Fact Families: Printable Fact Family Worksheets

How to use the fact families worksheet tool

1. Type a heading in Title on the sheet. The default is Fact Families.
2. Choose a range in Fact families: addition and subtraction with sums to 10 or to 20, or multiplication and division with tables to 5, 10 or 12. The default is sums to 10.
3. Choose a Number picture: Number triangle or Fact family house.
4. Choose What children do: Complete the 4 facts, Write the 4 facts, or Find the missing number, then write the facts.
5. Under Only families that include, keep Any numbers or pick one number from 1 to 12, such as 7.
6. Tick Include families with two equal numbers if you want families like 4 + 4 = 8.
7. Set the number of families (4, 6, 8, 9, 12 or 16) and the number across the page (2 or 3).
8. Keep Include answer key ticked to print the answers on a separate page.
9. Check the preview, then select Print or save as PDF. Paper size can be US Letter or A4.

New worksheet makes a different sheet with the same settings. Each sheet shows a worksheet code under the buttons. The page address stores your settings, so a bookmarked or shared link opens the same sheet again. Reset settings restores the defaults.

Choose Number triangle or Fact family house for the picture each family is drawn in.

What is a fact family in math?

A fact family is a set of three numbers linked by addition and subtraction, or by multiplication and division. The three numbers make four number sentences, and each sentence uses the same three numbers. For 2, 5 and 7, the family is 2 + 5 = 7, 5 + 2 = 7, 7 − 2 = 5 and 7 − 5 = 2.

Because all four sentences share the same numbers, knowing one fact helps you find the other three.

What are the four number sentences in a fact family?

The four sentences are two addition facts and two subtraction facts. The two parts can be added in either order, so a + b = c and b + a = c are both included. Subtraction cannot swap parts, so the total is taken away once by each part: c − a = b and c − b = a.

Subtraction is the reverse of addition. If you know that 2 + 5 makes 7, then 7 take away 5 must leave 2.

What are multiplication and division fact families?

Multiplication and division families follow the same pattern. For 3, 7 and 21, the four facts are 3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7 and 21 ÷ 7 = 3. Multiplication can be done in either order, and each division undoes one of the multiplications.

The two factors are the numbers you divide by, and the product is the number you divide. Table ranges set which factors appear. Factors start at 2, and the tables to 5, 10 and 12 limit the largest factor. The sheet also prints the operation symbols in the middle of each triangle or house as a reminder of which operations belong to the family.

Why does a fact family with two equal numbers have only two sentences?

When the two parts are equal, swapping them gives the same sentence. For example, 4 + 4 = 8 written in reverse is still 4 + 4 = 8. The subtraction facts also match: 8 − 4 = 4 is the only subtraction using the 4 as a part. That leaves two different facts, 4 + 4 = 8 and 8 − 4 = 4.

The same rule applies to multiplication. For 6 × 6 = 36, the facts are 6 × 6 = 36 and 36 ÷ 6 = 6. When the equal-numbers checkbox is ticked, the sheet shows two lines for these families instead of four.

Which fact family worksheets suit each grade?

The tool does not set a grade level, so choose the number range that matches what your class is learning. Sums to 10 suit early addition and subtraction practice, and sums to 20 extends that work to larger totals. Tables to 5 cover the first multiplication facts, while tables to 10 and 12 suit children who already know those tables.

To make a task easier, pick “Complete the 4 facts”, which shows all three numbers. For more recall, choose “Write the 4 facts” with every box blank. Setting “Only families that include” to one number lets you focus on a single set of facts.