In this unit, students learn to multiply fractions by whole numbers, extending their understanding of fractions to see that a nonunit fraction can be thought of as a multiple of a unit fraction. Students also deepen their understanding of multiplication from repeated addition to a comparison by using nonwhole numbers.
Students have previously worked with multiples of whole numbers only, and it may be a conceptual struggle to think of nonunit fractions as multiples of a unit fraction.
Key Concepts:
 A fraction a/b is a multiple of 1/b.
 A multiple of a/b is a multiple of 1/b: (n x a/b) = (n x a)/b.
 Because fractions are numbers, the meaning of multiplicative comparison does not change when fractions are involved.
Prior Knowledge Needed:
 Locate fractions on a number line; (Grade 3, Unit 5; 3.NF.A.2)
 Multiply whole numbers; (Grade 3, Unit 1; 3.NBT.A.3)
 Understand a fraction a/b with a › 1 as a sum of fractions 1/b; (Grade 4, Unit 3, 4.NF.B.3)
 Multiplication can be used to compare amounts; (Grade 4, Unit 7; 4.OA.A.1)
Units on the Horizon:
 Understanding the concept of multiplying fractions by fractions; (Grade 5, Unit 5)
 Interpreting multiplying fractions as scaling; (Grade 5, Unit 7)
Lessons

Lesson objective: Understand that every nonunit fraction is a multiple of the unit fraction with the same denominator. Students bring prior knowledge of adding fractions from 4.NF.B.3, as well as multiplication of whole numbers. This prior knowledge is...

Lesson objective: Multiply a unit fraction by a whole number. This lesson provides practice with multiplying a unit fraction by a whole number. Number lines are used here because they support the understanding that fractions are numbers and can be opera...

Lesson objective: Apply understanding of writing a nonunit fraction as the product of a whole number and a unit fraction in order to solve a problem involving running on tracks. This lesson provides an opportunity for students to apply their knowledge ...

Lesson objective: Understand that multiplying a nonunit fraction by a whole number results in a product that is a multiple of the unit fraction that makes up the nonunit fraction. Students bring prior knowledge of representing the fraction \(\frac{a}b...

Lesson objective: Practicing multiplying a nonunit fraction by a whole number. This lesson helps to build procedural skill with multiplying nonunit fractions by whole numbers. A number line is used here because it reinforces the understanding that fra...

Lesson objective: Practice multiplying a nonunit fraction by a whole number. This lesson helps students build procedural skill with multiplying a nonunit fraction by a whole number. Students will use both an area model and number lines. This work deve...

Lesson objective: Solve a realworld problem that involves multiplying nonunit fractions by whole numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplying nonunit fractions by whole numbers to...

Lesson objective: Understand that we can compare quantities using multiplication (such as "one quantity is n times as much as another quantity"), whether the quantities are whole numbers or fractions. Students bring prior knowledge of multiplicative com...

Lesson objective: Practice writing and solving equations when one quantity is some number of times as much as another number. This lesson helps to build procedural skill with using multiplication to compare amounts that include a fraction. All equations...

Lesson objective: Solve realworld problems involving multiplicative comparisons where a fraction is multiplied by a whole number. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplicative comparisons ...