Grade 4 Content overview
Strands
Operations and Algebra
Measurement and Data
Numbers and Computation
Geometry
LESSONS
TOPICS
1
16
2
15
14
3
13
Connected
Topics
4
GRADE 4
12
11
10
5
Connected
Topics
6
9
8
7
Connected topics develop related content that is broken into separate topics to allow
for assessment opportunities during the development.
F4
Contents
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F C R
FOCUS
COHERENCE
RIGOR
Content is developed with focus, coherence, and rigor. The attention to rigor
reflects a balance of conceptual understanding, procedural skill and fluency, and
applications. See each Topic Overview and Lesson Overview.
TOPICS
FOCUS ON
1 Generalize Place Value Understanding
In Topic 1, students expand their place value understandings
from numbers to 1,000 (Grade 3) to 1,000,000 (Grade 4).
2 Fluently Add and Subtract Multi-Digit Whole Numbers
3 Use Strategies and Properties to Multiply by 1-Digit Numbers
4 Use Strategies and Properties to Multiply by 2-Digit Numbers
5 Use Strategies and Properties to Divide by 1-Digit Numbers
In Topics 2–5, students create and explore strategies for
performing multi-digit calculations that involve breaking
numbers apart using place value.
6 Use Operations with Whole Numbers to Solve Problems
In Topic 6, students are introduced to multiplicative
comparison situations. They use understandings of operations
to solve multi-step problems.
7 Factors and Multiples
In Topic 7, students represent, analyze, and classify numbers
using understandings of multiplication.
8 Extend Understanding of Fraction Equivalence and Ordering
In Topic 8, students use models and mathematical procedures
to understand, recognize, and generate equivalent fractions.
9 Understand Addition and Subtraction of Fractions
10Extend Multiplication Concepts to Fractions
In Topics 9–10, students use their understanding of unit
fractions to add and subtract fractions with like denominators
and multiply a fraction by a whole number.
11Represent and Interpret Data on Line Plots
In Topic 11, students represent data visually using line plots.
Some data involve fractions and mixed numbers.
12Understand and Compare Decimals
In Topic 12, students learn the meaning of a decimal number
by connecting to their understanding of fractions. They
compare decimals using models and number sense.
13Measurement: Find Equivalence in Units of Measure
In Topic 13, students make measurement conversions within
the same measurement system.
14Algebra: Generate and Analyze Patterns
In Topic 14, students generate and analyze patterns that
grow or repeat in predictable ways.
15Geometric Measurement: Understand Concepts of Angles and
Angle Measurement
In Topic 15, students develop an understanding of angles.
They use unit angles to measure and draw angles, and to
add and subtract angle measures.
16Lines, Angles, and Shapes
In Topic 16, students classify two-dimensional shapes by their
sides and angles. They analyze and draw shapes with line
symmetry.
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1
16
TOPIC 1 Generalize Place Value
Understanding
2
15
14
3
13
4
GRADE 4
12
11
Planner.................................................................................................1I
Math and Science Project.........................................................................1
Review What You Know....................................................................... 2–4
Vocabulary Cards and Activities............................................................ 2–4
5
10
1–1
Numbers Through One Million . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5A
1–2
Place Value Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11A
1–3
Compare Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17A
1–4
Round Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23A
1–5
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29A
Construct Arguments
6
9
7
8
In Topic 1, students expand their place-value
understandings from numbers to 1,000 (Grade 3)
to 1,000,000 (Grade 4).
TOPIC 1 OVERVIEW
Math Background: Focus.................................................1A
Math Background: Coherence....................................... 1C
Math Background: Rigor...................................................1E
Problem Solving..................................................................1F
Differentiated Instruction................................................1G
The Language of Math.....................................................1H
Fluency Practice Activity.........................................................................35
Vocabulary Review...............................................................................36
Reteaching...........................................................................................37
Topic Assessment............................................................................. 39–40
Topic Performance Assessment.......................................................... 41–42
Placement Test....................................................................................42B
Basic-Facts Timed Tests........................................................................ 42D
This shows how
to find the values
of the digits in
a number.
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Contents
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1
16
TOPIC 2 Fluently Add and Subtract
Multi-Digit Whole Numbers
2
15
14
3
13
4
GRADE 4
12
11
5
10
6
9
8
7
In Topics 2–5, students create and explore
strategies for performing multi-digit calculations
that involve breaking numbers apart using
place value.
