The importance of mental maths skills for SATs success

LbQ (insert Darryl's preferred role) Darryl Keane, highlights why mental maths skills can play a vital role in SATs success.

During SATs week, children often prefer the relatively straightforward nature of Mathematics Paper 1 to the more cognitively demanding papers 2 and 3. On Paper 1, there are no abstract contexts or character names to get their heads around and usually no need to think about which operation to perform. It is basically a no-nonsense test of the skills that children have spent years diligently practising and developing.

Why are mental maths skills important?

In one word: time.

Children have only 30 minutes to complete 36 questions worth a total of 40 marks. This works out at 45 seconds for each mark on average. This may seem like a reasonable amount of time, yet many children do not finish all of the questions on the arithmetic paper.

Efficiency is king

What is the secret to being able to score high marks on Paper 1? Choosing the most efficient strategy every time.

On the 2022 arithmetic paper, it was possible for a child very proficient in mental calculations to not have to use a full written method for 28 of the 36 questions.

On some of the other questions, it was also possible to use mental strategies to make calculations easier or take some short cuts to arrive at a correct answer in the shortest possible amount of time.

Question 3 of this paper is a great example of where the child needs to be able to identify that this can be done mentally within a matter of seconds.

Making the mistake of setting out this question using a formal written method takes up valuable minutes, when it is much more efficient to subtract 1 ten from the 30 tens in 302. If they choose the most efficient methods, children have to perform approximately 108 individual mental calculations in the entire paper.

Choosing a written method each time more than doubles the number of individual calculations a child has to do, so they are much less likely to finish the test. Being able to quickly identify which questions should be answered mentally is vital.

Learning by Questions provides children with these opportunities as part of their National Curriculum Test style Question Sets, all of which guide children to efficient methods in the instant feedback.

Mental maths strategies or written?

Children may be extremely confident in following the rigid algorithms they have been practising for many years. Indeed, many children may be so efficient in written methods that they complete them in a similar time to a mental method. So, the choice is ultimately dependent on the individual child.

One interesting example from the 2022 paper is question 34:

Using a mental method of partitioning 2 ¼, the answer can be arrived at in two simple steps: 10 - 2 = 8 8 - ¼ = 7 ¾

By attempting a formal written method, or by converting both values to improper fractions, this question becomes much more complex:

There are now many more potential errors and the number of steps required has increased significantly using either of these methods..

Again, being confident in using mental strategies saves time and - just as importantly - minimises chances for common errors when exchanging. Interestingly, a similar question on LbQ’s version of Paper 1 was one of the questions answered incorrectly most often last year: 33% of all responses to the question 10 - 7.3 were incorrect.

Based on this analysis, Learning by Questions developed a Question Set that helps children to become experts at this kind of question: (Click on the link to sample this Question Set. Be sure to give some wrong answers to see the constructive feedback that your pupils will receive on the LbQ platform).

Number fact fluency

Virtually all questions on the 2022 paper require the use of basic number facts. Many questions include a mixture of operations. Children need to be able to instantly recall all addition, subtraction, multiplication and division facts.

Of course, it isn’t just paper 1 where children need to be able to use these key facts instantly. Quick recall and use of all number facts are required in the majority of questions across all three papers if children are to achieve well and complete each paper.

The maths specialists at LbQ have developed many practice Question Sets designed to help children become - and stay - fluent in these key facts. All of these sets include constructive feedback for the most likely mistakes and misconceptions.

Key mental maths strategies to develop

The curriculum does state that mental calculation should be taught: however, the exact methods that should be used are not stipulated. Learning by Questions has developed mastery and practice sets covering a range of mental strategies:

• partitioning

• compensation

• near-doubles

• number bonds

• related facts

• calculating efficiently

These sets typically feature image support in Level 1 to model the strategy, before the children attempt to use the strategy independently in Level 2.

LbQ has created SATs content that really helps your children improve their understanding of mental strategies (and ultimately improve their test scores). You can access our maths SATs practice papers here including our 10 new arithmetic sets focussed on developing fluency for Paper 1.

Sign up to the SATs Springboard and enjoy extended free access to our library of award-winning mastery and SATs content across.

KS2 Maths SATs paper analysis by @_MissieBee

Percentage of questions by content domain