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Pythagorean Theorem Group 7 CCLM^2 Spring 2013 Leadership for the Common Core in Mathematics (CCLM^2) Project University of Wisconsin-Milwaukee, 2012–2013 This material was developed for the Leadership for the Common Core in Mathematics project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. You may not use this work for commercial purposes. This project was supported through a grant from the Wisconsin ESEA Title II Improving Teacher Quality Program.

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Proving the Pythagorean Theorem Gerry ShinnersJason Thurow Nina Overholser Mindi MacLeish

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Launch Activity Plot the points (0, 0) and (4, 8) on the coordinate plane Connect the two points As you look at these two points, brainstorm ways that you could find the exact distance between these two points? 5.G.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

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Group Norms Active Participation Keep sidebar conversations to a minimum Ensure all electronic devices are silenced Presenters will raise their hands to signal the group to come back together

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Learning Intention & Success Criteria Learning Intention- We will learn how to explain a proof of the Pythagorean Theorem (8.G.6). Success Criteria- We will be successful when we can explain a proof of the Pythagorean Theorem and apply it to a given task.

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Activity 1 Pull out all 3 of the triangles. W hat do you know about all of these triangles? Match the squares to each of the side lengths of each triangle. What did you notice? 4.G.2: Classify two-dimensional figures based on...the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 3.MD.6: Measure areas by counting unit squares

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Activity 2 Lets pull out your triangles. Notice they are labeled leg 1, leg 2, and hypotenuse. Look at Leg 1 and use your tiles to build Leg 1 squared Look at Leg 2 and use your tiles to build Leg 2 squared Manipulate your tiles to create hypotenuse squared 2.G.2: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 3.MD.7: Relate area to the operations of multiplication and addition. 3.MD.7a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

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8.G.6 Explain a proof of the Pythagorean Theorem and its converse

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Activity 3 Pythagorean Theorem Area Activity Explore and answer activity questions. (Make notes to your observations for debrief). Work together.... You will have 8 minutes Open bags of shapes and try to make connections between them.

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Algebraic Proof of the Pythagorean Theorem

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Launch Activity Revisited Pull out your Launch Activity o Plot the points (0, 0) and (4, 8) on the coordinate plane o Connect the two points Find the distance between the two points o What is the length? o Explain how you found the distance 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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Learning Intention & Success Criteria Learning Intention- We will learn how to explain a proof of the Pythagorean Theorem (8.G.6). Success Criteria- We will be successful when we can explain a proof of the Pythagorean Theorem and apply it to a given task.

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Thank You! Have a great night! Closure

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