## Instructor Overview

Students use the Hot Air Balloon simulation to model integer subtraction. They then move to modeling subtraction on a number line. They use patterns in their work and their answers to write a rule for subtracting integers.

# Key Concepts

This lesson introduces the number line model for subtracting integers. To subtract on a number line, start at 0. Move to the location of the first number (the minuend). Then, move in the negative direction (down or left) to subtract a positive integer or in the positive direction (up or right) to subtract a negative integer. In other words, to subtract a number, move in the opposite direction than you would if you were adding it.

The Hot Air Balloon simulation can help students see why subtracting a number is the same as adding the opposite:

- Subtracting a positive number means removing heat from air, which causes the balloon to go down, in the negative direction.
- Subtracting a negative number means removing weight, which causes the balloon to go up, in the positive direction.

The rule for integer subtraction (which extends to addition of rational numbers) is easiest to state in terms of addition: to subtract a number, add its opposite. For example, 5 – 2 = 5 + (–2) = 3 and 5 – (–2) = 5 + 2 = 7.

# Goals and Learning Objectives

- Model integer subtraction on a number line.
- Write a rule for subtracting integers.

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