Multi-Step Reasoning Challenge
A multi-step reasoning question chains together two or more separate calculations, often from different areas of maths such as the four operations, fractions, and measures, where the answer to one step becomes an input to the next. 11+ papers use these to test whether a child can plan a solution path, not just execute a single known method, so they carry more marks than a one-step question and reward showing clear intermediate working.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem and identify how many separate facts or quantities it gives you, since each one is likely to feed into a different step.
- Plan the order of steps before calculating anything, working out what you need to know first before you can find what the question actually asks for.
- Label or note each intermediate answer clearly, since a later step will reuse it, and a mislabelled number is the most common cause of a wrong final answer.
- Carry out one step at a time, checking each intermediate answer looks sensible before moving to the next.
- On the final step, reread the question to confirm you are answering what was asked, not just the last thing you calculated.
- If short on time, write down the correct method and as many correct steps as possible, since many mark schemes award marks for a correct method even if the final answer is wrong.
Worked example
A tank starts with 64 litres of water. Every hour, 1/4 of the water currently in the tank leaks out. How much water is left in the tank after 2 hours?
- After hour 1, find 1/4 of 64: 64 / 4 = 16 litres leak out.
- Water remaining after hour 1: 64 - 16 = 48 litres.
- After hour 2, find 1/4 of the new amount, 48: 48 / 4 = 12 litres leak out.
- Water remaining after hour 2: 48 - 12 = 36 litres.
- The final answer is 36 litres.
Practice questions
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Q1A shop has 80 T-shirts. It sells 3/4 of them on Monday, then half of the remaining T-shirts on Tuesday. How many T-shirts are left?Show answer
Answer: 10 T-shirts
Q2Tom has 45 pounds. He spends 1/3 of it on a book, then 2/5 of what is left on a game. How much does he have left?Show answer
Answer: 18 pounds
Q3A class of 32 pupils is split into 4 equal teams. Each team then loses 2 pupils to another activity. How many pupils remain in each team?Show answer
Answer: 6 pupils per team
Q4A car travels 60 miles in the first hour and 3/4 of that distance in the second hour. What total distance has it travelled after 2 hours?Show answer
Answer: 105 miles
Q5A baker makes 96 rolls. She sells half in the morning, then a quarter of what remains in the afternoon. How many rolls are left at the end of the day?Show answer
Answer: 36 rolls
Q6A tank holds 200 litres. 30% is drained, then half of what remains is drained again. How much water is left?Show answer
Answer: 70 litres
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A charity collects 540 pounds. It donates 2/3 of the money to a local school, then splits the remaining money equally between 4 other causes. How much does each of the 4 causes receive?
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A gardener plants 120 bulbs. 40% of them are tulips, and the rest are split equally between daffodils and crocuses. How many crocus bulbs does she plant?
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Free printable worksheet
Want more practice on paper? Download the multi-step reasoning challenge worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 5 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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