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

a. 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).

b. 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.)

c. 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?

[divider] [/divider]Students are able to…

  • Model and explain using manipulatives, pictures, words and numbers, multiplication of a whole number by a fraction.
  • Solve a variety of problems involving multiplication of a whole number and a fraction.

[divider] [/divider]Students are able to…because teachers…

  • Provide students with manipulatives including fraction tiles, number lines and area models to use as they solve problems involving multiplication of a whole number and fraction.
  • Provides opportunities for students to make connections between whole number multiplication and multiplication of a whole number and a fraction.
  • Provide problem solving situations and facilitate discussion on the connections between whole number multiplication, repeated addition and multiplication of a whole number and a fraction.

[divider] [/divider]Questions to ask students:

  • See if students can explain the difference between multiplication of two whole numbers and multiplication of a whole number and a fraction. How is 3 x 4 similar to 3 x 1/4?
  • Sample answer that indicates understanding:  3 x 4 is 3 groups with 4 in each group while 3 x 1/4 is 3 groups with 1/4 in each group. 3 x 4 = 12 and 3 x 1/4 is 3/4, less than a whole.

          

  • See if students can correctly model multiplication between a whole number and a fraction. i.e. 3 x 2/5
  • Sample answer that indicates understanding:
  • Ask students to explain if 4 scoops of 3/5 cups would make a whole number of cups.
  • Sample answer that indicates understanding: No, because 4 scoops of 3/5 would be 12/5, and the numerator should be a number I could skip count by 5’s, like 10 or 15, to be a whole number.

[divider] [/divider]FSA Notes

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

Achievement Level Descriptors:

2-understands a fraction a/b as a multiple of 1/b including the use of visual fraction models or repeated addition

3-understands and solves one-step mathematical and real-world problems involving a fraction a/b as a multiple of 1/b, and uses this understanding to multiply a fraction by a whole number, using visual fraction model

4-understands and solves word problems by recognizing that fraction a/b is a multiple of 1/b, and uses that construct to multiply a fraction by a whole number (in general, n x a/b is (n x a)/b)

5-solves multi-step word problems

Assessment Limits:

Fractions may only be multiplied by a whole number.

Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.

[divider] [/divider]Additional Resources:

Additional in depth content knowledge

Video: Multiplying fractions and whole numbers visually

Multiplying fractions and whole numbers word problems

[divider] [/divider]Sample Formative Assessment Tasks:

[divider] [/divider]Resources/Tasks to Support Your Child at Home

Next time you order pizza for dinner, count the number of slices. What fraction does each slice represent? ( if there are 8 slices in the pie.) How would I represent the whole pie? ( ) Ask your child questions such as, “If I ate 5 slices, how much did I eat and how can I write that as a fraction multiplication problem?”

Ask your child to take a recipe and multiply the ingredients to make a larger portion of the recipe.

Khan Academy “Multiply Whole Number by a Unit Fraction Practice” – https://goo.gl/iRP2yL

Learnzillion “Use a fraction model…” – https://goo.gl/rOPksc

Khan Academy “Multiply Fractions by Whole Numbers” – https://goo.gl/eAs7Xp

XP Math “Multiply fractions by Whole Numbers…”- http://goo.gl/qY3S0y

Learnzillion “Solve word problems…” – https://goo.gl/22Mr8X