How to use the fact family worksheet generator
- Enter the number of problems, from 1 to 30, and a worksheet number.
- Choose Add and subtract or Multiply and divide for the facts.
- Tick Show the answer key to show the four facts for each problem.
- Print the sheet. Students write the four related facts for each pair of parts and whole.
Formula
Addition family: a + b = c, b + a = c, c - a = b, c - b = a
Multiplication family: a x b = c, b x a = c, c / a = b, c / b = a
The two parts and the whole are given, and the student writes all four facts
When the two parts are equal, the family has only two different facts
A fact family shows that addition and subtraction undo each other, and that multiplication and division do. Knowing one fact gives three more.
The first problems of worksheet number 1
Problem 1 gives the parts 8 and 2 and the whole 10. The family is 8 + 2 = 10, 2 + 8 = 10, 10 - 8 = 2 and 10 - 2 = 8. Problem 2 gives the parts 7 and 12 and the whole 19, so the family is 7 + 12 = 19, 12 + 7 = 19, 19 - 7 = 12 and 19 - 12 = 7.
Problem 3 gives 12, 5 and 17: 12 + 5 = 17, 5 + 12 = 17, 17 - 12 = 5 and 17 - 5 = 12. With multiplication and division on, parts 6 and 7 with a whole of 42 give 6 x 7 = 42, 7 x 6 = 42, 42 / 6 = 7 and 42 / 7 = 6.
What students learn
Fact families build the idea that operations are linked. A student who knows 8 + 2 = 10 can solve 10 - 8 without counting back. In the same way, a student who knows 6 x 7 = 42 can solve 42 / 6. The sheet asks for all four facts, so students practice both the order of the numbers and the choice of operation.
Parts in the addition sheets run from 2 to 12, and the multiplication sheets use factors from 2 to 9. For a calculator to check answers, use the long multiplication calculator or the fraction calculator.
Using the sheets
Give the addition sheet first, then the multiplication sheet once students know their times tables. For extra support, let students use counters or a number line. For a challenge, ask students to write a fact family from a number sentence they make up.
Combine the sheet with other practice, such as the elapsed time worksheet generator or the GCF and LCM calculator for factors.
Assumptions and limits
- Parts and wholes are whole numbers. Addition sheets use parts from 2 to 12, and multiplication sheets use factors from 2 to 9.
- Each problem gives both parts and the whole, and the student writes the four facts.
- The same worksheet number and choice of facts always make the same sheet.
- The sheet is general practice and is not matched to a particular curriculum.
Frequently asked questions
What is a fact family?
It is a group of related facts that use the same three numbers, such as 8 + 2 = 10, 2 + 8 = 10, 10 - 8 = 2 and 10 - 2 = 8.
Can I use multiplication and division?
Yes. Choose Multiply and divide, and each problem gives two factors and the product.
What if both parts are the same?
The family has only two different facts, since the two orders are the same. The key still lists four lines, one for each position.
How do I print the answers?
Tick Show the answer key, then print. Use the same worksheet number to match the student sheet.