Why do this problem?
This problem continues to investigate the sequence of
shapes introduced in
Building Gnomons Learners will need to use their skills of
representation to communicate their ideas and justify their
findings. This problem builds on learners' prior knowledge of
how the Fibonacci sequence grows.
Possible approach
Ask learners to work in small groups to investigate areas and
dimensions of gnomons.
After a short time, draw all the groups together to share
ideas about how they might organise their approaches and
record findings. Which groups are working systematically,
which have used effieicent recording methods?
It is most desirable for learners to develop their own
representations to justify any patterns they find. However,
if they are struggling the Hint contains one way of recording
edge lengths in terms of Fibonacci numbers that might be a
useful stimulus for discussion.
Is it possible to predict the dimensions of the gnomons in
the sequence?
Encourage the use of diagrams and notation to explain how the
pattern will continue and why.
Sharing findings and justifications might be achieved by the
use of posters which groups present to the rest of the group.
Use the opportunity for other learners to feedback on the
clarity of what is presented.
Key questions
How does the approach in the hint work?
How does the way you put pairs of gnomons together result in
new Fibonacci numbers?
Possible extension
Possible support
Try
Building Gnomons first.
Sheep Talk could be used as an introduction to Fibonacci
numbers.