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# What Makes A Good Resource - Trigonometry via Enlargement

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 08 September 2009 by ncetm_administrator
Updated on 03 September 2010 by ncetm_administrator

# Trigonometry via Enlargement

Resource description:
Pupils work in small groups of 2 or 3 with a set of nine photographs and a large sheet of plain paper.

They are required to 'sort out' the photographs using criteria of their own choice.

Teacher comment:
Trigonometry is always presented as a complicated topic in mathematics – one which gets you that magic ‘B’ grade. When you ask pupils what they know about trigonometry they will often give you the mnemonic which helps them remember a rule (Some Officers Have …) rather than tell you about the relationships between sides and angles on right angle triangles. By using this set of photographs, I wanted the pupils to 'get inside' a particular situation which I could use to develop their existing awareness and then explore some properties of right angle triangles.

What I did:
I began by asking the pupils to sort out the photographs. Most groups began to draw a map on their paper.

I particularly wanted pupils to think about the location so I asked if they could tell me anything particular about the situation. After some discussion we started to think about which pictures could have been taken from the same location and thought about ways to represent this on their 'map'.

Having got the sense that pupils were ‘there’, I wanted to explore the picture made by the telegraph pole, sign post and the viewer so we recreated the situation in the classroom with different pupils acting as the telegraph pole, sign post and viewer. Pupils suggested that they needed to stand on chairs to represent the telegraph post because it was so much taller than the sign post. Pupils then directed the 'viewer' to move further from and closer to the sign post to recreate the different views in photos A & D and then to draw the profile of these scenarios – creating some right-angle triangles.

Pupils were then ready to focus on right angle triangles. They sorted a whole set of triangles into three distinct categories; in each category were enlargements of an initial triangle. We started to note the similarities of the triangles in each group - focussing particularly on the ratios of the sides. There was certainly some surprise that the ratios of short : long or short : middle were always the same for the group, and the group was defined by one of the angles. It was then possible to make some more triangles to fit these criteria.

Reflection:
Using this activity enabled the pupils to enter into a real life situation and articulate some of the mathematics that was in it. It helped me to get a sense of their spatial awareness and ask questions to develop it.  I was really surprised that some of the pupils found it so difficult to link together the photographs. I tried to support them by asking them to tell me what they were doing and this often helped them move forward in their thinking. Alternatively, I tried placing an object (I used a can) on their paper and saying ‘does it make it easier if I put the telegraph pole here?’

We did have some good discussion about the heights of the two posts; how the two heights never change but the distance away from the posts does change, as does the angle of the viewer.(‘What stays the same?’ and ‘what changes?’). In subsequent lessons, this was a shared experience to which I was able to frequently refer.

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