It's Monday and that means counting circle. Today I thought we would work with some negative numbers so we started at -173 and went up by 4. Many were using their fingers or counting up by 1 four times aloud so I opted to stick to a simple counting circle today.
We did discuss the pattern in the one's digits after we finished, which some had not noticed. Hopefully that will give them another strategy for next time.
While I was away, my class took two days to work on similar triangles. I love that spiralling gives me the freedom to spend the time needed to properly work through each concept. As a result, what I wrote about here didn't happen on Friday so we did that today (handout). But first, we did a quick recap of solving for a missing side with similar triangles:
We colour-coded the corresponding sides, calculated the scale factor then solved for the missing sides.
Today's work was my attempt to tie together similar triangles with linear and quadratic relations. I was happy with the questions that came out of filling in this table:
They had to really understand what the scale factor represents to be able to use it appropriately in this table. They also had to understand that the pattern didn't help them for the last two entries as the scale factor is no longer going up by 1. There were a lot more issues that came up out of this work than I expected, but it is great that they were able to put it all together with a little guidance. I don't know how many times I asked "How much bigger is a 6-8-10 triangle than a 3-4-5 triangle?" and "If the scale factor is 17, what does that mean?". They were making connections and I made them keep trying even when they wanted to quit. We will consolidate tomorrow then move on to trig.