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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

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Session 5 modeling with functions

Session 5 Modeling with Functions

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

5.1


Agenda
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 & 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


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 criteria1
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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