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Milwaukee Public Schools Curriculum Guide- Grade 4
Houghton Mifflin Math Expressions
1st Quarter
Houghton Mifflin Expressions
Grade 4
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 4
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 4
Time
Curricular
Connections
Units/Lessons
MPS Learning Targets
Curriculum Guide Expressions Grade 4
1st Quarter
Version 2.0
Houghton Mifflin Math Expressions
Wisconsin State Framework Assessment Descriptors
1st Quarter
Connections
District Model
CABS
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
2
Milwaukee Public Schools Curriculum Guide- Grade 4
September
19 teaching
days
Number Operations and
Relationships#1
Use strategies fluently to make
estimates, solve, and pose realworld problems (e.g., single and
multi-step) for all operations, to
compare and rename numbers,
and to find factors and
multiples.(1.1, 1.2, 1.3 ,1.4, 1.5,
1.6, 1.7, 1.10, 1.11, 1.12, 1.14,
1.15, 1.16, 1.17)
Statistics and Probability #7
Design and conduct data
investigations, display and
describe data, summarize data
sets (e.g., range, median, and
mode), and draw conclusions.
(1.4, 1.7, 1.15, 1.16)
Algebraic Relationships #9
Represent and extend patterns and
describe rules for functional
relationships(1.1, 1.2, 1.4 ,1.6,
1.7, 1.8, 1.10, 1.11, 1.12, 1.13,
1.15)
Algebraic Relationships #10
Use symbols to represent problem
situations and use properties and
order of operations to solve
equations involving all operations
(1.2, 1.6, 1.7, 1.13, 1.15)
Houghton Mifflin Math Expressions
Number Operations and Relationships
B.a:2 Read, write, and represent numbers using words, numerals,
pictures (e.g., base ten blocks), number lines, arrays, expanded forms
(243=200+40+3), and symbolic renaming e.g., 243=250-7
(1.1, 1.2, 1.3, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11 , 1.12, 1.17)
B.a:4 Use basic facts to determine the first ten multiples of 2-10 and
determine factors for numbers up to 100. Recognize the divisibility
potential of numbers (divisors of 2, 5, 10, 25). Count using whole
numbers less than 10,000 and by any number 1-12 and ‘friendly
numbers’ through 100 (ex. 20, 25, etc.)
(1.1, 1.2, 1.3, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.14, 1.15, 1.17)
1st Quarter
MPS Number
Operations and
Relationships
CABS #4, #5
MPS Algebra #1
CABS
MPS Statistics and
Probability CABS
#3
B.b:10 Use all operations in everyday situations to solve single or
multi-step word problems.
(1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9, 1.11, 1.16, 1.17)
B.b:11 Solve three- and four-digit addition and subtraction with
regrouping; multiplication of two-digit by one-digit numbers;
division with single-digit divisors and two-digit dividends and with
two-step or mixed operation problems with single-digit numbers.(1.2,
1.4)
B.b:13 Solve problems using basic multiplication and division
facts.(1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.9, 1.10, 1.11, 1.12, 1.14, 1.16,
1.17)
B.b:16 Determine reasonableness of answers.(1.1, 1.2, 1.3, 1.4, 1.5,
1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.15, 1.16, 1.17)
Statistics and Probability
E.a:1 Formulate questions to collect, organize, and display data
(1.15)
Statistics and Probability
E.a:2 Collect, organize, and display data in appropriate graphs or
charts. (1.15)
E.a:3 Draw reasonable conclusions based on contextual data.
(1.4, 1.15, 1.16)
Curriculum Guide Expressions Grade 4
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 4
Houghton Mifflin Math Expressions
September
E.a:4 Use data to predict outcomes or trends from graph or table.
(1.15)
19 teaching
days
E.a:5 Read and interpret information from single bar graphs, line
plots, picture graphs, and Venn diagrams. (1.4, 1.7)
1st Quarter
Algebraic Relationships
F.a:1 Recognize, extend, describe, create and replicate a variety of
patterns including attribute, numeric, and geometric patterns.
(1.1, 1.2, 1.5, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.15)
F.a:2 Represent patterns and relationship with pictures, tables, and
charts. (1.1, 1.2, 1.4, 1.5, 1.6, 1.8, 1.9, 1.10, 1.11, 1.15)
F.a:3 Describe a rule that explains a functional relationship or pattern
using addition, subtraction, or multiplication rules. (1.8, 1.10, 1.12)
F.b:5 Solve simple one-step open sentences involving all operations
in context. (1.4, 1.5, 1.10, 1.11, 1.12)
F.b:6 Describe a given set of data of seven items/numbers or fewer
using the terms range, mode, and median in problems with and
without context (1.8, 1.9, 1.14)
F.b:7 Solve simple, one-step open sentences including missing factor
in problems with and without context e.g., “box” or letter variable
and whole number coefficients. (1.6)
F.b:8 Represent problem situations with one-step equations involving
multiplication and division with simple open sentences. (1.6, 1.7, 1.8,
1.9)
F.b:9 Represent problem situations with one-step equations or
expressions using one of the four operations (1.6, 1.7, 1.8, 1.9, 1.15)
F.c:10 Use the commutative property of multiplication with positive
single digits. (1.2, 1.12, 1.13)
Number Operations and Relationships
Number and Operations #1
Use strategies fluently to make
estimates, solve, and pose realworld problems (e.g., single and
Curriculum Guide Expressions Grade 4
1st Quarter
Version 2.0
B.a.4 Use basic facts to determine the first ten multiples of 2-10 and
determine factors for numbers up to 100. Recognize the divisibility
potential of numbers (divisors of 2, 5, 10, 25). Count using whole
MPS Measurement
CABS #11
MPS Algebraic
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
4
Milwaukee Public Schools Curriculum Guide- Grade 4
multi-step) for all operations, to
compare and rename numbers,
and to find factors and multiples.
