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## Session 5 Modeling with Functions

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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