Stack Coins for Integer Action!
Topics: Middle School, Math
Positive or negative 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!
- 10 pennies
- 10 nickels
- pencil
- paper
What You Do:
- Place 10 pennies and 10 nickels on the table. Explain that the pennies represent positive integers and the nickels represent negative integers.
- Write a simple addition problem using integers:
- Place 5 pennies in a line and 3 nickels underneath the pennies.
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) =
P P
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 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)
- Now that you've got adding integers covered, it's time to subtract! Subtracting integers is all about changing the signs first. For example:
4 – (-1) becomes 4 + (+1)
Show coins
Answer: 5 pennies (5)
(-4) – (1) becomes (-4) + (-1)
Show coins
Answer: 5 nickels (-5)
(-4) – (-1) becomes (-4) + (+1)
Show coins
Answer: 3 nickels (-3)
(5) + (-3) =
Tips:
- 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.
Comments from readers
We've always said that subtracting is "taking away" something but what do you do when you're taking away more than what you have? For instance, 10 - 13? You don't have 13 pennies to take away! So to get those extra pennies on the table (so you can eventually take them away) remember that the penny on top of the nickel "cancel each other out" (they equal zero). So put 3 penny-nickel pairs on the table with the 10 pennies that are already there. Now you have 13 pennies that you can take away (subtract) - and what are you left with? 3 nickels, better known as negative 3.
When you have 5 - (-3), you read this as "5 take away -3". You start out with 5 pennies on the table, but since you don't have 3 nickels to take away, you place 3 nickel-penny pairs on the table with the 5 pennies (remember the 3 nickel-pennies on the table are canceling each other out and not really changing the 5 that you had to start with). With the nickel-penny pairs on the table, you now have 3 nickels (3 negatives) that you can take away - and the remaining 8 pennies is your answer! 5 - (-3) = 8 Once you learn integer subtraction this way then it makes more sense why you can just "change the signs" when you're subtracting.