Grade 8 Module 4 Planning Guide
Topic A
Topic B
Topic C
Topic D
Writing and Solving Linear
Equations
Linear Equations in Two
Variables and Their Graphs
Slope and the Equations of
Lines
Systems of Linear Equations
and Their Solutions
12 days
8 days
9 Days
8 Days
In Module 4, students extend what they already know about unit rates and proportional relationships (6.RP.A.2, 7.RP.A.2) to linear equations and
their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module (8.EE.B.5, 8.EE.B.6).
Also in this module, students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality
(6.EE.A.2, 7.EE.A.1, 7.EE.B.4) to transcribe and solve equations in one variable and then in two variables.
In Topic A, students begin by transcribing written statements using symbolic notation. Then, students write linear and non-linear expressions leading
to linear equations, which are solved using properties of equality (8.EE.C.7b). Students learn that not every linear equation has a solution. In doing so,
students learn how to transform given equations into simpler forms until an equivalent equation results in a unique solution, no solution, or infinitely
many solutions (8.EE.C.7a). Throughout Topic A students must write and solve linear equations in real-world and mathematical situations.
In Topic B, students work with constant speed, a concept learned in Grade 6 (6.RP.A.3), but this time with proportional relationships related to
average speed and constant speed. These relationships are expressed as linear equations in two variables. Students find solutions to linear equations
in two variables, organize them in a table, and plot the solutions on a coordinate plane (8.EE.C.8a). It is in Topic B that students begin to investigate
the shape of a graph of a linear equation. Students predict that the graph of a linear equation is a line and select points on and off the line to verify
their claim. Also in this topic is the standard form of a linear equation, 𝑎𝑥+𝑏𝑦=𝑐, and when 𝑎,≠0, a non-vertical line is produced. Further, when 𝑎 or
𝑏=0, then a vertical or horizontal line is produced.
In Topic C, students know that the slope of a line describes the rate of change of a line. Students first encounter slope by interpreting the unit rate of
a graph (8.EE.B.5). In general, students learn that slope can be determined using any two distinct points on a line by relying on their understanding of
properties of similar triangles from Module 3 (8.EE.B.6). Students verify this fact by checking the slope using several pairs of points and comparing
their answers. In this topic, students derive 𝑦=𝑚𝑥 and 𝑦=𝑚𝑥+𝑏 for linear equations by examining similar triangles. Students generate graphs of
linear equations in two variables first by completing a table of solutions, then using information about slope and 𝑦-intercept. Once students are sure
that every linear equation graphs as a line and that every line is the graph of a linear equation, students graph equations using information about 𝑥and 𝑦-intercepts. Next, students learn some basic facts about lines and equations, such as why two lines with the same slope and a common point are
the same line, how to write equations of lines given slope and a point, and how to write an equation given two points. With the concepts of slope and
Grade 8 Module 4 Planning Guide
lines firmly in place, students compare two different proportional relationships. represented by graphs, tables, equations, or descriptions.
Finally, students learn that multiple forms of an equation can define the same line.
Simultaneous equations and their solutions are the focus of Topic D. Students begin by comparing the constant speed of two individuals to determine
which has greater speed (8.EE.C.8c). Students graph simultaneous linear equations to find the point of intersection and then verify that the point of
intersection is in fact a solution to each equation in the system (8.EE.C.8a). To motivate the need to solve systems algebraically, students graph
systems of linear equations whose solutions do not have integer coordinates. Students use an estimation of the solution from the graph to verify
their algebraic solution is correct. Students learn to solve systems of linear equations by substitution and elimination (8.EE.C.8b). Students
understand that a system can have a unique solution, no solution, or infinitely many solutions, as they did with linear equations in one variable.
Finally, students apply their knowledge of systems to solve problems in real-world contexts, including converting temperatures from Celsius to
Fahrenheit.
Grade 8 Module 4 Planning Guide
Grade 8 Module 4 Planning Guide
Grade 8 Module 4 Planning Guide
Lesson
Big Idea
Emphasize
Suggested
Examples and
Exercises
Suggested Exit Ticket
Problems
Suggested
Days
TOPIC A
Lesson 1:
writing
equations using
symbols
Write math statements
using symbols; know what
written description they
represent.
Translating
Example 1, 2, 3, 4, Problem
5
Set
Yes
1
Lesson 2:
Linear vs. NonLinear
Expressions in x
Knowing properties,
transcribing and
identifying linear and
non-linear equations
Linear vs. Non-Linear
Discussion
Problem
Example 1, 2, 3, 6 Set
1-5, 7-9
Yes
1
Lesson 3:
Linear
Equations
in x
Understand that a
linear equation is a
statement of equality
between 2 expressions.
