SATs Mental Maths Strategies
Although there is no longer a ‘formal’ mental arithmetic element to the KS2 SATs, there are still a good many opportunities for children in Year 6 to demonstrate their ability to quickly manipulate numbers mentally.
In Paper 1 particularly, there are likely to be several questions where mentally calculating the answer is preferable to formally writing it out. Mentally calculating answers saves time, enabling children to work through the paper quicker. In total, there are 36 questions in Paper 1 that need to be answered in 30 minutes, giving an average of only 50 seconds per question!
Below are some examples from the 2017 paper, showing how a good grasp of mental strategies is key to succeeding in this area:
Although it may sometimes be instinctive for children to write out the calculation, particularly if they find maths difficult, this question is a good example of where a secure understanding of place value is essential.
Once the child has established the value of each digit within both numbers (and recognised that although the second number is longer than the first, it will not affect how the calculation happens), they should be able to simply add 3 and 2, and insert the 0.7 into the currently ‘empty’ tenths position, giving an answer of 5.714.
The potential pitfall here could come if the child does not recognise the values of the digits within each number, or writes the calculation out, but misaligns the values of the digits, resulting in an incorrect answer.
At first, this may seem like a simple calculation. However, the ‘reverse’ nature of this addition may prove confusing for some children, particularly those who only recognise the symbol ‘=’ as meaning ‘is the answer’ and not its true meaning of ‘the same as’ or ‘equal to’.
In other words, it’s effectively a balance scale, with one side of the number sentence having the same value as the other. As the total of the two numbers on the right of the calculation is 5,100, this should be the answer in the empty box.
This may seem like quite a difficult calculation but it’s actually a good example of the kind of mental multiplication expected of KS2 children today. Once children have learned their times tables well, they are encouraged to expand their use, using place value in order to complete calculations using larger numbers.
In this example, a child who understands 8 x 3 = 24, should also understand that 8 x 30 = 240. Adding those two components together would achieve the correct answer of 264.
A child with less-secure times table/place value knowledge may instead rely upon simpler facts, such as 10 x 8 (three times) + 3 x 8. Bearing in mind the limited time allowed to complete each question, the first method is more efficient.
Again, some children may fall into the trap of setting out this calculation in a formal way, using columns and the decomposition method. This would likely take longer than 50 seconds to complete, so it would be faster to mentally calculate by subtracting 824 in stages.
Firstly, 4,912 – 800 is 4,112. The final stages could either be 4,112 – 20 (4,092) and then 4,092 – 4 = 4,088 or in one final calculation of 4,112 – 24.
Another example of a question relying on the child’s understanding of the ‘=’ sign and its meaning. In this calculation, making both sides of the number sentence have the same value means finding a number which, when 100 is subtracted, results in 1,059. In other words, the initial number should be 100 more than 1,059, which is 1,159.
This is another example of a question that may initially seem like it needs to be written out formally but can, in actual fact, be solved more speedily with mental calculation. In this case, a strong knowledge of the seven times table and a good understanding of place value are needed. Knowing that 7 x 8 = 56 should help the child conclude that 7 x 80 = 560. The remaining 21 is, of course, 7 x 3, giving a final answer of 83.
This question can therefore be calculated using multiplication facts and not formal division, which many children find difficult. Children would, of course, need to understand the concept division being a grouping of the same number and recognise its relationship to multiplication.
Being able to mentally manipulate decimal numbers is a key skill and requires a secure understanding of the value of each digit. Furthermore, in this question, an understanding of number bonds, or pairs that equal 100, would also be useful.
Some children may transfer this question to a number line (with 3.45 on the left and 9 on the right) and use it to find the difference between the two numbers. It is also possible (and faster) to calculate the answer by recognising that 0.55 is added to 3.45 to get to 4, and then a further 5 is added to get to 9, giving a total answer of 5.55.
This could be achieved either entirely through mental calculation, or at the very least through the jotting of the number needed at each stage.
There are countless ways to solve mental calculations, and everyone has a preferred method. The method itself is not really the key issue here, but rather the ability to see how numbers can be manipulated mentally and without the need for formal methods of calculation. This ability will not only give the child confidence, it will crucially save them valuable seconds, which should leave a little extra time to answer the harder questions.