Mental Maths: Is it still relevant?

We all know by now that the  former mental mathematics test is to be replaced by a 30-minute arithmetic test. Does this mean that we should stop teaching Mental Maths? No! Maths Advisor, Caroline Clissold, explains why.

The National Curriculum requires children in every year group to answer appropriate calculations mentally. However, there is very little mention of the strategies that they could use to do this. One of the successes of the National Numeracy Strategy was the emphasis on the importance of teaching specific strategies for mental calculation. Now that the strategy has been replaced, the teaching of mental calculation strategies is often not a priority and therefore not done in enough depth in the primary classroom. The idea behind this was that the children should be able to decide which method to use to answer different calculations. Could they do them in their heads? Could they use jottings? Would it be more efficient to use a written method? From my experience working in schools, I find that many children in Years 4, 5 and 6 use written methods as their default method, even if they are not the quickest and most efficient methods to use.

The new Arithmetic Test Paper expects the children to answer 36 questions in 30 minutes. Less than a minute per question! Clearly, having a bank of mental calculation strategies would help the children to answer some of these questions with speed and fluency. Some of the questions are set out to encourage written methods, for example those requiring the children to answer long multiplication and division calculations but most of the others can clearly be answered mentally. This will only happen if the children have a bank of strategies to choose from.

The teaching of mathematics in schools these days requires mastery. All children need to master the requirements for their year group. This means that they need to spend longer on the key topics that they are taught. One of these topics should be mental calculation. These days, I advise teachers to spend a week or two teaching key strategies before teaching written methods. These should be taught using variation so that the children can spot patterns and understand their underlying structure in order to be able to apply these confidently and accurately to calculations that can be answered in this way. When written methods are introduced, it is useful to give the children a variety of calculations to look at and discuss, sharing the methods that would be the most efficient to use to answer them. Often a mental calculation would be the most efficient.

 

There are several important mental calculation strategies that need introducing from Year 1. These include:

  • Partitioning and recombining leading to sequencing (keeping one number whole and partitioning the second, for example 245 + 165 = 245 + 100 + 60 + 5)

  • Doubling and near doubling. For example, if I know that double 250 is 500 then 250 + 260 will double 250 add 10.

  • Using number pairs to 1, 10, 100 etc. For example, 136 + 214, I know 6 add 4 equals 10, so I can add the tens and then the hundreds.

  • Adding near multiples of ten and adjusting. For example, to subtract 1998 from 3456, it would be efficient to subtract 2000 and add 2.

  • Using known number facts. For example, if I know that 8 multiplied by 7 equals 56, I can work out eight multiplied by 70 and eight multiplied by 35.

  • Bridging though ten. For example, 78 add 34, I can partition 34 into 32 and 2, add 2 to 78 to make 80 and then add the remaining 32.

  • Use relationships between operations. For example, if I know that three multiplied by 4 equals 12, I also know that 4 multiplied by 3 equals 12, 12 divided by 3 equals 4 and 12 divided by 4 equals 3.

  • Counting on. For example, because the difference between 134 and 128 is going to be small, I can count on from 128 to 134.

Others need teaching when appropriate, for example:

  • x 4 by doubling and doubling again

  • x 5 by x10 and halving

  • ÷4 by halving and halving again

  • ÷ 5 by ÷10 and doubling

  • In the sample Arithmetic paper, examples of calculations that can be answered using a mental calculation strategy include 1 034 + 586 (1 034 + 500 + 80 + 6), 472 – 9 (472 – 10 + 1}. 5 x 4 x 7 (7 x 5 doubled and doubled again), 630 ÷ 9 (using knowledge that 63 ÷ 9 equals 7 so 630 divided by nine must be 70), 20% of 1500 (finding 10% and doubling) and 12 – 6.01 (12 – 6 – 0.1)

So in answer to the question, is Mental Maths still relevant? Yes! Teaching mental calculation strategies is still as relevant as it always has been and we should ensure that we spend sufficient time working on these so that our children have a bank of methods to consider for different calculations.

Want more Mental Maths practice? Find out more about our New Curriculum Mental Maths series and download some free samples.


Tags

arithmetic, caroline, clissold, ks2, maths, mental, paper, preparation, sats

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