Solutions are those
numbers x that satisfy a
given equation.
Equality
Examples: All
Problem
Exercises:1-6, and Set
7 as a
1-4
discussion
Yes
1
Lesson 4:
Solving a linear
equation
Using properties of equality Solving Linear Equations with Examples 1-3
Exercises 1-5
to solve linear equations
Rational Coefficients
with rational coefficients.
1-3
Modify to
solve and
check only
2
1, 2, 3, 5
Problem
Set
1-5
Grade 8 Module 4 Planning Guide
Lesson
Big Idea
Lesson 5: SKIP
UNTIL LATER
Using geometry to Writing Linear
write and solve
Equations
linear equations
 Good review
lesson prior to
exam.
Using distributive Solving Linear
property of
Equations
simplify
equation. Not
every linear
What
represents
Classification of
equation
has a
asolution.
linear equation Solutions
with one
* Can be correlated
solution, no
with OnRamp
solution, or
infinite
solutions?
Using properties Solving Complex
of equality to
Proportions using
solve non-linear
Cross Multiplication
equations
Rewriting an
Application
exponential
expression that
represents a
series as a linear
equation
Lesson 6:
Solutions of a
Linear equation
Lesson 7:
Classification of
solutions
Lesson 8: Linear
equation in
disguise
Lesson 9:
SKIP-
Emphasize
Suggested
Examples and
Exercises
Examples
Exercises
Suggested
Problems
Exit Ticket
Suggested
Days
Examples 1-4
Exercises 1-2
Plus 4,5,6 if
time permits
Problem
Set
1-3, 5,7
1-2
2-3
Examples none Problem
Exercises 1-3, 4- Set
1-3
7 (only
transform until
equation can be
classified) and
8-10
1-3
1-2
Problem
Set
1-4
Yes
1
Examples 3-4
Exercises 1,3
Examples
Exercises
Grade 8 Module 4 Planning Guide
TOPIC B
Lesson
Big Idea
Emphasize
Lesson 10: A
critical look at
proportional
relationships
Using average and
constant speed to
write a linear
equation in 2
variables, then
answer questions
about distance
and time.
Constant Rate & Writing
Proportions
* Lesson 10 should be
combined with lesson 11.
Lesson 11:
constant rate
Seeing constant
Constant Rate used with:
rate in context:
 Table of Variable
Graphing points
 Graph
on a coordinate
plane, defining
constant rate
using 2 variables
(where one is
time)
Using a table to
ax + by = c (2 variables) in
find solutions to
relationship to tables and
linear equations
graphs
and then plot on
coordinate plane.
Lesson 12: linear
equations in two
variables
Suggested
Examples and
exercises
Examples 1,2
Examples 1,2
Exercises
Suggested Exit
Problems Ticket
Suggested
Days
Problem
Set
1-5
all
1.5
Examples 1-2
Exercises 1
Problem
Set
1-4
All
1.5
Problem
Set
1,2
all
2
Examples none
Exercises: opening
exercise as whole
group
1-5 exploratory in
pairs
Grade 8 Module 4 Planning Guide
Lesson
Big Idea
Emphasize
Lesson 13:
The graph of a
linear equation in
two variables
Find and plot
solutions to
linear equations
on a coordinate
plane to predict
shape of a graph.
Explaininglinear
shape
Graphing
of graph ininterms
equations
of
a givenform
linear
standard
equation.
that
produce a
horizontal or
vertical line.
Graph of a Linear Equation
* This Lesson 13 should be
combined with Lesson 14.
Lesson 14: The
graph of a linear
equation –
horizontal and
vertical lines
Suggested
Examples and
exercises
Vertical and Horizontal Lines
(a=0, b=0)
Exercise 1 as minilesson
Exercises 1-3
Suggested
Problems
Exit Ticket Suggested
Days
Problem Set
1
1
Problem Set
1,2
1
TOPIC C
Lesson 15: the
slope of a nonvertical line
Understanding
that slope is the
slant of a line,
and that it
represents a unit
rate.
Determining slope based on a Day 1/2: Lesson 15,
graph, and using the formula Examples 1-4.
to calculate slope.
Lesson 16 examples
1-3, but allow for
gradual release with
independent
practice.
Lesson 16: the
computation of
the slope of a nonvertical line
Using slope
formula to
compute slope,
and similar
triangles to
explain why slope
is the same
between 2 distinct
points.
Use similar triangles to
emphasize that you can pick
any two points on a line, to
find slope and the ratio is
always the same.
Lesson
Big Idea
Day 3:
Lesson 15, Example
5: An Application.
More Practice on
Slope.
Lesson
15/16, all
problems
sets are
helpful.
Choose
based on
student
need.
Day 1:
2-3
Lesson 15 1&2
Suggested
Problems
Exit Ticket Suggested
Days
Day 2:
Lesson 16 1
(Look at discussion so that
when looking at examples you
can reference this.)
Emphasize
Suggested
Examples and
exercises
Grade 8 Module 4 Planning Guide
Lesson 17 : the line The line joining
The 𝒎 of 𝒚=𝒎𝒙+𝒃 is the
joining two distinct two distinct points number that describes the
points of the graph of the graph of the slope.
y = mx + b has
linear equation
slope m
𝒚=𝒎𝒙+𝒃 has slope
𝒎.
Exercises: 1-5
1-3
1
1-4
*Use exercises 6, 7,
and 8 at teacher
discretion. These
problems are
expectations for
level 4 only
according to the
performance level
descriptions
document.
Lesson 18 : there is Understand that Students need to recognize that Examples 1 - 3
Do even or 1 - 2
1
only one line
Exercises 1 – 4
odd sets.
straight lines with the y-intercept is named as a
passing through a the same slope and point (x, y) and a solution to the *Use exercises 5
Make sure
given point with a one common point linear equation.
and 6 at teacher
students do
given slope
discretion. These question 8 or
are the same line,
problems are
9.
using equations in
expectations for
the form y=mx +b
level 4 according to
the performance
level descriptions
document.
Lesson
Big Idea
Emphasize
Suggested
Suggested Exit Ticket Suggested
Examples and
Problems
Days
exercises
Grade 8 Module 4 Planning Guide
Lesson 19 : the
graph of a linear
equation in two
variables is a line
Using y=mx+b to Graphing using intercepts.
show that a line is
made up of a series
of points.
Skip Proofs
Using intercepts is
an easier way to
graph a line than
making a table of
solutions.
Lesson 20: every Y=mx+b represents
line is a graph of a any non-vertical
linear equation
line, with b as a
constant. Write the
equation that
represents the
graph of a line.
Lesson
Big Idea
Lesson 21: some
facts about graphs
of a linear
equation in two
variables
Writing an
equation when
given 2 points and
a slope. Know the
forms of a slope
formula and slopeintercept equation.
Skip Exercises 1 – 8,
but use exercise 5’s
equation as example
1 so you can find
other integer
coordinates points
that are solution.
1-3
Opening, Examples Exercises 1,2,
1-3,
4, 6
Emphasize
1-4
Suggested
Examples and
exercises
Suggested
Problems
Example 1, 2
Exercises 1-4 1, 2
1
1
Exit Ticket Suggested
Days
2 Days
Grade 8 Module 4 Planning Guide
Lesson 22:
Constant rates
revisited
SKIP
Students know that any
constant rate problem
can be described by a
linear equation in two
variables where the
slope of the graph is
the constant rate.
TOPIC D
Lesson 24:
Introduction to
Simultaneous
Equations
Understanding of
systems of
equations and
notation.
Comparing graphs
for systems in the
context of rate
Opening Exercises 1- Exercise 4
3
Lesson 25:
Geometric
interpretation of
the solutions of a
linear system
Graphing equations
to find point of
intersection,
identified as
solution. Solution
also determined by
computation.
Lesson 26:
A System of
Characterization of equations with no
parallel lines
solution will be
parallel lines
Lesson
Big Idea
Emphasize
1
1 day
Exercises 1,2, 5, 6
Problem Set 1
1, 3, 4
2 days
Exercise 1-3
Problem Set 1-3
1-4
1 day
Suggested
Examples and
exercises
Suggested
Problems
Exit Tickets Suggested
Days
Grade 8 Module 4 Planning Guide
Lesson 27: Nature
of solutions of a
system of linear
equations
Students must
know if a system of
equations has one
unique solution, no
solution, or
infinitely many
solutions.
Exercises 1-3, 4
Example 1, 2
Exercise 5, 6 1-3
2 Days
(Hint: use
substitution,
not
elimination)
Lesson 28:
Another
Computational
Method of Solving
a Linear System
Elimination
method, rational
number properties
using substitution
to solve a system of
linear equations.
Examples
1, 2
Problem set 1, 2
2, 4, 9, 10
Lesson 29: Word
Problems
SKIP
Writing and solving
linear equation
system word
problems using
substitution and
elimination
methods
A real world
application of linear
equations.
Lesson 30:
Conversion
between Celsius
and Fahrenheit
SKIP
Exercise 1
2 Days