Lesson 6

The purpose of this lesson is for students to understand that dividing an amount into a whole number of equal parts can be interpreted as multiplying the same amount by a unit fraction.

In previous lessons, students interpreted a fraction as division of the numerator by the denominator, and equivalently, as a whole number divided into equal sized pieces. In this lesson, students relate division of two whole numbers to multiplying a whole number by a unit fraction. In the first activity, students are given an opportunity to solve a division problem using any strategy and, in the synthesis, they examine how the solution can be interpreted in terms of multiplication or division.  In the second activity, students continue to explore the relationship between a fraction, a division expression, and a multiplication expression.

In grade 4, students multiplied a unit fraction by a whole number and in this lesson they begin to explore how to interpret a whole number multiplied by a unit fraction.

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