Why do this problem?
This problem encourages learners to examine the relationships
between the ratios of sides of right angled triangles, and how
those ratios vary over changing angles. The aim is to look in
detail at the under-pinning structure of the animation.
Ask the group to watch the animation carefully, explaining
that you will ask them to recall in detail what they saw. They
should not make notes as they need to watch the animation carefully
- seeing it as a whole will help them make connections.
Spend some time trying to recreate the animation - checking by
running the animation and pausing the screen after major
Ask the learners to work in pairs "making sense" of the data
that the animation produces. Trying to think about connections? As
you move around the group encourage recording of findings and ideas
to share. You may even like them to produce a display of what they
discover. It may be useful to ask them to think about mathematics
they have met before that might be useful (e.g. Pythaogoras
theorem) or encourage them to think about drawing some graphs (what
would the independent and dependent variables be?).
There may be points in this part of the lesson when you will
want to stop and share some of the ideas learners have and if
others agree or have found similar or conflicting things.
- What do the numbers refer to?
- Are they the same value at different points during the dot's
motion around the circle?
- Are the three values connected and if so how?
- What can graphs of the values tell you?
The problem "Trigonometric
" is designed to build on the ideas presented
Spending some time talking together about the animation and
what it is showing and creating a story board of key moments will
help to unpick the underpinning structure.