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# Reasoning with Pythagoras

Lesson 2 of 10

## Objective: SWBAT measure the length of the hypotentuse of a right triangle and use this measurement to find other lengths.

*65 minutes*

#### Launch

*10 min*

The video below explains how I begin today's lesson. Although the task is not challenging, my students like to be called on to perform it. And, I think it gets their minds started off in the right direction.

**Source Url**: http://www.screencast.com/t/Yw7BHP0SJOl (accessed December 3 2014)

#### Resources

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#### Access Prior Knowledge

*15 min*

Next, I want to review concepts from our previous lesson before launching our main activity for today. I will project the PPT Access Prior K Lesson 2 slides on the board and ask students to:

- Analyze the triangles
- Share what they think with their immediate partner
- Reach an agreement with their partner
- Raise their hand to respond.

To be successful, my students must recall that the area of the square above the hypotenuse equals the sum of the areas of the squares drawn upon each leg (see Answers).

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#### Activity

*30 min*

Breaking up students into small groups works well for Activity Parts 1 and 2. Yet, each student should have their own worksheet. For this lesson, I try to form groups of students that usually don´t work together. Sometimes this works better when some students understand the concepts well and others need more assistance. My students are often more willing to take risks with application tasks when they are not working with their closest friends.

Part 1 of the Activity asks students to find square roots of values using square polygons. The level of difficulty increases as students move from problem 1 to problem 6.

In Part 2 students find the length of the hypotenuse geometrically. Again, the level of difficulty is progressive.

As my students work, I encourage them to discuss their ideas with their partners. I walk around listening, and I stop to spark conversations with groups that are too quiet. Of course, as I do so I am assessing the students' work.

#### Resources

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#### Closing

*10 min*

To conclude today's lesson, I ask groups to come together and check their work and discuss any differences between them.

Most of the time, groups will have almost all the same correct answers except for maybe one or two. Therefore their discussions will not take more than a few minutes. I plan to collect the students work at the end of the lesson to assess individual students' understanding.

#### Resources

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- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
- UNIT 7: Functions
- UNIT 8: Advanced Equations and Functions
- UNIT 9: The Pythagorean Theorem
- UNIT 10: Volumes of Cylinders, Cones, and Spheres
- UNIT 11: Bivariate Data

- LESSON 1: A thought is an idea in transit
- LESSON 2: Reasoning with Pythagoras
- LESSON 3: Fluency with Pythagorean Triples
- LESSON 4: Hypotenuse Hype
- LESSON 5: Missing a Leg (Day 1)
- LESSON 6: Missing a Leg (Day 2)
- LESSON 7: Pythagorean Theorem Converse
- LESSON 8: Draw a Right triangle! You can´t go wrong.
- LESSON 9: Applying Pythagoras' Theorem with 7 "Choice" Problems
- LESSON 10: Round Robin Review (Unit 9/L1-7)