### 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.