I have been teaching proportional reasoning in my year 11 lessons and then I was given the topics of similarity and congruence for my year 9 class. I am also teaching fractions at Ks3. So I started thinking about how students try to use LCM to find common denominators when adding fractions but when asked if two shapes are similar students usually try to find a scale factor.

I trialled a few questions with year 9 first… the biggest issues were with addition being used that wasn’t rated addition and not understanding that they could look at the scale factor between length/width in the same shape as well as length to length and width to width. If I looked at 3/4.2 and 5/7 I might consider that 3/4.2=30/42=15/21 so they are similar.

Update: After a discussion on Twitter with @petergates3 – he made the comment below. So i rethought the task and came up with something a little different. I am glad i did. In the lesson students were able to make sense of the different ways to check if two shapes are similar. They drew, they discussed and when it came to trying questions they referred to different approaches

I wanted to share a few resources I have made for students who are looking at similar triangles. I the first worksheet I wanted students to realise/note that when two shapes are similar there is a scale factor between all 3 sides from one triangle to another but also there is a connection between the sides. For example; side B is always 3 times the length of A no matter what triangle is drawn (if they are similar)

I also wanted students to notice that you can use all the method they use in ratio to answer these questions. So if they are working from a length of 8cm to a length of 6cm. They can divide the 8cm by 4 then multiply by 3 or multiply by 6 and divide by 8 and so on. This would also work quite well in a pythagoras lesson as a starter. You could remove the right angle and fill in some of the values and ask students to decide whether the triangles were right angled or not and how you can tell.

Here the questions have a repeated length.

Here is the ppt for this lesson with a number starter.