Education Technology

Multiplication of Integers--Repeated Addition and Subtraction

Published on 06/09/2008

Activity Overview

In this activity, students investigate how repeated addition or subtraction is related to multiplication.

Before the Activity

  • Access the NUMLINE application and select the number line option

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

  • Use red and blue chips to multiply integers (blue chips stand for positive integers and red chips stand for negative integers)

    Multiply 3 x 4
  • Put in (positive 3) three groups, each group contains (positive 4) four blue chips to get the answer + 12

    Multiply 3 x - 4
  • Put in (positive 3) three groups, each group contains (negative 4) four red chips to get the answer - 12

    Multiply - 3 x 4
  • Take away (negative 3) three groups, each group contains (positive 4) four blue chips, add enough zeros (12 red and 12 blue chips) so there are enough blue chips to take away, take away three groups of four blue chips (12) to leave 12 red chips and get the answer - 12

    Multiply - 3 x - 4
  • Take away (negative 3) three groups, each group contains (negative 4) four red chips, add enough zeros (12 red and 12 blue chips) so there are enough red chips to take away, take away three groups of four red chips (12) to leave 12 blue chips and get the answer + 12

  • Add a positive integer x, 4 times (x + x + x + x) and observe the distance moved on the number line
  • Observe this is the same as four times the integer (4 * x)
  • Similarly, add a negative integer four times (0 + -x + -x + -x + -x), this is the same as 4 * - x
  • Compute (0 - x - x - x - x) and notice that this is equivalent to - 4 * x
  • Compute (0 - -x - -x - -x - -x) and observe this is equivalent to - 4 * - x
  • Solve other multiplication problems by repeated addition or repeated subtraction

After the Activity

Students complete the Student Activity sheet.

Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary