1. Plenary 1

2. Estimate these percents as they apply to you. The percent of your daily calorie intake that is snacks The percent of your life that you’ve been a teacher/consultant/etc. The percent of your staff that is male. Getting acquainted

3. Write the percents in random order. Ask your neighbour to guess which percent is which. Getting acquainted

4. Estimate these percents for you. The percent of your daily calorie intake that is snacks The percent of your life that you’ve been a teacher/consultant/etc. The percent of your staff that is male. Getting acquainted

5. Focus on the big ideas in algebraic thinking and proportional reasoning Focus on using open questions and parallel tasks for DI and richer mathematics classrooms Past two camps

6. We want to build on what we’ve dealt with before. We will continue to talk about the big ideas in both of those topics, but we will focus more on how to respond to student thinking in these areas. And now

7. We will share the big ideas related to proportional reasoning we have been focusing on as a download on the wiki.

8. Let’s get to it Let’s try some problems.

9. A giant baseball bat is about 175 cm long. A giant pair of scissors is about 90 cm long. Think of at least three different ways to compare their lengths. Which way do you think is better? How long are they?

10. I need one group to talk about their thinking. The rest of you think about what you’d say in response. Then I will respond and talk about my rationale. What kind of feedback?

11. Spinning colours Work with a partner. Create a spinner where you are likely to spin 3 more reds than blues in 10 spins. How many more reds than blues are you likely to spin in 15 spins?

12. I need one group to talk about their thinking. The rest of you think about what you’d say in response. Then I’ll actually do it and talk about my rationale. What kind of feedback?

13. Mixing colours Jane mixed 2 containers of yellow paint with 3 same-sized containers of blue paint to make green. Lianne mixed 2.5 containers of yellow paint with 3.5 same-sized containers of blue paint. Are the paints the same shade? Explain why or why not.

14. Mixing colours Jane mixed 2 containers of yellow paint with 3 same-sized containers of blue paint to make green. Lianne also mixed yellow and blue paint. But her paint was just a little more blue than Jane’s. What numbers of same–sized containers could she have mixed?

15. Proportional reasoning involves the deliberate use of multiplicative relationships to compare quantities and to predict the value of one quantity based on the values of another. Proportional reasoning

16. How did the problems you tried relate to proportional reasoning? Talk to a partner. We’ll share a few ideas. Proportional reasoning

17. You think of a number as a group of units of another. For example, if you think of 15 as three 5s, you are thinking proportionally. When you think of 15 as 8 + 7, you are NOT thinking proportionally, even though there is nothing wrong. Another “definition” of pr

18. The variables p and q are related proportionally if the ratio of p to q doesn’t change when values of p and q change by the same factor. Or someone might say…..

19. This lunch is Papa Bear’s. Draw a sandwich that would be right for baby bear. Example of proportional reasoning

20. How does the picture show you that is less ? o o o o x o o o o o o o o o x o o o o x Example of proportional reasoning

21. When you decide that an increase from 1 to 5 is more significant than an increase from 96 to 106 because the percent increase is much more substantial, you are using proportional reasoning. Example of proportional reasoning

22. If when solving the problem: If you get a penny every time someone in Ontario sneezes, how long would it take to become a millionaire? you take a relatively small sample and multiply to generalize, you are using p.r. Example of proportional reasoning

23. When a student figures out the height of the tree, the student is using proportional reasoning. Example of proportional reasoning

24. Create your own interesting example of proportional reasoning. Try to use a different context than you just saw. What is proportional reasoning?