Addition & subtraction word problems
Theory
Addition and subtraction word problems are a Year 3 maths skill: reading a story, deciding whether to add or subtract, and working out the answer. This page explains keyword clues, the part-whole bar model, how to find a missing part or starting number, and how to solve two-step problems including money and change. Curriculum: VC2M3N08 / AC9M3N06.
A word problem is a maths question written as a short story. Your job is to work out whether to add or subtract, then find the answer.
Every add-or-subtract story is really about parts and a whole. When two parts are joined together, you add to find the whole. When you take one part away, or compare two amounts to find how many more, you subtract.
Some words give clues. Altogether, total and in all usually mean add. Left, fewer, how many more and change usually mean subtract. A bar model is a picture that helps you see the parts and the whole so you can choose the right operation.
Word problems do not use one set formula, but the part-whole idea and these fact links help you decide whether to add or subtract.
How to solve an addition or subtraction word problem
- Read and picture. Read the story twice and picture what is happening: joining two groups, taking some away, or comparing two amounts.
- Choose add or subtract. Join two parts, so add. Take away or compare, so subtract. Draw a bar model and look for clue words to help you decide.
- Work it out. Line up the hundreds, tens and ones, then add or subtract, regrouping when you need to carry or borrow.
- Check it fits. Ask if the answer makes sense in the story, and check a subtraction by adding the parts back together.
Two groups are joined, so add.
| \(328 + 245\) | \(=\) | \(573\) |
Altogether \(573\) visitors came.
The missing part is the whole take away the known part.
| \(220 - 85\) | \(=\) | \(135\) |
There are \(135\) blue counters. Check: \(85 + 135 = 220\).
How many more is a difference, so subtract.
| \(74 - 59\) | \(=\) | \(15\) |
Room 5 scored \(15\) more points.
First the total, then the change.
| \(\$18 + \$9\) | \(=\) | \(\$27\) |
| \(\$50 - \$27\) | \(=\) | \(\$23\) |
Maya gets \(\$23\) change.
Common pitfalls
Frequently asked questions
How do you know whether to add or subtract in a word problem?
Picture the story. If two parts are joined into a whole, add. If you take one part away, or compare to find how many more or fewer, subtract. Clue words like altogether usually mean add, while left, change and how many more usually mean subtract.
What is a bar model in maths?
A bar model is a picture that shows the parts and the whole as rectangles. A long bar is the whole and the shorter bars below are the parts. It helps you see whether to add the parts or subtract to find a missing part.
Does how many more mean add or subtract?
How many more means subtract. You are comparing two amounts to find the difference, so take the smaller number away from the larger one. For example, how many more is \(74\) than \(59\) is \(74 - 59 = 15\).
How do you solve a two-step word problem?
Do one step at a time. Work out the first answer, such as a total, then use it in the second step, such as finding the change or the difference. Write both steps down so you do not stop after the first one.
How do you find a missing starting number?
Use the opposite operation. If some were taken away and you know how many are left, add them back. For example, if a bus loses \(17\) students and \(25\) are left, the start is \(25 + 17 = 42\).
What are keyword clues for addition and subtraction problems?
Words like altogether, total and in all usually point to addition. Words like left, fewer, how many more, difference and change usually point to subtraction. Always read the whole sentence, because clue words are hints, not fixed rules.