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Mental Calculations

The principles of teaching mental calculation Important that children have a rapid recall of known number facts (for example, number bonds to 10, multiplication tables). If children can recall these key facts, they can concentrate on a more challenging calculation. If children cannot recall key facts, they treat each maths problem as a new one and start from scratch each time.

What is mental calculation? It is more than just recalling number facts. Mental maths is an important part of each maths lesson. Time is devoted to this aspect in each lesson and children are given the opportunity to use facts which they already know to work out more facts. Numbers are seen as quantities rather than just digits. Children are also given the opportunity to talk through their strategies and compare alternatives.

Different aspects of maths which involve mental calculations.

Recalling facts What is 3 add 7? How many days are there in a week?... in four weeks? Applying facts Tell me two numbers that have a difference of 12. Hypothesising or predicting Roughly, what is 51 times 47?

Designing and comparing procedures How could you subtract 37 from 82? Interpreting results So what does that tell us about numbers that end in 5 or 0? Applying reasoning The seven coins in my purse total 23p. What could they be?

How do children develop a range of mental strategies? Children are made aware of all the possible strategies Practise the different strategies Discuss and choose which is the most efficient for the calculation in question

Using practical equipment Mental calculating can involve the use of practical equipment such as: counters interlocking cubes coins counting sticks bead strings number lines 100-squares place-value cards structural apparatus like base 10 blocks (Diennes) diagrams of shapes divided into fractional parts

Using pencil and paper Pencil and paper jottings can also be used to support mental calculations. These can be to: Show the intermediate steps in a calculation Use models and diagrams (e.g. a number line)

Is the speed at which children calculate important? It is firstly important that children become secure with a method They are then encouraged to better their own performance, trying to compete against themselves

Progression in mental calculation skills See handout

A feature of mental calculation is that it is a type of calculation that can often be worked out in several different ways. Which method is the best will depend on the numbers involved, the age of the children and the range of methods that they are confident with.

Example… A group of Year 4 children is working on mental addition of two- digit numbers –Jo explains that , a near double, must be 71, since it is double 35 plus 1. –Sam explains that is 36 plus 30, making 66, plus 4 to make 70, plus 1 more, to make 71. He has worked this out by partitioning the second number into tens and ones, then counting on the tens, then the ones, bridging through 70. –Jane explains that is 30 plus 30, or 60, plus 6 add 5, which is 11, giving a total of 71. She has partitioned both numbers into tens and ones, and added the tens first. She has also recalled a known fact that she knows by heart: = 11.

Addition and Subtraction Strategies Counting forwards and backwards Reordering Partitioning: counting on or back Partitioning: bridging a multiple of 10 Partitioning: compensating Partitioning: using ‘near’ doubles Partitioning: bridging through 60 to calculate a time interval

Multiplication and Division Strategies Knowing multiplication and division facts to 10 × 10 Doubling and halving Multiplying and dividing by multiples of 10 Multiplying and dividing by single-digit numbers and multiplying by two-digit numbers Finding fractions, decimals and percentages.

Once mental calculations methods are secure, the children are able to calculate using larger numbers and find answers to trickier calculations by applying this knowledge to written methods.