Four main operations underpin the whole of maths:

· adding
· subtracting
· multiplying
· dividing

in that order and in varying degrees of complexity according to age and natural ability.

Maths is to do with space, bigger and smaller, more and less, the order in which things come and the beauty and elegance inherent in order. A lot of early learning has to do with developing a sense of space, size and number. Nursery rhymes encourage a sense of timing; board and card games develop a child’s ability to count backwards and forwards. Playing these types of ‘maths’ games should be just as much a part of children’s learning at an early stage as reading to them and listening to them read.

The approach to number is progressive and follows roughly the following steps in Years 1 - 4:

1) learning how to count
2) what comes before and what comes after specific numbers (to develop a sense of sequence and order)
3) addition - simple number bonds under 10. e.g. 3 + 4 = 7
4) addition - number bonds up to 20, e.g. 8 + 16 = 14
5) subtraction – under ten, e.g. 7 – 3 = 4
6) subtraction – using numbers up to 20 (e.g. 14 – 9)
7) subtraction – numbers over 20 (e.g. 34 – 9, 34 – 27)
8) multiplication – some times tables are easier than others (e.g. 2x 5x 9x 10x 11x 12x)
9) multiplication – 3x 4x
10) multiplication – 6x 7x 8x
11) multiplication by 10, 100, 1000 …etc
12) multiplication – e.g. 56 x 7
13) multiplication – e.g. 56 x 27
14) division – within the tables 2x – 10x
15) division – short division involving numbers beyond 100, e.g. 151 ÷ 7
16) division – long division 432 ÷ 16 = 27
17) division – long division 433 ÷ 16  = 27 r1
18) division by 10, 100, 1000 … etc

Into this work measurement can gradually be integrated in Years 3 & 4: weight, distance, area, perimeter, time and conversion from one unit to another, e.g. centimetres to metres, hours to minutes.

After a solid foundation in basic number work, more advanced topics can be approached in Years 5 & 6:

1) Fractions
2) Ratios
3) Percentages
4) Decimals

In fact fractions, percentages and decimals are closely related and pupils need to know and understand such equivalences as ¼ , 25% and .25 so that they can exchange one for the other to make word problems simple to solve. For example, it is easier to work out ¼ of 168 than 25%, if that is what the problem requires.

By the end of Year 6, the aim is for pupils to be able to …

1. Recite all tables to 10 x 10, especially for division,
e.g. 63 ÷ 7 = 9, and quickly work out remainders.
2. Multiply and divide decimals by 10 or 100 in their heads,
e.g. 2.61 x 10, 53.2 ÷ 100.
3. Put numbers, including decimals, in order of size,
e.g. 1.06, 0.099, 0.25, 1.67.
4. Use pencil and paper to add and subtract decimals, e.g. 3.91 + 8.04 + 24.56, or 13.3 -1.27.
5. Use pencil and paper to multiply and divide, e.g. 387 x 46, 21.5 x 7, 539 ÷ 13, 307.6 ÷ 4.
6. Cancel fractions e.g. reduce 4/20 to 1/5, and work out which of two fractions is bigger, e.g. 7/12 or 2/3.
7. Work out simple percentages of whole numbers, e.g. 25% of £90 is £22.50.
8. Work out the perimeter and area of simple shapes that can be split into rectangles
9. Solve one and two stage word problems and explain their methods
10. Use co-ordinates to plot the position of points.
11. Understand and use information in graphs, charts and tables.

In my experience many pupils at the beginning of Year 5 do not know their times tables and this is the single main contributing factor in poor performance in maths. This is not simply a question of intelligence but a lack of thorough knowledge as acquired through constant repetition and practice. Parents concerned about their child’s performance in maths should ensure in the first place that their child learns the times tables. A little and often is all that is required.

It is also worth checking that a child knows how to use the basic mathematical operations. Adding is rarely a problem, but many children have a poor understanding of subtraction, multiplication and division in the last years of primary school. And without these basic skills they are poorly equipped to tackle a maths SATs paper at Key Stage2 or to extend their knowledge of maths at Secondary Level.

Posted in Maths ~ 1 Comment