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.

5.3

5.4

Homework Review and DiscussionActivity 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.

5.5

Modeling Olympic Times

• 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?

Activity 2:

5.6

Modeling Olympic Times

•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.

Activity 2:

5.7

Modeling Olympic Times

• 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?

Activity 2:

5.8

Modeling Olympic Times

• 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?

Activity 2:

5.9

Team Planning

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?

Activity 3:

Break

5.10

5.11

Modeling Pendulums

•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?

Activity 4:

5.12

Modeling Pendulums

• 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, ...)?

Activity 4:

5.13

Reading N-Q.1-3

• 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?

Activity 5:

5.14

Reading N-Q.1-3

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?

Activity 5:

5.15

Mathematical Practices

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

Activity 6:

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.

5.16

5.17

Homework and Closing RemarksActivity 7:

Homework (to be included in journal): • Day 5 Math Tasks: Modeling Kidneys and

Basketball Bounces• Day 5 Class Reflection