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Milwaukee Public Schools Curriculum Guide- Grade 4
Everyday Mathematics
2nd Quarter
Everyday Mathematics
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 5)
1) Reasoning: Use reasoning and logic to:
• Perceive patterns
• Identify relationships
• Formulate questions
• Pose problems
• Make conjectures
• Justify strategies
• Test reasonableness of results
Curriculum
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 Everyday Mathematics
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 4
Time
November
13 Teaching
days
Curricular Connections
Units/Lessons
MPS Learning Targets
Take time to complete
any lessons that have not
yet been completed.
Numbers and Operations #1
Use strategies fluently to
make estimates, solve, and
pose real-world problems
(e.g., single and multi-step)
for all operations, to compare
and rename numbers, and to
find factors and multiples.
(4.1, 4.2, 4.3, 4.4, 4.5, 4.6)
Number Operations and Relationships
Numbers and Operations #2
Represent commonly used
fractions (e.g., pictures,
number lines) and decimals
(i.e., money) and use informal
reasoning to rename,
compare, add, and subtract
them with and without
context. (4.2, 4.3, 4.4, 4.5,
4.6)
B.a:3 Compare and order numbers less than 10,000
represented in numbers, arrays, symbols (<, >, =) and
words. (4.3, 4.4)
Unit 4 Decimals and
Their Uses
4.1 Decimal Place Value
(NO&R,AR)
4.2 Review of Basic
Decimal Concepts
(NO&R)
4.3 Comparing and
Ordering Decimals
(NO&R)
4.4 Estimating with
Decimals (NO&R,
Stat/Prob)
4.5 Decimal Addition
and Subtraction
(NO&R)
4.6 Decimals in Money
(NO&R, Stats/Prob)
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.
(4.4, 4.6)
Algebraic Relationships #9
Represent and extend patterns
and describe rules for
functional relationships. (4.1)
Curriculum Guide Everyday Mathematics
2nd Quarter
Version 2.0
Everyday Mathematics
Wisconsin State Framework Assessment
Descriptors
B.a:1 Recognize and apply place-value concepts to
whole numbers less than 1,000,000. (4.1, 4.5)
2nd Quarter
Connections
District Model
CABS
MPS NO&R
CABS #15
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. (4.2, 4.3, 4.4, 4.5)
B.a:7 Represent fractions (1/4s, 1/2s, 1/8s, 1/10s,
1/16s) using numbers, pictures (e.g., drawings or base
ten blocks), and number lines. (4.2, 4.3, 4.5)
B.b:10 Use all operations in everyday situations to
solve single or multi-step word problems. (4.3)
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.
(4.5)
B.b:12 Add and subtract decimals in the context of
money. (4.6)
B.b:13 Solve problems using basic multiplication and
division facts. (4.8, 4.10)
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
Everyday Mathematics
2nd Quarter
Number Operations and Relationships
November
13 Teaching
days
B.b:15 Estimate: multiplication of two-digit by onedigit problems, addition and subtraction of decimals
using money, and division in context. Estimate:
multiplication of two-digit by one-digit problems,
addition and subtraction of decimals using money, and
division in context. (4.4, 4.6)
B.b:16 Determine reasonableness of answers. (4.4, 4.5,
4.6)
Statistics and Probability
E.a:2 Collect, organize, and display data in appropriate
graphs or charts. (4.6)
E.a:4 Use data to predict outcomes or trends from
graph or table. (4.4)
Algebraic Relationships
F.a:1 Recognize, extend, describe, create and replicate
a variety of patterns including attribute, numeric, and
geometric patterns. (4.1)
F.a:2 Represent patterns and relationship with pictures,
tables, and charts. (4.1)
Curriculum Guide Everyday Mathematics
2nd 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
Unit 4 Decimals and
Their Uses
December
15
Teaching
days
4.7 Thousandths(NO&R)
4.8 Metric Units of
Length(NO&R, M)
4.9 Personal References
for Metric Length(M)
4.10 Measuring in
Millimeters(NO&R,
M)
4.11 Progress Check 4
Unit 5 Big Numbers,
Estimation, and
Computation
5.1 Extended
Multiplication
Facts(NO&R)
5.2 Multiplication
Wrestling(NO&R,
AR)
5.3 Estimating
Sums(NO&R,
Stat/Prob)
5.4 Estimating
Products(NO&R,
Stat/Prob)
5.5 Partial-Products
Multiplication (Part
1)(NO&R, AR)
5.6 Partial-Products
Multiplication(Part
2)(NO&R, AR)
5.7 Lattice Muliplication
(NO&R)
Numbers and Operations #1
Use strategies fluently to
make estimates, solve, and
pose real-world problems
(e.g., single and multi-step)
for all operations, to compare
and rename numbers, and to
find factors and multiples.
