Clip 1/5: lesson part 1
Patty introduces her lesson by charging students to identify the “big ideas” they should be thinking about when they work with right triangles. Students pair-share their ideas, and Patty notes when they are making reference to available tools and supports, such as anchor charts, around the room.
In her commentary, Patty notes that this lesson is intended to develop students’ capacity to engage in modeling mathematical situations. Students identify the Pythagorean Theorem, and Patty prompts them to attend to precision and communicate precisely. In a whole-group sharing, she engages all students to add on to, critique, extend, and clarify each other’s thinking. Students deepen their capacity to make sense of the problem or situation.
Patty presents student work from a previous assessment and asks students to critique the person’s strategies and precision, giving advice to each exemplar learner about how to improve their approach.
Some kids were really good with the geometry we had been doing. They were really good with all these procedures of writing equations, but they were still struggling with making sense of it. I like having it integrated, so students can shine in different ways. I was still making sense of a lot of it myself, too.
The day before this lesson, students had a choice of two problems on comparing costs of gym memberships and rate plans. And they actually brainstormed very low-level questions like, "What is the constant rate of change?" But we got the high-end questions, like, "When will the cost be the same at the same time?" They chose which one they wanted to work on, and then they were going to be working on that. I wanted to address "modeling the situation," to help them solve that problem. I just think that that knowing what they know and don’t know makes every decision for me.
I was excited to see what they could do, based on what their experiences were before. Then I really wanted them to write advice to their peers about an upcoming assessment. Like, "What do you do? What do you do if you get stuck? What kind of strategies can you do?"
I found that many students understood the relationship and could verbalize and relate it to the areas of the land. When the length of the legs were given, students could use the Pythagorean Theorem. But when a hypotenuse and a leg were given, there was some difficulty finding out the length of the other leg. There was some confusion with the relationship.
A lot of the language, you could still hear in their voice, they were struggling with being super precise all the time. I know they referred to the conceptual understanding, which I think supported them. They looked at the anchor poster, and they were able to make connections to the story of the area of land, and the relationship between the two areas and the one area.
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