(1.21, 1.22, 1.23, A.4, A.5, A.6,
October
2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7)
20 teaching
days
Geometry #3
Describe, compare, and classify
two-and three-dimensional figures
according to their properties
including symmetry (A.1, A.2,
A.3, A.4, A.5, A.6)
Houghton Mifflin Math Expressions
numbers less than 10,000 and by any number 1-12 and ‘friendly
numbers’ through 100 (ex. 20, 25, etc.) (1.23, A.4, A.5, A.6)
1st Quarter
Relationships
CABS #5, #6, #7
B.b:10 Use all operations in everyday situations to solve single or
multi-step word problems. (1.21, 1.22, 1.23, A.4, A.5, A.6)
B.b:13 Solve problems using basic multiplication and division facts.
(1.21, 1.22, 1.23, A.4, A.5, A.6)
B.b:16 Determine reasonableness of answers. (1.18, 1.19, 1.20, 1.21,
1.22, 1.23. A.1, A.2, A.3, A.4, A.5, A.6)
Geometry
Measurement #6
Identify and compare measurable
attributes, estimate and measure,
and make conversions (e.g., area,
perimeter, temperature) in both
customary and metric systems,
and solve problems with elapsed
time. (A.4, A.5, A.6)
Statistics and Probability #7
Design and conduct data
investigations, display and
describe data, summarize data
sets (e.g., range, median, and
mode), and draw conclusions.
(1.19)
Algebraic Relationships #10
Use symbols to represent problem
situations and use properties and
order of operations to solve
equations involving all
operations. (1.8, 1.22, A.4, A.5,
A.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6)
C.a:1 Identify, describe and compare properties of 2-and 3dimensional figures, comparing sides, faces, vertices and edges of
regular figures including parallel and perpendicular lines and line
segments. (A.1, A.2, A.3, A.4, A.5, A.6)
C.b:3 Use pattern blocks and dot paper (geoboards) to describe,
model, and construct plane figures. (A.1, A.2, A.5)
C.b:5 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) (A.1)
C.b:6 Discern a shape with one line of symmetry. (A.1)
Measurement
D.a:1 Identify appropriate units to measure length, liquid capacity,
volume, weight/mass, time, and temperature. Units include:
inches, feet, yards, miles, millimeters, centimeters, meters,
kilometers, ounces, cups, quarts, gallons, liters, seconds, minutes,
hours, days, months, years, ounces, pounds, grams, kilograms, and
degrees Fahrenheit/Celsius. (A.4)
D.c:9 Determine perimeter and area of regular shapes and the area of
plane rectangular shapes. (A.4, A.5, A.6)
D.c:10 Determine perimeter and area of irregular shapes when given
a reference tool such as a grid. (A.6)
Curriculum Guide Expressions Grade 4
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 4
Houghton Mifflin Math Expressions
1st Quarter
Statistics and Probability
E.a:1 Formulate questions to collect, organize, and display data
(1.19)
October
Algebraic Relationships
19 teaching
days
F.a:9 Represent problem situations with one-step equations or
expressions using one of the four operations (1.18)
F.b:5 Solve simple one-step open sentences involving all operations
in context. (1.22)
F.b:7 Solve simple, one-step open sentences including missing factor
in problems with and without context e.g., “box” or letter variable
and whole number coefficients. (A.6)
F.b:8 Represent problem situations with one-step equations involving
multiplication and division with simple open sentences. (A.4, A.5)
F.c:10 Use the commutative property of multiplication with positive
single digits. (A.4, A.5)
Number Operations and
Relationships #1
Use strategies fluently to make
estimates, solve, and pose real-
Curriculum Guide Expressions Grade 4
1st Quarter
Version 2.0
Number Operations and Relationships
B.a:1 Recognize and apply place-value concepts to whole numbers
less than 1,000,000 (2.8, 2.9, 2.11, 2.12)
MPS Number
Operations and
Relationships
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
6
Milwaukee Public Schools Curriculum Guide- Grade 4
world problems (e.g., single and
multi-step) for all operations, to
compare and rename numbers,
and to find factors and multiples
(2.8, 2.9, 2.10, 2.11, 2.12, 2.13,
November
2.14)
7 teaching
days
Algebraic Relationships #9
Represent and extend patterns and
describe rules for functional
relationships (2.8)
Algebraic Relationships #10
Use symbols to represent problem
situations and use properties and
order of operations to solve
equations involving all operations
(2.10)
Houghton Mifflin Math Expressions
1st Quarter
CABS # 2
B.a:2 Read, write, and represent numbers using words, numerals,
pictures (e.g., base ten blocks), number lines, arrays, expanded forms
(243=200+40+3), and symbolic renaming e.g., 243=250-7 (2.8, 2.9)
B.a:3 Compare and order numbers less than 10,000 represented
in numbers, arrays, symbols (<, >, =) and words (2.10)
B.b.11 Solve three- and four-digit addition and subtraction with
regrouping; multiplication of two-digit by one-digit numbers;
division with single-digit divisors and two-digit dividends and with
two-step or mixed operation problems with single-digit numbers
(2.12, 2.13, 2.14)
B.b:16 Determine reasonableness of answers (2.8, 2.9, 2.10, 2.11,
2.12, 2.13, 2.14)
Algebraic Relationships
F.b.2 Represent patterns and relationship with pictures, tables, and
charts (2.8)
F.b:6 Demonstrate a basic understanding of equality and inequality
using symbol (<, >, =) with all operations. (2.10)
Curriculum Guide Expressions Grade 4
1st Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
7