Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
Vocabulary
Instructional
Strategies
8.4 The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.
8.4(A) use similar
Construct triangles
The line ABC is graphed below.
Slope
Use graph paper to model
right triangles to develop
between two points on a
Jordan says the slope of the line
Rise
the slope with right
an understanding
line and compare the
segment AB is not the same for
Run
triangles.
that slope, m, given as
sides to understand the
line segment BC. Kyla says the
the rate comparing
slope is same between
slope is the same for both line
Associate the legs of the
the change in y-values to
any two points on a line. segments. Which student is
right triangles with the rise
the change in x-values, (y2 correct?
and run.
y1)/ (x2 - x1), is the same
State that m is the
for any two points (x1, y1)
frequently used variable
Use the slope formula.
and (x2, y2) on the same
for slope.
line;
Introduce the slope
ELPS
formula and connect this
http://ritter.tea.state.tx.us/r
Supporting Standard
concept to 8.4C lessons.
ules/tac/chapter074/ch074a
.html
College Readiness
A. Jordan, because AB  BC
Standard:
C.1F
http://www.thecb.state.tx.us/c
ollegereadiness/crs.pdf
Connections: A1.b
2 4

3 6
2 6

C. Jordan, because
3 4
Resources/
Weblinks
Motivation Math 8:
Unit 8
Texas Go Math 8:
Explore Activity #2 p210
Engaging Math 8, Vol II:
P 68, 70
http://learnzillion.com/les
sons/1414-describe-a-linewith-a-unique-slope
Google Drive: Exemplar
Lesson 8.4A
B. Kyla, because
D. Kyla, because 2 AB  BC
Correct answer: B
2016-2017
Page 1
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.4(B) graph proportional
relationships, interpreting
the unit rate as the slope of
the line that models the
relationship.
Unit rate
Slope
y-intercept
Ensure students
understand that the graph
of a proportional
relationship will always
have a y-intercept at the
origin (0,0).
The table shows the distance Ms.
Long traveled as she went to the
beach. Graph the relationships
between time and distance and
state the unit rate as the slope.
Readiness Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/c
ollegereadiness/crs.pdf
Algebraic C2d
Unit rate in a given
situation will become the
slope of the graph.
Slope is not always a
whole number.
Questions should include
explaining the meaning
of slope from given
situations in real-world
applications including
equations, tables and
graphs
Correct answer:
The slope is ¾ , which means for
every 4 minutes Ms. Long drives,
she travels 3 miles.
Vocabulary
Instructional
Strategies
Model graphing
proportional relationships
from tables and equations.
Guided Practice using
graphing calculators to
convert slope to unit rate
Demonstrate finding slope
from various proportional
relationships including
word problems, tables and
graphs
ELPS
http://ritter.tea.state.tx.us/r
ules/tac/chapter074/ch074a
.html
C.1F
Resources/
Weblinks
Motivation Math 8:
Unit 9
Texas Go Math 8:
3.3
Engaging Math 8, Vol II:
P 108, 110, 112, 114
http://learnzillion.com/less
ons/3219-determine-theunit-rate-of-a-proportionalrelationship-using-a-graph
7th AIRR Activity 164
7th AIRR Activity 165
7th AIRR Activity 167
Misconceptions:
 The student may graph a non-proportional relationship and interpret the
slope as the unit rate.
 The student may not understand a linear proportional relationship goes
through the origin.
2016-2017
Page 2
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.4(C) use data from a table or
graph to determine the rate of
change or slope and y-intercept
in mathematical and real-world
problems.
Have students
determine the slope
or rate of change
from a graph or a
table.
y-intercept
Slope
Rate of change
Rise
Run
Origin
Readiness Standard
Discuss y-intercept
differences between a
proportional
relationship and a
non-proportional
relationship.
College Readiness Standard:
http://www.thecb.state.tx.us/colleg
ereadiness/crs.pdf
Connections B1c
Use the formula for
slope.
A weightlifter is adding plates of
equal weight to a bar. The table
below shows the total weight,
including the bar, that he will lift
depending on the total number of
plates on the bar.
