Applying Rates of Similar Triangles

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SWBAT use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line.

Big Idea

Through an exploration task and an application exercise, students will learn how similar triangles relate to slope and proportional reasoning.

Warm Up

8 minutes

To provide additional practice identifying unit rate, for today's Warm Up problems, I have provided a graph without numbers and a follow-up question. I want to check students' abilities to recognize the slope of the line and then compare it to another rate, 6/8. As students work, I will make note of any student who is still struggling with this task so that I can provide additional support during "Power Hour", a specific time set aside by our school twice a week for intervention. 

Once the timer sounds, I will select a student to share his answer and ask for class consensus using thumbs up (agree), thumbs down (disagree), or thumbs sideways (not sure). Students are encouraged to come to the SmartBoard to support their thinking through demonstration. Once class consensus is reached, I introduce today's Learning Objective.

Work Time: Explore Task

17 minutes

I have created an explore task for today's Work Time based on one from Illustrative Mathematics. It requires students to use knowledge from the week's previous lessons to analyze the work of three fictitious students. On a graph, three similar triangles have been drawn. After working through the Explore Task- Applying Rates of Similar Triangles, students should be able to explain how similar triangles relate to a linear graph.

Slope Triangles

15 minutes

Once students have completed the Explore Task, I engage students in additional practice with Slope Triangles, to check for understanding. Students must decide which of the given triangles match the each graph. Students can drag and drop the given slope triangles onto the graph to check their answers. While some students will have made the connection between slope and the side-side relationship of the given triangles in the Explore Task, with proper facilitation, I can help all students understand this concept.

Concept Check

5 minutes

To provide essential feedback regarding conceptual understanding, students will complete a brief Concept Check. This formative assessment asks students to graph a given linear equation and draw two slope triangles on the graph. Then, students need to provide a written explanation about how they know that the slope triangles they have drawn are similar.

Student responses on this Concept Check- Slope Triangles will reveal which students continue to struggle with this concept. I can then provide appropriate levels of intervention based on their needs. These interventions occur during Advisory period, before or after school, or during Power Hour.