MENTAL CALCULATION

Mental Calculation

Mental Calculation

Task 1:

Mental calculation: expectations for each year

It is important that teachers of all years should address all the strategies, including the basic strategies, to ensure that they are well covered. This section reinforces the expectations set out by the Framework for teaching mathematics. Teachers should refer to the 'Framework' for further examples of mental calculations. (Koshy 2000)

Rapid recall

Children should be able to recall rapidly:

Mental strategies

Children should be able to use the following strategies, as appropriate, for mental calculations:

Year 1:

- All pairs of numbers with a total of 10, e.g. 3 + 7;

- Addition and subtraction facts for all numbers to at least 5;

- Addition doubles of all numbers to at least 5, e.g. 4 + 4.

- count on or back in ones;

- reorder numbers in a calculation;

- begin to bridge through 10, and later 20, when adding a single-digit number;

- use known number facts and place value to add or subtract pairs of single-digit numbers;

- add 9 to single-digit numbers by adding 10 then subtracting 1;

- identify near doubles, using doubles already known;

- use patterns of similar calculations.

Year 2:

- Addition and subtraction facts for all numbers to at least 10;

- All pairs of numbers with a total of 20, e.g. 13 + 7;

- All pairs of multiples of 10 with a total of 100, e.g. 30 + 70;

- Multiplication facts for the 2 and 10 times-tables and corresponding division facts;

- doubles of all numbers to ten and the corresponding halves;

- multiplication facts up to 5 x 5, e.g. 4 x 3.

- count on or back in tens or ones;

- find a small difference by counting up from the smaller to the larger number;

- reorder numbers in a calculation;

- add three small numbers by putting the largest number first and/or find a pair totalling 10; (Thompson 2001)

- partition additions into tens and units then recombine;

- bridge through 10 or 20;

- use known number facts and place value to add or subtract pairs of numbers;

- partition into '5 and a bit' when adding 6, 7, 8 or 9, then recombine;

- add or subtract 9, 19, 11 or 21 by rounding and compensating;

- identify near doubles;

- use patterns of similar calculations;

- use the relationship between addition and subtraction;

- use knowledge of number facts and place value to multiply or divide by 2, 5 or 10;

- use doubles and halves and halving as the inverse of doubling.

Mental calculations

Children should be able to calculate mentally:

- add or subtract a single-digit to or from a single-digit, without crossing 10, e.g. 4 + 5, 8 - 3;

- add or subtract a single-digit to or from 10;

- add or subtract a single-digit to or from a 'teens' number, without crossing 20 or 10, e.g. 13 + 5, 17 - 3;

- Doubles of all numbers to 10, e.g. 8 + 8, double 6.

- add or subtract any single-digit to or from any two-digit number, without crossing the tens boundary, e.g. 62 + 4, 38 - 7;

- add or subtract any single-digit to or from a ...