Complete number sentences (find the unknown) - One-step
Theory
A number sentence such as \(\;\rule{1.2cm}{0.4pt}\; + 9 = 21\) has a missing number. The equals sign means both sides have the same value, so the missing number is the one that makes the sentence true. This Year 5 maths page shows how to find it with number facts, how to check by substituting it back in, and how to write a number sentence for a story.
The equals sign \(=\) means “has the same value as”. It does not mean “the answer comes next”. \(11 + 5 = 24 - 8\) is true because both sides are \(16\).
A missing number (the unknown) can be anywhere in the sentence: at the start, in the middle or at the end.
To substitute means to put a number in place of the gap. If the sentence is then true, the number is correct.
A word problem can be written as a number sentence with a gap for the unknown amount. “Some cards, then \(14\) more, makes \(41\)” is \(\;\rule{1.2cm}{0.4pt}\; + 14 = 41\).
The equals sign balances the two sides:
How to find a missing number
- Read the sentence as a question (what plus \(9\) makes \(21\)?).
- Use a fact you know, or the opposite operation, to find the number.
- Substitute it into the gap.
- Check that both sides have the same value.
| \(21 - 9\) | \(=\) | \(12\) |
\(12\). Check: \(12 + 9 = 21\).
| \(36 \div 4\) | \(=\) | \(9\) |
\(9\). Check: \(9 \times 4 = 36\).
(i) \(48 \div \;\rule{1.2cm}{0.4pt}\; = 6\)
(ii) \(\;\rule{1.2cm}{0.4pt}\; - 19 = 33\)
(iii) \(120 - \;\rule{1.2cm}{0.4pt}\; = 75\)
| \(6 \times 8\) | \(=\) | \(48\) |
| \(33 + 19\) | \(=\) | \(52\) |
| \(120 - 75\) | \(=\) | \(45\) |
(i) \(8\)
(ii) \(52\)
(iii) \(45\)
| \(13 \times 5\) | \(=\) | \(65\) |
\(65\). Check: \(65 \div 5 = 13\).
| \(11 + 5\) | \(=\) | \(16\) |
| \(24 - 8\) | \(=\) | \(16\) |
True: both sides have the value 16.
| \(\;\rule{1.2cm}{0.4pt}\; + 14\) | \(=\) | \(41\) |
| \(41 - 14\) | \(=\) | \(27\) |
\(\;\rule{1.2cm}{0.4pt}\; + 14 = 41\); she started with \(27\) cards.
| \(13 - 5\) | \(=\) | \(8\) |
Both sides must be equal. \(5 + 18\) is \(23\), not \(13\). The missing number is \(8\).
Common pitfalls
Frequently asked questions
What does the equals sign mean?
Both sides have the same value. \(11 + 5 = 24 - 8\) is true because both sides equal \(16\).
How do you find a missing number?
Ask what number makes the sentence true, using a fact or the opposite operation. For \(\;\rule{1.2cm}{0.4pt}\; \times 4 = 36\), \(36 \div 4 = 9\).
What does substitute mean?
Put the number into the gap and work out both sides to see if they are equal.
Can the missing number be first?
Yes. In \(\;\rule{1.2cm}{0.4pt}\; \div 5 = 13\) the missing number is \(65\).
How do you write a word problem as a number sentence?
Follow the story in order and use a gap for the unknown: some cards plus \(14\) makes \(41\) is \(\;\rule{1.2cm}{0.4pt}\; + 14 = 41\).