Stack Coins for Integer Action!

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 Need:

• 10 pennies
• 10 nickels
• 3 penny-nickels (3 pennies stacked on 3 nickels)
• pencil
• paper

What You Do:

1. 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.
2. Write a simple addition problem using integers: -3 + 5=
3. Place 5 pennies in a line and below that put 3 nickels in a line.

   P P P P P

   N N N

4. 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)
5. 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!

6. 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!
7. Subtracting integers is all about changing the signs first. For example:

   4 – (-1) becomes 4 + (+1)

8. Show this with the coins by placing four pennies down, then include one penny-nickel.

9. 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)

Tips:

1. Always use the new term “integer” rather than “number”.
2. 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!