate units to measure length,
liquid capacity, volume, time, weight/mass,
temperature, including measures. Units include: inches,
feet, yards, (i.e. 1 foot 3 inches) miles, centimeters,
millimeters, meters, kilometers, ounces, cups, quarts,
gallons, liters, hours, minutes, seconds (i.e. 1 hour 15
minutes), days, months, years, ounces, pounds, grams,
kilograms, and degrees Fahrenheit/Celsius. (A.6)
D.a:2 Compare attributes of length, volume, and weight
by observation or when given actual
measurements.(A.6)
D.a:3 Make measurement conversions within a system
between units (e.g., feet and yards; inches and yards;
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
5
Milwaukee Public Schools Curriculum Guide - Grade 5
October
20 teaching
days
Unit 2
Addition and
Subtraction with
Whole Numbers and
Decimals
Houghton Mifflin Math Expressions
1st Quarter
quarts and gallons; meters and centimeters; seconds and
hours (A.6, 2.3)
D.b:4 Measure down to the nearest 1/8-inch,
centimeter, or millimeter.
(A.5, 2.3)
D.b:7 Determine and compare elapsed time in problemsolving situations. (2.12)
D.c:9 Determine the area of regular shapes including
right triangles. (A.2, A.3, A.4, A.5, A.6)
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
6
Milwaukee Public Schools Curriculum Guide - Grade 5
November
7 teaching
days
Houghton Mifflin Math Expressions
1st Quarter
Number Operations and Relationships
Unit 2
Addition and
Subtraction with
Whole Numbers and
Decimals
2.14 Introduce Line
Graphs (Stats/Prob)
2.15 Graphs With
Decimal Numbers
(Stats/Prob)
2.16 Classify Word
Problems (AR)
2.17 Situation and
Solution Equations
(AR)
2.18 Comparison
Problems (AR)
2.19 Two-Step Word
Problems (NO&R,
Stats/Prob)
Numbers Operations and
Relationships #1
Pose real-world problems, and use
strategies, including number theory
concepts and place value, to compare
numbers, make estimates, and solve
single and multi-step word problems
(2.19)
Statistic and Probability # 6
Conduct data investigations, interpret
and summarize (e.g., mean, median,
mode, range) data sets and displays
(e.g., line plots, Venn diagrams), and
make context-based conclusions and
predictions (2.14, 2.15, 2.19)
Algebraic Relationships #9
Apply and justify use of equations,
inequalities, properties (e.g.,
distributive, 4x27=4x25+4x2), and
order of operations to represent and
solve one-step and two-step problems
with and without context (2.16, 2.17,
2.18)
B.b:13 Use all operations in everyday situations to
solve single or multi-step word problems (2.19)
MPS Statistics
and Probability
CABS #8
Statistics and Probability
E.a:2 Collect, organize, and display data in appropriate
graphs or charts (2.14, 2.15)
E.a:3 Draw reasonable conclusions based on contextual
data (2.14, 2.15)
E.a:5 Extract, interpret, and analyze data from single
bar graphs, tables and charts, line plots, context, circle
graphs, and Venn diagrams (2.14, 2.15)
E.a:6 Describe a given set of data of ten or fewer
items/numbers using the terms mean, median, mode,
and range to extract information from organized charts,
tables, graphs, and Venn diagrams in problems with and
without context (2.19)
Algebraic Relationships
F.b:7 Solve one-step equations with “box” variable and
whole number coefficients in problems with and
without context using whole number coefficients (2.17)
F.b:9 Represent problem situations with one or twostep equations or expressions. Solve simple two-step,
two-operation patterns (2.16, 2.17, 2.18)
Curriculum Guide Expressions Grade 5
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
7