Function Understanding

Kimberly TarnowieckyiOctober 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 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

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

Time Elapsed

Time Elapsed

Time Elapsed

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Math Practice #1Mathematically 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. Anticipating2. Monitoring3. Selecting4. Sequencing5. Connecting

Five practices for orchestrating effective discussionSmith and Stein, 2011

Remember the two reasons to ask questions is to: - probe students to thinking - push students understanding

How fast does Dash run?Sp

eed

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 shareHow 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?

KimberlyTarnowieckyi5-6 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?