1. Summer Institute Summer 2009
Quadratic & Trigonometric Relations
Session 2
Summer Institute Summer 2009
<Welcome participants.>
Tom Chapman
Judy Mendaglio

2. Modeling in a Parallel Universe
Quad & Trig Relationships - Day2 2

3. Quad & Trig Relationships - Day2
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
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4. Minds On – Parallel Tasks
Determine the equation of a function with the following properties:
Option 1
Option 2
Quadratic
Passes through (–1, 5)
Has zeros 4 and 5
Has zeros and
Debrief with next slide
MO – task and debrief – 10 min
Note about follow-up with expectations and processes – just a reminder to include process expectations?????
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5. Quad & Trig Relationships - Day2
Follow-up Questions
Did you draw a graph?
Did you use algebra?
Which did you do first? Why?
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6. Quad & Trig Relationships - Day2
Follow-up Questions
Could you have predicted whether the ‘a’ value was positive or negative before you actually calculated it?
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7. Quad & Trig Relationships - Day2
Follow-up Questions
Is the value of ‘a’ what you expected?
Explain.
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8. Quad & Trig Relationships - Day2
Follow-up Questions
Did you need all three pieces of information?
Why? Or Why not?
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9. Quad & Trig Relationships - Day2
Follow-up Questions
How did you determine the equation?
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10. Quad & Trig Relationships - Day2
Follow-up Questions
How would the function change if the given point (-1, 5) changed to (-1, -5)?
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11. 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
MO – task and debrief – 10 min
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12. Break Time

13. Action! – Parallel Tasks
Walk the Walk & Talk the Talk
Quad & Trig Relationships - Day2

14. Quad & Trig Relationships - Day2
Action! … continued
Record your thinking on your handout
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15. Quad & Trig Relationships - Day2
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.
Quad & Trig Relationships - Day2

16. Quad & Trig Relationships - Day2
Action! … continued
Quad & Trig Relationships - Day2

17. Quad & Trig Relationships - Day2
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???
Our turn to share: How we opened up the task…
Started with an existing task (Hula Hoop Activity from TIPS)
Developed learning goals based on the overall/specific expectations
Focus on the big ideas
Quad & Trig Relationships - Day2

18. 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.
MO – 25 minutes – do you think this is enough? Also, rather than have them write all the BI and expectations, lets have them code it someway to make it faster.
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19. Consolidate – Revisiting ll Tasks
Join with another pair
Exchange parallel tasks for feedback
Write suggestions on sticky notes
Consolidate – 30 minutes
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20. Quad & Trig Relationships - Day2
Consolidate / Debrief
Reflection
Quad & Trig Relationships - Day2

21. Consolidate – Exit Cards
Please fill in your exit card and hand it in to one of us as you leave!
Ask the participants to complete the statement: "What's important about parallel tasks is …".
Participants complete on a sticky and post on the door as they leave.
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