Fact Family Worksheets (Addition and Subtraction)

Fact families and missing numbers go together: a fact family is a group of facts that use the same three numbers, and a missing-number problem asks which of the three is hidden. The six PDFs on this page have fact family triangles to 10 and to 20, number bonds to 20, missing numbers in subtraction to 10 and to 20, and missing addends to 20.

Every sheet has an answer key. They follow standards 1.OA.B.4 and 1.OA.D.8 of the Common Core standards for grade 1 operations and algebraic thinking, and the notes below count the families, show where the box can hide and give a way to solve each kind.

What is a fact family?

A fact family is a group of facts that use the same three numbers. The numbers 4, 6 and 10 make two addition facts and two subtraction facts:

• 4 + 6 = 10 and 6 + 4 = 10
• 10 − 6 = 4 and 10 − 4 = 6

Knowing one fact means knowing the whole family. That is the main reason fact families matter: a child who knows 7 + 8 = 15 can solve 15 − 8 without counting.

What is on these worksheets

• Fact family triangles: the whole sits at the top and the two parts at the bottom corners. Children write all four facts beside each triangle.
• Number bonds: find the missing part or whole.
• Missing numbers: problems like 13 − ☐ = 6 or ☐ + 5 = 12, where children use the related fact to find the unknown.

Teaching tips

• Point out that the biggest number is always the whole: it comes last in addition and first in subtraction.
• For a missing number in subtraction, turn it around: 13 − ☐ = 6 becomes 6 + ☐ = 13.
• Doubles such as 5 + 5 = 10 only make two facts, so the triangles on these sheets always use two different parts.

Fact families and missing numbers worksheets: what is in the set

There are 6 fact families and missing numbers worksheets on this page, and every one has an answer key except for any cut-out games. Two sheets of triangles, one of bonds, and three of missing numbers make a path from writing the four facts to finding a box that can be anywhere.

Fact families and missing numbers: how many families are there?

Fact families and missing numbers are easiest when children know how big the topic is. A family is made from a whole and two parts, so for every whole there is one family for each way of splitting it into two different parts, and one more if the whole is even (the double). This table lists the families for five wholes, with the smaller part first:

Each family has four facts, two additions and two subtractions, except for the double, which has two. The picture above shows the family for 7, 8 and 15. Counted over all the wholes, this is the whole of the work:

All the addition and subtraction facts within 20 come from just 100 families, and the facts within 10 from 25. A child who learns the family together does not need to learn 380 separate facts. The families with a part of 0 are left out, since they have only a trivial fact (0 + 7 = 7).

Fact families addition and subtraction: how the triangle works

Fact families addition and subtraction can be shown in a triangle with the whole on top and the two parts at the bottom. The worksheets use this picture because it shows that the whole is special: it is the sum in the addition facts and the starting number in the subtraction facts. This table shows five triangles, to 10 and to 20, with the four facts, or two for a double:

Fact family worksheets: the two triangle sheets

The fact family worksheets with triangles come in two levels. The first has six triangles with wholes up to 10, and the second has six with wholes from 11 to 20. Each triangle shows the three numbers, and children write two addition facts and two subtraction facts beside it. Together the two sheets give twelve families to practice.

When children write the facts, ask them to say the family aloud: “seven, eight, fifteen”. Then they can say any of the facts, and see that they all use the same three numbers. The addition worksheets and subtraction worksheets pages use the same facts in different orders.

Missing number subtraction worksheets: where the box can hide

The missing number subtraction worksheets put a box in a fact, and the box can be in three places. One fact family gives 12 different missing-number problems, since each of its four facts can hide one of three numbers. A double gives only 6. This table shows how the problems divide by the place of the box, and how to think about each one:

Counted over all the families, there are 270 different missing-number problems to 10 and 1,140 to 20. The table below shows how a family multiplies into problems:

The hardest of the three kinds is the box at the start of a subtraction, as in ☐ − 7 = 8, because the answer to the question is bigger than both of the numbers that can be seen. Children who think of the family 7, 8 and 15 see at once that the whole is the missing number. The subtraction within 10 and subtraction within 20 pages have the plain facts, and the same fact families are used for the missing numbers.

Missing addend worksheets: three ways to find the box

The missing addend worksheets ask for the part that goes with a given part to make a whole, as in 8 + ☐ = 13. A missing addend is just a subtraction in disguise, and children can find it in three ways. They can think addition (“what goes with 8 to make 13?”), count up from the first number, or subtract. This table shows the three ways for five problems:

The count-up way uses the make-ten idea: to go from 8 to 13, first go to 10 (2) and then to 13 (3), so the missing number is 2 + 3 = 5. This connects to the making 10 page and the ten frame tool. The standard 1.OA.B.4 describes this: children understand subtraction as an unknown-addend problem.

Related facts worksheets: number bonds to 20

The related facts worksheets use number bonds to show how the parts of a number fit together. A number bond to 20 shows a whole and its two parts, and it is another way to draw the same family. This table shows how many ways there are to split five numbers into two parts:

For 10 there are 11 ordered splits, from 0 + 10 to 10 + 0, and 6 splits if the order is ignored. For 20 there are 21 ordered splits and 11 unordered ones. The sheet of bonds to 20 asks for the missing part or whole, so the child must decide which of the three numbers is hidden and which fact family to use.

Common mistakes with fact families and missing numbers

Most mistakes come from not being sure which number is the whole. This table lists five of them, with what went wrong and the fix:

Fact families and missing numbers word problems

Fact families come up in stories in which a group is split or joined. Ask children to say which number is the whole, to write a fact with a box, and to solve it:

Games and activities for fact families and missing numbers

Children learn fact families and missing numbers best when they play with it. These games use things that are found at home or in a classroom:

• Triangle cards: make cards with the whole on top and ask a partner to say all four facts
• Hide a number: write a fact on a card and cover one number with a cube; the partner says what is hidden
• Family roll: roll two dice for the parts, add for the whole, and write the four facts
• Bond snap: deal number bond cards and snap when two bonds make the same whole
• Missing number hunt: hide cards with a missing number around the room and solve each one
• Fix the family: a teacher writes a family with one wrong fact, and children find the mistake

Extra support and extra challenge with fact families and missing numbers

For children who need more support: use counters in two colors and a part-part-whole mat, and let the child slide the counters apart and together to see all four facts. Start with wholes up to 5, then up to 10. For missing numbers, cover one number with a cube and ask “which part of the mat is it?”.

For children who need more challenge: ask for all the families with a whole of 12 (there are six), for a missing number with the box in every place in one family, and for the number of facts in all the families with wholes up to 10 (90). Move on to missing numbers with 2-digit numbers, such as ☐ + 25 = 60.

How to tell that a child is ready to move on from fact families and missing numbers

Before moving on from fact families and missing numbers, check that the child can do all four of these things:

1. The child can name the whole and the parts in any three numbers that make a family.
2. The child writes all four facts of a family, or two for a double.
3. The child finds a missing number in any of the three places.
4. The child uses an addition fact to solve a subtraction with a box.

When all four are true, fact families and missing numbers is secure, so move on to subtraction within 20 or the addition and subtraction word problems page.

A 20-minute lesson on fact families and missing numbers

A short lesson is the best way to introduce fact families and missing numbers. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where fact families and missing numbers fits across the grades

No skill stands alone. This table shows what children learn before and after fact families and missing numbers, with the standard that goes with each step:

This page is the main page for fact families. The whole sequence is on the subtraction worksheets page.

Helping at home with fact families and missing numbers

Parents do not need to be experts to help with fact families and missing numbers. These suggestions work well, and each takes only a few minutes:

• Use three numbers on cards, such as 4, 6 and 10, and ask for all the facts.
• Ask “which one is the whole?” before every problem.
• Cover a number in a fact with your finger and ask what is under it.
• Use dominoes: the two sides are the parts and the total is the whole.
• Praise a child who says a fact in a different order.

How to check progress in fact families and missing numbers

A teacher or parent can check progress in fact families and missing numbers with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for fact families and missing numbers

Most children need about a week of short sessions for fact families and missing numbers. This plan follows the order of the worksheets on this page:

When the plan for fact families and missing numbers is complete, move on to subtraction within 20. The whole sequence is on the subtraction worksheets page.