MFM2P - Day 18 (Modelling Perimeter & Area of Triangles)

Today's warm up is a Daily Desmos-like challenge:

The great part about this is that, if all goes according to plan*, this is the perfect segue to what is coming next today. (*I am out of town and don't know how far the class got yesterday.) I want students to come up with the equation of the line shown (likely by finding the slope and noticing the y-intercept) and then check their equation using Desmos.

On to the main event. I wanted to tie triangles back to the linear and quadratic work we did earlier this semester so I made this handout. Students will begin by calculating the perimeter for all the triangles from family 1 (from our similar triangles work) and add a few more triangles to the list. They will look at the pattern of the results and hopefully notice that is is constant when the scale factor increases by 1 and a multiple of the previous pattern when the scale factor increases by more than one.

Next they will graph the results and determine a model which will allow them to answer some questions about larger triangles. You may notice that I am giving them a graph with the scale set up for them and the axes labeled. As we progress through the course, I will give them less and expect more.

On to area:

I predict a lot more issues coming up here. They have a column with the length of the hypotenuse, but don't use it to calculate area. All the triangles used here are right triangles which they have drawn, so they can refer back to them for help with finding the area, but will they think to do that? The pattern and pattern in the pattern (1st and 2nd differences) should work nicely if they calculate the area correctly. It will be interesting to see what their graphs look like and how many come up with an equation to represent the relationship.

On Monday I will see how it all went. I do love how this connects linear, quadratic and similar triangles - like a spiral within the first spiral : )