TOPICS 2–5 OVERVIEW
Math Background: Focus...............................................43A
Math Background: Coherence.....................................43C
Math Background: Rigor................................................ 43E
Problem Solving............................................................... 43F
Differentiated Instruction............................................. 43G
The Language of Math.................................................. 43H
Planner...............................................................................................43I
Steps to Fluency Success.......................................................................43K
Math and Science Project.......................................................................43
Review What You Know................................................................... 44–46
Vocabulary Cards and Activities........................................................ 44–46
2–1
Mental Math: Find Sums and Differences . . . . . . . . . . . . . . . . . . . . . . . . 47A
2–2
Mental Math: Estimate Sums and Differences . . . . . . . . . . . . . . . . . . . 53A
2–3
Add Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A
2–4
Subtract Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65A
2–5
Subtract Across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71A
2–6
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77A
Reasoning
Fluency Practice Activity.........................................................................83
Vocabulary Review...............................................................................84
Reteaching...........................................................................................85
Topic Assessment............................................................................. 87–88
Topic Performance Assessment.......................................................... 89–90
This shows one
way to add whole
numbers.
1 1
9,263
+ 7,951
17,214
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1
16
TOPIC 3 Use Strategies and Properties to
Multiply by 1-Digit Numbers
2
15
14
3
13
4
GRADE 4
12
11
5
10
3–1
Mental Math: Multiply by Multiples of 10, 100, and 1,000 . . . . . . . 95A
3–2
Mental Math: Round to Estimate Products . . . . . . . . . . . . . . . . . . . . . 101A
3–3
The Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107A
3–4
Mental Math Strategies for Multiplication . . . . . . . . . . . . . . . . . . . . . . 113A
3–5
Arrays and Partial Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119A
3–6
Use Partial Products to Multiply by 1-Digit Numbers . . . . . . . . . . . 125A
3–7
Multiply 2- and 3-Digit Numbers by 1-Digit Numbers . . . . . . . . . . 131A
3–8
Multiply 4-Digit by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A
3–9
Multiply by 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143A
3–10
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149A
Model with Math
6
9
8
7
In Topics 2–5, students create and explore
strategies for performing multi-digit calculations
that involve breaking numbers apart using
place value.
TOPICS 2–5 OVERVIEW
Math Background: Focus...............................................43A
Math Background: Coherence.....................................43C
Math Background: Rigor................................................ 43E
Problem Solving............................................................... 43F
Differentiated Instruction............................................. 43G
The Language of Math.................................................. 43H
This shows how to
use partial products
to multiply.
6 hundreds 12 tens 15 ones
245
× 3
15
120
+ 600
735
F8
Planner............................................................................................. 91A
Math and Science Project.......................................................................91
Review What You Know................................................................... 92–94
Vocabulary Cards and Activities........................................................ 92–94
Fluency Practice Activity.......................................................................155
Vocabulary Review.............................................................................156
Reteaching................................................................................. 157–158
Topic Assessment......................................................................... 161–162
Topic Performance Assessment...................................................... 165–166
Partial
products
Contents
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16
TOPIC 4 Use Strategies and Properties to
Multiply by 2-Digit Numbers
2
15
14
3
13
4
GRADE 4
12
11
Planner........................................................................................... 167A
Math and Science Project.....................................................................167
Review What You Know............................................................... 168–170
Vocabulary Cards and Activities.................................................... 168–170
5
10
4–1
Mental Math: Multiply Multiples of 10 . . . . . . . . . . . . . . . . . . . . . . . . . . 171A
4–2
Use Models to Multiply 2-Digit Numbers by Multiples of 10 . . . . 177A
4–3
Estimate: Use Rounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183A
4–4
Estimate: Use Compatible Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189A
4–5
Arrays and Partial Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195A
4–6
Multiply Using the Distributive Property . . . . . . . . . . . . . . . . . . . . . . . 201A
4–7
Use Partial Products to Multiply by 2-Digit Numbers . . . . . . . . . . . 207A
4–8
Multiply 2-Digit Numbers by Multiples of 10 . . . . . . . . . . . . . . . . . . . 213A
4–9
Multiply 2-Digit by 2-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219A
4–10
Continue to Multiply by 2-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . 225A
4–11
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231A
Make Sense and Persevere
6
9
8
7
In Topics 2–5, students create and explore
strategies for performing multi-digit calculations
that involve breaking numbers apart using
place value.
