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# What Makes A Good Resource - Degree Radian Conversion

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Created on 09 August 2010 by ncetm_administrator
Updated on 03 September 2010 by ncetm_administrator

Resource description:
The resource consists of two body movements to help students remember what radians are and a sheet of dominos where students match radian measures to equivalent degree measures.

Maths Poster (PDF)

Teacher comment:

I tend to teach waving my arms about and these two shapes just sort of happened. Now I use them regularly because the students remember them well. The finger one gives a good feel for what a single radian is, so students can relate a radian angle to an angle they can see. I use it to get students to estimate an answer where they can see it in circle questions, or in complex number questions in Further Mathematics. The whole body one is very useful. When students who should already know, ask me what

$\frac{\pi}{3}$

is in degrees, I don’t answer, but stand in the 'pi' stance, and they work it out for themselves.

What I did:

To explain the concept of a radian I use hands. Make an equilateral triangle with three fingers.

Each of your fingers have the same length (theoretically!). Now imagine two of the fingers are radii of a circle and bend the other finger to be the arc of the circle.

Your fingers are still all the same length, so the angle between your two straight fingers is one radian.

To remember that 180° is π radians I stand in front of the class with my feet astride and my arms held out and ask them to imagine my head is chopped off and ask them if they can see a π shape. If you move from both hands together on one side, arcing an arm over your head to the other side, you move through 180° or π radians.

$0^o=0radians$                    $90^o=\frac{1}{2}\pi radians$

I find this works well for thirds and quarters as well.

I also use a set of 24 dominos to reinforce conversions. Students work in pairs to cut out the dominos and make a complete snake from start to finish, matching equivalent angles.

Reflection:

The three radian angles which are not given as multiples of $\pi$ always trip students up. I find this useful to reinforce the fact that the π is three and a bit, not a symbol to represent radians. It is interesting to start a lesson soon after doing degree/radian conversion with the question “Is $\pi$ bigger or smaller than 180?” and see what they answer.

(With thanks to Hugh and Arthur for being models!)

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