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Milwaukee Public Schools Curriculum Guide - Grade 5
Houghton Mifflin Math Expressions
2nd 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 6)
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
2nd 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
November
13 teaching
days
Curricular
Connections
Units/Lessons
*Complete any lessons
previously not taught.
(8 days)
Unit 2 Review and
Test (2 days)
Unit B Circles,
Polygons, and Angles
B.1 Lines and Angles
(G, M)
B.2 Polygons and
Angles (G, M)
B.3 Compare and
Contrast Polygons (G,
M)
MPS Learning Targets
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. (B.1,
B.2, B.3)
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.(B.1, B.2)
Houghton Mifflin Math Expressions
2nd Quarter
Wisconsin State Framework Assessment Descriptors
Geometry
Connections
District Model
CABS
MPS Geometry
CABS #1,2 & 8
C.a:1 Recognize and name polygons with 3, 4, 5, 6 or
8 sides.(B.2, B.3)
C.a: 2 Identify lines and line segments in a plane
figure.(B.1)
C.a:3 Classify plane figures by characteristics of
angles (acute, obtuse, and right) and describe rays
found in open-angle situations. (B.1, B. 2)
C.b:5 Identify figures that are congruent and/or
similar. (B.3)
Measurement
D.b:5 Determine angle measurement to nearest five
degrees using a protractor. (B.1, B.2)
Curriculum Guide Expressions Grade 5
2nd Quarter
Version 2.0
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
December
15 teaching
days
Unit B Circles,
Polygons, and Angles
B.4 Circles and Angles
(G, M)
B.5 Symmetry (G, M)
B.6 Circle Graphs
(Stats/Prob)
Review and Unit Test
(2 days)
Unit 3
Fraction Concepts
3.1 Build Unit Fractions
(NO&R)
3.2 Compare Fractions
(NO&R)
3.3 Subtract
Fractions(NO&R)
3.4 Fractional Addends
of One (NO&R)
Numbers and Operations #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.(3.1, 3.2, 3.3, 3.4)
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. (B.4,
B.5,)
Geometry #4
Evaluate the results of transformations
from rigid motions and movement
between polyhedral and nets, and
describe three-dimensional figures
from multiple perspectives.(B.4)
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.(B.4)
Statistics 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.(B.6)
Curriculum Guide Expressions Grade 5
2nd Quarter
Version 2.0
Houghton Mifflin Math Expressions
2nd Quarter
Numbers Operations and Relationships
B.a:10 Represent fractions using numbers, pictures,
and number lines. (3.1,3.2,3.3,3.4)
Geometry
MPS
Measurement
CABS #9
MPS CABS
Statistics and
Probability #2
C.a:3 Classify plane figures by characteristics of
angles (acute, obtuse, and right) and describe rays
found in open-angle situations. (B.4)
C.b:7 .Use slides, flips, and turns on figures. Identify
congruent shapes using figures that have been
manipulated by one or two motions (slides, flips, and
turns). ( B.4, B.5)
C.b:8 Identify lines of symmetry and the number of
lines of symmetry in figures, and design shapes that
have at least one line of symmetry. (B.5)
Measurement
D.b:5 Determine angle measurement to nearest five
degrees using a protractor. (B.1, B.2, B.4)
Statistics and Probability
E.a:2 Collect, organize, and display data in
appropriate graphs or charts.(B.6)
E.a:3 Draw reasonable conclusions based on
contextual data.(B.6)
E.a:5 Extract, interpret, and analyze data from single
bar graphs, tables and charts, line plots, context, circle
graphs, and Venn diagrams.(B.6)
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
January
15 teaching
days
Unit 3
Fraction Concepts
3.5 Relate Fractions and
wholes (NO&R)
3.6 Fractions Greater
Than One (NO&R)
3.7 Add Fractions
Greater Than One (Like
Denominators) (NO&R,
AR)
3.8 Subtract Mixed
Numbers ( Like
Denominators) (NO&R)
3.9 Comparison
Situations (NO&R, M)
3.10 Mixed Practice
With Like Fractions
(NO&R)
3.11 Discover
Equivalent Fractions
(NO&R)
3.12 Equivalent
Fractions and
Multipliers (NO&R)
3.13 Solve Equivalence
Problems (NO&R)
3.14 Probability and
Equivalent Fractions
(NO&R, Stats/Prob)
Numbers and Operations #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.
(3.12, 3.13)
Numbers and Operations #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.(3.5, 3.6, 3.7, 3.8, 3.9, 3.10,
3.11, 3.12, 3.13, 3.14)
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.(3.9)
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.
(3.14)
Houghton Mifflin Math Expressions
2nd Quarter
Numbers Operations and Relationships
B.a:10 Represent fractions using numbers, pictures,
and number lines. (3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 3.11,
3.12, 3.13, 3.14)
MPS CABS
Statistics and
Probability
#1&4
B.a: 9 Read, write, identify, order, and compare mixed
fractions. (3.6, 3.7, 3.8, 3.9, 3.10,)
B.a:11 Rename improper fractions to mixed numbers
in lowest terms. (3.6, 3.7, 3.8, 3.9, 3.10)
B.b:17 Rename improper fractions. (3.6, 3.7, 3.8,3.9,
3.10)
B.a:12 Identify and represent equivalence between
fractions, percents, and decimals. (3.11, 3.12,3.13)
B.b:16 Solve problems using basic multiplication and
division facts. (3.12, 3.13)
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. (3.9)
Statistics and Probability
E.a: 7
Determine the likelihood of future events, predict
outcomes of future events, and test predictions using
data from a variety of sources. (3.14)
E.a:9 Determine the probability of events in context
using words, percents, or fractions. (3.14)
Curriculum Guide Expressions Grade 5
2nd Quarter
Version 2.0
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
January
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. (3.7)
Houghton Mifflin Math Expressions
2nd Quarter
Algebraic Relationships
F.c:14 Simplify (evaluate) two-step numerical
expressions using correct order of operations. (3.7)
Adjustments made to the 2nd quarter curriculum guide reflect feedback from teachers regarding the pacing in the 1 st quarter guide. Please note that
continuing at this pace could inhibit completion of the math program as it is written. The committee recommends teachers to consider combining similar
mathematical ideas. This may assist students in developing a deeper conceptual understanding of mathematics as well as help to improve the current
pacing as outlined in the 2nd quarter curriculum guide.
Curriculum Guide Expressions Grade 5
2nd Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
5