If children know a range of ways to tackle multiplication increases the ability of a child to handle multiplication problems. There are two ways to approach it:
- Repeated aggregation structure - language used is "so many sets of/lots of" and "How many altogether". An important use of aggregation is in shopping, for example buying 8 tins of tomatoes at 31p each, how much does it cost altogether?
- Scaling Structure - increasing a quantity by a scale factor, language used is "doubling", "trebling", "so many times bigger/longer than", "so many times as much as/as many as". Comparisons are important in scaling operations, for example I paid 50p for my drink, Daddy paid three times as much, how much did he pay?
Many children find it helpful to hand ideas on an image to help with remembering and understanding them. Multiplication can be associated with the 'rectangular array' which means that 3 x 4 can be represented visually on graph paper as three squares up and four squares along. This leads naturally on to using multiplication to find out the area of a rectangle in the future!
Children need to have concrete, hands on working of multiplication secure before they move onto mental arithmetic techniques.
With all this in mind I put together a few ideas to try alongside our living maths book called 'Anno's Mysterious Multiplying Jar'
We played a game from Peggy Kaye's book 'Games for Maths' which comes under the 'repeated aggregation' format of multiplying. This game was popular, and quick using scrap paper, pens and a dice. You roll it once and draw that many circles then roll it again and draw that number of dots inside each circle. The player with the highest number of dots wins.
This game was also from her book and was useful for introducing the 'commutative law' idea as the dice roll this time gave two side of a rectangle which was completed using the squared paper then the area was calculated by multiplying the sides. It showed the commutative law idea as I pointed out to Eve that is was easier to count in two's which she knew confidently, than struggle with counting in fours and get it wrong!
The skip counting in this lead to us making a skip counting bracelet with flower beads and pipe cleaners for practising counting in threes. Having the bracelet on prompted them to count in threes quite often and progress was made in learning them. We also used colouring sheets from 'The Multiplication Tables Colouring Book' which the girls enjoyed as colouring the numbers in a pattern that were multiples of two for example, revealed a picture of something, such as a mouse. There is a multiplication table which asks them to colour in the multiples of two to reveal the pattern of numbers that are multiples of that number. This was the first time they had come across the idea of 'multiples of' and the language associated with that and it caused a false start or two but was generally successful.
It was in reading about multiplication and researching activities to support this book that I realised just what a huge topic multiplication is and how it needs to be tackled regularly in small chunks rather than one dose, like the symmetry could be for instance. The girls enjoy multiplying and often come and tell me little snippets such as 'what four threes are' and so on. The idea of using cuisenaire rods popped up several times and that led me to another maths book which has added in a new dimension to our maths, it has also derailed my 'living maths' planning for a while as we swerved to one side to accommodate a new direction. I have got my head around it now though so will hopefully be back to posting a few more living maths explorations!!