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Stage 3: Second guided practice

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Stage 3

Second guided practice

In the third stage, another worked example is practised. This time, using another problem, more students are asked to say each step of the process and write it on the board. It is important to try to include as many students as possible in this stage, including those who may be reluctant to respond.

Because the steps in the process have now been modelled twice, most students will be able to provide an appropriate answer and the teacher can continue to affirm students’ understanding.

It is this experience of success that engages students in their learning and can be used to engage all students in learning mathematics.

Video transcript

Presenter

[Talking head]

This time, using another question, more students are asked to say each step and write it on the board, including students who are normally silent or reluctant. This reluctance is overcome because the steps have been modelled twice, so that all students can now give an appropriate answer, and because the teacher is continually affirming all answers. It’s this experience of success and affirmation that engages students in learning, and can be used to engage all students in learning mathematics.

Teacher

Now let's see … read the question loudly.

Student

[Students scribe on smartboard as teacher guides]

In a triangle PQR, angle Q is 90 degrees, side QR is 17 centimetres, side PR is 21 centimetres. Find the value of angle R.

Teacher

OK, what's the next step?

Student

Write down all the important points.

Teacher

Write down all the important points, all the important information from the question. First one?

Student

Angle Q is a right angle.

[Student writes]

Teacher

OK … What is the next important thing in that question?

Student

Side QR is 17 centimetres.

Teacher

OK, can you put that on the board?

[Student writes]

What is the next important point in that one?

[Student writes]

Student

Side PR is equal to 21 centimetres.

Teacher

OK, can you put that on the board. Any other important points in the question?

Student

Angle R is theta.

Teacher

OK, put that on the board.

[Student writes]

OK, what is the next step?

Student

Draw the diagram.

Teacher

OK, you can go on the board and people will help you draw the diagram.

[Student writes]

Let's put in the information there. What is the first information?

Student

Angle Q is 90 degrees.

[Student writes]

Teacher

So 90 degrees will be where?

Student

At the bottom left corner.

[Student writes]

Teacher

OK, at the bottom left corner. Q is 90 degrees. Side Q equals to 17 centimetres. Who can help him?

Student

Bottom right.

[Student writes]

Teacher

Bottom right. What else is missing in that one?

Students

21 centimetres.

[Student writes]

Teacher

Where should it go?

Students

Between P and R.

[Student writes]

Teacher

In between P and R. Who agrees with him that this is the right diagram for using all the information?

[Students raise hands]

Obviously somebody disagrees. I'll ask them why. Obviously everybody’s agreeing with him. Thank you. OK, next step. What is the next step after that?

Student

You level the ratios.

[Student writes]

Teacher

OK, write down all the ratios related to the right angle triangle. Who can remember the first ratio?

Student

Cos theta equal to 17 over PR.

[Student writes]

Teacher

OK, then write down that here. Think about the next ratio when he's writing. … I'm going to ask you about the next ratio. What's the next ratio?

Student

Sine theta equals PQ over 21.

[Student writes]

Teacher

He said sine theta is equal to PQ over 21. Is he right?

Students

Yes.

Teacher

Go and write on the board.

[Student writes]

What's the next ratio?

Student

PQ over 17 centimetres.

Teacher

Can you put that on the board there?

[Student writes]

What's the next? Can you come on the board here and eliminate the ones that are wrong. Can you tell me why?

Student

Those two are givens so I'll tick that.

[Student marks the equations on the board]

This one has two unknowns, that's PQ and theta, so that’s wrong. And this one has two unknowns, that's PQ and theta.

Teacher

Is he correct?

Students

Yes.

Teacher

OK, what is the next step? Really? Yes, you want to go there? Let’s go there, come on. OK, what is he going to end up?

Student

17 centimetres over 21 centimetres.

[Student writes]

Teacher

OK, he said '17 over 21'. OK, what is the next step?

Student

Cos and then to the power of minus 1.

Teacher

Is anything one the left hand side?

Student

Yes, and then theta is equal to.

Teacher

OK, he's saying put down 'theta is equal to'. What's he saying?

Student

Cos to the power of minus 1.

[Student writes]

Teacher

Cos to the power of minus 1. Is he right?

Students

Yes.

Teacher

OK, what is the next step?

Student

Using a calculator to calculate the equation.

Teacher

Using calculator to calculate the equation.

Student

The answer is 35 degrees, 57 minutes.

[Student writes]

Teacher

35 degrees, 57 minutes. Give him a round of applause.

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