Vocabulary
Instructional
Strategies
Model creating and reading
tables and graphs from
real-world situations
Think-Alouds
Determine slope from a
graph by finding the y
value when x=1 or by
drawing right triangles and
determining rise and run.
Connect change in
dependent variable
(y)/change in independent
variable(x) to ordered
pairs.
Based on this information, what is
the slope and y-intercept?
A. m=35 and y-intercept is (0,45)
B. m=80 and y-intercept is (0,35)
C. m=45 and y-intercept is (0,35)
D. m=70 and y-intercept is (0,0)
Correct answer: A
Resources/
Weblinks
Motivation Math 8:
Unit 10
Engaging Math 8, Vol II:
P 72, 74, 76, 78
Alg 1 Engaging
Mathematics
Pg. 88-89 Activity 1 Pg,
90-91 Activity 2
Pg. 92-93 Activity 3
Pg. 102-102 Activity 1
Pg. 108-109 Activity 1
ELPS
http://ritter.tea.state.tx.us/r
ules/tac/chapter074/ch074a
.html
C.3G
Misconceptions:
 The student may confuse the x-intercept with the y-intercept.
 The student may not relate the data from the table to the rate of change or
slope.
 The student may think the slope is the unit rate, y/x, for a non-proportional
linear relationship.

The student may do
instead of
2016-2017
run
as the slope when using data from the graph
rise
rise
.
run
Page 3
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
Vocabulary
Instructional
Strategies
Resources/
Weblinks
8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
8.5(A) represent
linear proportional
situations with tables,
graphs, and equations in
the form of
y = kx
Integrate with 8.5A,
8.5H, and 8.5F
Emphasize that
proportional situations
on a graph will have a yintercept of (0,0)
Supporting Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/c
ollegereadiness/crs.pdf
Algebraic c2d
Connect the variable k to
the constant of
proportionality (slope).
Susan is able to bike 6 miles in 4
hours. Create a table, graph, and
equation to represent any distance
if her rate stays constant.
Correct Answer:
Sample table:
Hours
(x)
2
4
5
8
Equation:
y
3
x
2
Miles
(y)
3
6
7.5
12
Constant of
proportionality
Graphic Organizers
Motivation Math 8:
Unit 11
Demonstrate going from
table, equation and graph
(in any order)
Texas Go Math 8
3.1
Card Sort with situations,
graph, table, and equation.
Engaging Math 8, Vol II:
P 116, 118
Google Drive:
Exemplar Lesson 8.5A/B
TPT Free
http://www.teacherspayteache
rs.com/Product/LinearFunctions-LessonFrameworks-Bundle-148490
Graph:
2016-2017
Page 4
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.5(B) represent linear
non-proportional situations
with tables, graphs, and
equations in the form of y
= mx + b, where b ≠ 0
Slope
y-intercept
non-proportional
Supporting Standard
Integrate with 8.5(A) and
8.5(H) and 8.5(F)
Emphasize that nonproportional situations
will have a y-intercept
that does NOT go
through the origin (0,0).
Connect the y-intercept
to the variable b in the
formula.
Connect the rate of
change to the variable m
for slope.
2016-2017
Joshua buys film through the
mail. The standard shipping cost
is always $5.50, regardless of
how many rolls of film he buys.
The cost of each roll of film
equals $7.50. Construct a table to
show Joshua’s total cost when he
buys 5, 10, 15, and 20 rolls, write
the equation for the situation and
create a graph of the results.
Correct answer:
y  7.50 x  5.50
Rolls (x)
5
10
15
20
Cost (y)
43
80.50
118
155.50
Vocabulary
Instructional
Strategies
Model writing equations in
slope intercept form
y=mx+b from tables,
equations and graphs.
Card Sort with situations,
graph, table, and equation.
