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

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

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 Quad & Trig Relationships - Day2 3

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????? Quad & Trig Relationships - Day2 4

Quad & Trig Relationships - Day2 Follow-up Questions Did you draw a graph? Did you use algebra? Which did you do first? Why? Quad & Trig Relationships - Day2 5

Quad & Trig Relationships - Day2 Follow-up Questions Could you have predicted whether the ‘a’ value was positive or negative before you actually calculated it? Quad & Trig Relationships - Day2 6

Quad & Trig Relationships - Day2 Follow-up Questions Is the value of ‘a’ what you expected? Explain. Quad & Trig Relationships - Day2 7

Quad & Trig Relationships - Day2 Follow-up Questions Did you need all three pieces of information? Why? Or Why not? Quad & Trig Relationships - Day2 8

Quad & Trig Relationships - Day2 Follow-up Questions How did you determine the equation? Quad & Trig Relationships - Day2 9

Quad & Trig Relationships - Day2 Follow-up Questions How would the function change if the given point (-1, 5) changed to (-1, -5)? Quad & Trig Relationships - Day2 10

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 Quad & Trig Relationships - Day2 11

Break Time

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

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

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

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

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

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. Quad & Trig Relationships - Day2 18

Consolidate – Revisiting ll Tasks Join with another pair Exchange parallel tasks for feedback Write suggestions on sticky notes Consolidate – 30 minutes Quad & Trig Relationships - Day2 19

Quad & Trig Relationships - Day2 Consolidate / Debrief Reflection Quad & Trig Relationships - Day2

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. Quad & Trig Relationships - Day2 21