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AMP 2012-2013: Saturday #3

AMP 2012-2013: Saturday #3. Ted Coe, Scottsdale Community College, 2012. Some materials were also created or refined as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. . Speak meaningfully

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AMP 2012-2013: Saturday #3

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  1. AMP 2012-2013: Saturday #3 Ted Coe, Scottsdale Community College, 2012. Some materials were also created or refined as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project.

  2. Speak meaningfully • Exhibit intellectual integrity • Strive to make sense • Respect the learning process of your colleagues • Marilyn Carlson, Arizona State University The Rules of Engagement

  3. The Plot...

  4. The Broomsticks

  5. The Broomsticks The RED broomstick is three feet long The YELLOW broomstick is four feet long The GREEN broomstick is six feet long

  6. Is perimeter a one-dimensional, two-dimensional, or three-dimensional thing? • Does this room have a perimeter? Perimeter

  7. What do we mean when we talk about “measurement”? Measurement

  8. How about this? • Determine the attribute you want to measure • Find something else with the same attribute. Use it as the measuring unit. • Compare the two: multiplicatively. Measurement

  9. Using objects at your table measure the angle Angles

  10. Define: Area

  11. Area of whole square is 4r^2 Area of red square is 2r^2 Area of circle is…

  12. Image from wikipedia. cc-sa

  13. Area of one green triangle = a b Area of blue square = a c Area of whole (red) square = c b OR This means that: b c c a b a

  14. Speaking of areas… • Is “Area” a measure? • Or is it an attribute to be measured?

  15. Find the dimensions of the rectangle • Find the area of the rectangle • Find a rectangle somewhere in the room similar to the shaded rectangle

  16. “Similar means same shape different size.” • “All rectangles are the same shape. They are all rectangles!” • “Therefore all rectangles are similar.” Working with similar figures

  17. Two figures are similar if…

  18. Scale Factors

  19. Teaching Geometry According to the Common Core Standards, H. Wu Revised: April 15, 2012. Grade 7 notes, p.49: What is a scale factor?

  20. CCSS: Grade 2 (p.17)

  21. CCSS: Grade 7 (p.46)

  22. CCSS: Grade 7 (p.46)

  23. CCSS: Grade 8 (p.52)

  24. CCSS: Grade 8 (p.54)

  25. CCSS: Grade 8 (p.56)

  26. CCSS: HS Geometry (p.74)

  27. CCSS: HS Geometry (p.74)

  28. CCSS: HS Geometry (p.74)

  29. CCSS: Grade 8 (p.56)

  30. CCSS: HS Geometry (p.77)

  31. Pythagorean Theorem?

  32. Everything is better in 3D!

  33. What is volume? • What do students find challenging about understanding volume? Volume

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