Modelling in a Parallel Universe

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

Notes from the Exit Cards• Common threads in student struggles for our

group– Algebraic manipulation (factoring, completing the

square, expanding, etc…)– Connecting the concrete to abstract concepts– Understanding graphs– Connecting representations– Making connections in general

Notes from the Exit Cards• Common threads in our own struggles

– How do we find time to create all this ‘stuff’– How do we find time to deliver all this ‘stuff’– How to modify favourite activities to incorporate high

yield strategies– Connecting abstract and concrete ideas

• How do we use algebra tiles effectively in the classroom

– The meaning/differences between the big ideas and writing lesson goals

• How do we get to the skills too?

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

Follow-up Questions

• Did you draw a graph?

• Did you use algebra?

• Which did you do first? Why?

Follow-up Questions

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

Follow-up Questions

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

• Explain.

Follow-up Questions

• Did you need all three pieces of information?

• Why? Or Why not?

Follow-up Questions

• How did you determine the equation?

Follow-up Questions

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

this activity address

How did Why did Did

the big ideas?

the lesson goal?

Minds On – Parallel Tasks con’t

• 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

Minds On – Parallel Task 4 U 2 do• Identify one struggle that you believe your

students have when studying quadratics and the corresponding expectations

• Find a like-minded partner

• Develop one parallel task as well as the follow-up questions

Action – Algebra Tiles

this activity address

How did Why did Did

the big ideas?

the lesson goal?

Consolidate – Revisiting ll Tasks• Join with another pair

• Exchange parallel tasks for feedback, using the probing questions

• Write suggestions on sticky notes

this activity address

How did Why did Did

the big ideas?

the lesson goal?

Consolidate – Exit Cards

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