Bone up on multiplication

20th February 2004 at 00:00
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I recommend Napier's Bones for pupils who, as John Napier (1550-1670) put it, find that "there is nothing that is so troublesome to mathematical practice than the multiplication of great numbers".

The Scottish theologian, who became better known for his mathematical work, devised among other things a way to multiply which children less confident with the multiplication tables will love. Knowing the tables up to nine enables them to work out the products of large multiplications. They will need to be reminded of the value of each digit because, unlike partitioning, where 36 would be 30 and 6, with Napier's Bones the number is represented just by its composite digits.

Start with an example using just two two-digit numbers, such as 34 x 66.

Draw a two-by-two grid and put the partitioned digits (not their correct place value) at the top and to the side of each square (Diagram 1).

Then bisect each square in the grid from the top right corner diagonally to the bottom left (Diagram 2).

Do the multiplication. The 10s go in the top half of the bisected square, the units in the bottom half (Diagram 3).

"Slice" along the diagonals and add up the digits in each "slice". You carry over as you would in vertical addition. You will be able to see how well the children are able to read the figures and understand place value when they give their answers. The units will be the first digits on the right-hand side, followed by the 10s and so on (Diagram 4).

Napier's Bones can be used to multiply any size of numbers and children get a lot of satisfaction knowing they can work out large products without a calculator or needing anything higher than their nine times table. There's background info about Napier at: www-ah.st-andrews.ac.uk mgstudreflectnapier.html

Veronica Poku, maths co-ordinator, William Morris Primary School, Mitcham, Surrey, and leading maths teacher for Merton

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