Red & Black Chips
Manipulatives and More

Red and black chips are often used to model addition and subtraction of integers. A red chip represents -1 and a black chip represents +1. Click here to open a new browser window in which you can experiment with colored chips. Use your left mouse button to drag the chips.

Addition

Addition is modelled by combining collections of chips. A red chip and a black chip "cancel" each other, so that any collection of chips with an equal number of reds and blacks represents the number 0. Experiment a little by modelling each of these addition problems.

• 2 + 3
• -1 + (-2)
• 5 + (-3)
• -4 + 2

Subtraction

Subtraction is modelled by taking away chips. You will frequently have to add 0 chips (i.e. an equal number of red and black chips) in order to have enough of one kind to take away. Try these problems.

• 5 - 2
• -3 - (-2)
• 3 - 5
• -2 - (-4)

Steve Kifowit Prairie State College Chicago Heights, IL 60411 6-6-2002