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By TopicBy Standard
Grade 3Grade 4
  • 4.NF.1
  • 4.NF.2
  • 4.NF.3a
  • 4.NF.3b
  • 4.NF.3c
  • 4.NF.3d
  • 4.NF.4a
  • 4.NF.4b
  • 4.NF.4c
  • 4.NF.5
  • 4.NF.6
  • 4.NF.7
Grade 5Grade 6Grade 7
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Grade 4 - 4.NF - Number and Operations - Fractions

4.NF.1

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Model an Equivalent Fraction

4.NF.1 practice problems model an equivalent fraction
Fraction bar digital manipulative indicator
4.NF.1 practice problems model an equivalent fraction
Fraction bar digital manipulative indicator

Cutting Pieces to Build Equivalents

4.NF.1 practice problems cutting pieces to build equivalents
Fraction circle digital manipulative indicator
4.NF.1 practice problems cutting pieces to build equivalents
Fraction bar digital manipulative indicator

Gluing Pieces to Build Equivalents

4.NF.1 practice problems gluing pieces to build equivalents
Fraction circle digital manipulative indicator
4.NF.1 practice problems gluing pieces to build equivalents
Fraction bar digital manipulative indicator

Finding Equivalent Fractions Using Models

4.NF.1 practice problems finding equivalent fractions using models
Fraction bar digital manipulative indicator
4.NF.1 practice problems finding equivalent fractions using models
Fraction bar digital manipulative indicator

Modeling the Algorithm for Relating Equivalents

4.NF.1 practice problems modeling the algorithm for relating equivalents
Fraction bar digital manipulative indicator
4.NF.1 practice problems modeling the algorithm for relating equivalents
Fraction bar digital manipulative indicator

Finding Equivalent Fractions

4.NF.1 practice problems finding equivalent fractions
4.NF.1 practice problems finding equivalent fractions

Equivalence on the Number Line

4.NF.1 practice problems equivalence on the number line
Number line digital manipulative indicator
4.NF.1 practice problems equivalence on the number line
Number line digital manipulative indicator

Identifying Equivalent Fractions

4.NF.1 practice problems identifying equivalent fractions
4.NF.1 practice problems identifying equivalent fractions

Building Equivalents

4.NF.1 practice problems building equivalents
Fraction bar digital manipulative indicator
4.NF.1 practice problems building equivalents
Fraction bar digital manipulative indicator

One Half of Shapes and Sets

4.NF.1 practice problems one half of shapes and sets
4.NF.1 practice problems one half of shapes and sets
Set digital manipulative indicator

One Fourth of Shapes and Sets

4.NF.1 practice problems one fourth of shapes and sets
4.NF.1 practice problems one fourth of shapes and sets
4.NF.1 practice problems one fourth of shapes and sets
Set digital manipulative indicator

One Third of Shapes and Sets

4.NF.1 practice problems one third of shapes and sets
4.NF.1 practice problems one third of shapes and sets
Set digital manipulative indicator

Equivalent Fractions in Partitioning Sets.

4.NF.1 practice problems equivalent fractions in partitioning sets.
Set digital manipulative indicator
4.NF.1 practice problems equivalent fractions in partitioning sets.
Set digital manipulative indicator

Introduction to Simplifying

4.NF.1 practice problems introduction to simplifying
Fraction circle digital manipulative indicator
4.NF.1 practice problems introduction to simplifying
Fraction bar digital manipulative indicatorNumber line digital manipulative indicator

Simplifying in Context

4.NF.1 practice problems simplifying in context

Simplifying Fractions Using Models

4.NF.1 practice problems simplifying fractions using models
4.NF.1 practice problems simplifying fractions using models

Modeling Fractions in Simplest Form

4.NF.1 practice problems modeling fractions in simplest form
Fraction bar digital manipulative indicator
4.NF.1 practice problems modeling fractions in simplest form
Fraction bar digital manipulative indicator

Simplifying with Models and Symbols

4.NF.1 practice problems simplifying with models and symbols
Fraction bar digital manipulative indicator
4.NF.1 practice problems simplifying with models and symbols

Simplifying Given Fractions

4.NF.1 practice problems simplifying given fractions

4.NF.2

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Ordering Fractions

4.NF.2 practice problems ordering fractions
4.NF.2 practice problems ordering fractions

Comparing Fractions to Benchmark 1/2

4.NF.2 practice problems comparing fractions to benchmark 1/2
Fraction bar digital manipulative indicator
4.NF.2 practice problems comparing fractions to benchmark 1/2
Fraction bar digital manipulative indicator
4.NF.2 practice problems comparing fractions to benchmark 1/2
Fraction bar digital manipulative indicator
4.NF.2 practice problems comparing fractions to benchmark 1/2
4.NF.2 practice problems comparing fractions to benchmark 1/2
4.NF.2 practice problems comparing fractions to benchmark 1/2
4.NF.2 practice problems comparing fractions to benchmark 1/2
4.NF.2 practice problems comparing fractions to benchmark 1/2

Ordering Multiple Fractions

4.NF.2 practice problems ordering multiple fractions
4.NF.2 practice problems ordering multiple fractions
4.NF.2 practice problems ordering multiple fractions

4.NF.3a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Adding Fractions with Like Denominators

4.NF.3a practice problems adding fractions with like denominators
Fraction circle digital manipulative indicator
4.NF.3a practice problems adding fractions with like denominators
Fraction circle digital manipulative indicator

Completing Addition Sentences

4.NF.3a practice problems completing addition sentences
4.NF.3a practice problems completing addition sentences

Sums Greater Than 1 Using Models

4.NF.3a practice problems sums greater than 1 using models
Fraction bar digital manipulative indicator

Subtracting Fractions with Like Denominators

4.NF.3a practice problems subtracting fractions with like denominators
Fraction bar digital manipulative indicator
4.NF.3a practice problems subtracting fractions with like denominators
Fraction bar digital manipulative indicator

Completing Subtraction Sentences

4.NF.3a practice problems completing subtraction sentences
4.NF.3a practice problems completing subtraction sentences

Introduction to Addition of Fractions

4.NF.3a practice problems introduction to addition of fractions
Fraction bar digital manipulative indicator
4.NF.3a practice problems introduction to addition of fractions
Fraction circle digital manipulative indicator

Review Adding with Like Denominators

4.NF.3a practice problems review adding with like denominators
Fraction circle digital manipulative indicator
4.NF.3a practice problems review adding with like denominators
Fraction bar digital manipulative indicator

Subtracting with Like Denominators in Context

4.NF.3a practice problems subtracting with like denominators in context
Fraction circle digital manipulative indicator
4.NF.3a practice problems subtracting with like denominators in context
Fraction circle digital manipulative indicator

Review Subtracting with Like Denominators

4.NF.3a practice problems review subtracting with like denominators
Fraction bar digital manipulative indicator
4.NF.3a practice problems review subtracting with like denominators
Fraction circle digital manipulative indicator

4.NF.3b

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Mixed Numbers and Improper Fractions on a Number Line

4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers and improper fractions on a number line
Number line digital manipulative indicator

Modeling Mixed and Improper Fractions

4.NF.3b practice problems modeling mixed and improper fractions
Fraction circle digital manipulative indicator
4.NF.3b practice problems modeling mixed and improper fractions
Fraction circle digital manipulative indicator

Mixed Numbers on the Number Line

4.NF.3b practice problems mixed numbers on the number line
Number line digital manipulative indicator
4.NF.3b practice problems mixed numbers on the number line
Number line digital manipulative indicator

Improper Fractions on the Number Line

4.NF.3b practice problems improper fractions on the number line
Number line digital manipulative indicator
4.NF.3b practice problems improper fractions on the number line
Number line digital manipulative indicator

Mixed and Improper Fractions in Context

4.NF.3b practice problems mixed and improper fractions in context
Fraction circle digital manipulative indicator

Mixed to and from Improper with Simplifying

4.NF.3b practice problems mixed to and from improper with simplifying
4.NF.3b practice problems mixed to and from improper with simplifying

4.NF.3c

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Adding Whole Numbers and Fractions

4.NF.3c practice problems adding whole numbers and fractions
Fraction circle digital manipulative indicator
4.NF.3c practice problems adding whole numbers and fractions

Adding Mixed Numbers and Fractions Using Models

4.NF.3c practice problems adding mixed numbers and fractions using models
Fraction bar digital manipulative indicator

Adding Simple Mixed Numbers

4.NF.3c practice problems adding simple mixed numbers
4.NF.3c practice problems adding simple mixed numbers

Subtracting Fractions from Mixed Numbers

4.NF.3c practice problems subtracting fractions from mixed numbers
Fraction circle digital manipulative indicator
4.NF.3c practice problems subtracting fractions from mixed numbers

Subtracting Simple Mixed Numbers

4.NF.3c practice problems subtracting simple mixed numbers
4.NF.3c practice problems subtracting simple mixed numbers

Subtracting Mixed Numbers and Proper Fractions with Borrowing

4.NF.3c practice problems subtracting mixed numbers and proper fractions with borrowing
4.NF.3c practice problems subtracting mixed numbers and proper fractions with borrowing

4.NF.3d

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Sums Greater Than 1 Using Number Line

4.NF.3d practice problems sums greater than 1 using number line
Number line digital manipulative indicator

Adding Mixed Numbers and Fractions Using Number Line

4.NF.3d practice problems adding mixed numbers and fractions using number line
Number line digital manipulative indicator

Subtracting Fractions from Whole Numbers

4.NF.3d practice problems subtracting fractions from whole numbers
4.NF.3d practice problems subtracting fractions from whole numbers

4.NF.4a

Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

Multiplication of a Fraction by a Whole Number

4.NF.4a practice problems multiplication of a fraction by a whole number
Fraction circle digital manipulative indicator
4.NF.4a practice problems multiplication of a fraction by a whole number
Fraction circle digital manipulative indicator

Multiplication of Unit Fractions Using Number Line

4.NF.4a practice problems multiplication of unit fractions using number line
Number line digital manipulative indicator

4.NF.4b

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

Multiplication of Fractions Using Models

4.NF.4b practice problems multiplication of fractions using models
Fraction circle digital manipulative indicator
4.NF.4b practice problems multiplication of fractions using models

4.NF.4c

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Multiplication of a Whole Number by a Fraction Using Sets

4.NF.4c practice problems multiplication of a whole number by a fraction using sets
Set digital manipulative indicator
4.NF.4c practice problems multiplication of a whole number by a fraction using sets

Multiplication of a Whole Number by a Fraction Using Number Line

4.NF.4c practice problems multiplication of a whole number by a fraction using number line
Number line digital manipulative indicator
4.NF.4c practice problems multiplication of a whole number by a fraction using number line
Number line digital manipulative indicator

Multiplication of a Fraction by a Whole Number Using Models

4.NF.4c practice problems multiplication of a fraction by a whole number using models

Multiplication of a Fraction by a Whole Number with Number Lines

4.NF.4c practice problems multiplication of a fraction by a whole number with number lines
Number line digital manipulative indicator
4.NF.4c practice problems multiplication of a fraction by a whole number with number lines
Number line digital manipulative indicator

Choosing a Strategy for Multiplying Whole Numbers by Fractions

4.NF.4c practice problems choosing a strategy for multiplying whole numbers by fractions
4.NF.4c practice problems choosing a strategy for multiplying whole numbers by fractions

4.NF.5

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Naming Models as Decimals

4.NF.5 practice problems naming models as decimals
Base ten block digital manipulative indicator
4.NF.5 practice problems naming models as decimals
Base ten block digital manipulative indicator

Building Tenths from Hundredths

4.NF.5 practice problems building tenths from hundredths
Base ten block digital manipulative indicator
4.NF.5 practice problems building tenths from hundredths
Base ten block digital manipulative indicator

Comparing Models to the Benchmark 1/2

4.NF.5 practice problems comparing models to the benchmark 1/2
Base ten block digital manipulative indicator
4.NF.5 practice problems comparing models to the benchmark 1/2
Base ten block digital manipulative indicator

Decomposing Decimals

4.NF.5 practice problems decomposing decimals
Base ten block digital manipulative indicator

Breaking Tenths into Hundredths

4.NF.5 practice problems breaking tenths into hundredths
Base ten block digital manipulative indicator
4.NF.5 practice problems breaking tenths into hundredths
Base ten block digital manipulative indicator

Decomposing Decimals into Fractions on the Number Line

4.NF.5 practice problems decomposing decimals into fractions on the number line
Number line digital manipulative indicator

4.NF.6

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Introducing Tenths on the 1x10 Grid

4.NF.6 practice problems introducing tenths on the 1x10 grid
Base ten block digital manipulative indicator
4.NF.6 practice problems introducing tenths on the 1x10 grid
Base ten block digital manipulative indicator

Tenths Expressed as Decimals

4.NF.6 practice problems tenths expressed as decimals
Base ten block digital manipulative indicator
4.NF.6 practice problems tenths expressed as decimals
Base ten block digital manipulative indicator

Introducing Hundredths on the 10x10 Grid

4.NF.6 practice problems introducing hundredths on the 10x10 grid
Base ten block digital manipulative indicator
4.NF.6 practice problems introducing hundredths on the 10x10 grid
Base ten block digital manipulative indicator

Hundredths Expressed as Decimals

4.NF.6 practice problems hundredths expressed as decimals
Base ten block digital manipulative indicator

Composing and Writing Decimals

4.NF.6 practice problems composing and writing decimals
Base ten block digital manipulative indicator
4.NF.6 practice problems composing and writing decimals
Base ten block digital manipulative indicator

Locating Tenths on the Number Line

4.NF.6 practice problems locating tenths on the number line
Number line digital manipulative indicator
4.NF.6 practice problems locating tenths on the number line
Number line digital manipulative indicator

Measuring Tenths on the Number Line

4.NF.6 practice problems measuring tenths on the number line
Number line digital manipulative indicator
4.NF.6 practice problems measuring tenths on the number line
Number line digital manipulative indicator

Labeling Tenths on the Number Line

4.NF.6 practice problems labeling tenths on the number line
Number line digital manipulative indicator
4.NF.6 practice problems labeling tenths on the number line
Number line digital manipulative indicator

Composing Decimals on the Number Line

4.NF.6 practice problems composing decimals on the number line
Number line digital manipulative indicator
4.NF.6 practice problems composing decimals on the number line
Number line digital manipulative indicator

Locating Hundredths on the Number Line

4.NF.6 practice problems locating hundredths on the number line
Number line digital manipulative indicator
4.NF.6 practice problems locating hundredths on the number line
Number line digital manipulative indicator

Labeling Hundredths on the Number Line

4.NF.6 practice problems labeling hundredths on the number line
Number line digital manipulative indicator
4.NF.6 practice problems labeling hundredths on the number line
Number line digital manipulative indicator

Comparing Decimals on the Number Line

4.NF.6 practice problems comparing decimals on the number line
Number line digital manipulative indicator
4.NF.6 practice problems comparing decimals on the number line
Number line digital manipulative indicator

Ordering Decimals on the Number Line

4.NF.6 practice problems ordering decimals on the number line
Number line digital manipulative indicator
4.NF.6 practice problems ordering decimals on the number line
Number line digital manipulative indicator

4.NF.7

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Relative Size of Hundredths

4.NF.7 practice problems relative size of hundredths
Base ten block digital manipulative indicator

Solidifying Place Value with Models

4.NF.7 practice problems solidifying place value with models
Base ten block digital manipulative indicator

Solidifying Place Value without Models

4.NF.7 practice problems solidifying place value without models
4.NF.7 practice problems solidifying place value without models

Estimating Decimals on the Number Line

4.NF.7 practice problems estimating decimals on the number line
Number line digital manipulative indicator
4.NF.7 practice problems estimating decimals on the number line
Number line digital manipulative indicator

Comparing Decimals on the Number Line

4.NF.7 practice problems comparing decimals on the number line
Number line digital manipulative indicator
4.NF.7 practice problems comparing decimals on the number line
Number line digital manipulative indicator

Ordering Decimals on the Number Line

4.NF.7 practice problems ordering decimals on the number line
Number line digital manipulative indicator
4.NF.7 practice problems ordering decimals on the number line
Number line digital manipulative indicator