Resources/
Weblinks
Motivation Math 8:
Unit 11
Texas Go Math 8
4.1
Engaging Math 8, Vol II:
P 100, 102, 104
ELPS
http://ritter.tea.state.tx.us/rules
/tac/chapter074/ch074a.html
Google Drive: Exemplar
Lesson 8.5A/B
1A, 4F
TPT Free
http://www.teacherspayteache
rs.com/Product/LinearFunctions-LessonFrameworks-Bundle-148490
Page 5
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.5(F) distinguish between
proportional and nonproportional situations using
tables,
graphs, and equations in
the form
y = kx or y = mx + b,
where b ≠0;
Supporting Standard
Proportional
Non-proportional
Integrate instruction
with 8.5(H)
Identify tables, graphs
and equations that are
proportional and nonproportional
Which equation describes a
proportional relationship.
A. y = 3x + 5
B. 4x + 2 = y
C. y  1 x
3
D. y  15
x
Correct answer: C
Which graph represents a nonproportional situation?
Vocabulary
Instructional
Strategies
Use Example/Nonexample to help student
develop the understanding
of the difference between
the two types of
relationships.
Card Sort tables, graphs,
and equations into
Proportional and Nonproportional groups.
ELPS
http://ritter.tea.state.tx.us/rules
/tac/chapter074/ch074a.html
I.
II.
III.
A. I
B. II and III
C. I, II and III
D. I and II
Correct answer: A
2016-2017
c2C
Resources/
Weblinks
Motivation Math 8:
Unit 15
Texas Go Math 8
4.4
Engaging Math 8, Vol II:
P 124
Alg. 1 Engaging Mathematics
Proportional Relationships
Activity 2
Google Drive:
Card Sort Activity 8.5F
http://learnzillion.com/lessons/
3210-identifying-proportionalrelationships-by-examining-agraph
TPT Free
http://www.teacherspayteacher
s.com/Product/ProportionalRelationship-InteractiveNotes-378891
Page 6
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.5(G) identify functions
using sets of ordered pairs,
tables, mappings, and graphs
Relation
Function
Domain
Range
Input
Output
Vertical line test
Readiness Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/coll
egereadiness/crs.pdf
Determine whether a
relation is a function by
using ordered pairs,
tables, maps, and
graphs.
Emphasize that the x
values cannot repeat but
it is ok for y’s to repeat.
Given that y is a function of x,
which of the following represents
a function?
I.
II.
{(-1,2),(1,1),(1,-1), (2,1)}
Functions A1a
Vocabulary
Instructional
Strategies
Provide students examples
and non-examples of
functions to develop the
definition of a function.
Resources/
Weblinks
Motivation Math 8:
Unit 16
Texas Go Math 8:
6.1
Introduce vocabulary by
connecting domain to input
and range to output.
Engaging Math 8, Vol II:
P 220, 222, 224, 228
Have students use pipe
cleaners or pencils to
implement the vertical line
test.
Google Drive:
Exemplar Lesson and activity
8.5G
ELPS
III
http://ritter.tea.state.tx.us/rules
/tac/chapter074/ch074a.html
c4F
Misconceptions:
 The student may think two x-values mapped to the same y-value is not a
function.
 The student may think only linear data can represent a function.
IV.
A. I only
B. I I and III
C. I and IV
D. None
Correct answer: C
2016-2017
Page 7
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.5(H) identify examples of
proportional and
non-proportional
functions that arise from
mathematical and real-world
problems;
Supporting Standard
Function
Non-proportional
Proportional
Integrate instruction
with 8.5(F)
Establish factors that
non-proportional
relationships in the realworld will have such as
flat fee, base charge,
initial fee, starting
amount, annual fee, etc.
Which of these situations do
NOT represent a proportional
relationship?
Vocabulary
Instructional
Strategies
Proportional vs. Nonproportional reflective
discussion/guided practice
A. A recipe calls for 1.5 cups of
lemon juice for every 6 cups of
water.
B. A local pool charges $3 per
day to visit over the summer, plus
an annual fee of $25.00.
C. Jimmy can clean 2 pools every
hour.
D. A cookie recipe requires 2
sticks of butter for every cup of
sugar.
Think-Alouds (discussions
about flat rates/flat fees)
Correct answer: B
c2C
Resources/
Weblinks
Motivation Math 8:
Unit 15
Texas Go Math 8:
4.4
Engaging Math 8, Vol II:
P 128, 132, 134, 136
Quick- Writes defending
why a situation is
proportional or not.