TOPICS 2–5 OVERVIEW
Math Background: Focus...............................................43A
Math Background: Coherence.....................................43C
Math Background: Rigor................................................ 43E
Problem Solving............................................................... 43F
Differentiated Instruction............................................. 43G
The Language of Math.................................................. 43H
This shows how
you can represent
partial products
to help multiply.
10 3 5 5 50
10 3 10 5 100
15
Fluency Practice Activity.......................................................................237
Vocabulary Review.............................................................................238
Reteaching................................................................................. 239–240
Topic Assessment......................................................................... 243–244
Topic Performance Assessment...................................................... 247–248
Cumulative/Benchmark Assessment Topics 1–4.....................................248B
12
2 3 10 5 20
2 3 5 5 10
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16
TOPIC 5 Use Strategies and Properties to
Divide by 1-Digit Numbers
2
15
14
3
13
4
GRADE 4
12
11
5
10
5–1
Mental Math: Find Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253A
5–2
Mental Math: Estimate Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259A
5–3
Mental Math: Estimate Quotients for Greater Dividends . . . . . . . 265A
5–4
Interpret Remainders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271A
5–5
Division as Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277A
5–6
Use Partial Quotients to Divide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283A
5–7
Use Partial Quotients to Divide: Greater Dividends . . . . . . . . . . . . 289A
5–8
Divide with 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295A
5–9
Continue to Divide with 1-Digit Numbers . . . . . . . . . . . . . . . . . . . . . . 301A
5–10
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307A
Model with Math
6
9
8
7
In Topics 2–5, students create and explore
strategies for performing multi-digit calculations
that involve breaking numbers apart using
place value.
TOPICS 2–5 OVERVIEW
Math Background: Focus...............................................43A
Math Background: Coherence.....................................43C
Math Background: Rigor................................................ 43E
Problem Solving............................................................... 43F
Differentiated Instruction............................................. 43G
The Language of Math.................................................. 43H
This shows how
place value can
help you divide.
13 R3
4) 55
-4
15
- 12
3
F10
Planner........................................................................................... 249A
Math and Science Project.....................................................................249
Review What You Know............................................................... 250–252
Vocabulary Cards and Activities.................................................... 250–252
Fluency Practice Activity.......................................................................313
Vocabulary Review.............................................................................314
Reteaching................................................................................. 315–316
Topic Assessment......................................................................... 319–320
Topic Performance Assessment...................................................... 323–324
Contents
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16
TOPIC 6 Use Operations with Whole
Numbers to Solve Problems
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................325I
Math and Science Project.....................................................................325
Review What You Know.......................................................................326
Vocabulary Activities...........................................................................326
5
10
6–1
Solve Comparison Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327A
6–2
Continue to Solve Comparison Situations . . . . . . . . . . . . . . . . . . . . . . 333A
6–3
Solve Multi-Step Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339A
6–4
Solve More Multi-Step Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345A
6–5
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351A
Make Sense and Persevere
6
9
8
7
In Topic 6, students are introduced to
multiplicative comparison situations. They use
understandings of operations to solve multi-step
problems.
TOPIC 6 OVERVIEW
Math Background: Focus............................................325A
Math Background: Coherence.................................. 325C
Math Background: Rigor..............................................325E
Problem Solving.............................................................325F
Differentiated Instruction...........................................325G
The Language of Math................................................325H
Fluency Practice Activity.......................................................................357
Vocabulary Review.............................................................................358
Reteaching.........................................................................................359
Topic Assessment......................................................................... 361–362
Topic Performance Assessment...................................................... 363–364
This shows how
you can represent a
comparison situation.
42
3
n times as many
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1
16
TOPIC 7 Factors and Multiples
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................365I
Math and Science Project.....................................................................365
Review What You Know............................................................... 366–368
Vocabulary Cards and Activities.................................................... 366–368
7–1
Understand Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369A
7–2
Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375A
7–3
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381A
Repeated Reasoning
7–4
Prime and Composite Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387A
7–5
Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393A
5
10
6
9
8
7
In Topic 7, students represent, analyze, and
classify numbers using understandings of
multiplication.
TOPIC 7 OVERVIEW
Math Background: Focus............................................365A
Math Background: Coherence.................................. 365C
Math Background: Rigor..............................................365E
Problem Solving.............................................................365F
Differentiated Instruction...........................................365G
The Language of Math................................................365H
Fluency Practice Activity.......................................................................399
Vocabulary Review.............................................................................400
Reteaching.........................................................................................401
Topic Assessment......................................................................... 403–404
Topic Performance Assessment...................................................... 405–406
This shows how
you can use arrays
to model factor pairs
for a number.
