multiplication and division
Why does maths look different today?
How we teach multiplication and division.
If what you remember as multiplication and division is pages of sums you may sometimes feel confused when your child’s maths book contains writing, pictures, diagrams, jottings and not many ‘formal calculations’. Your children will record calculations in a variety of ways that do not necessarily look like the kind of ‘sums’ you remember. This is because written calculations are not the ultimate aim: the aim is for children to do calculations in their heads and, if the numbers are too large, to use a way of writing them down that helps their thinking.
As children develop their knowledge and understanding of multiplication through years 3,4,5 and 6 teachers will be asking them to look at any calculation and ask “Can I do this in my head?” Sometimes this will need to be supported by a drawing, diagram or numerical jotting (notes). If they can’t do it largely in their heads they should be looking for the most suitable written method or, during years 5 and 6, using a calculator for more complex calculations.
Did anyone ever tell you that you only needed to learn about half of the multiplication tables in order to know them all? If they didn’t it was a bit mean because if you know 3x4=12 you also know 4x3=12, so why learn it twice?
Did anyone ever say that once you knew the 2 times table, which is only double the 1 times, then the 4 times was easy because you just double the 2 times? Then you can double the 4 times to get the 8 times. The 3 times doubles to the 6 times and 12 times, the ten times can be halved to give 5 times and so on. This uses the knowledge children are developing through addition and subtraction and makes important connections for them.
It’s also possible that you weren’t told that you knew your division tables. If you were shown that division was the opposite of multiplication you will understand that knowing 3x4=12 or 4x3=12 also means you know 124=3 and 123=4. So knowing one number fact, like 3x4=12, immediately means we know at least four.
But did you also realise that knowing any one of these facts helps you to know a lot more than four without actually learning them?
The early work children do will introduce them to the ideas of multiplication and division. They will be counting in different patterns, helped to see how multiplication is repeated addition and division is repeated subtraction, shown how division is the opposite of multiplication and taught to understand place value (that in 234 the 2 is 200, the 3 is 30 and the 4 is 4 ones (units)). This knowledge and understanding, with much of the work being done in their heads, opens up a whole world of facts for them and they don’t all have to be memorised. That can make dealing with numbers feel a lot easier.
Children are introduced to the concept of multiplication in Year 1 & 2.
| Unit 1 (Years 1 & 2) | In Key Stage 1 we begin teaching multiplication by regularly counting in multiples of 2’s, 10’s and 5’s. Initially children will use practical situations and counters to do this, progressing to the more abstract use of numbers. Children become familiar with the pattern of numbers. For example by counting in 2’s as in 0, 2, 4, 6, numbers are always even. When counting in 5’s numbers always end in 5 or 0. Children are also being taught to double and half numbers to at least 10. This is the foundation for the 2 x table and the inverse or opposite operation of dividing by 2. Multiplication and division operations are usually taught simultaneously although division is a difficult concept that requires lots of practical sharing type activities. In Year 2 the children progress to learning to multiply and divide by 2, 10 and 5 and symbols of x and ÷ are usually introduced together with the accompanying language of ‘groups of’, ‘arrays’ and ‘repeated addition’ referring to multiplication and ‘repeated subtraction’ in relation to division. Here is an example of what these terms mean: 4 x 2 = 8 or 2 + 2 + 2 +2 = 8 repeated addition
4 groups of 2: ■ ■ ■ ■ ■ ■ ■ ■
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| Unit 2 (Years 3 & 4)
| Multiplication and division are taught in Years 3 and 4 as inverse operations. If I know a multiplication fact, I know the related division, for example:
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| Unit 3(Years 5 & 6)
| As they move into years 5 & 6 children will still be encouraged to choose the most suitable method of calculation, mentally if possible. Where this is not possible they will be using expanded or compact methods and a calculator for more complex and involved work. Most children will be expected to multiply 3 digits x 1 digit and 3 digits x 2 digits using a written method.
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Your child will bring home a maths leaflet showing you the different methods of multiplication and division that we teach, in line with the UK National Curriculum.
Multiplication & Division Vocabulary may have changed since you were in school…
Remainder – The number left when you cannot equally divide (share).
Chunking – informal method of division which uses repeated multiplication