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Stage 1

Teacher modelling

In the first stage, the teacher demonstrates the mathematical process with a worked example that has been carefully planned beforehand. The teacher explicitly describes each step of the process as it is modelled.

The first step is to read the problem which may be written on the board or appear in a text. After reading, the students are asked to identify key information in the problem/question. The teacher writes this information sequentially on the board. The teacher then demonstrates how to use the information to solve the problem.

This video demonstrates a mathematical process for solving a trigonometry problem.

Teachers have varying approaches to explaining mathematical processes. The approach demonstrated in this video may be different to approaches you are familiar with. For example, the teacher here makes some steps more explicit and deals with students’ responses that are not perfectly correct.

Video transcript

Presenter

[Talking head]

In the Year 9 Maths lesson here, the process being modelled is trigonometry with right angle triangles. The teacher explicitly names each step, as he explains and writes it on the board. Teachers have varying approaches to explaining processes. The approach the teacher demonstrates here may be different from approaches you’re familiar with. For example, he makes some steps more explicit than other teachers might. The point is to watch the demonstration followed by guided practice.

Teacher

We are going to look at questions relating to trigonometry. So what I will do, I will model one question in trigonometry here.

[Teacher demonstrates process on whiteboard]

OK. First thing is let's read the question. In a right angle triangle LMN, angle M is 90 degrees, side LN is 9.2 metres and side LM is 8.2 metres. Find the angle L to the nearest degree.
OK, step 2. Step 2 says you write down all the important points from the question. Who can tell me what's the first important point? Put your hand up.

Student

Right angle triangle.

Teacher

First it's a right angle triangle. It is a right angle triangle. First important point. Next one?

Student

Angle M is 90 degrees.

Teacher

Angle M is 90 degrees. What is the next important thing? Yes, Justin.

Student

Side LN is 9.2 metres.

Teacher

Side LN …. OK, let's use this information and draw this diagram.

Next one, step 3. Let's label angle L as theta. So read the question. Step 2, write down all the information that is given in the question. And put all this information into a diagram.
Step 4. Since this is a trigonometry question we're going to write down all the trig ratios related to the question. We'll write down sine theta, cos theta and tan theta. So looking from the sine of theta, sine theta is equal to opposite divided by hypotenuse. Therefore MN divided by hypotenuse which is 9.2. Second cos theta. Cos theta is equal to adjacent side divided by hypotenuse. And the last is tan theta. Tan theta is equal to opposite side divided by adjacent side. Therefore MN divided by 8.2.

Now the next step. Choose the right ratio to apply to find the angle theta. Let's decide which one to use here. Sine theta is equal to MN over 9.2. We don't know MN, we don't know theta. So there are two unknowns in this one. So that is not going to work. Cos theta is 8.2 divided by 9.2. So there is only one unknown in that one, which is theta. So cos theta is equal to...

OK, cross-multiply now. 9.2 multiplied by cos theta is equal to 8.2. We want to find the value of theta here so leave cos theta on that side. Then theta equals shift cos 8.2 divided by 9.2.

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