Summer Institute Mathematics Summer Institute Quadratic & Trigonometric Relationships Sessions 4 and...
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Transcript of Summer Institute Mathematics Summer Institute Quadratic & Trigonometric Relationships Sessions 4 and...
Summer Institute
Mathematics
Summer Institute
Quadratic & Trigonometric Relationships
Sessions 4 and 5
Quad & Trig Relationships - Day2 2
Summer Institute
Modeling in a Parallel Universe
Quad & Trig Relationships - Day2 3
Summer Institute
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
Summer Institute
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
Summer Institute
Follow-up Questions
• Did you draw a graph? • Did you use algebra? • Which did you do first? Why?
Quad & Trig Relationships - Day2 6
Summer Institute
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
Summer Institute
Follow-up Questions
• Is the value of ‘a’ what you expected?
• Explain.
Quad & Trig Relationships - Day2 8
Summer Institute
Follow-up Questions
• Did you need all three pieces of information?
• Why? Or Why not?
Quad & Trig Relationships - Day2 9
Summer Institute
Follow-up Questions
• How did you determine the equation?
Quad & Trig Relationships - Day2 10
Summer Institute
Follow-up Questions
• How would the function change if the given point (-1, 5) changed to (-1, -5)?
Quad & Trig Relationships - Day2 11
Summer Institute
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
Summer Institute
Break Time
Quad & Trig Relationships - Day2 13
Summer Institute
Action! – Parallel Tasks
Walk the Walk & Talk the Talk
Quad & Trig Relationships - Day2 14
Summer Institute
Action! … continued
Record your thinking on your handout
Quad & Trig Relationships - Day2 15
Summer Institute
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
Summer Institute
Action! … continued
Quad & Trig Relationships - Day2 17
Summer Institute
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
Summer Institute
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
Summer Institute
Consolidate – Revisiting ll Tasks
• Join with another pair• Exchange parallel tasks for feedback• Write suggestions on sticky notes
Quad & Trig Relationships - Day2 20
Summer Institute
Consolidate / Debrief
Reflection
Quad & Trig Relationships - Day2 21
Summer Institute
Consolidate – Exit Cards
Please fill in your exit card and hand it in to one of us as you leave!