Mental arithmetic in P5/6

In P5/6 we are currently having a big focus on mental arithmetic – we are spending a minimum of 30 minutes each day on this area.

As we are spending so much curricular time on this, here is a brief summary of:

  • what we are doing in mental arithmetic;
  • why we are doing it;
  • how you can help.

The 72 Key Facts

Our arithmetic programme is based around 72 key ‘number facts’, which form the foundation for all other number calculation.

There are 36 key addition facts, and 36 key multiplication facts. The aim is for pupils to know these facts – i.e. be able to answer straight away without having to count.

We are working on learning our facts in school. Every week, we have a number fact challenge. Pupils are given a sheet containing 72 questions – one for each number fact – and given three minutes to complete as many questions as possible.

Three minutes may seem a very short time, but the whole point is to encourage instant recall of these facts. Our target is for pupils to improve their scores as their number fact knowledge and recall improves.

What are the Key Facts?

You can download the Addition key facts and Multiplication key facts here to print and cut out. They are in triangle form with each fact being presented in the shape of an individual triangle.

triangleAt the base of the triangle are the two smaller numbers, and at the top is the bigger number.

You can use these triangles to test your child (for example, cover up the 9 and ask 5 + 4? Or cover up the 4 and ask 9 – 5.)

Why are these facts important?

Each ‘key fact’ contains the answer to four basic calculations.

For example, if a child knows that 2 + 3 = 5:

2 + 3 = 5

3 + 2 = 5

5 – 3 = 2

5 – 2 =3


Moving on from this, knowledge of the key number fact 2 + 3 = 5 also allows pupils to understand ‘missing number’ calculations such as ? – 3 = 2, or 5 – ? = 2.


What is the benefit of knowing these facts?

Once a child comfortably knows a number fact, he / she can use it to solve more complicated arithmetic problems. For example, if 2 + 3 = 5, then 20 + 30 = 50 and 200 + 300 = 500.

Pupils in P5/6 are expected to complete 2 digit addition sums such as 23 + 45 or 56 + 36 in their heads. This is easy if you know your number facts; but almost impossible if you have to count up in your head or on fingers.

What  if children know all 72 facts?

A small number of our pupils already know all 72 facts – during the number fact challenge, these pupils are given harder calculations which are based on their number facts. E.g. instead of being given 5 x 4, they might be given ? x 40 = 2000, or 2000 ÷ ? = 5.

Firstly – does your child really know all the facts? (e.g. can he / she give answers instantly and without having to hesitate or count up in their head?)

Secondly – can your child answer all the questions relating to a number fact? For example, if he / she knows that 6 x 7 = 42, can he / she also answer 7 x 6… 42 ÷ 6… x ÷ 7 = 6 etc?

If both the above are true, then you can encourage your child to use these facts to solve harder calculations. I will cover this in the blog at a later date.

What about times tables?

Times tables are a good way of organising the multiplication number facts. However, merely learning to recite a times table can sometimes lead to problems. Children sometimes ‘learn a table’ but cannot recall individual facts within that table. They also sometimes find it hard to link the times table to division.

There is nothing wrong with learning tables, but children should ensure that they are also learning division facts.

What about written sums?

In P5/6, we do not work on formal written methods for addition or multiplication (i.e. ‘tower sums’ or ‘chimney sums’.

This is to ensure that we are fully focused on developing our mental calculation skills. There is considerable evidence to suggest that teaching children formal written methods before they have a good grasp of mental arithmetic leads to confusion and lack of understanding.

In addition, if children have a firm understanding of mental arithmetic, then there is no need to lay out a formal written method for a sum such as 36 + 53.

We do use informal written methods to solve harder addition, subtraction, multiplication and division sums. This is outwith the scope of this current blog but will be covered at a later date.

I appreciate that the majority of parents will have learned written methods at school and may wish to teach these to your child. Please ensure that before you teach your child any written methods, he / she has a good grasp of the relevant number facts. After all, it is pointless using the written method to solve 87 + 48 if your child cannot confidently recall that 8 + 4 = 12 and 7 + 8 = 15.

How can I support this at home?

Short, regular practice is the best way for children to learn and consolidate their number facts. You can download the fact triangles using the link above. Test your child every so often and encourage your child to work on remember the ones that he / she has not yet learned.

If your child is more confident and knows the number facts, then you can try and ask more challenging questions based on the number facts – e.g. 400 x 600 – to develop your child’s arithmetic further.

You can also visit – this is a speed challenge website which your child uses each day in school as extra practice. Set the time limit and type of question for an endless source of challenge questions.

Where can I find out more?

Please feel free to ask me about our mental arithmetic work – I am happy to provide  support if necessary. I will also be further outlining our numeracy work at the forthcoming curricular evening on Thursday 9th February.


This entry was posted in P5-7 Homework, P5/6 2016-17, Uncategorized. Bookmark the permalink.

One Response to Mental arithmetic in P5/6

  1. sampringle says:

    Every day is a school day! This is really interesting and I can see that it’s the foundation of later work. Thank you for sharing the work sheets and website

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