freesabaiMath squares puzzle
3×3 grids of numbers with plus and minus signs (and times, as an option) between them and the result at the end of every row and column. Some numbers are missing and the child works back to find them. Every grid is checked to have one answer only: arithmetic and reasoning in one.
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How to use it
- Choose the signs, the numbers, the level and how many grids. The sheet appears on the right at once; "New random sheet" draws new ones.
- The child fills the empty squares so that every row (read left to right) and every column (read top to bottom) gives the result at its end.
- Press "Print / Save as PDF". The key fills in the missing numbers.
Good to know
- Rows and columns are worked in order, left to right and top to bottom, with no "times first": 2 + 3 × 4 = 20. The sheet says so. No step goes below zero.
- Every grid has been checked by trying every number of its range (1-9 or 1-20) in every empty square: exactly one way works. Easy grids can mostly be solved one square at a time; hard ones need rows and columns together.
- Build the basics first with the arithmetic drills, or keep reasoning with sudoku.
Report a problem or suggest an idea
Found a grid with two answers, or want bigger grids? Tell us on the feedback page.
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Questions and answers
How are the rows and columns worked?
Rows left to right and columns top to bottom, in order, with no times first: 2 + 3 × 4 = 20. Each must give the number at its end.
How do I know there is one answer?
Every grid is checked by trying every number of the range chosen, 1-9 or 1-20, in every empty square; exactly one way works. Grids with more than one answer are thrown away.
How do the levels differ?
Easy leaves 3 of the 9 numbers out, medium 5, hard 6. Easy grids can mostly be filled one square at a time; hard ones need rows and columns together.
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