ALGEBRA I
LENGTH 18 DAYS
UNIT TWO: FUNCTIONS & GRAPHS
UNIT OVERVIEW: Students will interpret, build and graph functions.
UPDATED
2/6/14
NUMBER AND QUANTITY (N), FUNCTIONS (F)
PLANNING CONSIDERATIONS PRIOR TO UNIT INCLUDING PRIOR KNOWLEDGE/SKILLS:
KEY UNDERSTANDING (S):
1. Functions can be used to describe real-world situations.
2. Functions can be used to demonstrate a relationship between two quantities.
3. Not all relations are functions.
4. Functions can be shown in different types of function notation.
ESSENTIAL QUESTION (S):
1. What is the best way to represent a function?
2. How can we use graphs to describe relationships?
3. What strategies can we use to identify patterns?
STANDARD CODE/
COMMON CORE STANDARDS FOR MATHEMATICAL CONTENT
FUNCTIONS
COMMON CORE FOCUS STANDARDS OF
MATHEMATICAL PRACTICE
Interpreting Functions: Understand the concept of a function and use function notation
1. Make sense of problems and
persevere in solving them.
F.IF.1
2. Reason abstractly and quantitatively.
F.IF.2
F.IF.3
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).
Use function notation, evaluate functions for inputs in their domains, and interpret statements
that use function notation in terms of a context.
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.
Interpreting Functions: Interpret functions that arise in applications in terms of the context.
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.*
3. Construct viable arguments and
critique the reasoning of others.
4. Model of mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
F.IF.9
Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say which has the larger maximum.
Building Functions: Build new functions from existing functions
F.BF.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them
to model situations, and translate between the two forms.*
F.BF.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative); find the value of k given the graphs. Experiment with
cases and illustrate an explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic expressions for them.
KNOWLEDGE
SKILLS
DECLARATIVE AND FACTUAL KNOWLEDGE
STUDENTS WILL KNOW…
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SKILLS
STUDENTS WILL BE ABLE TO….
Relations vs. Functions
The concept of functions as relationships between independent
variables and dependent variables
Function notation that is expressed explicitly and recursively
Vertical and horizontal transformations
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Determine if a relation is a function
Write an equation in function notation
Evaluate functions in function notation
Recognize that sequences are functions
Write explicit and recursive equations using appropriate function
notation
Determine an appropriate domain for a given situation
Compare properties of two functions represented in different ways
Recognize and apply vertical and horizontal transformations in
functions represented algebraically and graphically
Find the value of k given a graph and its transformation
Determine whether a function is even, odd, or neither from a graph
or equation
MATHEMATICAL VOCABULARY
NEW:
Relation, Function, Function Notation, Independent Variables, Dependent
Variables, nth Term, Arithmetic Sequence, Explicit Equation, Recursive
REVIEW:
formula, Domain, Range, Vertical Transformations, Horizontal
Transformations, Even Function, Odd Function
ASSESSMENTS
FORMATIVE ASSESSMENT (S)
SUMMATIVE ASSESSMENT(S)
Function Notation Exit Slip
Function Notation Quiz
Unit 2 Assessment
ANCHOR RESOURCES
Textbooks
Manipulatives
Notes
Function Notation Notes
Function Transformations Notes
Even and Odd Functions Notes
Independent & Dependent Variables Notes
Sequences Notes
Learning Experiences
Class Party Project (1) Guidelines (2) Link Sheets
Functions Hunt
Functions Hunt Answer Sheet
Hexagon Trains
Resources
Khan Academy video introducing Functions
Dan Meyer's Graphing Stories
Worksheets
Graphs of Functions
What is a Function?
Function Notation Practice
Distance/Time Graphs
Transformations Up and Down
Transformations Left and Right
Transformations Two Directions
Recursion Problem Set
Handouts Unit 2 Learning Targets
SCAFFOLDED RESOURCES FOR THIS UNIT
INTERVENTION
ENRICHMENT
ELL
LITERATURE/ART/MUSIC CONNECTIONS:
MEDIA CONNECTIONS/ONLINE WEBSITE RESOURCES: