Missing numbers and inverse operations: what children learn
Year 4 pupils solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use. Missing-number problems build the inverse thinking those problems need.
In this game children match missing-number calculations, such as □ + 1,150 = 5,000, to the missing number. Using the inverse operation turns each puzzle into a calculation children already know how to do.
This topic covers the Year 4 statutory requirement in the National Curriculum in England (Number – addition and subtraction): pupils should be taught to “estimate and use inverse operations to check answers to a calculation”. Year 4 pupils are usually aged 8–9.
For families following US standards, the closest Common Core standard is 4.NBT.B.4, which is taught in Grade 4.
How to play
Pick a card on the left, then the card on the right that matches it. Each game has 6 pairs. Wrong matches are counted as mistakes, and you get three stars for a game with no mistakes.
Step by step
- Read the box as a missing number. □ + 1,150 = 5,000 means 'what plus 1,150 makes 5,000?'
- Use the inverse for addition. If □ + 1,150 = 5,000, then □ = 5,000 − 1,150.
- Subtraction with a missing part. If 7,500 − □ = 1,200, then □ = 7,500 − 1,200.
- Check. Put the answer back in the box and see if the calculation works.
Worked examples
Example 1: □ + 1,150 = 5,000
Working: 5,000 − 1,150 = 3,850.
Answer: 3,850
Example 2: 7,500 − □ = 1,200
Working: 7,500 − 1,200 = 6,300.
Answer: 6,300
Example 3: 10,000 − □ = 3,000
Working: 10,000 − 3,000 = 7,000.
Answer: 7,000
Common mistakes and how to fix them
- Adding the two numbers you can see, every time. Ask what the calculation means in words first.
- Using the wrong inverse for a missing subtracted number. If 7,500 − □ = 1,200, the box is the part taken away: 7,500 − 1,200.
- Not checking the answer. Put the number in the box and calculate to check.
Activities to try at home
- Ask: I had some money and spent £1,150. I have £3,850 left. How much did I start with?
- Play 'what's my number?' with addition clues.
- Use a bar model drawing to show missing parts.
Ideas for the classroom
- Pupils draw bar models for missing-number problems.
- Pupils write their own missing-number puzzles for a partner.
- Link missing numbers to fact families: 1,150 + 3,850 = 5,000, so 5,000 − 3,850 = 1,150.
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Why use boxes instead of letters?
A box is easier to understand at first. Letters for unknowns come in Year 6 algebra.
What is a bar model?
A drawing of a whole split into parts. It shows which numbers to add or subtract.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it, then pick its partner.