Establishing meaning for fraction multiplication by building on whole number multiples and providing various concrete models will support the extension to division as well as lay key groundwork for future study of ratio and proportion.
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See the standards throughout the grades: http://www.corestandards.org/Math/Content/NF/
Multiplication
NF3.d. Understand a fraction a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. Apply and extend this understanding to multiply a fraction (or mixed number) by a fraction (or mixed number). Solve word problems involving the multiplication of fractions.
NF2.a. Use concrete (set, area and length models) and pictorial (set, area and length models) to represent problems involving the addition, subtraction, multiplication, or division of fractions. Compare and contrast the different models.
NF2.b. Recognize common student errors involving fraction operations. (Involving multiplication)
Division
NF3.e. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
NF4.a. Interpret a fraction as division of the numerator by the denominator. (a/b = a Ă· b) Explain why b cannot be 0. Extend this understanding to divide a fraction (or mixed number) by a fraction (or mixed number). Solve word problems involving the division of fractions.
NF2.a. Use concrete (set, area and length models) and pictorial (set, area and length models) to represent problems involving the addition, subtraction, multiplication, or division of fractions. Compare and contrast the different models.
NF2.b. Recognize common student errors involving fraction operations. (Involving division)
Similar to addition and subtraction fraction computation, the focus of these topics should emphasize reasoning and sense-making about the procedures for multiplication and division of fractions. Students should develop, connect, and represent addition and subtraction fraction procedures using manipulatives, area models, number line models, and bar diagrams.
Beyond Invert & Multiply: Making Sense of Fraction Computation Book (Julie McNamara)
Extending Children's Mathematics: Fractions and Decimals Book (Susan Empson and Linda Levi)
Mine the Gap for Mathematical Understanding, Grades 6-8 Book ( John SanGiovanni and Jennifer Novak)
Uncomplicating Fractions to Meet Common Core Standards in Math, K-7 Book (Marian Small)
"From whole numbers to invert and multiply." Article in Teaching Children Mathematics, vol. 20, issue 6, pgs. 375-383.
"Student representations at the center: Promoting classroom equity." Article in Mathematics Teaching in the Middle School, vol. 13, issue 8, pgs. 458-463.
"Measurement and fair-sharing models for dividing fractions." Article in Mathematics Teaching in the Middle School, vol. 12, issue 9, pgs. 490-496.
Beckmann (2018) Resources:
Chapters 5 and 6
Activity 5A Extending Multiplication to Fractions, Part I
Activity 5C Extending Multiplication to Fractions, Part II
Activity 5D Explaining Why the Procedure for Multiplying Fractions is Valid
Activity 5E When Do We Multiply Fractions
Activity 5F What Fraction is Shaded?
Activity 6M How-Many-Groups Fraction Division Problems
Activity 6O Dividing Fractions by Dividing the Numerators and Dividing the Denominators
Activity 6P How-Many-Units-in-1-Group Fraction Division Problems
Activity 6Q Are These Division Problems?
Billstein (2016) Resources:
Section 6-3
Sowder (2017) Resources:
Chapter 7
Activity 4 Juanita and Jaime Again
Activity 5 Dividing by Unit Fractions
Activity 6 Can We Draw Pictures?
Activity 7 An Alternative Approach - Draw
Activity 8 Illustrating
Van De Walle (2019) Resources:
Chapter 15
Contextual Examples
Models
Estimation
Factors Greater Than 1