(4.7, 4.8, 4.10, 5.1, 5.2, 5.3,
5.4, 5.5, 5.6, 5.7)
Number Operations and Relationships
Numbers and Operations #2
Represent commonly used
fractions (e.g., pictures,
number lines) and decimals
(i.e., money) and use informal
reasoning to rename,
compare, add, and subtract
them with and without
context. (4.7)
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.) (5.1, 5.2, 5.4,
5.5)
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. (4.8, 4.9,
4.10)
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.
(5.3, 5.4)
Curriculum Guide Everyday Mathematics
2nd Quarter
Version 2.0
Everyday Mathematics
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. (4.7, 4.8, 5.1, 5.2,
5.5, 5.6)
2nd Quarter
MPS
Measurement
CABS #3
B.a:3 Compare and order numbers less than 10,000
represented in numbers, arrays, symbols (<, >, =) and
words. (4.7)
B.a:7 Represent fractions (1/4s, 1/2s, 1/8s, 1/10s,
1/16s) using numbers, pictures (e.g., drawings or base
ten blocks), and number lines. (4.7)
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.
(5.2, 5.5, 5.6, 5.7)
MPS NO&R
CABS #7a-7c
B.b:13 Solve problems using basic multiplication and
division facts. (4.8, 4.10, 5.1, 5.2, 5.5, 5.6, 5.7)
B.b:15 Estimate: multiplication of two-digit by onedigit problems, addition and subtraction of decimals
using money, and division in context. Estimate:
multiplication of two-digit by one-digit problems,
addition and subtraction of decimals using money, and
division in context. (5.3, 5.4, 5.5, 5.6)
B.b:16 Determine reasonableness of answers. (5.3)
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
December
Algebraic Relationships #10
Use symbols to represent
problem situations and use
properties and order of
operations to solve equations
involving all operations. (5.2)
15
Teaching
days
Everyday Mathematics
2nd Quarter
Measurement
D.a:2 Compare attributes of length and weight by
direct observation or when given actual measurements.
(4.8)
D.a:3 Make measurement conversions within a system
between units (e.g., feet and yards; inches and feet;
quart and gallons; meters and centimeters; minutes and
hours; hours and days; months and years). (4.8, 4.10)
D.b:4 Read, interpret, and use measuring instruments
to determine the measurement of objects with nonstandard and standard units to the nearest 1/4-inch or
centimeter. (4.8, 4.9, 4.10)
D.c:8 Estimate measurement using U.S. customary and
metric measurements. (4.9)
Statistics and Probability
E.a:4 Use data to predict outcomes or trends from
graph or table. (5.3)
E.a: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. (5.4)
Algebraic Relationships
F.c:12 Demonstrate understanding of order of
operations by solving two-step open sentences
involving all operations. (5.2)
Curriculum Guide Everyday Mathematics
2nd 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
January
15
Teaching
days
Unit 5 Big Numbers,
Estimation, and
Computation
5.8 Big Numbers
(NO&R, AR)
5.9 Powers of 10
(NO&R, Stats/Prob)
5.10 Rounding and
Reporting Round
Numbers (NO&R,
Stats/Prob)
5.11 Comparing Data
(NO&R, Stats/Prob)
5.12 Progress Check 5
Unit 6 Division; Map
Reference Frames;
Measures of Angles
6.1 Multiplication and
Division Number
Stories (NO&R)
6.2 Strategies for
Division (NO&R)
6.3 The PartialsQuotients Division
Algorith, Part I
(NO&R)
6.4 Expressing and
Interpreting
Remainders (NO&R)
6.5 Rotations and Angles
(NO&R, G)
6.6 Using a Full-Circle
Protractor (G)
6.7 The Half-Circle
Protractor (G)
Numbers and Operations #1
Use strategies fluently to
make estimates, solve, and
pose real-world problems
(e.g., single and multi-step)
for all operations, to compare
and rename numbers, and to
find factors and multiples.
