1. Grand Canyon University, 2013. Ted Coe, Ph.D.
AMP 2013: Week Geometry
Grand Canyon University, 2013.
Ted Coe, Ph.D.
cc-by-sa 3.0 unported unless otherwise noted

2. THE Rules of Engagement
Speak meaningfully — what you say should carry meaning;
Exhibit intellectual integrity — base your conjectures on a logical foundation; don’t pretend to understand when you don’t;
Strive to make sense — persist in making sense of problems and your colleagues’ thinking.
Respect the learning process of your colleagues — allow them the opportunity to think, reflect and construct. When assisting your colleagues, pose questions to better understand their constructed meanings. We ask that you refrain from simply telling your colleagues how to do a particular task.
Marilyn Carlson, Arizona State University
THE Rules of Engagement

3. 08/13/09
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The Plot... 3

4. The Foot

5. Square Triangle Angle
Define

6. A square is a rectangle.
True or False?

8. Quadrilaterals

9. Quadrilaterals

10. Quadrilaterals

13. Downloaded from the PARCC website 6/2/2013

14. From the AZ Glossary, 2008:

15. Wolframalpha.com (6/11/2013)

16. But that isn’t the only possibility…
Some are based on symmetry

17. An Example of CCSS 5.G…

18. From Illustrativemathematics.org

19. From Illustrativemathematics.org

20. From Illustrativemathematics.org

21. From the Progression Documents http://ime. math. arizona

22. Act I Scene II

23. From http://www. healthreform. gov/reports/hiddencosts/index

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The Broomsticks 24

25. The Broomsticks The RED broomstick is three feet long
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The Broomsticks
The RED broomstick is three feet long
The YELLOW broomstick is four feet long
The GREEN broomstick is six feet long 25

26. The Burj is ______________ times as large as the Willis tower.
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The Willis tower (formerly the Sears tower) is 1730 feet high. The Burj Khalifa (formerly Burj Dubai) is 2717 feet high.
The Burj is ______________ times as
large as the Willis tower.
The Willis tower is _____________times as
large as the Burj
The Burj is _____________ percent the
size of the Willis tower.
The Willis tower is _____________ percent
the size of the Burj. 26

27. Perimeter What is “it”? Is the perimeter a measurement?
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What is “it”?
Is the perimeter a measurement?
…or is “it” something we can measure?
Perimeter 27 27

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Is perimeter a one-dimensional, two- dimensional, or three-dimensional thing?
Does this room have a perimeter?
Perimeter 28

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31. Perimeter Perimeter: the sum of all lengths of a polygon. Discuss
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From the AZ STD's (2008)
Perimeter: the sum of all lengths of a polygon.
Discuss
Perimeter 31 31

32. Progressions Progressions: http://ime.math.arizona.edu/progressions/
_2012_07_21.pdf p.16.

33. 4/18/2013:
Wolframalpha.com

34. From the CCSS, Grade 3:

35. Measurement What do we mean when we talk about “measurement”? 08/13/09
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What do we mean when we talk about “measurement”?
Measurement

36. 3636
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“Technically, a measurement is a number that indicates a comparison between the attribute of an object being measured and the same attribute of a given unit of measure.”
Van de Walle (2001)
But what does he mean by “comparison”?
Measurement 36

37. Measurement How about this?
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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 37

38. From Fractions and Multiplicative Reasoning, Thompson and Saldanha, 2003. (pdf p. 22)

39. What is a circle?

41. What is circumference?

42. Circumference From the AZ STD's (2008)
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From the AZ STD's (2008)
the total distance around a closed curve like a circle
Circumference 42

43. 4343
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So.... how do we measure circumference?
Circumference 43

44. Tennis Balls

45. The circumference is about how many times as large as the diameter?
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The circumference is about how many times as large as the diameter?
The diameter is about how many times as large as the circumference? 45 45

46. Circumference
If I double the RADIUS of a circle what happens to the circumference?

47. How many Rotations?

48. 4848
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What is an angle?
Angles 48

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Using objects at your table measure the angle
Angles 49

50. Angles What attribute are we measuring when we measure angles? 5050
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What attribute are we measuring when we measure angles?
Angles 50

51. CCSS, Grade 4, p.31

53. What is the length of “d”? You may choose the unit.
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What is the length of “d”? You may choose the unit.

54. What is the measure of the angle? You may choose the unit.
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What is the measure of the angle? You may choose the unit.

55. 5555
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How is measurement an application of multiplicative thinking?
How does this apply to angles?
Reflection 55

56. Define: Area 56

57. Area has been defined* as the following:
“a two dimensional space measured by the number of non-overlapping unit squares or parts of unit squares that can fit into the space”
Discuss...
*State of Arizona 2008 Standards Glossary 57

58. Area: Grade 3 CCSS

59. 59

60. What about the kite?

62. In the CCSS…
“Simplify”
And
“Copies of”

63. Page 7: CCSS SoMP
“Simplify” in the CCSS

64. “Simplify” in the CCSS

65. CCSS, p.89