Missing number subtraction

A missing number can hide anywhere in a subtraction. A bar model or a fact family shows how to find it.

Three places a number can hide

The last row surprises many children: a subtraction with a missing start is solved by adding. That makes sense once you see that the start is the whole, made of the two parts.

Use a bar model

Draw a bar for the whole and split it into two parts. In any subtraction, the first number is the whole, and the other two numbers are the parts.

• If you know both parts, add to find the whole.
• If you know the whole and one part, subtract to find the other part.

This one rule solves every missing number problem in addition and subtraction.

Fact families and counting up

For small numbers, a fact family gives the answer straight away. 12 − ? = 5: the family is 5, 7 and 12, so the missing number is 7.

For bigger numbers, count up. 63 − ? = 38: count up from 38 to 63, which is 2 to 40 and 23 more, so 25. Check: 63 − 25 = 38.

Balancing

Some puzzles have numbers on both sides: 15 − 6 = ? − 2. The = sign means both sides are equal. 15 − 6 = 9, so the right side must also be 9: ? − 2 = 9, so the missing number is 11. Puzzles like this build the idea of balance that algebra needs later.

Missing numbers in stories

Word problems often hide the missing number in a different place from the end:

• Start unknown: “Some birds were on a tree. 5 flew away and 8 are left. How many were there at first?” ? − 5 = 8, so 13.
• Change unknown: “There were 15 cakes. Some were eaten and 6 are left. How many were eaten?” 15 − ? = 6, so 9.
• Result unknown: “There were 15 cakes and 9 were eaten. How many are left?” 15 − 9 = ?, so 6.

The start-unknown problems are the hardest for most children, because the story says “flew away” but the answer needs adding. Drawing a bar model first makes it clear that the start is the whole.

Write the missing-number sentence first, with a box or question mark, before solving. It shows exactly what the story says and helps your child choose between adding and subtracting.

Where this fits: subtraction step by step

1. What is subtraction
2. Subtraction within 10
3. Counting back
4. Subtraction on a number line
5. Counting up
6. Fact families
7. Make 10 subtraction strategy
8. Subtraction within 20
9. Subtracting tens and hundreds
10. 2-digit subtraction
11. Subtraction with regrouping
12. 3-digit subtraction
13. Subtracting across zeros
14. Mental subtraction strategies
15. Checking subtraction with addition
16. Missing number subtraction (this page)
17. Estimating differences
18. Multi-digit subtraction
19. Subtraction word problems

What to say to your child

More worked examples

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

1. 9 − ? = 4
2. ? − 3 = 6
3. 14 − ? = 8
4. ? − 7 = 7
5. 20 − ? = 13
6. ? − 25 = 30
7. 70 − ? = 45
8. Raj had some sweets. He ate 4 and has 9 left. How many did he have?
9. Stretch: 18 − 9 = ? − 3

Common mistakes

How to teach it at home

Hidden objects

Show 10 toys, hide some, and ask how many are hiding from what is left.

Box puzzles

Write puzzles like 15 − ? = 9 on sticky notes around the house.

Mystery number

“I’m thinking of a number. Take away 6 and you get 8. What is it?”

By grade

• Grade 1 (1.OA.B.4, 1.OA.D.8): find the unknown number in addition and subtraction equations within 20.
• Grade 2 (2.OA.A.1): solve word problems with unknowns in all positions within 100.
• Grade 3 (3.OA.A.4): find unknown numbers in equations, a step towards algebra.
• Next: subtraction word problems.

More for each grade: Grade 1 math and the CBSE class 1 maths guide; Grade 2 math and the CBSE class 2 maths guide; Grade 3 math and the CBSE class 3 maths guide.

Worksheets and practice

Fact families worksheet: printable PDF with an answer key. · Make a fresh test

Subtraction practice · subtraction speed test · subtraction chart · subtraction for kids