Discussion on similar triangles and other figures

Today was focused on students sharing and discussing responses to the questions they completed on the Similar Triangles and Other Figures investigation packet.

I first asked several students which of the five conjectures they thought were true. I wrote the conjecture numbers on the board. After getting responses from five of them, I had various students explain why they either thought the conjecture was true or not. Students were providing good counter-examples to disprove some conjectures and had solid reasoning to explain why other conjectures would be true.

As we proceeded through the questions, I called on different students. Overall, the responses were mathematically sound. We had a nice discussion around the AAA and AA theorems. We went through the proportion solutions and the only questions that came up were on the last two: one involving an expression in the denominator and the other involving square roots. I worked through these two problems and explained my thinking and results as I completed the problems.

For the last problem, the issue always comes up about simplifying radicals and results. For my part, I typically don't care the form in which the final answer is given; I care more about the thinking that went into finding the answer. However, I realize that standardized tests, especially multiple choice tests, typically simplify a response.

With this idea in mind, I explained to my class that while I would not mark them off for not simplifying, they should still practice since, as sophomores, they will be taking the PSAT test this Spring and the SAT test next year. I went through my thinking process for simplifying and what I was trying to accomplish. Student comments as I worked through the process showed they were making connections and understanding the hows and whys.

It turns out I had made copies of a selection of SAT style multiple choice questions covering quadrilaterals and similarity. I passed these out and asked students to work through them. I'll go over any problems they struggled with over the weekend and then work through and indirect measurement investigation in preparation for our unit test next week.