Adding Integers Using Integer Chips
Concept
The term “integer” was adapted in Mathematics from Latin. Integer means intact or whole. Integers are very much like whole numbers, but they also include negative numbers among them. For example, 11, 8, 0, and −1,908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses.
Addition generally means to increase the value. But, in the case of integers, the addition operation might lead to an increase or decrease in the value of the given number. If we add a negative integer, the value of the given number will decrease and if we add a positive integer the value will increase.
When modeling integers, we can use colored chips to represent these integers. One color can represent a positive number and another color can represent a negative number. Here, a yellow chip will represent a positive integer and a red chip will represent a negative integer. A zero pair is the pair of the positive and negative form of the same number.
Rules
1. Model the addends using integer chips. If the addend is positive, use yellow chips. If the addend is negative, use red chips.
2. Equal amounts of red and yellow counters create zero pairs and cancel each other out.
3. Determine the amount and color of the remaining counters and write the corresponding integer.
Example
Add.
-12 + 4
Solution
1. Model the addends using integer chips. If the addend is positive, use yellow chips. If the addend is negative, use red chips.
2. Equal amounts of red and yellow counters create zero pairs and cancel each other out.
3. Determine the amount and color of the remaining counters and write the corresponding integer.
-12 + 4 = -8
Practice Adding Integers Using Integer Chips
Practice Problem 1
Use the counters to model the expression and then find the solution.
8 + (-3)
Practice Problem 2
Use the counters to model the expression and then find the solution.
(-7) + 5
Practice Problem 3
Use the counters to model the expression and then find the solution.
(-6) + 10 + (-3)
An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
Positive Integers: An integer is positive if it is greater than zero. Example: 1, 2, 3 . . .
Negative Integers: An integer is negative if it is less than zero. Example: -1, -2, -3 . . .
Zero is defined as neither negative nor positive integer. It is a whole number.
A zero pair – A pair of the positive and negative form of the same number.
Absolute value – the positive distance that a number is from 0 on a number line.
Additive inverses – two integers that are opposites.
Integer chips – Are colored chips with signs. One color represents a positive number and another color represents a negative number.
Pre-requisite Skills
Integers and Absolute Value
Order of Operations