Clone of Wonderful Number Patterns
Why do this problem?
This activity , I have found to be very enjoyable for pupils,
because it opens up a new world for most of them - that they can
create their own number patterns and explore them! It's a healthy
change for many of them to feel that they are not just being handed
something that the teacher already knows an awful lot about. So if
these thoughts encourage you then present it to your pupils.
Possible approach
I've found it valuable to
use this with the whole class and focus on an introduction where
they're meeting the usual number patterns. As they look at some
familiar patterns, I note down for all to see the comments that
pupils are making. I've usually numbered their findings and got to
at least number six for each one! This then leads into the idea of
them creating their own, to explore in similar ways.
Key questions
Tell me about your
rules.
Do you notice anything
that you want to tell me about?
Possible extension
See the 'Then choose'
suggestions at the end of
the problem itself.
Possible support
Calculators are useful
here so that the pupls are free to explore rather than getting tied
down by the calculations.
For the
highest-attaining
The pupils could go to Become a Maths
Detective which is an interactive version of this activity.
They can then explore much further and do some powerful comparisons
of results. Further ideas relating to that later activity can be
found by following the link in Become a Maths Detective for the
NRICH Projects site where other pupils' ideas can be viewed and
commented on once you have registered.
Extra
The patterns that are generated can be very exciting. I find it
useful if the children have already met things like the patterns
that are evident in the ninetimes table to take things a bit go
further and investigate
Digital Roots . I have also found that following the a, b, c,
d, e parts as suggested in this activity, writing what they notice,
changing something slightly and repeating etc. to be a very good
investigational process for the youngsters to get used to. Caleb
Gattegno in the 1960's said; "Mathematics is the study of the
invariances under a set of transformation". Or if you prefer it, in
my words now; "Doing mathematics is taking something, changing it
in some way and observing what is the same and what is
different."
BE WARNED it may be hard
to stop some children once they get going!