F12
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16
TOPIC 8 Extend Understanding of
Fraction Equivalence and Ordering
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................407I
Math and Science Project.....................................................................407
Review What You Know............................................................... 408–410
Vocabulary Cards and Activities.................................................... 408–410
5
10
8–1
Equivalent Fractions: Area Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411A
8–2
Equivalent Fractions: Number Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417A
8–3
Generate Equivalent Fractions: Multiplication . . . . . . . . . . . . . . . . . 423A
8–4
Generate Equivalent Fractions: Division . . . . . . . . . . . . . . . . . . . . . . . . 429A
8–5
Use Benchmarks to Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . . . 435A
8–6
Compare Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441A
8–7
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447A
Construct Arguments
6
9
7
8
In Topic 8, students use models and mathematical
procedures to understand, recognize, and
generate equivalent fractions.
TOPIC 8 OVERVIEW
Math Background: Focus............................................407A
Math Background: Coherence.................................. 407C
Math Background: Rigor..............................................407E
Problem Solving.............................................................407F
Differentiated Instruction...........................................407G
The Language of Math................................................407H
Fluency Practice Activity.......................................................................453
Vocabulary Review.............................................................................454
Reteaching.........................................................................................455
Topic Assessment......................................................................... 457–458
Topic Performance Assessment...................................................... 459–460
Cumulative/Benchmark Assessment Topics 1–8.....................................460B
This shows how
fraction strips can
be used to determine
equivalent fractions.
1
1
4
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
8
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1
16
TOPIC 9 Understand Addition and
Subtraction of Fractions
2
15
14
3
13
4
GRADE 4
12
11
5
10
In Topics 9–10, students use their understanding
of unit fractions to add and subtract fractions with
like denominators and multiply a fraction by a
whole number.
TOPICS 9 AND 10 OVERVIEW
Math Background: Focus............................................461A
Math Background: Coherence.................................. 461C
Math Background: Rigor..............................................461E
Problem Solving.............................................................461F
Differentiated Instruction...........................................461G
The Language of Math................................................461H
This shows how you
can use fraction strips
to model the addition
of fractions.
F12B
1
10
9–2
Decompose Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471A
9–3
Add Fractions with Like Denominators . . . . . . . . . . . . . . . . . . . . . . . . . 477A
9–4
Model Subtraction of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483A
9–5
Subtract Fractions with Like Denominators . . . . . . . . . . . . . . . . . . . . 489A
9–6
Add and Subtract Fractions with Like Denominators . . . . . . . . . . . 495A
9–7
Estimate Fraction Sums and Differences . . . . . . . . . . . . . . . . . . . . . . . . 501A
9–8
Model Addition and Subtraction of Mixed Numbers . . . . . . . . . . . 507A
9–9
Add Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513A
9–10
Subtract Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519A
9–11
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525A
Model with Math
Fluency Practice Activity.......................................................................531
Vocabulary Review.............................................................................532
Reteaching.........................................................................................533
Topic Assessment......................................................................... 535–536
Topic Performance Assessment...................................................... 537–538
1
1
10
Model Addition of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465A
7
8
1
10
9–1
6
9
1
10
Planner.............................................................................................461I
Math and Science Project.....................................................................461
Review What You Know............................................................... 462–464
Vocabulary Cards and Activities.................................................... 462–464
1
10
1
10
1
10
Contents
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TOPIC 10 Extend Multiplication
Concepts to Fractions
2
15
14
3
13
4
GRADE 4
12
11
Planner........................................................................................... 539A
Math and Science Project.....................................................................539
Review What You Know............................................................... 540–542
Vocabulary Cards and Activities.................................................... 540–542
5
10
10–1
Fractions as Multiples of Unit Fractions: Use Models . . . . . . . . . . . 543A
10–2
Multiply a Fraction by a Whole Number: Use Models . . . . . . . . . . . 549A
10–3
Multiply a Fraction by a Whole Number: Use Symbols . . . . . . . . . . 555A
10–4
Multiply a Whole Number and a Mixed Number . . . . . . . . . . . . . . . . 561A
10–5
Solve Time Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567A
10–6
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573A
Model with Math
6
9
7
8
In Topics 9–10, students use their understanding
of unit fractions to add and subtract fractions with
like denominators and multiply a fraction by a
whole number.
