Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a.  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.)

 

Students are able to… 

  • Explore what happens when they multiply a whole number by a fraction when solving word problems in different contexts using models, pictures, words, and numbers.
  • Explore multiplying a fraction by a fraction using models, pictures, words, and numbers when solving a variety of word problems.
  • Explain their reasoning of multiplying a whole number by a fraction and a fraction by a fraction to partners, small groups, and to the class.
  • Look for patterns when multiplying fractions and explain why the patterns work using models, pictures, numbers, and words.
  • Apply knowledge of patterns found to determine a procedure for multiplying fractions.

Students are able to…because teachers:

  • Connect multiplying whole numbers to multiplying fractions through situations students can model and scaffold instruction to begin with unit fraction factors before building to multiplying with other fractions and mixed numbers.
  • Provide students time to work within groups to explore solutions using area models, fraction bars, and number lines.
  • Use formative assessment tasks to gauge student learning.
  • Provide students time to explore patterns and to determine a procedure for multiplying fractions.

Questions to ask students:

  • Make a model demonstrating what happens when you multiply 5 x .
    • Sample answer that indicates understanding: Five groups of one-fourth looks like this:

  • What patterns have you noticed when multiplying a whole number by a unit fraction?
    • Sample answer that indicates understanding: When I multiply a whole number by a unit fraction, the product is less than the whole number I multiplied by. For example, with 2 x 1/3 , the product is 2/3 and that is less than 2. With 8 x 1/4 , the product is 8/4  or 2 when simplified. So when multiplying by fractions, the product is not always greater than the factors like it is when multiplying two whole numbers.
  • Use words, pictures, or numbers to multiply  1/2 x 1/4

 

 

FSA Notes

Cognitive Complexity Level: Level 2: Basic Application of Skills & Concepts

Achievement Level Descriptions:

Level 2: shows the product of a fraction by a whole number using visual fraction models; solves realworld problems involving multiplication of a fraction by a whole number by using visual fraction models or equations to represent the problem

Level 3: finds the product of two fractions by using an area model; generalizes that a/b x c/d = (ac)/(bd) and uses it to solve mathematical or realworld problems involving multiplication of fractions

Level 4: solves real-world problems involving multiplication of fractions and mixed numbers; creates a real-world context involving multiplication of fractions and/or mixed numbers

Level 5: finds the possible fractional dimensions of a rectangle given the area; solves multistep mathematical and real-world problems involving multiplication of whole numbers, fractions, and/or mixed numbers

Assessment Limits: 

  • Visual models may include:
    • Any appropriate fraction model (e.g., circles, tape diagrams, polygons, etc.)
    • Rectangle models tiled with unit squares
  • For tiling, the dimensions of the tile must be unit fractions with the same denominator as the given rectangular shape.
  • Items may not use the terms “simplify” or “lowest terms.”
  • Items may require students to interpret the context to determine operations.
  • Fractions may be greater than 1.
  • For given fractions in items, denominators are limited to 1‐20.

Note MAFS.5.NF.2.4 also assesses MAFS.5.NF.2.6

 

Context? – Allowable for  MAFS.5.NF.2.4.  Required for MAFS.5.NF.2.6

 

Additional Resources:

Additional in depth content knowledge:

 

Video: Multiplication of Fractions Progression (Part 1)

 

Video: Multiply 2 fractions using a fraction model:

 

Video: Multiply 2 fractions using a number line:

 

Sample Formative Assessment Tasks:

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Write a story problem to match the expression 1/3 of 9

 

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[divider] [/divider] Resources/Tasks to support your child at home:

• Use an area model to multiply these fractions:

• LearnZillion Video: Multiply Fractions by Fractions Using Area Models
• LearnZillion Video: Multiply Mixed Numbers by Mixed Numbers Using Visual Representations