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Stage 2: First guided practice

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Stage 2

First guided practice

In this stage, a second problem is selected and written on the board. The teacher asks students to say each step of the process they would use to solve the problem.

Because the teacher has explicitly modelled each step previously, students’ responses approximate what has already been modelled. Although responses may not be exact, it is important to acknowledge the response and adjust as necessary. In this way, students’ understanding is affirmed.

Each step is then written on the board.

Video transcript

Presenter

[Talking head]

This time, the question has been written on the board by a student. The teacher asks students to say each step, sharing this task around the class. Because he’s explicitly modelled each step, each answer is appropriate and he is able to continually affirm the students. Answers may not be exact, but the important point is to affirm and adjust as necessary.

Teacher

OK, first step says there 'read the question'. Read the question.

Student

[Students scribe on smartboard as teacher guides]

In the triangle A B C, there is a right angle at B. Side AC 30 centimetres, side AB 22 centimetres. Find the value of angle C.

Teacher

Second step.

Student

Write the main, important stuff.

Teacher

OK, write down number one.

[Student writes]

OK, what is the second most important thing in the diagram?

Student

AB is 22 centimetres.

Teacher

AB is 22 centimetres.

[Student writes]

OK, while he's writing. What is the third most important thing?

Student

There's a right angle at B.

Teacher

There's a right angle at B. Come up quickly and write on the board.

[Student writes]

The right angle is at B. Anything else which we are missing here?

Student

The theta is at C.

Teacher

Angle theta is level at C. What is the next step?

Student

Draw the diagram.

Teacher

Draw the diagram. OK, let's see how you can draw the diagram.

[Student writes]

Who can tell him where to put B?

Student

Bottom left.

Teacher

Bottom left. Where would C go?

[Student writes]

Student

Bottom right.

Teacher

Bottom right. And obviously A should go at the top. Where should 30cm go?

[Student writes]

Student

Between A and C.

Teacher

Between A and C. And where do you think 22 cm will go?

[Student writes]

Student

Between A and B.

Teacher

Between A and B. Where do you think the angle should go? Theta.

[Student writes]

Student

It should go at angle C.

Teacher

At C. What is the next step?

[Student writes]

Student

You write the ratios.

Teacher

Who can come up and write all the ratios at the same time?

Student

Cos theta equal to adjacent over the hypotenuse which is BC over 30.

[Student writes]

Teacher

Who can do the next ratio? Yes, Justin.

Student

Sine.

[Student writes]

Teacher

OK, Justin says sine ratio. Justin, sine theta over what?

Student

That's 22 over 30.

[Student writes]

Teacher

Go ahead. Tan theta?

Student

Tan theta which is 22 over BC.

[Student writes]

Teacher

Tan theta is 22 over BC. Very good.

What is the next process we do after that step?

Student

Elimination.

Teacher

Process of elimination. We're going to do the process of elimination to find which of these ratios will give us the value of angle theta. Is the first one going to give you the value of angle theta?

Students

No.

Teacher

Why? Because this is unknown and that's also unknown. Let's look at the second one. How many unknowns are here?

Students

One unknown.

Teacher

One unknown, only theta is unknown. How many unknowns are here?

Students

Two.

Teacher

Two unknowns, that one and that one. So we have found out what ratio to use?

Student

Sine theta is equal to 22 over 30.

Teacher

Sine theta is equal to 22 over 30. So what is the next step we do?

Student

We solve the equation.

Teacher

OK, go ahead and see.

Student

Sine theta 22 over 30. Now theta, that's what it's equal to...

[Student writes]

Teacher

OK …use a converter to find the value of theta.

Student

Shift sine 22 divided by 30 is equal to 47 minutes, 9 degrees.

[Student writes]

Student

That's why angle C equals to 47 degrees and 9 minutes.

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