This is an idea I took from my all-time favourite project, the Build a School Project. This time however, I used it to investigate and discover the Trig ratios.
I did this with my Year 9 class, who had met trig in Year 8, but needed a good reminding of what it was about (and after it worked successfully with them, I used it to teach my Year 8 about Trig, using this resource).
I started the lesson by asking the simple question "How tall is the school?". We had lots of random guesses (estimatimations as they called them). I then asked "How could we find out?". This again generated lots of ideas such as finding the plans of the school building and finding the height there. "How would we use the plans to find the height?" was my response, and they said that we would measure the height and use the scale.
Although a brilliant idea, we did not have access to the plans, so "How could we go about measuring the height of the school?". This is the point when suggestions of climbing on the roof and hanging a tape measure from there to the floor came. "How could we do it without me losing my job?" came my rather sarcastic reply.
After a few discussions around the class, one group finally said "Draw a scale drawing!".
At this point I pulled out a selection of Clinometers and Tape Measures, and we discussed what measurements we could take that would be useful (the angle to the top and the distance from that point to the wall), and how this information would give us a right angled triangle. We all headed outside. I split them into groups of 3, and told them they needed to take at least two sets of measurements for accuracy, but preferably 3 or 4.
After 5 minutes of running around and taking the measurements they needed, we headed back into the classroom. The students then had to use the ideas we talked about previously, to work out the height of the school (using similar triangles).
Generally, most groups got two results that were similar, and they were relatively in line with each other. We then discussed what might cause the discrepencies: human error in measuring; human error in drawing; forgetting that the clinometer was 1m above the ground when used (though some did get to the floor to compensate for this).
This led to another discussion of the fact that no matter the height was constant, but with a different length we needed a different angle. I then flipped the thinking from here to "What if the angle was the same, but the length was different?". They all responded that the height would change accordingly (if the length was longer, the height was taller).
Now we were heading into the realm of constant ratios, and this led to the tangent ratio being fixed for a given angle...
The activity was great as it really made the class think about what we needed and how it worked, as well as combining a practical element into the lesson (which they obviously enjoyed, even if it was raining outside). I will definitely be using this idea again to introduce students to the idea of similar triangles and how they can relate to Trig.
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.