Why do this
problem?
This problem can be done when the group are occupied with
making straight-line graphs of multiplication tables and
similar material. It could just nudge certain learners into
something new. If they do not know the triangular numbers they
could be shown how to work them out first. Drawing the graphs
on paper is most satisfactory, although a graphing calculator
or a computer can be used.
Key questions
Is this a straight-line graph?
Which times tables have you done?
Do you know the figures you need for the triangular numbers?
What about the square numbers? How far do you think you will
be able to get on that paper?
Possible extension
Learners could try sequences such as doubling or adding
successively one, two, three. Alternatively this
Matchsticks problem could be used.
Possible support
Some children might benefit from drawing the graphs of
multiplication tables on paper. A graphing calculator or on a
computer can also be used.