Multi-Step Word Problems

Multi-step word problems are the backbone of the CSSE 11+ maths paper. Unlike some other 11+ exams, the CSSE does not have a separate verbal reasoning or non-verbal reasoning paper — the maths paper carries significant weight, and it is well known for challenging, wordy problems that require more than one calculation. This lesson will give you a reliable method for breaking down and solving any multi-step problem.

Why Multi-Step Problems Matter on the CSSE

The CSSE maths paper is designed to test your reasoning as well as your arithmetic. Many questions look simple at first glance, but they contain two, three, or even four steps before you reach the answer. Students who rush often miss a step and get the wrong answer.

The RICE Method

Use this four-step approach for every word problem:

Step	Letter	What to do
1	R — Read	Read the entire question carefully. Read it a second time.
2	I — Identify	Identify the key numbers and what the question is asking. Underline them.
3	C — Calculate	Carry out the calculations step by step. Write each step clearly.
4	E — Evaluate	Check your answer. Does it make sense in the context of the question?

Top Tip: On the CSSE paper, the final answer is not always the last number you calculate. Always re-read the question before writing your answer.

Key Words That Signal Operations

Recognising key words in a problem helps you decide which operation to use at each step.

Key words	Operation
total, altogether, sum, combined, increase	Addition
difference, fewer, less than, reduce, remain, left	Subtraction
times, product, each, every, groups of, per	Multiplication
share, split, divide, per (sharing context), equally	Division
of (with fractions or percentages)	Multiplication

Watch out: "How many more" means you need to subtract, not add!

Worked Example 1: Shopping Problem

Emma buys 3 notebooks at £2.75 each and 2 pens at £1.40 each. She pays with a £20 note. How much change does she receive?

Step 1 (Read): We need the total cost first, then the change from £20.

Step 2 (Identify): 3 notebooks at £2.75, 2 pens at £1.40, paid with £20.

Step 3 (Calculate):

Cost of notebooks: 3 × £2.75 = £8.25
Cost of pens: 2 × £1.40 = £2.80
Total cost: £8.25 + £2.80 = £11.05
Change: £20.00 - £11.05 = £8.95

Step 4 (Evaluate): £8.95 is reasonable — the items cost just over £11, so change from £20 should be just under £9. Correct!

Worked Example 2: Distance, Speed, and Time

A cyclist travels at 12 km per hour. She sets off at 09:45 and arrives at 11:15. How far does she cycle?

Step 1: Find the time taken, then use it to calculate the distance.

Step 2: Speed = 12 km/h. Departure = 09:45. Arrival = 11:15.

Step 3:

Time taken: from 09:45 to 11:15 = 1 hour 30 minutes = 1.5 hours
Distance = speed × time = 12 × 1.5 = 18 km

Step 4: 18 km in 1.5 hours at 12 km/h — that checks out.

Worked Example 3: Fractions in a Real Situation

A farmer has 240 sheep. He sells 3/8 of them in the morning. In the afternoon, he sells 1/3 of the remaining sheep. How many sheep does he have left?

Step 1: This is a three-step problem involving fractions.

Step 2: 240 sheep, sells 3/8, then sells 1/3 of the remainder.

Step 3:

Morning sales: 3/8 × 240 = 90 sheep sold
Remaining after morning: 240 - 90 = 150 sheep
Afternoon sales: 1/3 × 150 = 50 sheep sold
Remaining: 150 - 50 = 100 sheep

Step 4: 90 + 50 + 100 = 240. All sheep accounted for. Correct!

Worked Example 4: Interpreting Remainders

A school needs to transport 155 children on a trip. Each coach holds 45 children. How many coaches are needed?

Step 1: Divide and think about what the remainder means.

Step 2: 155 children, 45 per coach.

Step 3:

155 ÷ 45 = 3 remainder 20
You cannot leave 20 children behind!
4 coaches are needed.

Step 4: 3 coaches hold 135 children, leaving 20 who need a fourth coach. The answer is 4, not 3.

CSSE Tip: The CSSE loves remainder questions. Always ask yourself: do I round up or down in this situation?

Worked Example 5: Percentage and Profit

A market trader buys 80 oranges at 25p each. He sells them in bags of 5 for £2.00. He sells all the oranges. What is his total profit?

Step 1: Find the total cost, total income, then subtract.

Step 2: 80 oranges at 25p each. Sells in bags of 5 for £2.00.

Step 3:

Total cost: 80 × £0.25 = £20.00
Number of bags: 80 ÷ 5 = 16 bags
Total income: 16 × £2.00 = £32.00
Profit: £32.00 - £20.00 = £12.00

Common Mistakes to Avoid

Mistake	How to avoid it
Answering the wrong question	Re-read the final sentence before writing your answer
Forgetting a step	Write every calculation down, even simple ones
Mixing up units (e.g. pence and pounds)	Convert everything to the same unit at the start
Rounding at the wrong stage	Only round at the very end, if at all
Ignoring remainders	Think about the real-life meaning of the remainder

Practice Problems

A box of 12 cupcakes costs £6.60. A single cupcake costs 75p. Which is cheaper per cupcake — the box or buying individually? How much do you save per cupcake by choosing the cheaper option?
A train leaves London at 14:35 and arrives in Cambridge at 15:52. The return train takes 12 minutes longer. What time does the return train arrive back in London if it departs Cambridge at 17:20?
Mr Shah earns £2,400 per month. He spends 1/4 on rent, 1/5 on food, and saves the rest. How much does he save each month?

Answers:

Box price per cupcake: £6.60 ÷ 12 = 55p. Individual: 75p. Box is cheaper. Saving per cupcake: 75p - 55p = 20p.
Outward journey: 15:52 - 14:35 = 1 hour 17 minutes. Return journey: 1 hour 17 minutes + 12 minutes = 1 hour 29 minutes. Departure 17:20 + 1 hour 29 minutes = 18:49.
Rent: 1/4 × £2,400 = £600. Food: 1/5 × £2,400 = £480. Spent: £600 + £480 = £1,080. Saved: £2,400 - £1,080 = £1,320.

Summary

Multi-step word problems are the most important question type on the CSSE 11+ maths paper. Use the RICE method every time: Read, Identify, Calculate, Evaluate. Break each problem into small, manageable steps, write your working clearly, and always check that your final answer makes sense in the context of the question. With regular practice, you will become faster and more confident at these problems.