Home > #MTBoS, Maths, Resources, SSM, Starters, Teaching > Similarity, and other stories

Similarity, and other stories

Recently I have been looking into a variety of things. One thing is “Inquiry Maths” and another is something I found on the #matheme site through the explore the MTBoS project called “Notice and wonder”.

These got me thinking about how I could introduce some of their elements into some of my lessons. I had just introduced similarity to my year elevens and I was going to move to similar area and volume problems. So I came up with this starter:


I put it on the board and gave them ten minutes (I think) and let them get their teeth into it. A few were a little confused at first, but the discussions on each table enabled all pupils to make their own way to the correct answer. I didn’t know what they would notice or wonder, but I was pleasantly surprised to hear some of their comments:

“I notice that the area has gone up by four, not two. Does that mean you double the scale factor for area?”

-I loved this one, and refused to answer it, instead I asked him to enlarge the shape sf3 and see if the area was enlarged by six. I then got:

“It’s nine, not six. Why’s it nine? Stupid thing. Oh hang in, it’s squared. Oh, of course it’s squared! you times each side by it [the scale factor] and you times them together! Duh!”

Others I particularly liked were:

“I wonder if there’s a way of doing Pythagoras on triangles without right angles” (I told her that we would be meeting the cosine rule soon enough).

“the angles are the same! Wait, that’s how this SOHCAHTOA thing works isn’t it, cos it’s ratios an that.” (I said “very good, but can we use the proper name please!” then another pupil interjected with “Trigonometry”)

The lesson goes on to pose question prompts similar to those I’ve seen on inquiry maths in which we discussed similar volume and then I included a set of questions for then to attempt. I have uploaded the resource to TES:

  1. November 18, 2013 at 12:56 am

    That’s a great way to introduce students to the ratios of perimeters/areas/volumes of similar figures. I’ve taught this explicitly before and always thought it would be an easy thing for students to discover on their own. Thanks for posting this!

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