freesabaiFact families
Number triangles with the result on top and the two parts below, for children to write the four number sentences of a family, such as 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3. Choose addition and subtraction or multiplication and division, the range, and whether the triangle is complete, has a corner missing, or comes with one sentence given.
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How to use it
- Choose the operations, the range, the kind and how many families. The sheet appears on the right at once; "New random sheet" gives another set.
- "All three numbers given" introduces fact families; "one corner missing" has the child find the missing number first; "one sentence given" practises writing the rest from the relationship.
- Press "Print / Save as PDF". The answer key on the last page lists all four sentences of every family and the missing corner (untick it to leave it out).
Good to know
- A fact family is three related numbers, such as 3, 5 and 8, which give four sentences: 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5 and 8 − 5 = 3. Multiplication and division work the same way: 3, 5 and 15 give 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5 and 15 ÷ 5 = 3.
- The two parts are always different (no 4 + 4 = 8), so the four sentences differ. Multiplication families start at 2; addition families start at 1.
- "Numbers 2-12" draws both parts from the 2 to 12 times tables (products up to 144); with addition and subtraction it gives sums up to 24.
- To drill the facts of one table, use the times tables maker; for written division, the long division sheets.
Report a problem or suggest an idea
Would you like circles or number houses instead of triangles, or other ranges? Tell us on the feedback page.
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Questions and answers
What is a fact family?
Three numbers related by addition and subtraction or by multiplication and division, such as 3, 5 and 8, which give four sentences: 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3. Each is drawn as a triangle, result on top.
How do the three kinds differ?
All given: see the three numbers and write four sentences. One corner missing: find the missing number first. One sentence given: read it and write the other three. The key covers every kind.
Why is there no family like 4 + 4 = 8?
Equal parts give only two different sentences, so the sheet draws only families whose two parts differ, which always gives four distinct sentences.
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