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Grade 3Grade 4Grade 5
  • 5.NBT.2
  • 5.NF.1
  • 5.NF.2
  • 5.NF.3
  • 5.NF.4a
  • 5.NF.4b
  • 5.NF.5
  • 5.NF.6
  • 5.NF.7a
  • 5.NF.7b
  • 5.NF.7c
Grade 6Grade 7
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Grade 5 - 5.NBT - Number and Operations in Base Ten

5.NBT.2

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Decimal Point Patterns

5.NBT.2 practice problems decimal point patterns
Base ten block digital manipulative indicator

Grade 5 - 5.NF - Number and Operations - Fractions

5.NF.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Completing Addition Sentences

5.NF.1 practice problems completing addition sentences
5.NF.1 practice problems completing addition sentences

Adding Fractions Using Models

5.NF.1 practice problems adding fractions using models
Fraction circle digital manipulative indicator
5.NF.1 practice problems adding fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems adding fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems adding fractions using models
Fraction bar digital manipulative indicator

Adding Fractions

5.NF.1 practice problems adding fractions
5.NF.1 practice problems adding fractions
5.NF.1 practice problems adding fractions
5.NF.1 practice problems adding fractions
5.NF.1 practice problems adding fractions
5.NF.1 practice problems adding fractions

Adding Proper Fractions Using Models

5.NF.1 practice problems adding proper fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems adding proper fractions using models

Adding Proper Fractions Using Symbols

5.NF.1 practice problems adding proper fractions using symbols
5.NF.1 practice problems adding proper fractions using symbols

Adding Mixed Numbers

5.NF.1 practice problems adding mixed numbers

Subtracting Fractions Using Models

5.NF.1 practice problems subtracting fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems subtracting fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems subtracting fractions using models
Fraction bar digital manipulative indicator
5.NF.1 practice problems subtracting fractions using models
Fraction bar digital manipulative indicator

Subtracting Fractions

5.NF.1 practice problems subtracting fractions
5.NF.1 practice problems subtracting fractions
5.NF.1 practice problems subtracting fractions
5.NF.1 practice problems subtracting fractions

Subtracting Fractions Using Number Line

5.NF.1 practice problems subtracting fractions using number line
Number line digital manipulative indicator
5.NF.1 practice problems subtracting fractions using number line
Number line digital manipulative indicator

Subtract Mixed Numbers

5.NF.1 practice problems subtract mixed numbers

Borrowing with Common Denominators on the Number Line

5.NF.1 practice problems borrowing with common denominators on the number line
Number line digital manipulative indicator

Borrowing with Uncommon Denominators

5.NF.1 practice problems borrowing with uncommon denominators
5.NF.1 practice problems borrowing with uncommon denominators

5.NF.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Estimate Sums

5.NF.2 practice problems estimate sums
Fraction circle digital manipulative indicator
5.NF.2 practice problems estimate sums
Fraction circle digital manipulative indicator

Adding Fractions in Context

5.NF.2 practice problems adding fractions in context
5.NF.2 practice problems adding fractions in context
5.NF.2 practice problems adding fractions in context
5.NF.2 practice problems adding fractions in context

Subtracting Fractions from Whole Numbers on Number Line

5.NF.2 practice problems subtracting fractions from whole numbers on number line
Number line digital manipulative indicator
5.NF.2 practice problems subtracting fractions from whole numbers on number line
Number line digital manipulative indicator

Subtracting Fractions in Context

5.NF.2 practice problems subtracting fractions in context
5.NF.2 practice problems subtracting fractions in context

5.NF.3

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Interpreting and Expressing a/b

5.NF.3 practice problems interpreting and expressing a/b
Fraction circle digital manipulative indicator
5.NF.3 practice problems interpreting and expressing a/b

Interpreting and Expressing a/b when a>b

5.NF.3 practice problems interpreting and expressing a/b when a>b
Set digital manipulative indicator
5.NF.3 practice problems interpreting and expressing a/b when a>b

