1. Quadratic and Trigonometric Relations Session 1 Summer Institute August 2009 Donna Del Re David Zimmer

2. 2 Welcome Introductions –Tell us your name and Board –Share one thing that you hope to get out of this breakout session OR –Share one success that you have had teaching relations

3. 3 Learning Goals Explore the Big Ideas of Quadratic and Trigonometric relations Make connections between the overall expectations and the big ideas of Quadratic and Trigonometric relations Making sense of Big Ideas

4. 4 Minds On: Four Corners Four big ideas for quadratic relations and four big ideas for trigonometric relations are posted, one on each side of each corner of the room.

5. 5 Minds On: Four Corners (continued) At your table, you will find two envelopes. Each envelope contains overall expectations from various grade 10, 11 and 12 courses related to quadratic relations OR trigonometric relations. Select a partner. Choose an envelope and then select one expectation (so each pair will have two expectations) from that envelope.

6. 6 Minds On: Four Corners (continued) With your partner, walk around the room and discuss the Big Ideas through the lens of your expectations. With your expectation, go to the corner that it best connects to. (You and your partner may need to separate.)

7. 7 Minds On: Four Corners (continued) In your corner, discuss your rationale for matching the overall expectation to that big idea. You may change your corner if your discussion made you rethink your choice. When you are ready, post your overall expectation under the big idea.

8. 8 Minds On: Four Corners (continued) Corner Share: How are the expectations for quadratic and trigonometric relations the same for that Big Idea? Different? Gallery Walk

9. 9 Minds On: Turn and Talk Corner Share: Find three new people to work with. Questions to consider… –How easy / difficult was it to assign an overall expectation to a big idea? Why? –Are the overall expectations sufficient to get at the big ideas? Why or why not? –What role do students’ prior experiences play in the development of their understanding of the big ideas? –What challenges might you as a teacher face when providing students with learning opportunities that focus on developing understanding of the big ideas?

10. 10 Big Ideas of Quadratic Relations, Q1 Algebraic reasoning can help you to describe and analyze generalized quadratic relations and change using words and symbols.

11. 11 Big Ideas of Quadratic Relations, Q2 Different representations of quadratic relations highlight different characteristics and serve different purposes.

12. 12 Big Ideas of Quadratic Relations, Q3 Comparing quadratic relations with other relations (e.g. linear) provides insight into the defining characteristics of a quadratic relation.

13. 13 Big Ideas of Quadratic Relations, Q4 Limited information about a quadratic relation can sometimes, but not always, reveal other information about that relation.

14. 14 Big Ideas of Trigonometric Relations, T1 Trigonometric relations can help you to describe and analyze periodic relationships and change using words and symbols.

15. 15 Big Ideas of Trigonometric Relations, T2 A trigonometric function can be represented in multiple ways (numerically, graphically, geometrically and algebraically) and each representation highlights different characteristics or behaviours, and can serve different purposes.

16. 16 Big Ideas of Trigonometric Relations, T3 When comparing trigonometric relations to other relations, the periodic nature becomes a defining characteristic.

17. 17 Big Ideas of Trigonometric Relations, T4 Limited information about a periodic relationship can sometimes, but not always, reveal other information about that relationship.

18. 18 Action: Match Me Up! In pairs, match each question to the big idea that it is most likely to elicit.

19. 19 Action: Match Me Up! (continued) Group Share: Questions to consider… –Which questions were easiest / most difficult to map? Why? –What common elements are evident in the questions that help students develop understanding of the big ideas?

20. 20 Exit Card Select a Big Idea and write your own question (for Quadratic or Trig relations) that gets at that Big Idea. Remember to label the Big Idea on your sticky. Write your name on the back. Post it on your way out.