Same Math › Grade 7 › Integer chips
What are integer chips?
Integer chips are counters with a + side and a − side. A positive and a negative chip together make zero, called a zero pair. To work out −5 + 3, kids lay out the chips, cancel the zero pairs, and count what's left: two negatives, so −2.
- + chips stand for positive 1.
- − chips stand for negative 1.
- A + and a − together make zero. Cancel them, count the rest.
Why schools teach it
It replaces rules kids forget
Seventh graders add and subtract positive and negative numbers and explain what's happening (7.NS.A.1). Many of us memorized sign rules like “same signs add, different signs subtract.” Chips show why those rules work, so kids can rebuild them when they forget.
Subtracting a negative is the classic stumbling block. With chips, −3 − (−5) means taking away five negatives from three negatives, which requires adding zero pairs first. Kids see why it turns into adding.
At the kitchen table
What to say, and what to skip
Say this
How many zero pairs can you make?
What's left after the zero pairs cancel?
Is the answer positive or negative? How do you know?
More of which color?Can you check it on a number line?
Skip this
Two negatives make a positive.
True for multiplying, not adding. −2 + −3 is −5.- Jumping straight to Keep Change Change.It's a fine shortcut later. First make sure the chips make sense.
- Doing the problem in your head for them.Ask them to show the chips or a quick sketch.
See it in action
Working out −2 + 6
Lay out 2 negative chips and 6 positive chips
Pair them up: 2 zero pairs cancel
2 pairs = 0Count what's left
4 positives: −2 + 6 = 4
Drawing circles with + and − works just as well as real chips.
Free practice sheet
Make an integer chips sheet
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Parents also ask
Do we need real chips?
No. Drawing + and − circles works fine. Coins with heads and tails also work.
How do chips show subtraction?
Take away chips. If there aren't enough to take, add zero pairs first, which doesn't change the value.
What is Keep Change Change?
A shortcut: keep the first number, change subtract to add, change the sign of the second. It works, but kids should know why first.
Do chips work for multiplying?
Yes, with groups of chips. Most classes switch to rules for multiplying once adding makes sense.