Speak Meaningfully What You Say Should Carry Meaning;

Geometry: week 1, 2013. p.1 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

2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected] Geometry: week 1, 2013. p.2 Define:

Square:

Triangle:

Angle:

Square:

Triangle:

Angle:

2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected]

This handout was originally created by Ted Coe in 2011 as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. Geometry: week 1, 2013. p.3

2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected] Geometry: week 1, 2013. p.4

This handout 2013 Tedwas Coe, originally Arizona Mathematics created byPartnership Ted Coe & Grand in 2011 Canyon as University,part of the [email protected] development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. Geometry: week 1, 2013. p.5 From http://www.healthreform.gov/reports/hiddencosts/index.html (6/3/2011):

Discuss.

2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected] Geometry: week 1, 2013. p.6 Multiplicative Thinking I - The Broomsticks

You have three broomsticks: The RED broomstick is three feet long The YELLOW broomstick is four feet long The GREEN broomstick is six feet long

1. How much longer is the GREEN broomstick than the RED broomstick?

2. How much longer is the YELLOW broomstick than the RED broomstick?

3. The GREEN broomstick is ______times as long as the YELLOW broomstick.

4. The YELLOW broomstick is ______times as long as the GREEN broomstick.

5. The YELLOW broomstick is ______times as long as the RED broomstick.

6. The RED broomstick is ______times as long as the YELLOW broomstick.

This handout was originally created by Ted Coe and modified in 2011 as part of the development of the “Math 5: Geometry” 2013 curriculum Ted Coe, forArizona Arizona Mathematics State University’s Partnership & TeachingGrand Canyon Foundations University, [email protected] Project. Geometry: week 1, 2013. p.7 7. A certain stock started at a value $74. One year later it was valued at $89.54. By what percent did the stock’s value increase?

8. The Willis tower (formerly the Sears tower) is 1730 feet high. The Burj Khalifa (formerly Burj Dubai) is 2717 feet high. a. The Burj is ______times as large as the Willis tower.

b. The Willis tower is ______times as large as the Burj

c. The Burj is ______percent the size of the Willis tower.

d. The Willis tower is ______percent the size of the Burj.

a 9. How can you think about ? b

a 10. If you are given  c , how can you think about c? b

11. On the broomstick questions (#3-#6) we did not need to mention “feet” in the answer. Why is that?

12. Which bank account grew more in one year? Account “A” grew from $100 to $145. Account “B” grew from $50 to $76.

13. Consider a bank account that grew from $95 to $120 over THREE years.

a. Use an additive comparison for these two numbers. What does your answer mean?

b. Use a multiplicative comparison for these two numbers. What does your answer mean?

14. If the terms of growth remained constant,

a. What is the annual additive growth for this account? What does your number mean?

b. What is the annual multiplicative growth (factor) for this account? What does your number mean?

15. Repeat the above with an account that went from $150 to $130 over four years.

16. Write every relationship you see in this diagram:

(From Thompson and Saldanha, 2004.)

Question 16 from Thompson, P. W., & Saldanha, L. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, G. Martin & D. Schifter (Eds.), Research companion to the Principles and Standards for School Mathematics (pp. 95-114). Reston, VA: National Council of Teachers of Mathematics.

This handout 2013 was Ted originally Coe, Arizona created Mathematics by Ted Partnership Coe in 2011 & Grand as partCanyon of University,the development [email protected] of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Geometry: week 1, 2013. p.12

This handout was originally created by Ted Coe in 2011 as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. 2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected] Geometry: week 1, 2013. p.14

This handout was originally created by Ted Coe in 2011 as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. 2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected] Geometry: week 1, 2013. p.15

2013 Ted Coe, Arizona Mathematics Partnership & Grand Canyon University, [email protected]