Adding and Subtracting Integers with Counters

Adding and Subtracting Integers with Counters

A visual approach to understanding positive and negative numbers Grade 7 Mathematics

What Are Integer Counters?

Red counters represent negative numbers (-1 each) Yellow counters represent positive numbers (+1 each) Zero pairs: one red + one yellow = 0 We can model any integer using these counters

Let's Model Some Integers!

Model +3 using yellow counters Model -5 using red counters Model 0 using zero pairs Try modeling +2 and -7 on your own

Adding Positive Integers

Example: 3 + 2 Start with 3 yellow counters Add 2 more yellow counters Count total: 5 yellow counters = +5

Adding Negative Integers

Example: (-2) + (-3) Start with 2 red counters Add 3 more red counters Count total: 5 red counters = -5

Adding Integers with Different Signs

{"left":"Example: 4 + (-3)\nStart with 4 yellow counters\nAdd 3 red counters","right":"Make zero pairs (3 pairs)\nRemove zero pairs\nResult: 1 yellow counter = +1"}

Practice Adding Integers

Try these problems with your counters: 5 + (-2) = ? (-3) + 7 = ? (-4) + (-1) = ? Work with a partner and check each other's work!

Subtracting Integers - The Key Insight

Subtraction means 'take away' But what if we don't have enough to take away? Solution: Add zero pairs first! Then take away the required counters

Subtraction Example: 2 - 5

Quick Check: What Have We Learned?

How do we add integers with the same sign? How do we add integers with different signs? What's the key strategy for subtraction? Why do zero pairs work?