Wednesday, 17 April 2013

Similar Triangles

As I've hinted at in another recent post, I have been part of an exciting project the TES Maths Panel have been putting together - 'Topic Progressions'.

These documents have already been a great resource to me and my teaching and I have recently used the Shape - Similar Shapes 'Topic Progression' to find resources/questions for my teaching of this topic. One of the resources I therefore subsequently used from the TES was this resource -->

If you click on the link in the resource it will bring up the 'Teach Maths' website ( On this page of the site it details an activity involving 24 similar triangles and is a lovely open ended task to give to students.

So, with the resource saved, the teacher notes read and the documents printed I was ready to go for my Y9 set 1 lesson on similarity of shapes. This would be the class' 1st lesson on the topic and as such I left the activity as open as possible to see what learning they may have had previously or thoughts they already had towards the task. As suggested on the site, I gave each group (my classes are all sat in groups now) a print out of the 24 triangles and got them to 'group'/'classify' the triangles as they saw best.
The interesting thing here is that, of the 5 groups of 6/7 students, 4 groups chose to classify the triangles by grouping them into 'equilateral', 'isosceles', 'right-angle' and 'scalene' triangles. There was one group that grouped them by size i.e. small triangles, middle sized triangles and large triangles. After this class discussion on how each group had classified the 24 triangles I asked them what they knew about similar shapes. One of my students then said that they were shapes where all the angles were the same. This then lead to us discussing that the similar shapes are enlargements of one another and that we can use the scale factor to work out missing lengths.

The class then had their task set - they were to find all 3 lengths of each triangle using their knowledge of similarity. They were not permitted the use of rulers or protractors but I hinted at placing triangles on top of one another to see if their angles were the same (and therefore they were similar triangles). I set the groups off on the task and this is how they started...

I gave each group one of my A1 sized magic whiteboard sheets to work on (these are available from They were given a good 10-15 minutes to attempt to find the missing lengths of the triangles with little input from me needed at this stage.
 Here's one of the groups attempt at beginning to sort out the triangles into similar triangles groupings

After about 10-15 minutes, when the groups were getting to the point where they were missing a few triangles' lengths, and they had done the perhaps, 'easier' ones I hinted that there were 8 groups of 3 similar triangles at this should help them work out which 3 triangles go together to work out the missing lengths.

At the end of the lesson I showed the class the correct lengths of all the 24 triangles and they marked their work as a group. The majority of groups got between 15-17 out of the 24 correct. One group got 22 correct. So, there's a little more work we need to do as a class on similarity and we'll be continuing with this next week.

I'd definitely recommend running this activity to others and I'll probably be using this with my Y10's too as Similarity and Congruence is a topic that comes up in both Unit 1 and 2 of the METHODS in Mathematics exam they are currently sitting - it'll be a chance for us to revise and reinforce our previous learning earlier in the year!

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