Summer Institute

Mathematics

Summer Institute

Quadratic & Trigonometric Relationships

Sessions 4 and 5

Quad & Trig Relationships - Day2 2

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Modeling in a Parallel Universe

Quad & Trig Relationships - Day2 3

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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

Quad & Trig Relationships - Day2 4

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Minds On – Parallel TasksDetermine the equation of a function with the following properties:

Option 1 Option 2• Quadratic• Passes through

(–1, 5) • Has zeros 4 and 5

• Quadratic• Passes through

(–1, 5)• Has zeros and 65

65

Quad & Trig Relationships - Day2 5

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Follow-up Questions

• Did you draw a graph? • Did you use algebra? • Which did you do first? Why?

Quad & Trig Relationships - Day2 6

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Follow-up Questions

• Could you have predicted whether the ‘a’ value was positive or negative before you actually calculated it?

Quad & Trig Relationships - Day2 7

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Follow-up Questions

• Is the value of ‘a’ what you expected?

• Explain.

Quad & Trig Relationships - Day2 8

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Follow-up Questions

• Did you need all three pieces of information?

• Why? Or Why not?

Quad & Trig Relationships - Day2 9

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Follow-up Questions

• How did you determine the equation?

Quad & Trig Relationships - Day2 10

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Follow-up Questions

• How would the function change if the given point (-1, 5) changed to (-1, -5)?

Quad & Trig Relationships - Day2 11

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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

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Break Time

Quad & Trig Relationships - Day2 13

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Action! – Parallel Tasks

Walk the Walk & Talk the Talk

Quad & Trig Relationships - Day2 14

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Action! … continued

Record your thinking on your handout

Quad & Trig Relationships - Day2 15

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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

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Action! … continued

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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???

Quad & Trig Relationships - Day2 18

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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.

Quad & Trig Relationships - Day2 19

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Consolidate – Revisiting ll Tasks

• Join with another pair• Exchange parallel tasks for feedback• Write suggestions on sticky notes

Quad & Trig Relationships - Day2 20

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Consolidate / Debrief

Reflection

Quad & Trig Relationships - Day2 21

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Consolidate – Exit Cards

Please fill in your exit card and hand it in to one of us as you leave!