# Graphs

This activity shows how times tables plotted on a graph result in a straight line. The gradient varies with each table – the higher the table the steeper the gradient. It also shows that multiplication and division can be calculated from the lines produced – or a very close estimate.

 With a sheet of graph paper in portrait position, children draw x and y axes (arrowed at the ends to indicate that the scales could continue).
 The x axis is numbered on the cm lines from the origin 0 to 15 or as far as it will go and labelled ‘Times’.
 The y axis is numbered on the cm lines from the origin 0 in tens to 200 or as far as it will go and labelled ‘Multiples’.
 Explain that all the tables will begin at the origin as 0 times any number is 0.
 Use a times table as an example, say, the fives and ask the children to plot 10 × 5 on the graph – following the ten times line up from the x axis until it meets the 50 multiple line across from the y axis.
 To be sure, plot also the 5 × 5 (where 5 from the x meets 25 from the y).
 A ruler is aligned through the two points and the origin – which should be in a straight line – and a line drawn from the zero through the two points and right to the edge of the paper.

 Show how multiplication of 5 and division by 5 can be calculated using the line, e.g. for 14 × 5 follow the 14 line up from the x axis until it meets the drawn line, read across from that point to the y axis which should be 70. And for 43 ÷ 5 follow the 43 line across from the y axis until it meets the drawn line, read down from that point to the x axis which should be 8.6 or very close.
 Other tables can now be plotted using the same procedure with the known amounts of ten times and five times together with the origin. If several different tables are plotted on the same sheet of paper, it will clearly show the comparative gradients. Children must remember to label each line with the respective table.
 The lines can be used to calculate some tricky multiplication and division questions.