Magic Square Worksheets
Free printable 3 by 3 magic square worksheets. Fill in the empty boxes so every row, column and diagonal adds to the total. Answer key included.
A magic square is a 3 by 3 grid where every row, every column and both long diagonals add to the same total. Each square on this sheet has five boxes filled in and four empty, with the total printed above it. Fill in the empty boxes, then add each line to check: if a line is off, a number is wrong.
Five filled boxes leave exactly one way to finish a square, so there is never a choice between two answers. The largest number sets the difficulty: 9 gives the classic squares of the numbers 1 to 9, with a total of 15, and 20, 50 and 100 give bigger numbers to add and take away.
No two squares on a page are the same while there are enough different squares to pick from. At 9 there are only eight, so eight on a page is the most that can all differ.
What this worksheet covers
- Add and subtract to find the missing numbers in a 3 by 3 square
- Check every row, column and diagonal against the total
Frequently asked questions
Why is the total printed above each square?
It is the rule every line must meet, and it is what the child checks against. It also helps: the middle box of any 3 by 3 magic square is a third of the total, so a total of 15 puts a 5 in the middle.
Is there only one way to finish each square?
Yes. The five boxes that are filled in are chosen so that only one set of numbers makes every line add to the total. A child who finds a different fill has made a mistake in one of the lines.
What does the largest number change?
The size of the numbers in each square. At 9 every square uses 1 to 9 once each. At 20, 50 and 100 the numbers are further apart, so more of the work is two-digit adding and subtracting.