Missing numbers in number sentences
Theory
Missing numbers in number sentences is a Year 3 maths number and algebra skill: finding the number that fills a box so an addition or subtraction sentence is true. This page explains what the equals sign really means, how to use inverse operations and part-part-whole bar models to work backwards, and how to decide if a number sentence is true or false. Curriculum: VC2M3A01 / AC9M3A01.
A number sentence is a line of maths with numbers, operation signs and an equals sign, like \(6 + 4 = 10\). The equals sign means "the same as": whatever is on the left must have the same value as whatever is on the right. It does not mean "the answer comes next".
A box \(\square\) (or a blank) stands for a number we do not know yet. Our job is to find the number that makes the sentence true, such as the \(8\) in \(7 + \square = 15\).
Addition and subtraction are inverse operations — one undoes the other. That lets us work backwards to find the box. A part-part-whole bar model helps too: two parts join to make the whole, so a missing part is the whole take away the known part.
There are no formulas to memorise, but these inverse facts show how to find the box. Match your sentence to one of these shapes.
How to find a missing number
- Read the whole sentence. Find the equals sign and see which side has the box.
- Choose the inverse. If the box is added, subtract to undo it. If the box is a start that has been subtracted, add to undo it. If a sentence has two sides, work out the full side first.
- Work it out and check. Do the calculation, then put your number back into the box to make sure both sides are the same.
The box is added, so subtract to undo it.
| \(\square\) | \(=\) | \(17 - 8\) |
| \(\square\) | \(=\) | \(9\) |
Check: \(8 + 9 = 17\). The box is \(9\).
The box is the start that was subtracted, so add to undo it.
| \(\square\) | \(=\) | \(25 + 16\) |
| \(\square\) | \(=\) | \(41\) |
Check: \(41 - 16 = 25\). The box is \(41\).
Take the known part from the whole.
| \(27 + \square\) | \(=\) | \(62\) |
| \(\square\) | \(=\) | \(62 - 27\) |
| \(\square\) | \(=\) | \(35\) |
Check: \(27 + 35 = 62\). The missing part is \(35\).
Work out the full left side first, then balance the right.
| \(45 + 8\) | \(=\) | \(53\) |
| \(40 + \square\) | \(=\) | \(53\) |
| \(\square\) | \(=\) | \(53 - 40 = 13\) |
Check: \(40 + 13 = 53\). The box is \(13\).
Common pitfalls
Frequently asked questions
What does the equals sign mean?
The equals sign means "the same as". It shows that the amount on the left has the same value as the amount on the right. It does not mean the answer comes next.
How do you find a missing number in a number sentence?
Use the inverse operation to work backwards. To find the box in \(\square + 6 = 11\), subtract: \(11 - 6 = 5\). To find the box in \(\square - 6 = 11\), add: \(11 + 6 = 17\).
What is a number sentence?
A number sentence is a line of maths that uses numbers, operation signs like plus and minus, and an equals sign, such as \(6 + 4 = 10\). A missing number is often shown with a box.
What does the box or blank stand for in a number sentence?
The box or blank stands for the number you do not know yet. Your job is to find the number that makes the sentence true.
How do you check a missing number answer?
Put your number back into the sentence in place of the box and work it out. If both sides are the same, the answer is correct. For example, \(8 + 9 = 17\) checks the answer \(9\).
What are inverse operations?
Inverse operations are operations that undo each other. Addition and subtraction are inverses, so subtraction can undo an addition and addition can undo a subtraction.