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### Session 5 Modeling with Functions

Common Core High School Mathematics: Transforming Instructional Practice for a New Era

5.1

Agenda

- Homework review and discussion
- Modeling Olympic times
- Team planning
- Break
- Modeling pendulums
- Reading N-Q.1-3
- Mathematical Practices
- Homework and closing remarks

5.2

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics.

Success Criteria:

We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task.

Homework Review and Discussion

Activity 1:

- Table Discussion:
- Discuss your write up for the day 4 math task Foxes and Rabbits:
- Compare your strategies with others at your table.
- Reflect on how you might revise your own solution and/or presentation.

5.4

Modeling Olympic Times

Activity 2:

- Study the handout showing Men’s and Women’s winning Olympic times in various events since 1908.
- In your groups, discuss any stories that you can read from the data. What questions do the data raise for you?

5.5

Modeling Olympic Times

Activity 2:

- Will the women’s time for the Olympic 100 meter event ever equal the men’s?
- Answer this question, justifying your answer by using the data from the handout.

5.6

Modeling Olympic Times

Activity 2:

- Thinking about the modeling cycle, evaluate the strengths and weaknesses of your linear model for Olympic times.
- How might you change the model to take account of one or more of the weaknesses you identified?

5.7

Modeling Olympic Times

Activity 2:

- Consider an exponential model of the form y = abx + c (where y is the winning time in year x); how might you determine the parameters a, b and c?:
- According to your exponential model, will the women’s time ever equal the men’s? If so, when?

5.8

Team Planning

Activity 3:

- Thinking about the start of the next school year:
- What are your next steps as a district team?
- What one change will you, as a classroom teacher, work to make in your own instruction as a result of your learning in this institute?

5.9

Modeling Pendulums

Activity 4:

- Measure the period of a pendulum, and build a table of values for the period corresponding to different lengths of the pendulum. Keep the mass of the pendulum bob constant.
- Does changing the mass of the pendulum bob have any effect on the period?

5.11

Modeling Pendulums

Activity 4:

- Draw a scatter plot of your pendulum data.
- If you were asked to build a mathematical function that fit this data, what type of function would you choose (linear, exponential, trigonometric, ...)?

5.12

Reading N-Q.1-3

Activity 5:

- Read these content standards from the Number and Quantity conceptual category.
- Turn and talk: what is meant by “[u]se units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas;” in N-Q.1?
- How can you apply this idea to refine your pendulum model?

5.13

Reading N-Q.1-3

Activity 5:

- Notice that the standards N-Q.1-3 are starred (*).
- What is the meaning of this symbol?
- How often does this symbol appear throughout the high school standards?

5.14

Mathematical Practices

Activity 6:

- As a group, pick the two mathematical practice standards that you think were most evident in today’s activities, and justify your choices.

5.15

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics.

Success Criteria:

We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task.

Homework and Closing Remarks

Activity 7:

- Homework (to be included in journal):
- Day 5 Math Tasks: Modeling Kidneys and Basketball Bounces
- Day 5 Class Reflection

5.17

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