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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 - PowerPoint PPT Presentation
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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.
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