Education Technology

Partitions--How Many Ways Can we Split a Number?

Published on 06/09/2008

Activity Overview

In this activity, students explore multiple representations of positive integers. They also learn how to partition positive integers using the number line.

Before the Activity

  • Access the NUMLINE application and select the Number Line option
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 54 - 56 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

  • Find the number of partitions for the number 3
  • Enter 1 + 1 + 1 as the first partition and observe the number line
  • Enter 1 + 2, 2 + 1, and 3 and observe the number line
  • Observe that there are three unique ways to split the number 3
  • Similarly, find the number of partitions for the number 6, and sketch the expressions
  • Predict the number of partitions for numbers 1 through 10
  • Use the number line, cups, and marbles to determine the exact number of partitions possible for each number and compare with the prediction
  • After the Activity

    Review student results:

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