ELPS
Alg 1 Engaging Mathematics
Proportional Relationships
Activity 3 Pg. 24-26
Activity 4 Pg. 28-29
http://ritter.tea.state.tx.us/rules
/tac/chapter074/ch074a.html
Google Drive: Activity 8.5H
TPT Free
http://www.teacherspayteacher
s.com/Product/LinearFunctions-LessonFrameworks-Bundle-148490
2016-2017
Page 8
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
8.5(I) write an equation in
the form y = mx + b to
model a linear relationship
between two
quantities using verbal,
numerical, tabular, and
graphical representations.
Readiness Standard
Constant rate of
change
Equation
Linear relationship
Slope
Slope-intercept
form (y=mx+b)
y-intercept
College Readiness
Standard:
http://www.thecb.state.tx.us/c
ollegereadiness/crs.pdf
Problem Solving C2c
Given two quantities,
determine which quantity
is the independent and
dependent variables.
Student must determine
slope (m) and yintercept(b) from a
verbal, numerical, table,
or graphical
representation in order to
write the equation in
y=mx+b form.
A graph is shown below.
Which equation represents the
graph?
A. y   3 x  2
2
3
B. y  x  3
2
C. y  2 x  2
3
D. y  2 x  3
3
Correct answer: C
Vocabulary
Instructional
Strategies
Graphic Organizers
Reflective discussion and
writing about how to
determine the slope and yintercept to generate the
equation
Use four corner model to
have students connect
verbal, table, graph, and
equation to each other.
Resources/
Weblinks
Motivation Math 8:
Unit 17
Texas Go Math 8:
5.1
5.2
Engaging Math 8, Vol II:
P 80, 84, 86, 88, 92
Google Drive:
8.5I Activities
ELPS
http://ritter.tea.state.tx.us/rules
/tac/chapter074/ch074a.html
c3B
Engaging Math 8:
Multiple representations:
p116-122
Supporting STAAR
Achievement: Grade 8
p54
Misconceptions:
 The student may confuse the x-intercept with the y-intercept.
 The student may not relate the data from the table (ie: change in y ) to the rate
change in x
of change or slope.
 The student may think the slope is always equal to y/x.
 The student may do run as slope when using data from the graph.
rise
2016-2017
Page 9
Mathematics
Course: 8th Grade Mathematics
Unit 3: Slope and Rate of Change
Unit 4: Proportional and Non-Proportional Relationships; Linear and
Non-Linear Relationships.
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 2nd
Days to teach: 23
Vocabulary
Instructional
Strategies
Resources/
Weblinks
8.9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations.
8.9(A) identify and
Developing the concept
Verify that the ordered pair on the Verify
Use the intersection feature Motivation Math 8:
verify the values
of solving systems by
intersection on the graph satisfies Intersection
on graphing calculator to
Unit 28
of x and y that
graphing.
both equations for lines
Systems of
find the ordered pair for
simultaneously satisfy two
Equations
the solution.
Texas Go Math 8
y  2 x  1 and y   x  5 .
linear equations in the
Relate “simultaneously
4.5
form y = mx + b from the
satisfy” to intersection of
Provide points in tables
intersections of the graphed lines.
and as ordered pairs for
Engaging Math 8, Vol II:
equations.
verification.
P 94, 96, 98
Have students use the
ELPS
http://ritter.tea.state.tx.us/rules
solution ordered pair to
Supporting Standard
/tac/chapter074/ch074a.html
verify the values for x
c1A
and
y
are
correct.
College Readiness
Standard:
http://www.thecb.state.tx.us/c
Provide opportunities for Correct answer:
y  2x  1
ollegereadiness/crs.pdf
points to not
Yes,
because
3
 2( 2)  1
simultaneously satisfy
Algebraic C2c
3  4 1
the equations.
33
Only two linear
equations .
Focus on graphs rather
than situations.
2016-2017
y  x  5
and 3  (2)  5
33
Page 10