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Instructor Overview

Students explore whether multiplying by a number always results in a greater number. Students explore whether dividing by a number always results in a smaller number.

Key Concepts

In early grades, students learn that multiplication represents the total when several equal groups are combined. For this reason, some students think that multiplying always “makes things bigger.” In this lesson, students will investigate the case where a number is multiplied by a factor less than 1.

Students are introduced to division in early grades in the context of dividing a group into smaller, equal groups. In whole number situations like these, the quotient is smaller than the starting number. For this reason, some students think that dividing always “makes things smaller.” In this lesson, students will investigate the case where a number is divided by a divisor less than 1.

Goals and Learning Objectives

  • Determine when multiplying a number by a factor gives a result greater than the number and when it gives a result less than the number.
  • Determine when dividing a number by a divisor gives a result greater than the number and when it gives a result less than the number.