Non-Calculator Reasoning Paper A
Non-Calculator Reasoning Paper A is a timed 11+ maths paper of multi-step problems that must be solved entirely by written and mental methods, with no calculator allowed. It mirrors the non-calculator sections used by GL Assessment and CEM, which test whether a pupil can choose an efficient method, carry out accurate column or short working, and estimate to check the answer is sensible.
Method
- Read the question and identify the calculation type (addition, subtraction, multiplication, division, or a mix) before picking a method.
- Choose the most efficient method for the numbers involved, for example a mental method for round numbers and a written column method for larger or awkward numbers.
- Estimate the answer first by rounding the numbers, so you can spot a badly placed decimal point or a slipped digit later.
- Show full working for every step of a written method, since method marks are awarded even when the final answer is wrong.
- Check your answer using the inverse operation, for example checking a division by multiplying the answer back up.
- Manage your time across the whole paper, moving on from any single calculation that is taking far longer than its mark value suggests.
Worked example
A market trader has 3 crates of oranges, each containing 144 oranges. She sells the oranges in bags of 8. How many bags can she fill?
- Find the total number of oranges: 3 x 144 = 432.
- Divide the total by the bag size: 432 / 8.
- Work this out step by step: 8 x 50 = 400, leaving 32 remaining.
- 32 / 8 = 4, so add this to the 50: 50 + 4 = 54.
- Final answer: 54 bags.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Work out 347 + 268 without a calculator.Show answer
Answer: 615
Q2Work out 503 - 176 without a calculator.Show answer
Answer: 327
Q3Work out 23 x 16 using a written method.Show answer
Answer: 368 (23 x 10 = 230, 23 x 6 = 138, 230 + 138 = 368)
Q4Work out 588 / 12 using a written method.Show answer
Answer: 49
Q5Estimate 68 x 31 by rounding each number to the nearest 10, then give the estimate.Show answer
Answer: 2100 (70 x 30)
Q6A stadium has 25 rows of 34 seats. How many seats in total?Show answer
Answer: 850 (25 x 34)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Without using a calculator, work out 456 x 23, showing your written method.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A school hall holds 480 chairs, arranged in equal rows of 24. (a) How many rows are there? (b) On the day of a concert, 15% of the chairs are left empty. How many chairs are occupied? Work without a calculator and show your method.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 6 available
Free printable worksheet
Want more practice on paper? Download the non-calculator reasoning paper a 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 12 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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