1
Rigorous Curriculum Design
Unit Planning Organizer
Subject(s)
Middle Grades Mathematics
Grade/Course 8th
Unit of Study Unit 4: Functions
Unit Type(s)
❑Topical
X Skills-based
Pacing
17 days
❑ Thematic
Unit Abstract
In this unit of study students will investigate examples and non-examples of functions
displayed algebraically, numerically, graphically, and verbally. They will compare the rate
of change of two functions represented in different ways.
Common Core Essential State Standards
Domain: Functions (8.F)
Cluster: Define, evaluate, and compare functions.
Standards:
8.F.1 UNDERSTAND that a function is a rule that assigns to each input exactly one
output. The graph of a function is the set of ordered pairs consisting of an input and the
corresponding output. (Note: Function notation is not required in Grade 8.)
8.F.2 COMPARE properties of two functions each REPRESENTED in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). For example,
given a linear function represented by a table of values and a linear function represented
by an algebraic expression, determine which function has the greater rate of change.
Revised 7/15/13
2
Standards for Mathematical Practice
1. Make sense of problems and persevere 4. Model with mathematics.
in solving them.
5. Use appropriate tools strategically.
2. Reason abstractly and
6. Attend to precision.
quantitatively.
3. Construct viable arguments and critique 7. Look for and make use of structure.
the reasoning of others.
8. Look for and express regularity in
repeated reasoning.
“UNPACKED STANDARDS”
8.F.1 Students understand rules that take x as input and gives y as output is a function.
Functions occur when there is exactly one y-value is associated with any x-value. Using y
to represent the output we can represent this function with the equations y = x2 + 5x + 4.
Students are not expected to use the function notation f(x) at this level.
Students identify functions from equations, graphs, and tables/ordered pairs.
Graphs
Students recognize graphs such as the one below is a function using the vertical line test,
showing that each x-value has only one y-value;
whereas, graphs such as the following are not functions since there are 2 y-values for
multiple x-values.
Revised 7/15/13
3
Tables or Ordered Pairs
Students read tables or look at a set of ordered pairs to determine functions and identify
equations where there is only one output (y-value) for each input (x-value).
Function
x
y
0
3
1
9
2
27
Not A Function
x
16
16
25
25
y
4
-4
5
-5
{(0, 2), (1, 3), (2, 5), (3, 6)}
Equations
Students recognize equations such as y = x or y = x2 + 3x + 4 as functions; whereas,
equations such as x2 + y2 = 25 are not functions.
8.F.2 Students compare two functions from different representations.
Example 1:
Compare the following functions to determine which has the greater rate of change.
Function 1: y = 2x + 4
Function 2:
x
y
-1
-6
0
-3
2
3
Solution:
The rate of change for function 1 is 2; the rate of change for function 2 is 3. Function 2
has the greater rate of change.
Example 2:
Compare the two linear functions listed below and determine which has a negative slope.
Function 1: Gift Card
Samantha starts with $20 on a gift card for the bookstore. She spends $3.50 per week to
buy a magazine. Let y be the amount remaining as a function of the number of weeks, x.
Revised 7/15/13
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Function 2: Calculator rental
The school bookstore rents graphing calculators for $5 per month. It also collects a nonrefundable fee of $10.00 for the school year. Write the rule for the total cost (c) of renting
a calculator as a function of the number of months (m).
c = 10 + 5m
Solution:
Function 1 is an example of a function whose graph has a negative slope. Both functions
have a positive starting amount; however, in function 1, the amount decreases 3.50 each
week, while in function 2, the amount increases 5.00 each month.
NOTE: Functions could be expressed in standard form. However, the intent is not to
change from standard form to slope-intercept form but to use the standard form to
generate ordered pairs. Substituting a zero (0) for x and y will generate two ordered
pairs. From these ordered pairs, the slope could be determined.
Example 3:
2x + 3y = 6
Let x = 0:
2(0) + 3y = 6
3y = 6
3y = 6
3 3
y=2
Let y = 0:
Ordered pair: (0, 2)
2x + 3(0) = 6
2x = 6
2x = 6
2
2
x=3
Ordered pair: (3, 0)
Using (0, 2) and (3, 0) students could find the slope and make comparisons with another
function.
“Unpacked” Concepts
(students need to know)
8.F.1
 Functions
Revised 7/15/13
“Unwrapped” Skills
(students need to be able to do)
COGNITION
DOK

I can explain that a function is a
rule that assigns exactly one
output to each input.
1

I can give an example and a nonexample of a function using a
table, a graph or an equation.

I can explain that the graph of a
function is the set of ordered pairs
consisting of an input and the
corresponding output.
1
1
5
8.F.2
 Properties of two functions

I can compare two functions from
different representations.
Essential Questions
Corresponding Big Ideas
8.F.1
 What is a function?

3

Students will explain that a function is a
rule that assigns exactly one output to
each input.

Students will be able to give an example
and a non-example of a function.

Students will explain that the graph of a
function is the set of ordered pairs
consisting of an input and the
corresponding output.

Students will be able to give an example
and a non-example of a graph of a
function.

Students will determine which function
has the greater rate of change when the
function is represented algebraically,
graphically, numerically in a table, by
verbal description (the student derives
the rate of change from the context of
the problem.
How do I graph a function?
8.F.2
 How do you compare properties of two
functions each represented in a
different way?
Vocabulary
functions, y-value, x-value, vertical line test, input, output, rate of change, linear function,
non-linear function
Revised 7/15/13
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Language Objectives
Key Vocabulary
8.F.1 - 2
SWBAT Define and give examples of the specific vocabulary for this
standard: functions, y-value, x-value, vertical line test, input, output,
rate of change, linear function, non-linear function.
Language Function
8.F.1
SWBAT explain the difference between a function and a nonfunction to a partner.
8.F.2
SWBAT compare two functions represented in different ways using
a graphic organizer.
Language Skill
8.F.2
SWBAT explain how to determine the greater rate of change in two
functions represented in a different way and display in a table.
Grammar and Language Structures
8.F.1
SWBAT describe to a partner an example and a non-example of a
function.
8.F.2
SWBAT compare two functions represented in two different ways in
a journal entry.
Language Tasks
8.F.1
SWBAT give an example and a non-example of a function. Explain
to a partner why it is an example and why it is a non-example.
8.F.2
SWBAT explain step by step, to a partner, how to determine the
greater rate of change of two functions when represented in
different ways.
8.F.1 - 2
Revised 7/15/13
Language Learning Strategies
SWBAT use input/output table to determine the rate of change.
Share results with a partner.
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Information and Technology Standards
8.TT.1.1
Use technology and other resources for assigned tasks.
8.RP.1
Apply a research process to complete project-based activities.
Instructional Resources and Materials
Physical
Connected Math 2 Series
 Common Core Investigation 1
Technology-Based
WSFCS Math Wiki
NCDPI Wikispaces Eighth Grade
Partners in Math Materials
 Assembling Cubes
 Bob's Beam Task
 Skeleton Towers
 Mathematical Discourse
 Wi-Fi
 Modeling Relationships
 Matching Linear Equations
Georgia Unit
Illuminations NCTM Amazing Profit
Illuminations NCTM Bouncing Tennis Balls
Math.fullerton.edu/Linear_Equations
Themathpage.com/alg/
Mathematics Assessment Project (MARS)
UEN.org/Lessonplan/Grade=8
Book
 A Visual Approach to Functions by
Frances Van Dyke
Teachengineering.org/
Katm.org/8thFlipFinal
Access.bridges.com
Graniteschools.org/Pre-AlgebraLessons
Revised 7/15/13