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MFM2P - Day 16 (Similar Triangles)

We did two warms up today, as I did not think I should leave a warm up for the English teacher covering for me yesterday. This Estimation 180 was first, where they had to estimate the height of the lamppost:

They did a good job of saying that a "too low" guess was at least 6'4" as that is Mr. Stadel's height. Their reasoning for their actual estimates was solid - they said the lamppost seemed like it was 2.5 to 3 times his height so their estimates were in the 15' to 19' range. One student had said 15 m so we talked about the units they choose to use and that 15 m would be about 7 Mr. Stadel's stacked one on top of the other!

On to today's visual pattern:

I think the colours are very leading in how students saw the pattern. I would prefer to have all the blocks the same colour so that different students might see the pattern in different ways. It was great that one student thought the pattern was 3n + 2 and we talked about what that meant and why it was different from 3 + 2n.

I did show them a different way of seeing the pattern and how it was the same as what they had found.

I would like to say we took up the triangle families handout from yesterday, but they hadn't actually done it yet. So they drew triangles and measured the angles with protractors. They noticed that triangles in the same family have the same angles and there was a pattern in the sides. For the first family:

they saw this pattern as "add 3 (to the first number), add 4 (to the second number), add 5 (to the third number)". This was good, but I wanted to move toward finding the scale factor. I asked how they could get from 3-4-5 to 15-20-25. They had to think about it for a bit and came up with "multiply each number by 5". Yes! We looked at the next family and they all told me that they had to multiply by 2 this time.

We moved on to this handout which we went through a little faster than I would have liked because I will be out of town tomorrow and Friday. I had them use different colours/symbols for the corresponding angles, then I pulled out the highlighters and had them highlight corresponding sides. We measured angles and sides lengths and calculated the ratio of corresponding sides.

And that is where we had to stop.

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