Integer Operations Graphic Organizer


With integer multiplication and division, the rules are clean and concrete. A negative times a negative is literally the "opposite of a negative" and the rules are pretty simple to remember. With addition and subtraction the rules are a whole lot looser. For students who like things nice and clear, integers can be a real sticking point.


As part of my graduate thesis I made this integer operations manipulative that reduced my students' errors with integers by 62%. It allows students to "see" how the numbers relate to one another and helps concrete thinkers find success.

Yesterday a teacher asked if I could also come up with a cheat sheet for adding and subtracting integers that was like the one I had made for solving equations. I pulled together this graphic organizer. It works about the same as the manipulative and is geared towards students who don't need as much support as the manipulative offers.

How to use the graphic organizer:

1: Change any subtraction problem to addition (skip if already addition).

2: Now look at the integers' signs. Both positive? One negative, one positive? If so, which is "heavier"? (ie farther from zero).

3: Follow the column that matches the integers you have.

Example:

For a problem like...
5 - 14

1: change to addition.
5 + -14

2: The "heavier" number is negative because -14 is father from zero than 5 is. So we follow the 3rd column.

3: "subtract"* (find 14 - 5) and keep the -

5 + -14 = -9

*Since we're actually subtracting the absolute values of the numbers, I added a footnote on the graphic organizer. I will also ask my students, "how much farther from zero is 14 than 5?" when completing this last step.

A fun activity to practice integer addition and subtraction is this integers pennant. Students add and subtract integers then personalize their pennants with color. 


integer operations addition and subtraction math pennant

You can find this graphic organizer for free here



Can we really teach number sense? Visual math word wall references for integer addition and subtraction

There are some additional visuals for integer addition and subtraction in the post Can we really teach number sense?

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