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

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

3. We will know we are successful when we 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.
Discussion time: table first, then whole group share out.
Similarities among uses of the word “function” but differences too.
Have participants record their thinking for the last description.

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.
Which of the phrases comes closest to this standard?
How does the use of the word function in this standard relate to …
Didn’t put whole std as to focus on first part… not about graphs today?
(“…The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.”)

6. The circumference of a circle is a function of its area.
When describing this function after thinking about the standard, would your description change?
The circumference of a circle is a function of its area.
You can’t have an area of a circle with different circumferences. Revisit your description and talk about how it changed. Make sure that participants surface and describe the input and output of the relationship. Chart these ideas

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.
The amount of chicken depends on the amount of steak. And reverse is true.
A variety of descriptions is good.
Each group will chart their descriptions.
Gallery walk? Or whole group debrief/summary?

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.
Is there only one possible function? Surface different perspectives of the way function is being discussed at the tables.
What I have in mind here is something like:” it is decreasing and linear”. Given the context why is this a linear function.
Look for quantitative features such as intercepts, specific points, slope of the line.

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.
Can we use this or not…

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 when we 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?
You experienced function today in the context of launching, exploring, summarizing.
You sit in classrooms that don’t feel/look/sound like this.
What will you take back and USE in your day to day interactions with classroom teachers? How do teachers find and create opportunities for students to explore some mathematics?

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.