# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Number Sense and Operations

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book:
Walking the Line: Activities for the TI-73 Number Line.

The following materials are required for this activity:
• Paper cups
• Marbles

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

#### 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.

• 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