What you will learn
- Explain what the equals sign means.
- Find a missing number using the inverse (opposite) operation.
- Solve number sentences when the box is on the left or the right of the equals sign.
Some number sentences have a number missing, shown by a box. Finding it is like being a detective: the other numbers are your clues. In this lesson you will learn a trick that works every time: use the opposite operation.
What the equals sign means
A number sentence uses numbers and signs, like 300 + 200 = 500. The equals sign (=) does not mean “the answer comes next”. It means both sides have the same value, like a balance that is level.
So 500 = 300 + 200 and 300 + 200 = 400 + 100 are true number sentences too. When a number is missing, we draw a box: + 200 = 500.
Use the inverse
Adding and subtracting are inverse (opposite) operations. One undoes the other. To find a missing number, do the opposite.
Worked example 1
+ 1 250 = 3 400
Show me how
Something add 1 250 makes 3 400. To undo adding, subtract.
3 400 − 1 250 = 2 150.
Check: 2 150 + 1 250 = 3 400. So = 2 150.
Worked example 2
5 000 − = 1 800
Show me how
5 000 take away something leaves 1 800.
The missing number is the difference: 5 000 − 1 800 = 3 200.
Check: 5 000 − 3 200 = 1 800. So the box is 3 200.
The box can be anywhere
The box can be on the right of the equals sign: 900 = 400 + . It still means the same: 400 and what make 900? The answer is 500.
Sometimes both sides have two numbers: 400 + 300 = + 200. Work out the side you know first: 400 + 300 = 700. Now 700 = + 200, so the box is 500.
Watch out! A common mistake
Do not just add the numbers you can see. In 25 + = 60, the answer is not 85. Ask: 25 and what make 60? 60 − 25 = 35. Always put your answer in the box and check that both sides are equal.
Multiplying and dividing
Multiplying and dividing are inverse operations too. For 7 × = 42, think 42 ÷ 7 = 6. For 42 ÷ = 7, think 7 × 6 = 42, so the box is 6.
Try it
TRY ITBalance the number sentence
Choose a game, then tap the number that goes in the box. If you choose a wrong number, watch the balance tip.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. + 45 = 120
Hint
What do you add to 45 to make 120?
Show answer
120 − 45 = 75. The box is 75.
2. 2 300 + = 5 000
Hint
Subtract 2 300 from 5 000.
Show answer
5 000 − 2 300 = 2 700.
3. − 350 = 1 650
Hint
Use the inverse: add.
Show answer
1 650 + 350 = 2 000. Check: 2 000 − 350 = 1 650.
4. 6 000 − = 2 500
Hint
How much is taken away?
Show answer
6 000 − 2 500 = 3 500.
5. 800 = 500 +
Hint
The box is on the right. 500 and what make 800?
Show answer
300
6. 350 + 150 = + 100
Hint
Work out the left side first.
Show answer
350 + 150 = 500, and 500 − 100 = 400. The box is 400.
7. (a) 8 × = 56
(b) 63 ÷ = 9
Hint
Use your times tables.
Show answer
(a) 56 ÷ 8 = 7
(b) 9 × 7 = 63, so the box is 7.
8. Ria had some marbles. She won 125 more and now has 400. Write a number sentence with a box, then solve it.
Hint
What did she start with? That is the box.
Show answer
+ 125 = 400. 400 − 125 = 275, so Ria had 275 marbles.
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Balance Keeper badge.
Number sentences with a missing number: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. + 45 = 120
2. 2 300 + = 5 000
3. − 350 = 1 650
4. 6 000 − = 2 500
5. 800 = 500 +
6. 350 + 150 = + 100
7. (a) 8 × = 56
(b) 63 ÷ = 9
8. Ria had some marbles. She won 125 more and now has 400. Write a number sentence with a box, then solve it.
Part B: Quiz
1. □ + 300 = 1 000. What is □?
(a) 1 300
(b) 700
(c) 300
(d) 1 000
2. 4 500 − □ = 2 000. What is □?
3. Which number makes 1 250 + □ = 2 000 true?
(a) 750
(b) 3 250
(c) 850
(d) 650
4. In 900 = □ + 400, the missing number is 500.
True or False? Circle one: True / False
5. □ − 600 = 3 400. What is □?
6. 200 + 500 = □ + 300. What is □?
(a) 700
(b) 400
(c) 1 000
(d) 300
7. 6 × □ = 48. What is □?
8. To find □ in □ + 75 = 200, you add 200 and 75.
True or False? Circle one: True / False
9. 42 ÷ □ = 7. What is □?
(a) 6
(b) 7
(c) 35
(d) 49
10. Kezia gave away 1 250 stickers and has 3 750 left. Which number sentence shows how many she started with?
(a) □ − 1 250 = 3 750
(b) □ + 1 250 = 3 750
(c) 1 250 − □ = 3 750
(d) 3 750 + □ = 1 250
Answers (for the adult)
Part A
1. 120 − 45 = 75. The box is 75.
2. 5 000 − 2 300 = 2 700.
3. 1 650 + 350 = 2 000. Check: 2 000 − 350 = 1 650.
4. 6 000 − 2 500 = 3 500.
5. 300
6. 350 + 150 = 500, and 500 − 100 = 400. The box is 400.
7. (a) 56 ÷ 8 = 7
(b) 9 × 7 = 63, so the box is 7.
8. + 125 = 400. 400 − 125 = 275, so Ria had 275 marbles.
Part B
1. (b) 700
2. 2 500
3. (a) 750
4. True
5. 4 000
6. (b) 400
7. 8
8. False
9. (a) 6
10. (a) □ − 1 250 = 3 750
Recap
- The equals sign means both sides have the same value.
- A box stands for a missing number.
- Use the inverse to find it: subtraction undoes addition, and division undoes multiplication.
- The box can be on the left or the right of the equals sign.
- Check by putting your answer in the box: both sides must be equal.
Words to know
- number sentence
- Numbers and signs that make a statement.
Example: 400 + 100 = 500 is a number sentence. - equals sign
- The sign = which means both sides have the same value.
Example: In 6 = 2 + 4 the equals sign is first. - missing number
- A number that is not shown, often drawn as a box.
Example: In + 3 = 10 the missing number is 7. - inverse
- The opposite operation, which undoes another one.
Example: Subtraction is the inverse of addition. - balance
- When both sides are equal.
Example: 300 + 200 and 500 balance.
Try it at home
- Make a balance with a coat hanger, string and two plastic cups. Put the same number of beans or bottle caps on each side. Take some away from one side and ask someone at home to make it balance again.
- Mini project: write five missing-number puzzles on cards, with the box in different places. Swap cards with someone at home and check each other’s answers.
Test tips
Tips for class tests
- Look at the sign first. If it is +, the missing number is usually found by subtracting.
- Put your answer in the box and work out both sides. They must be equal.
- If both sides have two numbers, work out the side you know first.
For parents and teachers
After this lesson, your child should be able to:
- explain that the equals sign means “the same value as”;
- find a missing number by using the inverse operation;
- solve number sentences with the box on either side of the equals sign.
Multiplying and dividing here use only facts up to 10 × 10; these are practised fully in the multiplication lessons. Ask your child to check each answer by putting it back in the box.
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Next: Adding 4-Digit Numbers – Standard 3 Maths
Course: Standard 3 Maths
Updates
2026/11/04
– First version of this lesson.
Attributions to media used in this post:
Simple balance scales-02.jpg – Lilly_M – CC BY-SA 3.0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.
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