Integer Chips

Integer Chips model integer addition and subtraction. A yellow chip with a "+" sign represents positive 1. A red chip with a "-" sign represents negative 1. A neutral pair is a pair of opposite chips that represent 0, the sum of +1 and -1.

Modeling Integers

To show an integer, drag the desired number of chips to the top or bottom row in the work area. The chips in each row must all have the same sign.

To remove a chip, drag it out of the work area.

Neutral Pairs

A neutral pair consists of a +1 chip and a -1 chip. Since +1 + (-1) = 0, the value of a neutral pair is zero.

To add a neutral pair, drag it to the work area. (Note: you cannot add a neutral pair if both rows of tiles have the same sign.)

To remove a neutral pair, drag a chip on top of another chip that has the opposite sign. Both chips disappear (because +1 + (-1) = 0).

Adding Integers

To add two integers, model one addend in each row.

If the addends have the same sign, the sum is the total number of chips displayed. The sum has the same sign as the chips.

If the addends have different signs, remove neutral pairs by dragging chips on top of chips with different signs. The sum is the number of chips remaining after all neutral pairs have been removed.

Subtracting Integers

To subtract integers, start by modeling the minuend in one row.

If there are enough chips to "take away," remove the number of chips in the subtrahend from the work area. The difference is the number of chips remaining.

For example, to model -5 - (-2):

There are 3 negative chips left, so the difference is -3.

If there are not enough chips to "take away", OR if the minuend and the subtrahend have different signs, you need to add neutral pairs before subtracting. Drag neutral pairs into the work area until you have enough chips to subtract, then subtract as described above.

For example, to model -6 - 3:

There are 9 negative chips left, so the difference is -9.