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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.

slide4
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

slide5
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

slide6
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

slide7
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

slide8
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

slide9
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

slide11
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

slide12
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

slide13
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

slide14
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

slide15
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.

slide17
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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