Lesson Design
Subject Area: Algebra I
Grade Level: 8
Benchmark Period: II & IV
Duration of Lesson: 3 days
Standard(s):
Standard: 16.0 Understand the concepts of a relation & a function, determine whether a given relation
defines a function, & give pertinent information about given relations & functions.
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic
expression is a function and justify the conclusion.
Students will be able to apply the vertical line test to determine if a graph is a function.
Students will be able to determine if a set of ordered pairs is a function by examining values of x and y.
Big Ideas involved in the lesson:
Define function and relation. Given a set of ordered pairs or a graph, determine whether it is function or not.
As a result of this lesson students will:
Know:
 Vocabulary: relation, function, input, output, input-output table, domain, range, graph,
one-to-one, many-to-one, map onto, ordered pairs, horizontal axis, vertical axis,
coordinate plane, origin, discrete set, continuous set, data, vertical line, symbolic
expression, linear function, quadratic function, parabola, cubic graph, function notation
 Input-output tables.
 Vertical line test to determine if a graph is a function.
 Domain is the set of input values denoted by x and the range is the set of output values
denoted by y or f(x).
 In an ordered pair (x, y) = (x, f(x)) where y = f(x).
 Function notation: f ( x ) , (x, f ( x ) ), (x, y), x,  f (x).

Know the domain and range of previously studied parent functions, e.g.,
f(x) = x , f(x) = x2.

Understand:
 The difference and similarities between relations and functions.
 The difference between discrete and continuous functions.
 Relationships between variables may be expressed in numerical form as an input-output
table, algebraic form as an equation, in geometric form as a graph, or in words.
 A function input value cannot have more than one output value.
 Why a graph that passes the vertical line test is a function.
 Why a relation that passes the vertical line test is a function.
 How the domain and range are affected when the parent functions are translated.
Be Able To Do:
 Determine if a relation is a function
o Graphically by the vertical line test
o Numerically by verifying that each input value has exactly one output value.
 Recognize graphs and sets of ordered pairs that represent functions.
 Determine if a set of ordered pairs is a function by examining the values of x and y.
 Apply the vertical line test to determine if a graph is a function.
 Find the domain and range of a function, given its equation.
 Justify a relation is a function by describing it in one of four ways: input-output table, in
words, equation or graph.
1
Lesson Design
 Evaluate a function for given value(s) of the independent variable.
Assessments:
Formative:
CFU Questions
What will be evidence ABWA
 What is a function?
of student knowledge, Individual whiteboards
 What is a relation?
understanding &
Graphic Organizer
 What is the difference between
ability?
Pair share
a function and a relation?
Summative:
 What is the domain?
CST, BM, teacher created quiz
 What is the range?
Have students interpret the various forms of
 What is an input output table?
functions
 What do the values of the table
x = 3 , x = 0, and x =-4
represent?
f(x) = - (x – 2)
 What is the vertical line test?
g x  2x  3
 What does the vertical line test
determine?
The distance traveled by an elephant at a
 What is a discrete graph?
constant speed varies directly with the
 What is a continuous graph?
amount of time it travels. If the elephant
travels168 miles in four hours, how far will
it travel in 7 hours, 16 hours and 21 hours?
Lesson Plan
Anticipatory Set:
St. 16 Function PowerPoint.
a. T. focuses students
St. 18 Function & Relations PowerPoint slides 1-3
b. T. states objectives
a. Teacher focuses students with a Power-point Presentation
c. T. establishes purpose of
b. Teacher states objective as students read information from power-point:
the lesson
Define whether a graph is a function or a relation
d. T. activates prior knowledge c. The purpose of the lesson is stated in algebra standard 18.0 Students
determine whether a relation defined by a graph, a set of ordered pairs, or
a symbolic expression is a function and justify the conclusion.
d. Teacher activates students’ prior knowledge with a review of linear
equations. Discussion should include review vocabulary, quadrant
graphing, and reading a linear graph (y-intercept and slope).

Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide examples
 Model
b. Check for Understanding
 Pose key questions
 Ask students to explain
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples and nonexamples
 Encourage students to
2
Given a set of points we have a relation. If an input value is repeating
with different output values, then we don’t have a function. If all the
input values have distinct output values, then we have a function. For
example, if you have set of points, {(1,4),(-2,5),(2,7)}. This is a function
because all the have distinct outputs. This set of points {(4,5),(3,6),(3,9)}
is not a function because the input 3 repeats with different outputs (yvalues.)
Not a function
function
function
If instead of giving you a set of points, you have been given a graph; you
draw vertical lines to determine if the graph represents a function or not.
If any vertical line cuts the graph in more than one point then the graph
Lesson Design
generate their own
examples
 Use participation
does not represent a function.
CFU Questions
 What is a function?
 What is a relation?
 How do you determine if a graph is a function or not?
 How do you determine if a set of points is a function or not?
 What is the difference between a function and a relation?
Have student-pairs answer/evaluate the following questions and
shareout.
Do these points represent a function or relation? Why?
a) {(1,2), (-1,3), (1,5)}
b)
Input
Output
2
-3
3
1
5
1
5
7
c)
Std. 18 Functions and relations PowerPoint slides 1-6
Birthday Relations:
To further illustrate students’ knowledge of relations vs. functions, explain to
students that each person has a unique (discrete) birthday. However, two or
more people may share a birthday. Such as, Jane = 7/04, Vicki = 12/25, Mary
= 11/01, Kitty = 4/19, Bob = 11/01. Once students understand this concept,
transition them from names to numbers. Tell students you’re tired of writing
names and assign a number to a student. Student #1 = 7/04, 2 = 12/25, 3 =
11/01, 4 = 4/19, 5 = 11/01. On individual whiteboards, students should create
tables illustrating the data and determining if this is a function. Even though
Bob and Mary share the same birthday, this is still a function. You have made
the x-value their student number and their y-values their birthdays. The graph
will show two distinct points.
Rules: A function, two persons can have the same birthday. If we made the
3
Lesson Design
input birthdays, and the output people, then it would not be a function.
St. 18 PowerPoint Functions and Relations slide 4-8
Provide visual representations using PowerPoint presentation
 Cell phone cost and minutes used
 Categorize graphs
 Demonstrate the graphs of different functions.
 Show functions with their graphs

Have students graph the equation f x  3x  2 by making a table using
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same time
b. Elicit overt responses from
students that demonstrate
behavior in objectives
c. T. slowly releases student to
do more work on their own
(semi-independent)
d. Check for understanding
that students were correct at
each step
e. Provide specific knowledge
of results
f. Provide close monitoring
the values -2,0, and 2 for x.
Set Notation
Determine whether the given points represent a function or relation.
Why?
a) {(2,4),(4,2),(-2,5)}
b) {(-1,7),(3,6),(-1,6),(-3,9)}
Graphs
Which of these graphs represents a function? Why?
c)
d)
Tables
Do these tables represent a function? Or a relation? Why?
e)
Input Output
1
5
2
4
4
3
5
2
f)
Input Output
7
7
9
9
10
8
11
5
10
10
St. 18 Functions and Relations PowerPoint slides 9-15
Students fold a sheet of graph paper into four sections (fourths). Students
complete the following problems under teacher directives.
4
Lesson Design
Section 1: Have students interpret the various forms of functions
x = 3, x= 0 and x = -4
f(x) = - (x-2)
CFU: What do the values of the table represent?
What is an input output table?

Section 2: g x  2x  3
Section 3: The distance traveled by an elephant at a constant speed varies
directly with the amount of time it travels. If the elephant travels168 miles in
four hours, how far will it travel in 7 hours, 16 hours and 21 hours?
Section 4: Students create their own example. Criteria must include problem,
graph, and solution.
What opportunities will students
have to read, write, listen &
speak about mathematics?
Read the board.
Write in notebooks.
Listen to instruction.
Speak in pair shares.
PowerPoint
Activity: I have who has
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what and why
of the work
c. Have each student perform
behavior
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
5
Review what was learned.
1) {(0,2),(1,4),(2,6),(3,8)} Is this a function or just a relation? Why?
2)
Input Output
0
1
2
2
4
1
2
8
3) Is this a function or just a relation? Why?
Have class participate in the instructional game: I have . . . Who has? Each
student has a card and must find the correct match for their card (vocabulary
and definition). Cards are randomly distributed to all students and game is
played with students finding the correct match.
Correct matches are recorded on poster paper and posted on word wall.
Algebra I McDougal Littell book
pg. 255-256 16-24, 50-53 (all)
Students complete Independent Practice Problems.
Students graph the order pairs given in the problem. Students then assess
the graphs by using the vertical line test and write a sentence justifying why
the graph is or is not a function.
Lesson Design
Resources: materials needed
to complete the lesson
6
Computer, projector, PowerPoint, whiteboards, math journal, whiteboard
pens, overhead, overhead pens, textbook, equity cards, worksheet