Grand Canyon University, 2013. Ted Coe, Ph.D. AMP 2013: Week1 Geometry Grand Canyon University, 2013. Ted Coe, Ph.D. cc-by-sa 3.0 unported unless otherwise noted

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

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

The Foot

Square Triangle Angle Define

A square is a rectangle. True or False?

Quadrilaterals

Quadrilaterals

Quadrilaterals

Downloaded from the PARCC website 6/2/2013

From the AZ Glossary, 2008:

Wolframalpha.com (6/11/2013)

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

An Example of CCSS 5.G…

From Illustrativemathematics.org

From Illustrativemathematics.org

From Illustrativemathematics.org

From the Progression Documents http://ime. math. arizona http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_g_k6_2012_06_27.pdf

Act I Scene II

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

08/13/09 2424 08/13/09 The Broomsticks 24

The Broomsticks The RED broomstick is three feet long 2525 08/13/09 08/13/09 The Broomsticks The RED broomstick is three feet long The YELLOW broomstick is four feet long The GREEN broomstick is six feet long 25

The Burj is ______________ times as large as the Willis tower. 08/13/09 2626 08/13/09 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

Perimeter What is “it”? Is the perimeter a measurement? 08/13/09 2727 08/13/09 08/13/09 What is “it”? Is the perimeter a measurement? …or is “it” something we can measure? Perimeter 27 27

2828 08/13/09 08/13/09 Is perimeter a one-dimensional, two- dimensional, or three-dimensional thing? Does this room have a perimeter? Perimeter 28

08/13/09 2929 08/13/09 08/13/09 29 29

08/13/09 3030 08/13/09 08/13/09 30 30

Perimeter Perimeter: the sum of all lengths of a polygon. Discuss 08/13/09 3131 08/13/09 08/13/09 From the AZ STD's (2008) Perimeter: the sum of all lengths of a polygon. Discuss Perimeter 31 31

Progressions Progressions: http://ime.math.arizona.edu/progressions/ http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5 _2012_07_21.pdf p.16.

4/18/2013: Wolframalpha.com

From the CCSS, Grade 3:

Measurement What do we mean when we talk about “measurement”? 08/13/09 3535 08/13/09 What do we mean when we talk about “measurement”? Measurement

3636 08/13/09 08/13/09 “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

Measurement How about this? 3737 08/13/09 08/13/09 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

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

What is a circle?

What is circumference?

Circumference From the AZ STD's (2008) 4242 08/13/09 From the AZ STD's (2008) the total distance around a closed curve like a circle Circumference 42

4343 08/13/09 So.... how do we measure circumference? Circumference 43

Tennis Balls

The circumference is about how many times as large as the diameter? 08/13/09 08/13/09 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

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

How many Rotations?

4848 08/13/09 What is an angle? Angles 48

4949 08/13/09 Using objects at your table measure the angle Angles 49

Angles What attribute are we measuring when we measure angles? 5050 08/13/09 What attribute are we measuring when we measure angles? Angles 50

CCSS, Grade 4, p.31

What is the length of “d”? You may choose the unit. 5353 What is the length of “d”? You may choose the unit.

What is the measure of the angle? You may choose the unit. 5454 What is the measure of the angle? You may choose the unit.

5555 08/13/09 How is measurement an application of multiplicative thinking? How does this apply to angles? Reflection 55

Define: Area 56

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

Area: Grade 3 CCSS

59

What about the kite?

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

Page 7: CCSS SoMP “Simplify” in the CCSS

“Simplify” in the CCSS

CCSS, p.89