Write the following on the board. Encourage students to try to use an organized approach in responding to this story, such as making a table or list. Depending on your class, you might remind students that a and b may be the same number.
Find two numbers, a and b, each less than or equal to 10 so that (a × a) + (b × b) is a square number.
I listed all the square numbers from 1 × 1 through 10 × 10 and tried adding them together. I found out that if a = 3 and b = 4, then their sum is 25 (a square number). So a = 4 and b = 3 also works. I found out that a = 6 and b = 8 or a= 8 and b = 6 works.