Magic Squares

Room 221 mathematicians learned about magic squares in the first lessons of Chapter 3. A magic square is a 3 x 3 grid where the digits in each column, row and diagonal all add up to the same sum. The special sum for the above magic square is 15.

Third graders practiced using efficient addition strategies to complete magic squares. For example, when mathematicians are adding three numbers, they can find combinations of ten. For example in the center row, I would add 3 and 7 to make 10. Then, it is easy to add the 5 to 10. The sum of course, is 15. Similarly, third grade mathematicians can use sums they know, to solve sums they don't. For example, if third graders know that 7 + 7 = 14, they should also know that 6 + 7 = 13.

Third grade mathematicians also practiced finding missing addends when they knew the special sum of the square. For example, if we know that the special sum of the above grid is 15, but the last row is blank. We can add up the first column, 8 + 3 to make 11. Knowing that the special sum is 15, I can figure out that the last square in the first column is 4.

Ask your third grader to show you how they solve magic squares! Ask them what the special sum is for this magic square: