Subtracting Integers

The rule

Keep, Change, Change. Keep the first number, change the minus to a plus, change the sign of the second number. Then add.

What it is

Good news: nothing new to learn. Subtracting a number is the same as adding its opposite, so 8 - 3 and 8 + (-3) are the same question written two ways. Once they can do that swap, every subtraction becomes an addition they already know.

Why it matters

It makes this one skill instead of two. If they have the adding rules they already have every subtraction here - the rewrite is the only new part. It comes back in algebra, where treating the minus as part of the term is the only way to collect like terms without dropping a sign.

What they will get wrong

Changing only half of it. Keep, Change, Change means the operation changes AND the second number flips, and they very often do the first and forget the second: 5 - 3 becomes 5 + 3, giving 8 instead of 2. Watch that first box rather than only the final answer - you can see it happen there.

How to check an answer

Check your rewrite before you add. If a minus is still sitting between the two numbers, you have not finished - a done rewrite always has a plus in the middle.

What to say when they are stuck

• Say it plainly: "Two things change, not one. The sign in the middle, and the sign of the number after it."
• Point at their rewrite: "Did that second number change sign? If it looks the same, you only did half of it."
• For 5 - (-3): "Taking away something you owe leaves you better off." Cancelling a debt of 3 is gaining 3.
• If they can rewrite but stall on the adding, that is the last lesson talking. Go back and drill those two rules alone.
• When they get one right, have them say the three words out loud. Once they can chant it while working, it has stuck.