Function Understanding Kimberly Tarnowieckyi October 23, 2013

What is a function? Kimberly

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.  /watch?v=Imn_Qi3dlns&l ist=PL20023FA07684B9 37&index=15 /watch?v=Imn_Qi3dlns&l ist=PL20023FA07684B9 37&index=15

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.

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

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.

What a teacher does to orchestrate discussion/discourse 1. Anticipating 2. Monitoring 3. Selecting 4. Sequencing 5. Connecting Five practices for orchestrating effective discussion Smith and Stein, 2011 Remember the two reasons to ask questions is to: - probe students to thinking - push students understanding

How fast does Dash run? Speed Time

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 How will you group your students and have them share How will you monitor your students Look for ways to create discussions about the problem that push for students to show a deeper understanding

How to produce my own graph of a function?

Kimberly Tarnowieckyi 5-6 Function Tables 6-3 Functions 6-6 Functions and Equations Secret Codes and Number Rules Vending Machines Order Matters Which is Which?  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

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?