1. Summer Institute Mathematics Summer Institute Quadratic & Trigonometric Relationships Sessions 4 and 5

2. Summer Institute Quad & Trig Relationships - Day22 Modeling in a Parallel Universe

3. Summer Institute Quad & Trig Relationships - Day23 Learning Goals Practice posing parallel and open questions Refine understanding of how different representations of relationships highlight different characteristics or behaviours and can serve different purposes. Highlight the importance of being conscious and explicit about instructional decisions; specifically, the exploration of different models

4. Summer Institute Quad & Trig Relationships - Day24 Minds On – Parallel Tasks Determine the equation of a function with the following properties: Option 1Option 2 Quadratic Passes through (–1, 5) Has zeros 4 and 5 Quadratic Passes through (–1, 5) Has zeros and

5. Summer Institute Quad & Trig Relationships - Day25 Follow-up Questions Did you draw a graph? Did you use algebra? Which did you do first? Why?

6. Summer Institute Quad & Trig Relationships - Day26 Follow-up Questions Could you have predicted whether the ‘a’ value was positive or negative before you actually calculated it?

7. Summer Institute Quad & Trig Relationships - Day27 Follow-up Questions Is the value of ‘a’ what you expected? Explain.

8. Summer Institute Quad & Trig Relationships - Day28 Follow-up Questions Did you need all three pieces of information? Why? Or Why not?

9. Summer Institute Quad & Trig Relationships - Day29 Follow-up Questions How did you determine the equation?

10. Summer Institute Quad & Trig Relationships - Day210 Follow-up Questions How would the function change if the given point (-1, 5) changed to (-1, -5)?

11. Summer Institute Quad & Trig Relationships - Day211 Action! – Parallel Tasks … continued Select one of the parallel tasks Form a group with others working on the same task Complete the task by selecting one of the questions and then prompt each other using the follow-up questions provided Match the parallel task to a big idea and then find all the expectations that are addressed by the two parallel tasks

12. Summer Institute Break Time

13. Summer Institute Quad & Trig Relationships - Day213 Action! – Parallel Tasks Walk the Walk & Talk the Talk

14. Summer Institute Quad & Trig Relationships - Day214 Action! … continued Record your thinking on your handout

15. Summer Institute Quad & Trig Relationships - Day215 Action! … continued Form teams of four (walker, calculator operator, CBR manager, recorder). Select one of the walks pictured or create your own. See BLM 3.3. Discuss and record how you will “Walk the Walk” to make the graph and use this knowledge to create a similar graph with a graphing calculator and a CBR.

16. Summer Institute Quad & Trig Relationships - Day216 Action! … continued

17. Summer Institute Quad & Trig Relationships - Day217 Action! … continued Whole group share… –Why is this a parallel/open task??? –Scaffolding questions??? –Concepts covered??? Rates of change, periodic nature of walk, maximum, minimum, intervals of increase and decrease, points of inflection…. –Connection to big ideas??? –Talk the Talk???

18. Summer Institute Quad & Trig Relationships - Day218 Action! – Create a Parallel Task Select a big idea and an overall expectation from either a quadratic relations strand or a trig. functions strand. Consider the potential struggles that students might encounter with this big idea or expectation. Create a lesson goal and an appropriate parallel task that addresses that expectation.

19. Summer Institute Quad & Trig Relationships - Day219 Consolidate – Revisiting ll Tasks Join with another pair Exchange parallel tasks for feedback Write suggestions on sticky notes

20. Summer Institute Quad & Trig Relationships - Day220 Consolidate / Debrief Reflection

21. Summer Institute Quad & Trig Relationships - Day221 Consolidate – Exit Cards Please fill in your exit card and hand it in to one of us as you leave!