Teacher's Notes

This activity is designed to help students solve trigonometry problems by encouraging them to 'Speculate' about what might be possible. Students are asked to state different truths or complete different equations for a given diagram without being told what to solve for. Having completed the equations they are asked to think about which of them is most useful for solving for a particular variable. So often students feel that they must know 'the right thing to do' before they proceed and are afraid to try things out to see what happens. Yes it is possible to learn how to recognise certain types of problems but it is equally important to learn that problems can be solved by trying to use the different pieces of knowledge you have to make new ones. The sine rule and cosine rule can both be applied to any given triangle it is just that often only one of them generates an equation that can be solved. We can either learn to spot types of problems or to speculate with both. In practise one often leads to the other and then we are better equipped to solve more problems. 

How

The following is some practical advice about how the activity might be run.

Resources provided

This activity runs straight from the attached worksheet. 

Resources needed

A pencil and it helps if the teacher can project the tasks as well.

Time needs

This typically takes an hour if you want to really let students speculate. It does depend on the students and could be done faster.

Starting and finishing

The opening task - see diagram below - sets the tone for the activity and should be used to reinforce that the formulae associated with Pythagoras's theorem, SOHCAHTOA, Sine rule and Cosine rule can all be applied to different parts of this triangle where no values are associated to the variables. The last one looks tricky but is in fact correct and it is worth going through this with students if they don't get it themselves. It should have the advantage of showing how the list of 'true statements' we could make could go on and on.

After this the tasks are self explanatory and students can be left to have a go and the teacher can support and answer questions.

Records

The worksheet should provide a good record is worth keeping as a memory jogger.

What

I think the main thing to expect is some good discussion about the difference between knowing what to do and knowing that there are different things you can try.

More

This would be well timed after work done on  Discovering the Sine rule and before  3D uncovered.  Rearranging relations is an activity with similar aims that focusses on right-angled trigonometry.