A FUNCTIONing Classroom April 17, 2012

1. A FUNCTIONing ClassroomApril 17, 2012 Dorothy Schuller Hank Kepner Rosann Hollinger Kevin McLeod Mary Mooney

2. We are learning to deepen our understanding of “function”.

3. We will know we are successful whenwe can:decide whether a function can be used to model a given real-life context;describe an appropriate function when given a context.

4. Describe the word “function” in each of these phrases: • The car’s efficiency is a function of the car’s design. • Form follows function. • I don’t function well after lunch. • The circumference of a circle is a function of its area.

5. 8.F.1 Define, evaluate, and compare functions. 1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

6. When describing this function after thinking about the standard, would your description change? The circumference of a circle is a function of its area.

7. Chicken and Steak You have $100 to spend on a barbeque where you want so serve chicken and steak. Chicken costs $1.29 per pound and steak costs $3.49 per pound.

8. In the “Chicken and Steak” scenario: • Can a function be used to model this situation? Why or why not? • Choose a function that you identified above, sketch a graph of your function and describe your function qualitatively, as accurately as you can.. • Identify/label quantitative features to your graph.

9. 8th Grade Functions Use functions to model relationships between quantities. 5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g. where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

10. Reason Abstractly and Quantitatively Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.

11. We will know we are successful whenwe can:decide whether a function can be used to model a given real-life context;describe an appropriate function when given a context.

12. Debrief Discuss the interplay of the content standard and the Standard for Math Practice in the context of the Chicken and Steak Problem.

13. Making Connections How will your experiences in examining “function” through a launch, explore, summarize impact your future discussions with classroom teachers?

14. Professional Practice • Collaborate with a teacher to plan a lesson similar to the Chicken and Steak lesson. • Find problems that could be made more open, less structured to allow students to engage in the Standards of Mathematical Practice as they explore mathematical content. • Bring back lesson plan with student work and a short reflection.