Posing Powerful Questions

Lesson Title: Walk the Walk Talk the Talk Grade MHF4U Goals(s) for a Specific Lesson ◦ Trigonometric functions can help you to describe and analyze periodic behaviour ◦ Develop an understanding of rates of change of periodic functions

Curriculum Expectations 1.1 gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change (e.g., in words, numerically, graphically, algebraically) 1.2 recognize that the rate of change for a function is a comparison of changes in the dependent variable to changes in the independent variable, and distinguish situations in which the rate of change is zero, constant, or changing by examining applications, including those arising from real-world situations 3.1 compare, through investigation using a variety of tools and strategies (e.g., graphing with technology; comparing algebraic representations; comparing finite differences in tables of values) the characteristics (e.g., key features of the graphs, forms of the equations) of various functions (i.e., polynomial, rational, trigonometric, exponential, logarithmic)

Big Idea(s) Addressed by the Expectations T1 Trigonometric functions can help you to describe and analyze periodic relationships and change using words and symbols. T2 When a relationship appears to be periodic in nature, then it is appropriate to consider a trigonometric function to model the relationship.

Minds On… Sample Question(s)

Show CLIPS video Who Cares? For Periodic and Sine Functions and their Transformations. Highlight scenarios that describe periodic phenomenon.

Action! Sample Question(s) Walk the Walk Talk the Talk – parallel activity

Scaffolding Questions (posed to individuals as needed, written on popsicle sticks) (Written on popsicle sticks) . How do you know that you won’t start walking from …. . Will you always walk in one direction? . What if you were walking fast, how would the graph change?

Consolidate/Debrief Sample Question(s) Open questions to debrief the activity 1. How did you decide which graph you wanted to do? 2. What were some of the things you thought about when you were first trying to make your graph? 3. What were some of the adjustments that you had to make to get closer to your graph? 4. What was most challenging about creating your graph?

Open questions to debrief rates of change 1. How did you have to walk to get the turning points of your graph? 2. How did you know to increase or decrease speed? 3. How did you determine whether you would start slow and increase speed or start fast and decrease speed?

Question Planning Template, 2009 Question Planning Template, 2009