1. 1 Math CAMPPP 2011 Pursuing Broader Perspectives Proportional Reasoning Breakout # 1

2. As you enter…. You will be focussing on a course in the secondary math curriculum for our first afternoon activity Move to the corner that represents the grade level you would like to work on (see posters in the four corners of the room) Wait there until further instruction!!

3. Proportional Reasoning – Breakout 1 Learning Goals: Explore connections between key components of algebraic thinking and proportional reasoning. Find key components of algebraic thinking and proportional reasoning in the curriculum expectations for a specific course (participant to choose). Identify key proportional reasoning concepts in a sample grade 9 problem. Responding to students “in the moment“. 33

4. Proportional Reasoning – Breakout 1 Minds On ~ 5 minutes Consider the sticker dot graph of courses our group created on the first day showing what we have taught or will be teaching this year. Create ‘course’ groups of 3 or 4 participants to look at components of algebraic thinking and proportional reasoning in the curriculum expectations. 44

5. Proportional Reasoning – Breakout 1 Minds On ~ 15 minutes Using half of a sheet of chart paper, create a Venn Diagram. Use the Venn Diagram to illustrate similarities and differences between the key mathematical ideas related to Proportional Reasoning and Algebraic Thinking in general (not related to your specific course). Think about: information from our plenary sessions and the Big Ideas in the CAMPPP Programme. 55

6. Proportional Reasoning – Breakout 1 Minds On ~ 5 minutes Exchange Venn Diagrams with a neighbouring table. Use a post-it note to provide feedback: “We really like….”. Use a post-it note to provide feedback: “We are wondering….”. Return Venn Diagrams to original table group. 66

7. Proportional Reasoning – Breakout 1 Minds On ~ 20 minutes Focus on the course you chose to work with. Map out the expectations related to Proportional Reasoning and Algebraic Thinking on a Venn Diagram – look for similarities/differences. Set your Venn Diagram on the side table when your group is done. Will use again tomorrow. Resources: Hard copies of curriculum documents are available as well as on- line curriculum 77

8. Proportional Reasoning – Breakout 1 Action ~ 10 minutes Grade 9 Math Problem – Keepin’ Tabs A student council collects aluminium pop tabs to raise money to purchase a wheel chair. A company buys the pop tabs for $0.88 per kilogram. If 1267 pop tabs have a mass of one pound, how many pop tabs are needed to purchase a wheelchair worth $1500? THINK: What important proportional reasoning concepts do you see in this problem from a grade 9 content perspective? Show your work.Hint: 1 kilogram = 2.2 pounds 88 Solve with a partner

9. Proportional Reasoning – Breakout 1 Action ~10 minutes Craft a ‘student solution’. Think about possible student approaches/misconceptions as you create your solution. Plan out how you will ‘act it out’….you will be role playing the solution in a few minutes – take this time to jot down how you will ‘play student’ when you have to role play 99 With your partner

10. Proportional Reasoning – Breakout 1 Action ~15 minutes Find another pair. One pair takes the role of the student. Role play your solution. The other pair takes the role of the teacher. Practice “responding to students in the moment”. Reverse roles. 10

11. Proportional Reasoning – Breakout 1 Consolidate ~ 5 minutes Think about the Role Play. Shout Out ….words and/or phrases you used for feedback that you felt were effective. 11

12. Proportional Reasoning – Breakout 1 Consolidate ~ 5 minutes Perspective Passport / Math Map Individually reflect on your comfort level, learning and next steps related to giving feedback Record in your Passport or on your Math Map. 12