CCSS.Math.Content.5.NF.B
Standard Cluster
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Common Core State Standards for Mathematics
Cluster contents
Standards in This Cluster
CCSS.Math.Content.5.NF.B is a cluster heading. These are the individual standards under it.
- CCSS.Math.Content.5.NF.B.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 i...
- CCSS.Math.Content.5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- CCSS.Math.Content.5.NF.B.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.
- CCSS.Math.Content.5.NF.B.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 i...
- CCSS.Math.Content.5.NF.B.5
Interpret multiplication as scaling (resizing), by:
- CCSS.Math.Content.5.NF.B.5a
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.
- CCSS.Math.Content.5.NF.B.5b
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 n...
- CCSS.Math.Content.5.NF.B.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.
- CCSS.Math.Content.5.NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
- CCSS.Math.Content.5.NF.B.7a
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
- CCSS.Math.Content.5.NF.B.7b
Interpret division of a whole number by a unit fraction, and compute such quotients.
- CCSS.Math.Content.5.NF.B.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 ...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students find products involving fractions and solve division problems with unit fractions and whole numbers. They represent the work with equations, diagrams, or story contexts and explain how the result compares with the starting numbers.
What Mastery Looks Like
- Students calculate fraction products and solve division problems involving unit fractions and whole numbers. They use a model or equation to explain the result and judge whether it is reasonable.
Common Misconceptions
- Students may think multiplication always makes numbers larger and division always makes them smaller. They often reverse 4 ÷ 1/3 and 1/3 ÷ 4 or apply fraction rules without understanding the quantities.
How to Assess It
- Give an exit ticket: solve 3/4 × 2/5, 4 ÷ 1/3, and 1/3 ÷ 4. Draw a model and label the equation for one problem.
Lesson moves
Ways to Teach It
Use fraction strips to model 3 × 2/5, 3/4 × 2/5, 4 ÷ 1/3, and 1/3 ÷ 4.
Ask, “Can multiplying make a number smaller?” Students choose an example, draw a model, and explain their answer in three sentences.
Play Fraction Match: students pair product and quotient cards with answer cards, then earn a point by explaining one match.
Scale a recipe to 3/4 of a batch, then find how many 1/4-cup servings fit in a measured amount.
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Printable 5.NF.B Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.5.NF.B, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- CCSS.Math.Content.7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
- CCSS.Math.Content.6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- CCSS.Math.Content.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
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