Grade/Course: Algebra I (First Semester)
Instructional Unit 3: Linear Functions
Instructional Schedule: First Nine Weeks (suggested for 17 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
Evidence Of Standard:
(student should be able to…)
Prerequisite Knowledge:
Assessment Tools:
(standards linked to content taught in
(formative assessments, quizzes,
previous grades)
mastery tasks/activities)
Interpret functions that arise in applications in terms of the context. (key content)
(BA/PASS 2.2c.1) Calculate and
interpret the average rate of change
of a linear function (presented
symbolically or as a table) over a
specified interval. Estimate the rate
of change from a graph.
(Linear only)
-Calculate and interpret the average
rate of change of a function for a
function presented symbolically over
a specified interval.
-Calculate and interpret the average
rate of change of a function
presented in a table over a specified
interval.
-Calculate and interpret the average
rate of change of a function
presented in function notation over a
specified interval.
-Estimate the rate of change from a
graph.
Analyze functions using different representations. (supporting content)
(BA/PASS 2.2b, 2.2d) Graph square
root, cube root, and piecewisedefined functions, including step
functions and absolute value
functions. Recognize the parent
function of 𝑦 = 𝑘, 𝑦 = 𝑥, 𝑦 = |𝑥|.
(Graph linear relationships and
absolute value only)
-Graph linear functions f(x) = x and
understand point-slope form as
y-y1 = m(x-x1), slope-intercept form
as f(x) = mx + b, standard form as
Ax + By = C, and can determine the xand y-intercepts for each graph.
- Graph absolute value functions
f(x) = |x|, can understand that the
vertex of an absolute value function
is either the maximum or the
minimum, and can identify which it
will be by analyzing the equation. I
can determine the x- and y-intercepts
for an absolute value.
(BA/PASS 2.1d) Compare and
-Use tables, equations, graphs, or
evaluate properties of two functions
verbal descriptions to recognize and
each represented in a different way
compare properties of simple
(algebraically, graphically,
functions when represented in
numerically in tables, or by verbal
different ways.
descriptions). For example, given a
graph of one quadratic function and
an algebraic expression for another,
say which has the larger maximum.
Note: Linear only – (In this unit you
would compare the graph of one
linear function with the table of
another, and compare values of the
function for given points)
Build a function that models a relationship between two quantities. (supporting content)
(BA 2.1f) Determine an explicit
expression, a recursive process, or
steps for calculation from a context.
-Distinguish between an explicit and
recursive expression of a function.
-Write an explicit expression of a
function to describe a real-world
scenario.
-Write a recursive expression of a
function to describe a real-world
scenario.
-Determine steps for calculation for a
real-world scenario.
Construct and compare linear, quadratic, and exponential models and solve problems. (supporting content)
(Note: Linear aspect only)
(BA/PASS 2.5a) Match and construct - Match and construct linear and
linear and exponential functions,
exponential functions, including
including arithmetic and geometric
arithmetic and geometric sequences,
sequences, given a graph, a
given a graph, a description of a
description of a relationship, or two
relationship, or two input-output
input-output pairs (include reading
pairs (include reading these from a
these from a table).
table).
(BA 2.5c) Prove that linear functions
grow by equal differences over equal
intervals, and that exponential
functions grow by equal factors over
equal intervals.
-Distinguish between linear function
and exponential functions.
-Prove that a linear function has a
constant slope over equal intervals.
-Prove that an exponential function
grows by a constant multiplier over
equal intervals.
(BA/PASS 2.2e) Recognize situations -Recognize situations (real-world as
in which one quantity changes at a
well as theoretical) in which a
constant rate per unit interval
quantity grows or decays by a
relative to another.
constant percent rate per unit
interval relative to another.
-Recognize situations (real-world as
well as theoretical) in which one
quantity changes at a constant rate
per unit interval relative to another.
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 )