Estimating Quotients of Whole Numbers

5.NF.3 practice problems estimating quotients of whole numbers
Fraction circle digital manipulative indicator
5.NF.3 practice problems estimating quotients of whole numbers
Fraction circle digital manipulative indicator

Whole Number Divisors

5.NF.3 practice problems whole number divisors
Fraction circle digital manipulative indicator
5.NF.3 practice problems whole number divisors

5.NF.4a

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

Multiplication of Whole Numbers by Mixed Numbers

5.NF.4a practice problems multiplication of whole numbers by mixed numbers
Fraction circle digital manipulative indicator

Multiplication of Mixed Numbers by Whole Numbers Using Number Lines

5.NF.4a practice problems multiplication of mixed numbers by whole numbers using number lines
Number line digital manipulative indicator

Multiplication of Fractions Using Models

5.NF.4a practice problems multiplication of fractions using models
Fraction bar digital manipulative indicator
5.NF.4a practice problems multiplication of fractions using models
Fraction circle digital manipulative indicator

Multiplication of a Fraction by a Fraction Using the Algorithm

5.NF.4a practice problems multiplication of a fraction by a fraction using the algorithm
5.NF.4a practice problems multiplication of a fraction by a fraction using the algorithm

5.NF.4b

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Multiplication of a Fraction by a Fraction Using Area Model

5.NF.4b practice problems multiplication of a fraction by a fraction using area model
5.NF.4b practice problems multiplication of a fraction by a fraction using area model
5.NF.4b practice problems multiplication of a fraction by a fraction using area model
Area model digital manipulative indicator
5.NF.4b practice problems multiplication of a fraction by a fraction using area model
Area model digital manipulative indicator

5.NF.5

Interpret multiplication as scaling (resizing), by:
  1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  2. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Multiplication as Scaling - Understanding Magnitude

5.NF.5 practice problems multiplication as scaling - understanding magnitude
5.NF.5 practice problems multiplication as scaling - understanding magnitude

5.NF.6

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Multiplication of Fractions and Mixed Numbers

5.NF.6 practice problems multiplication of fractions and mixed numbers
Fraction circle digital manipulative indicator
5.NF.6 practice problems multiplication of fractions and mixed numbers

5.NF.7a

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Modeling Unit Fractions Divided by Whole Numbers

5.NF.7a practice problems modeling unit fractions divided by whole numbers
Fraction circle digital manipulative indicator
5.NF.7a practice problems modeling unit fractions divided by whole numbers
Fraction bar digital manipulative indicator

Unit Fractions Divided by Whole Numbers on a Number Line

5.NF.7a practice problems unit fractions divided by whole numbers on a number line
Number line digital manipulative indicatorFraction bar digital manipulative indicator
5.NF.7a practice problems unit fractions divided by whole numbers on a number line
Fraction circle digital manipulative indicator

Unit Fractions Divided by Whole Numbers

5.NF.7a practice problems unit fractions divided by whole numbers
Fraction bar digital manipulative indicator
5.NF.7a practice problems unit fractions divided by whole numbers

Estimating Quotients Involving Unit Fractions

5.NF.7a practice problems estimating quotients involving unit fractions

5.NF.7b

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

Modeling Whole Numbers Divided by Unit Fractions

5.NF.7b practice problems modeling whole numbers divided by unit fractions
Fraction bar digital manipulative indicator
5.NF.7b practice problems modeling whole numbers divided by unit fractions
Fraction circle digital manipulative indicator

Understanding Division as the Inverse of Multiplication

5.NF.7b practice problems understanding division as the inverse of multiplication
Fraction circle digital manipulative indicator
5.NF.7b practice problems understanding division as the inverse of multiplication
Fraction circle digital manipulative indicator

5.NF.7c

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Modeling Whole Numbers Divided by Unit Fractions

5.NF.7c practice problems modeling whole numbers divided by unit fractions
Number line digital manipulative indicator
5.NF.7c practice problems modeling whole numbers divided by unit fractions
Fraction circle digital manipulative indicator

Whole Numbers Divided by Unit Fractions

5.NF.7c practice problems whole numbers divided by unit fractions
5.NF.7c practice problems whole numbers divided by unit fractions