Pythagorean Theorem
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Transcript of Pythagorean Theorem
Pythagorean TheoremGroup 7
CCLM^2 Spring 2013
Leadership for the Common Core in Mathematics (CCLM^2) ProjectUniversity 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.
Proving the Pythagorean
TheoremGerry Shinners Jason
ThurowNina Overholser Mindi
MacLeish
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.
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
Learning Intention & Success CriteriaLearning 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.
Activity 1Pull out all 3 of the triangles. • What 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
Activity 2Let’s 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.
Activity 3Pythagorean 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.
Algebraic Proof of the Pythagorean Theorem
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 pointso 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.
Learning Intention & Success CriteriaLearning 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.
www.mytinyurl.com/triangles
Thank You!Have a great night!
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