TOPICS 9 AND 10 OVERVIEW
Math Background: Focus............................................461A
Math Background: Coherence.................................. 461C
Math Background: Rigor..............................................461E
Problem Solving.............................................................461F
Differentiated Instruction...........................................461G
The Language of Math................................................461H
Fluency Practice Activity.......................................................................579
Vocabulary Review.............................................................................580
Reteaching.........................................................................................581
Topic Assessment......................................................................... 583–584
Topic Performance Assessment...................................................... 585–586
You can use a number
line to help multiply
fractions and
whole numbers.
0
3
0
1
3
2
3
3
3
4
3
5
3
1
6
3
2
1×4=4
3
3
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TOPIC 11 Represent and Interpret Data
on Line Plots
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................587I
Math and Science Project.....................................................................587
Review What You Know............................................................... 588–590
Vocabulary Cards and Activities.................................................... 588–590
5
10
11–1
Read Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591A
11–2
Make Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597A
11–3
Use Line Plots to Solve Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603A
11–4
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609A
Critique Reasoning
6
9
8
7
In Topic 11, students represent data visually using
line plots. Some data involve fractions and mixed
numbers.
TOPIC 11 OVERVIEW
Math Background: Focus............................................587A
Math Background: Coherence.................................. 587C
Math Background: Rigor..............................................587E
Problem Solving.............................................................587F
Differentiated Instruction...........................................587G
The Language of Math................................................587H
Fluency Practice Activity.......................................................................615
Vocabulary Review.............................................................................616
Reteaching.........................................................................................617
Topic Assessment......................................................................... 619–620
Topic Performance Assessment...................................................... 621–622
This shows how
to create and use
a line plot to solve
problems.
5
F12D
10
15
20
Contents
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TOPIC 12 Understand and Compare
Decimals
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................623I
Math and Science Project.....................................................................623
Review What You Know............................................................... 624–626
Vocabulary Cards and Activities.................................................... 624–626
5
10
12–1
Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627A
12–2
Fractions and Decimals on the Number Line . . . . . . . . . . . . . . . . . . . 633A
12–3
Compare Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639A
12–4
Add Fractions with Denominators of 10 and 100 . . . . . . . . . . . . . . . 645A
12–5
Solve Word Problems Involving Money . . . . . . . . . . . . . . . . . . . . . . . . . 651A
12–6
12–6
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657A
Look For and Use Structure
6
9
8
7
In Topic 12, students learn the meaning of
a decimal number by connecting to their
understanding of fractions. They compare
decimals using models and number sense.
TOPIC 12 OVERVIEW
Math Background: Focus............................................623A
Math Background: Coherence.................................. 623C
Math Background: Rigor..............................................623E
Problem Solving.............................................................623F
Differentiated Instruction...........................................623G
The Language of Math................................................623H
Fluency Practice Activity.......................................................................663
Vocabulary Review.............................................................................664
Reteaching.........................................................................................665
Topic Assessment......................................................................... 667–668
Topic Performance Assessment...................................................... 669–670
Cumulative/Benchmark Assessment Topics 1–12...................................670B
This shows how to
represent 1.64 or
64
1 100
using grids.
64
1.64 = 1100
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TOPIC 13 Measurement: Find
Equivalence in Units of Measure
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................671I
Math and Science Project.....................................................................671
Review What You Know.......................................................................672
Vocabulary Cards and Activities.................................................... 673–674
5
10
13–1
Equivalence with Customary Units of Length . . . . . . . . . . . . . . . . . . . 679A
13–2
Equivalence with Customary Units of Capacity . . . . . . . . . . . . . . . . . 685A
13–3
Equivalence with Customary Units of Weight . . . . . . . . . . . . . . . . . . . 691A
13–4
Equivalence with Metric Units of Length . . . . . . . . . . . . . . . . . . . . . . . 697A
13–5
Equivalence with Metric Units of Capacity and Mass . . . . . . . . . . . 703A
13–6
Solve Perimeter and Area Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709A
13–7
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715A
Precision
6
9
8
7
In Topic 13, students make measurement
conversions within the same measurement system.
