Almost Squares

Almost Squares is a game designed to encourage students to derive multiplication facts. Students usually learn the square number facts (1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, …) quite early. Square numbers also have significant application in algebra and the measurement of area.
An array model can be used to illustrate the effect of reducing or increasing a factor by one.  Consider 5 x 5 = 25:

Students should realise that the lowest and highest numbers on the board are the hardest to get. All the other numbers can be obtained in two ways. For example, 56 can be obtained from 7 x 7 and 8 x 8. Therefore, it is sensible to cover 12 and 90 when the opportunity presents itself.

Students may wish to vary the game. For example, increase one factor by one or two and reduce the other by one or two. In this scenario, 6 x 6 becomes 7 x 5 or 8 x 4.
For this variation, the playing board would need these numbers:

Answers to Activity

A game using addition, subtraction, and multiplication.