(5.8, 5.9, 5.10, 5.11, 6.1, 6.2,
6.3)
Number Operations and Relationships
Geometry #3
Describe, compare, and
classify two-and threedimensional figures
according to their properties
including symmetry. (6.5,
6.6, 6.7)
B.a:3 Compare and order numbers less than 10,000
represented in numbers, arrays, symbols (<, >, =) and
words. (5.11)
Geometry #4
Identify and describe figures
constructed from blocks, nets,
and transformations. (6.5,
6.6)
Algebraic Relationships #9
Represent and extend patterns
and describe rules for
functional relationships (5.9)
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.(5.10, 5.11)
Curriculum Guide Everyday Mathematics
2nd Quarter
Version 2.0
Everyday Mathematics
2nd Quarter
B.a:1 Recognize and apply place-value concepts to
whole numbers less than 1,000,000. (5.8, 5.9)
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. (5.8, 5.9, 5.10,
5.11, 6.1, 6.2, 6.4)
MPS NO&R
CABS #2a-2c
MPS Stats/Prob
CABS #2
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.). (6.2, 6.3, 6.4,
6.5)
B.b:10 Use all operations in everyday situations to
solve single or multi-step word problems. (5.8, 6.1, 6.2,
6.3)
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.
(6.3)
MPS NO&R
CABS #4
B.b:13 Solve problems using basic multiplication and
division facts(6.4)
B.b:15 Estimate: multiplication of two-digit by onedigit problems, addition and subtraction of decimals
using money, and division in context. Estimate:
multiplication of two-digit by one-digit problems,
addition and subtraction of decimals using money, and
division in context.(5.8, 5.10)
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
Everyday Mathematics
2nd Quarter
Number Operations and Relationships
B.b:16 Determine reasonableness of answers.(5.8,
5.10)
January
Geometry
15
Teaching
days
C.a:1 Identify, describe and compare properties of 2and 3-dimensional figures, comparing sides, faces,
vertices and edges of regular figures including parallel
and perpendicular lines and line segments.(6.5, 6.6,
6.7)
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).(6.5, 6.6)
Statistics and Probability
E.a:4 Use data to predict outcomes or trends from
graph or table.(5.10, 5.11)
Algebraic Relationships
F.a:1 Recognize, extend, describe, create and replicate
a variety of patterns including attribute, numeric, and
geometric patterns.(5.9)
F.a:2 Represent patterns and relationship with pictures,
tables, and charts.(5.9)
F.a:3 Describe a rule that explains a functional
relationship or pattern using addition, subtraction, or
multiplication rules.(5.9)
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 2 nd quarter curriculum guide.
Curriculum Guide Everyday Mathematics
2nd Quarter
Version 2.0
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
7
Milwaukee Public Schools Curriculum Guide- Grade 4
Curriculum Guide Everyday Mathematics
2nd Quarter
Version 2.0
Everyday Mathematics
2nd Quarter
Developed by the Milwaukee Mathematics Partnership with support
by the National Science Foundation under Grant No. 0314898.
8