TOPIC 13 OVERVIEW
Math Background: Focus............................................671A
Math Background: Coherence.................................. 671C
Math Background: Rigor..............................................671E
Problem Solving.............................................................671F
Differentiated Instruction...........................................671G
The Language of Math................................................671H
Fluency Practice Activity.......................................................................721
Vocabulary Review.............................................................................722
Reteaching.........................................................................................723
Topic Assessment......................................................................... 725–726
Topic Performance Assessment...................................................... 727–728
This shows how
metric units are
related.
DATA
Metric Units of Length
1 m = 1,000 mm
1 cm = 10 mm
1 m = 100 cm
1 km = 1,000 m
F12F
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16
TOPIC 14 Algebra: Generate and Analyze
Patterns
2
15
14
3
13
4
GRADE 4
12
Planner.............................................................................................729I
Math and Science Project.....................................................................729
Review What You Know............................................................... 730–732
Vocabulary Cards and Activities.................................................... 730–732
11
5
10
14–1
Number Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733A
14–2
Patterns: Number Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739A
14–3
Patterns: Repeating Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745A
14–4
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751A
Look For and Use Structure
6
9
7
8
In Topic 14, students generate and analyze
patterns that grow or repeat in predictable ways.
TOPIC 14 OVERVIEW
Math Background: Focus............................................729A
Math Background: Coherence.................................. 729C
Math Background: Rigor..............................................729E
Problem Solving.............................................................729F
Differentiated Instruction...........................................729G
The Language of Math................................................729H
Fluency Practice Activity.......................................................................757
Vocabulary Review.............................................................................758
Reteaching.........................................................................................759
Topic Assessment......................................................................... 761–762
Topic Performance Assessment...................................................... 763–764
This shows how
to use a rule to
generate a pattern.
Rule: Add 7
+7
7
+7
14
+7
21
+7
28
35
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TOPIC 15 Geometric Measurement:
Understand Concepts of Angles and
Angle Measurement
2
15
14
3
13
4
GRADE 4
12
11
5
10
6
9
7
8
In Topic 15, students develop an understanding of
angles. They use unit angles to measure and draw
angles, and to add and subtract angle measures.
TOPIC 15 OVERVIEW
Math Background: Focus............................................765A
Math Background: Coherence.................................. 765C
Math Background: Rigor..............................................765E
Problem Solving.............................................................765F
Differentiated Instruction...........................................765G
The Language of Math................................................765H
Planner.............................................................................................765I
Math and Science Project.....................................................................765
Review What You Know.......................................................................766
Vocabulary Cards and Activities.................................................... 767–768
15–1
Lines, Rays, and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771A
15–2
Understand Angles and Unit Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777A
15–3
Measure with Unit Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783A
15–4
Measure and Draw Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789A
15–5
Add and Subtract Angle Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795A
15–6
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801A
Use Appropriate Tools
Fluency Practice Activity.......................................................................807
Vocabulary Review.............................................................................808
Reteaching.........................................................................................809
Topic Assessment......................................................................... 811–812
Topic Performance Assessment...................................................... 813–814
This shows how
to measure and
draw angles.
0
15
30
40
160
20
T
170
10
10
20
170 1
60
100
110
12
80
70
0
13
60
0
50
0
F12H
80
70
0 90
60 110 10
0
2
1
14
30
15
40
0
14
0
W
U
Contents
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16
TOPIC 16 Lines, Angles, and Shapes
2
15
14
3
13
4
GRADE 4
12
11
Planner.............................................................................................815I
Math and Science Project.....................................................................815
Review What You Know.......................................................................816
Vocabulary Cards and Activities.................................................... 817–818
16–1
Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821A
16–2
Classify Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827A
16–3
Classify Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833A
16–4
Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839A
16–5
Draw Shapes with Line Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845A
16–6
PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851A
Critique Reasoning
5
10
6
9
8
7
In Topic 16, students classify two-dimensional
shapes by their sides and angles. They analyze
and draw shapes with line symmetry.
TOPIC 16 OVERVIEW
Math Background: Focus............................................815A
Math Background: Coherence.................................. 815C
Math Background: Rigor..............................................815E
Problem Solving.............................................................815F
Differentiated Instruction...........................................815G
The Language of Math................................................815H
Fluency Practice Activity.......................................................................857
Vocabulary Review.............................................................................858
Reteaching.........................................................................................859
Topic Assessment......................................................................... 861–862
Topic Performance Assessment...................................................... 863–864
Cumulative/Benchmark Assessment Topics 1–16...................................864B
End-of-Year Assessment.................................................................... 864D
This shows how to
draw lines of symmetry
in a figure.
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