This week I will be introducing Trigonometry to Year 9 (UK Key Stage 3, age 13-14). I always like to begin trigonometry with students actually measuring lengths in triangles, I believe they get more of a feel for the meaning of the ratios of the sides of a triangle if they have actually measured the length of the sides and calculated the ratios themselves.

I decided what I need is some accurate drawings of triangles of various dimensions that they could work on. It took a few seconds (the third entry in the search results for introducing trigonometry) to discover not only the drawings I wanted but a perfect recording sheet! From NZmaths (New Zealand Maths) – a site I have mentioned before for its excellent resources comes Introducing Trig. As well as the resources, teachers’ notes are provided. (Scroll to the end, past the teachers’ notes for the resources)

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So after an introduction including a reminder of Pythagoras they met last year, we’ll just need to be clear on the terms opposite, adjacent and hypotenuse, how to complete the recording sheet and the measuring can begin! This is a very able group of students and I suspect several of them to be telling me for example by the end of the lesson that sin 60° is the same as cos 30°.

Checking a few more links in the results of the search I see the excellent Math Open Reference site which I have referred to on several occasions. I also see that I am in very good company in my desire to get the students measuring themselves and using the nzmath resource – see Dan Pearcy’s post.

Something else I like to do when discussing trigonometry is to discuss all the possible types of problems that can come up because whether they are disguised as buildings / trees / ladders or whatever there are still only a limited number of problem types, eg find the angle given the opposite and hypotenuse. The students can work out how many problems there are.

Thanks for this. I used the NZ resource in my lesson too. It went pretty well and inspired me to create a GeoGebra file which I have uploaded here: http://www.tes.co.uk/teaching-resource/Trigonometry-introduction-ratio-of-sides-6447101/
You can stretch the triangle and although the individual sides change the ratios don’t… until you change the angle. The class seemed to like it, anyway!

Glad it worked well Mark – and thanks for the GeoGebra file. Dan Pearcy also created one – see his post above. I like that NZ resource and would definitely use it again when introducing trigonometry.

Thanks for this. I used the NZ resource in my lesson too. It went pretty well and inspired me to create a GeoGebra file which I have uploaded here:

http://www.tes.co.uk/teaching-resource/Trigonometry-introduction-ratio-of-sides-6447101/

You can stretch the triangle and although the individual sides change the ratios don’t… until you change the angle. The class seemed to like it, anyway!

Glad it worked well Mark – and thanks for the GeoGebra file. Dan Pearcy also created one – see his post above. I like that NZ resource and would definitely use it again when introducing trigonometry.

Colleen big thanks

Colleen, your posts are always excellent, offer multiple resources.

Thank you !!

Great piece, I love trigonometry! http://wp.me/p2z9Lp-9F

I’m planning a new approach to it this year, will share when it’s done!

I like it too! Will report back on how it goes and look forward to hearing how your lessons go.