Grade/Course: Algebra I (First Semester)
Instructional Unit 2: Understanding Functions
Instructional Schedule: First Nine Weeks (suggested for 15 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
Evidence Of Standard:
(student should be able to…)
Prerequisite Knowledge:
(standards linked to content taught
in previous grades)
Understand the concept of function and use function notation. (key content)
(BA/PASS 2.1c) 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 𝑓is 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).
-Explain the difference between
domain and range.
-Identify domain and range of a
function.
-Comprehend the relationship
between the elements of domain and
range for a relation.
-Determine if a relation is a function.
-Determine the value of the function
with proper notation. (i.e. f(x) = y, the
y value is the value of the function at
a particular value of x).
(BA/PASS 2.1d) Use function
notation, evaluate functions for
inputs in their domains (using tables,
equations, or graphs), and interpret
statements that use function
notation in terms of a context.
-Identify mathematical relationships
and express them using function
notation.
-Define a reasonable domain, which
depends on the context and/or
mathematical situation, for a
function focusing on linear and
exponential functions.
-Evaluate functions at a given input in
the domain, focusing on linear and
exponential functions.
-Interpret statements that use
functions in terms of real world
situations, focusing on linear and
exponential functions.
Assessment Tools:
(formative assessments, quizzes,
mastery tasks/activities)
(BA 2.1e) 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.
-Analyze a set of integers (a
sequence) and create a function
whose domain is a subset of the
integers.
-Analyze a set of integers (a
sequence) and generate additional
integers according to the function
whose domain is a subset of the
integers.
-Determine any element of a
sequence by inputing its position into
a given formula.
-Interpret functions as they arise in
real-world applications.
Interpret functions that arise in applications in terms of the context. (key content)
(BA/PASS 2.2) Relate and interpret
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.
-Describe how the domain of a
function is conveyed in graph form
and, where applicable, to the
quantitative relationship it describes.
(The specific values that are
represented in the function).
-Relate the domain of a function to
its graph in a real-world scenario.
(BA/PASS 2.2d) For a function that
models a relationship between two
quantities, develop the equation of a
line, 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.
(PASS 2.1a) Distinguish between
linear and non-linear data.
(PASS 2.1b) Distinguish between
relations and functions.
-Recognize key information in written
problems as components of an
underlying function and sketch a
graph that conveys this information
and indicates all key features of the
underlying function.
-Interpret key features of graphs and
tables in terms of quantities for a
function that models a relationship
between quantities.
-Understand how relationships
between two quantities are conveyed
through:
1. x and y intercepts
2. ordered pairs
3. increasing intervals
4. decreasing intervals
5. positive intervals
6. negative intervals
-Recognize a linear or non-linear data
(table or graphical representation).
-Use prior knowledge to distinguish
between linear and non-linear data.
(table or graphical representation).
-Understand a relation as a set of
data representing input and output
values.
-Distinguish between a relation and a
function.
Analyze functions using different representations. (supporting content)
(BA/PASS 2.1d) Compare properties
-Use tables, equations, graphs, or
of two functions each represented in verbal descriptions to recognize and
a different way (algebraically,
compare properties of simple
graphically, numerically in tables, or
functions when represented in
by verbal descriptions) to evaluate
different ways.
functions. For example, given a graph
one quadratic function and an
algebraic expression for another, say
which has the larger maximum.
Note: comparison of simple
functions only – In this unit you
would compare the graph of one
function with the table of another,
and compare values of the function
for given points.
Note: Any italicized text denotes portions of a given standard that do not apply to identified standard content in this unit.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )