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Year 4 Maths Addition & Subtraction Problems

Multi-step addition & subtraction problems

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Theory

Multi-step addition and subtraction problems are a Year 4 maths problem-solving skill: word problems that need more than one calculation. This page shows how to turn each action into add or subtract, work through the steps in order, use a bar model to see the parts and the whole, and work backwards to find a starting amount for numbers to 1000 and money in dollars. Curriculum: VC2M4N09 / AC9M4N08.

A multi-step problem is a word problem that needs more than one step. You add or subtract two or three times before you reach the answer. Reading carefully matters just as much as the calculating.

The trick is to turn each action into add or subtract. Words like join, more, altogether, total and arrive mean add. Words like spend, leave, get off, give away and sold mean subtract. Then you work through the steps in order, keeping a running total after each one.

A bar model is a picture that helps you plan. The whole is one long bar and the parts sit underneath it. When you know the whole and some parts, you subtract to find a missing part. When you know all the parts, you add to find the whole.

Bar model with a whole of 250 split into parts 110, 75 and an unknown part A long top bar labelled 250 sits above three shorter bars. Two parts are 110 and 75; the third part is unknown, so 250 minus 110 minus 75 equals 65. Whole = 250 250 110 75 ? 250 − 110 − 75 = 65
A bar model: subtract the known parts from the whole to find the missing part.
Step chain showing 124 minus 36 equals 88, then plus 48 equals 136 Three boxes joined by arrows. The first box is 124, an arrow labelled minus 36 leads to 88, and an arrow labelled plus 48 leads to 136. 124 −36 88 +48 136 start now
Work in order: do each step and carry the running total forward.

Multi-step problems do not use a formula, but these word links help you write the number sentence for the whole story.

\[ \text{start} - \text{spent} + \text{received} = \text{now} \]
start-spent+received=now
\[ \text{goal} - \text{amount so far} = \text{still needed} \]
goal-amount so far=still needed
\[ 75 + 48 = 123 \quad \text{and} \quad 200 - 123 = 77 \]
75+48=123 and 200-123=77
Is it enough? Add up what you have, then compare it with the goal or the price. If the total is smaller, subtract to find how much more is needed: with \(\$75\) and \(\$48\) saved towards \(\$200\), you still need \(\$77\). If the total is bigger, subtract to find how much is left over. To test whether you can buy two things, add their prices and compare with the money you have.

How to solve a multi-step problem

  1. Read to the end. Read the whole story before you start so you know how many steps there are.
  2. Match each action. Turn each part of the story into add or subtract, using the meaning, not just a key word.
  3. Work in order. Do the first step, then use that answer in the next step, keeping a running total.
  4. Compare when asked. For "how many more", "is it enough" or "which statement is true", work out each amount first, then subtract to compare.
  5. Check it. Work backwards or ask if the answer makes sense for the story.
Finding a starting amount? Work backwards and undo each step. If an amount was added, subtract it back; if it was taken away, add it back. If \(30\) were added and then \(12\) taken away to leave \(100\), the start was \(100 + 12 - 30 = 82\).
Example 1 — Choose the number sentence
A ferry has \(162\) people aboard. At the wharf \(38\) get off and \(54\) get on. Which number sentence finds how many are aboard now?
Solution
\(\text{get off}\)\(\to\)\(-38\)
\(\text{get on}\)\(\to\)\(+54\)
\(162 - 38 + 54\)\(=\)\(178\)
162−38+54=178

The sentence is \(162 - 38 + 54\), which gives \(178\).

Example 2 — Total, then take away
A bakery made \(176\) rolls in the morning and \(158\) in the afternoon. It sold \(290\) rolls. How many rolls are left?
Solution
\(176 + 158\)\(=\)\(334\)
\(334 - 290\)\(=\)\(44\)
334−290=44

Add the two batches, then subtract what was sold: \(44\) rolls are left.

Example 3 — Bar model with money
Maya had \(\$180\). She spent \(\$75\) on a hoodie and \(\$46\) on a book. How much money is left?
Bar model with a whole of 180 dollars split into 75, 46 and an unknown left-over part A top bar of 180 dollars sits above three bars: 75 dollars, 46 dollars and an unknown part. So 180 minus 75 minus 46 equals 59. Whole = $180 $180 $75 $46 ? $180 − $75 − $46 = $59
Solution
\(180 - 75\)\(=\)\(105\)
\(105 - 46\)\(=\)\(59\)
180−75−46=59

Take away each amount she spent: \(\$59\) is left.

Example 4 — Find the starting amount
Ella spent \(\$60\) on shoes and \(\$35\) on a top. She has \(\$40\) left. How much money did she start with?
Solution
\(60 + 35\)\(=\)\(95\)
\(95 + 40\)\(=\)\(135\)
60+35+40=135

Add the spending back to what is left: she started with \(\$135\). Check: \(135 - 60 - 35 = 40\).

Common pitfalls

Stopping after one step. Watch out for answering too soon. Most of these problems have two or three steps, so read to the end before you write your answer.
Getting the order wrong. Keep the actions in the same order as the story. Money spent and then paid back is subtract, then add, not the other way round.
Trusting one key word. A word like "left" usually means subtract, but always check what is really happening in the story before you choose the operation.
Forgetting to undo when working backwards. To find a starting amount, subtract the parts that were added and add the parts that were taken away.

Frequently asked questions

What is a multi-step word problem?

A multi-step word problem needs more than one calculation to solve. You usually add or subtract two or three times, keeping a running total, before you reach the final answer.

How do you solve a two-step word problem?

Read the whole story first. Turn each action into add or subtract, do the first step, then use that answer in the second step. Working in order keeps a running total.

Do I add or subtract in a word problem?

Look at what is happening. Words like join, more, altogether and arrive mean add. Words like spend, leave, get off and sold mean subtract. Some problems use both.

How do you find the starting number in a word problem?

Work backwards and undo each step. If an amount was added, subtract it back. If an amount was taken away, add it back. Spending \(\$60\) and \(\$35\) and having \(\$40\) left means you started with \(60 + 35 + 40 = 135\).

What is a bar model in maths?

A bar model is a picture that shows the whole amount as one long bar and the parts as smaller bars underneath. It helps you see which parts to add and which to subtract to find a missing amount.

Why do I keep getting multi-step problems wrong?

The most common reason is stopping after one step. Read to the end, do every step, and keep the actions in the same order as the story. Checking your answer by working backwards helps too.

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