This week we explored similar triangles for the first time in MMF2P:

**Part 1:**

Students, in groups of 3, are provided with a set of triangles all cut out (my first class to ever do this activity cut them out & I save them in envelopes for re-use each year). This set of triangles was created by some teacher candidates in one of my courses a few years back.

Using a Pear Deck slideshow, I prompted each group to organize their triangles into groups using a common attribute; their choice. We discussed the groups they made; right triangles, acute, obtuse, scalene, isosceles, equilateral, and same shape but different size. One group had even stacked the similar triangles on top of each other, nested russian-doll style, which I showed off to the class. The discussion allowed a great review of vocabulary around triangles.

**Part 2:**

I asked all the groups to make groups of triangles that were the same shape, but different sizes now (which some had already done).

I introduced the terminology “similar triangles” and we drilled down as a group to a proper definition. Since we don’t take notes I asked students to find the definition in their course notes pack & highlight the keyword.

**Part 3:**

I showed a set of similar triangles with a missing side length to solve for. In 3-act-math style, I asked them a) What do you notice? b) What do you wonder? and c) Estimate the value of *x*:

They worked in their groups at their boards. Here is one group’s solution (I have to get back in the habit of photographing every group’s work) w/ my annotations written in red:

I then did a bit of direct teaching to show them how to write a proportion to solve algebraically:

Looking back at this, though, I’m not a fan of having them flip the proportion as I’m sure many don’t understand why that’s allowed (h/t to Nix the tricks). I wish I had showed them to set up the proportion in such a way that we start with the unknown value, x, in the top left position. Next time.

**Part 4:**

Individual practice solving similar triangle problems on Khan Academy. I gave them a second class period for this & what they didn’t get done was then for homework.

Lesson materials available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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