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Function Understanding

Function Understanding. Kimberly Tarnowieckyi October 23, 2013. ktarnowi@cloverpark.k12.wa.us. What is a function?. Kimberly Tarnowieckyi. ktarnowi@cloverpark.k12.wa.us. What is a function?. Standards assessed on End of Course Exams

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Function Understanding

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  1. Function Understanding Kimberly Tarnowieckyi October 23, 2013 ktarnowi@cloverpark.k12.wa.us

  2. What is a function? Kimberly Tarnowieckyi ktarnowi@cloverpark.k12.wa.us

  3. What is a function? Standards assessed on End of Course Exams A1.1.A Select and justify functions and equations to model and solve problems. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. http://www.youtube.com/watch?v=Imn_Qi3dlns&list=PL20023FA07684B937&index=15

  4. What is a function? F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

  5. A woman climbs a hill at a steady pace and the starts to run down one side Speed Speed Time Elapsed Time Elapsed Speed Speed Time Elapsed Time Elapsed

  6. Math Practice #1 Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

  7. What a teacher does to orchestrate discussion/discourse • Anticipating • Monitoring • Selecting • Sequencing • Connecting Remember the two reasons to ask questions is to: - probe students to thinking - push students understanding Five practices for orchestrating effective discussion Smith and Stein, 2011

  8. Speed Time How fast does Dash run?

  9. Practice/Collaboration Time • In small groups: • How will you add an activity to one of your lessons in the next few weeks. • What Performance Task looks like one you wish to give a try? • When are you will to try a CBR? • Be ready to present • Look for ways to create discussions about the problem that push for students to show a deeper understanding • How will you group your students and have them share • How will you monitor your students

  10. How to produce my own graph of a function?

  11. Real-World Math with Vernier Connecting Math and Science • By John Gastinueau, Chris Brueningsen, Bill Bower, Linda Antinone, and Elisa Kerner • TI-Instruments • Math N-spired • Function or Not a Function Activity • Domain and Range Activity • Performance Tasks/Activities KimberlyTarnowieckyi 5-6 Function Tables 6-3 Functions 6-6 Functions and Equations Secret Codes and Number Rules Vending Machines Order Matters Which is Which?

  12. Your exit slip • How do you help motivate students to persevere in math and specifically problem solving? • What questions or concerns do you still have about creating student discourse?

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