1. Dr. Betty Long Appalachian State University Sheila Brookshire Buncombe County Schools July 9-13, 2012

2. Norms Be on time Silence cell phones Limit sidebar conversations to activities Be respectful Be actively engaged Have Fun!

3. Goals Participants will: Become more familiar with the Common Core State Standards for grade 6-8 and how they progress horizontally and vertically Engage in tasks that can be used to develop students’ use of the Standards for Mathematical Practice Connect concepts among Common Core State Standards

4. Icebreaker How do you “picture” the Standards for Mathematical Practice?

5. Jelly Bean Video

6. What is Proportional Reasoning? Ability to scale up and down in appropriate situations and to supply justifications for assertions made about relationships in situations involving simple direct and inverse proportions (Lamon) Understanding: 1. Equivalent ratios can be created by iterating and/or partitioning a composed unit 2. If one quantity in a ratio is multiplied or divided by a particular factor, then the other quantity must be multiplied or divided by the same factor to maintain the proportional relationship 3. The 2 types of ratios – composed units and multiplicative comparisons – are related (NCTM)

7. Critical Components of Reasoning Rational Number Interpretations Relative Thinking Measurement Quantities and Covariation Reasoning Up and Down Unitizing Sharing and Comparing

8. Rational Number Interpretations Using a pizza as the unit, draw the following fractional parts: 1 (3/8 pizza) 3 (1/8 pizzas) 1 ½ (1/4 pizzas)

9. Relative and Absolute Thinking On a certain evening at a local restaurant, the five people sitting at Table A and the 7 people sitting at Table B ordered the drinks listed below. Later, the waitress was heard referring to one of the groups as “the root beer drinkers.” To which table was she referring? Table A: 2 Root Beers and 3 Colas Table B: 3 Root Beers and 4 Colas

11. Measurement This figure has an area of 1 square inch. Draw a figure that has an area of 2/3 inches squared..

12. Quantities and Covariation For each situation, list the changing Quantities: You are filling your car’s gas tank You travel by car from Milwaukee to Chicago You make several credit card purchases You are scuba diving You are draining the water in your bathtub

13. Reasoning Up and Down If the unit is Draw a picture for ½ represents ? If the unit is represents ?

14. Unitizing We are going to solve a problem that uses a case of soda (24 cans). What sort of mental picture do you get? Unitizing refers to the process of constructing chunks in terms of which to think about a given commodity.

15. Sharing and Comparing In Mr. Trent’s science class, students sit 3 to a table. One day for mid-morning break, Mr. Trent put 2 candy bars on each table and told the students to share them. “But before you do,” he said, “please push all 4 tables together.” If you are a candy lover, would you like to get your share of the candy before or after the tables are pushed together?

17. Bonita Bonita was given a problem about a leaky faucet through which 6 ounces of water dripped in 8 minutes. She needed to figure out how much water dripped in 4 minutes.