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# Secondary Magazine - Issue 51: Focus on

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 05 January 2010 by ncetm_administrator
Updated on 19 January 2010 by ncetm_administrator

# Focus on...multiplication tables

A tables square can be used to find a set of equivalent fractions. To find fractions equivalent to $\frac{3}{5}$ shade the row of the multiples of 3 and the row of the multiples of 5 producing the following diagram. The yellow row gives the numerator and the turquoise row the denominator of the fraction.

 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100

Areas on a tables square can be used to explore factors as this demonstration from Wolfram Mathworld shows:

How could writing songs help children learn their times tables? Read how Red Oaks Primary School in Swindon changed their teaching of the times tables with NCETM funding.

How can the tables square be used to introduce proportional reasoning? This departmental workshop gives an idea for you to work on in a department meeting.

In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table using Roman numerals. The rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144" and the columns showed each of these multiplied by every integer from two to fifty.

In 2002, one of the earliest known multiplication tables was found in South China. Dating from the Warring States period (475BC-221BC) the 22 cm-long and 4.5 cm-wide tablet clearly shows the eight times table.

John Mason has created a range of number grids. This times table grid might be used to construct understanding of multiplication with negative numbers. Ideas for using the grids are here.

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