This investigation could be revisited several times, trying
different approaches each time. Encourage the children to discuss
discoveries and suggest new things to try. For example, what
happens if the square box is enlarged to include nine numbers, or a
rectangular frame of six numbers? Test discoveries on other months.
Further explorations can be made by changing various parts and
carrying out more investigative work. Here we see what happens when
we pretend to have a four-day week and take our block to be 4 by 4.
The multiplication is done as follows;
This forms the first block of answers in the following table. The
table also includes some other pretend weeks. The answers to the 6
multiplications that can be done around the 4 by 4 square are then
shown as well as the digital roots of these answers.
Some of the blocks of 4 by 4 would not work because of the short
weeks - they are shown with hatching. The numbers 1 to 5 show the
starting number for each 4 by 4 block. Having given you this
starting point, pretend weeks of different lengths could be
explored in a similar way.
I found it very worthwhile to explore the digital roots that
resulted. You can then change the size of the blocks and continue
with more investigational work.
When working with your pupils in opening out a challenge it's
really good to get some first results from a change in the question
and then ask the pupils, "what do you see?". Then it's a matter of
being brave enough to follow some of those leads and not just push
for what you
You'll probably be very surprised about all the different things
that come up which may lead to further investigations.