Positive and negative whole numbers, called integers, can pop up anytime, anywhere in middle school math. Understanding how to add and subtract integers can be a challenge at first, but once you know how to handle the heat, it's a breeze! Remember when your middle schooler was a kindergartener and learned 2+2=4 using Cheerios? The same idea can be used with integers, however the Cheerios are now coins and the process requires a couple more steps!
What You Do:
Now that you've got adding integers covered, it's time to subtract!
- Place 10 pennies and 10 nickels on the table. Explain that the pennies represent positive integers and the nickels represent negative integers. If it helps - think P (pennies) for positive and N (nickels) for negative.
- Write a simple addition problem using integers: -3 + 5=
- Place 5 pennies in a line and below that put 3 nickels in a line.
P P P P P
N N N
- Place the 3 nickels on top of 3 pennies. Explain how positive and negative integers cancel each other out, and ask, “What do you have left?” (Answer: 2 pennies, or positive 2)
- Repeat the process using different addition problems:
(2) + (-6) =
N N N N N N
Place 2 pennies on top of 2 nickels. Ask “What do you have left?” (Answer: 4 nickels, or negative 4)
(-2) + (-6) =
N N N N N N
In this case, point out that there are no pennies (positives) to cancel out the nickels (negatives), so you can just add up the nickels. (Answer: 8 nickels, or negative 8)
- Set up three more nickels with a penny on top of each. (You'll have a total of 13 pennies, 13 nickels on the table.) Emphasize again how positive and negative integers cancel each other out - so these penny-nickel stacks equal zero!
- Subtracting integers is all about changing the signs first. For example:
4 – (-1) becomes 4 + (+1)
Show this with the coins by placing four pennies down, then include one penny-nickel.
Since you're taking away the negative, remove the nickel. What's left is your answer: 5 pennies (positive 5).
One rule to remember is subtracting an integer means you add its opposite!
Other example probelms to work with:
(-4) – (1) becomes (-4) + (-1)
Answer: 5 nickels (-5)
(-4) – (-1) becomes (-4) + (+1)
Answer: 3 nickels (-3)
- Always use the new term “integer” rather than “number”.
- Demonstrate the process 1-2 times, then do the process with your child. Next, have your child solve problems on her own and finally, have your child “teach” the process to someone else in your house!
Brigid Del Carmen has a Master's Degree in Special Education with endorsements in Learning Disabilities and Behavior Disorders/Emotional Impairments. Over the past eight years, she has taught Language Arts, Reading and Math in her middle school special education classroom.