By Jonathan Strange
Choose a Schofield & Sims Mental Arithmetic book around your child’s current understanding and the publisher’s placement guidance. Do not assume that the book number is the school year. Start by checking which series your teacher or tutor means.
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Build 7 × 8 from a fact you know
Start with 7 × 4
7 groups of 4 = 28.
Double the groups of 4
28 + 28 = 56.
Explain the connection
8 is double 4, so 7 × 8 is double 7 × 4.
First, identify the exact series
Mental Arithmetic, First Mental Arithmetic and Essential Mental Arithmetic are different titles. A recommendation for “Book 2” is incomplete without the series name. This article focuses on the Mental Arithmetic series listed in our student booklist.
Use the publisher’s entry guidance
Schofield & Sims provides entry tests and guidance for selecting a starting book. Its main placement article describes Entry Test A for Books 1–3 and Entry Test B for Books 4–6, alongside a separate guide for parents.
Visit the official entry-test guidance and follow the instructions for the resource you choose. Use its own marking and placement information rather than an unofficial score table.
Explain that the purpose is to find suitable work. Do not coach answers during the assessment: that can make the suggested starting point less useful. If the result seems inconsistent with everyday schoolwork, discuss it with the teacher.
Questions to ask before buying
- Does the full title match the recommendation?
- Is this the pupil book or the answer booklet?
- Does the edition match the supporting material?
- Are answers available through the publisher or school already?
- Is the copy unused if your child needs to write in it?
Do not automatically buy a separate answer booklet without checking what you already have. The publisher’s Mental Arithmetic downloads page includes supporting resources and answer downloads.
Turn marking into learning
A score tells you how many answers were correct. It does not tell you why the other answers went wrong. Before setting another page, choose one error and ask your child to explain their approach.
The worked strategy above uses 7 × 4 = 28 to find 7 × 8 = 56. That connection can help a child rebuild a forgotten fact. But it will not solve every kind of mistake: a child who chose multiplication when the question required subtraction needs different support.
Example 1: the fact is not secure
Suppose your child cannot recall 6 × 8. If they know 6 × 4 = 24, doubling gives 48. Ask them to explain why doubling is appropriate: each of the six groups contains twice as many.
Then try 6 × 9. One route is 6 × 10 − 6 = 54. The point is not to insist on one method, but to connect known facts with the fact being found. Return to the question later without supplying the starting fact.
Example 2: the calculation is right, but the operation is wrong
A notebook costs £3. Mia pays with a £10 note. How much change should she receive?
A child might calculate 10 + 3 = 13 accurately and still answer the question incorrectly. Ask, “Are we finding the total price or the money left after paying?” The required calculation is £10 − £3 = £7.
Drawing a simple £10 amount split into £3 spent and £7 left can make the relationship clear. Repeating addition facts would not address this particular misunderstanding.
Example 3: a units check catches an unreasonable answer
A ribbon is 1 metre long. A 35-centimetre piece is cut off. How much ribbon remains?
First express the quantities in the same unit: 1 metre = 100 centimetres. Then calculate 100 − 35 = 65 centimetres. Ask whether the answer is sensible: the remaining ribbon must be shorter than one metre.
All three are original examples for this guide. They illustrate different things to notice while marking; they are not questions copied from the Mental Arithmetic books.
Build a short practice session around one clear goal
A manageable session should leave time to understand a correction. Choose an amount of work your child can attempt with attention, then use this sequence:
- Attempt: let your child work independently so you can see what is secure.
- Discuss: choose an error or uncertain answer and ask for the method.
- Model: explain the missing idea with one clear example.
- Apply: give a similar question without repeating the prompt.
- Return: revisit the skill in a later session.
Keep a brief note such as “convert metres to centimetres before subtracting”. This is more useful for the next session than “needs to be more careful”.
What if the chosen book feels too hard or too easy?
If your child needs help with nearly every question, pause and compare the book with the publisher’s placement guidance and current schoolwork. Check whether the difficulty is the arithmetic, the language or the range of topics. Do not assume that frustration means a lack of effort.
If the work is consistently secure, ask your child to explain a method, estimate an answer or solve a related word problem. These are useful checks before seeking a recommendation for the next book.
Should I time every page?
Follow the teacher’s or publisher’s instructions for the activity. When teaching an unfamiliar idea, give room to explain and check it. Add timing where it serves a clear practice goal, rather than making speed the only sign of progress.
Does Book 3 mean Year 3?
No automatic school-year match should be inferred from the number. Use the exact series name and the publisher’s entry guidance to choose the starting point.
Will one arithmetic book cover everything for the 11+?
An arithmetic resource is one part of preparation. Check the requirements for the intended exam and make room for the wider reasoning and problem-solving it tests. Use the book to strengthen the relevant foundations.
When should you move to the next book?
Finishing pages is not the only check. Look for independent attempts, accurate methods and an explanation of mistakes. If your child needs prompts throughout, discuss whether to consolidate before moving on. Where work is consistently secure, seek the teacher’s next recommendation.
Find the matching resource
Explore our listings for Mental Arithmetic Introductory, Book 1, Book 2 and Book 3, or see the full student booklist. These are choices to match a recommendation, not a requirement to buy every volume.
For entrance preparation, our 11+ maths guide explains the wider role of foundations and problem-solving. For personal support, enquire about classes.