Unit #4
Developing and Understanding of Slope & Y-Intercept
Grade 8
5E Lesson Plan Math
Grade Level: 8th
Lesson Title: Developing an Understanding of
Slope and Y-Intercept
Subject Area: Mathematics
Unit Number: 4
Lesson Length: 8 days
Lesson Overview:
This unit bundles student expectations that address using tables and graphs to develop the
understanding of slope and y-intercept. According to the Texas Education Agency, mathematical process
standards including application, a problem-solving model, tools and techniques, communication,
representations, relationships, and justifications should be integrated (when applicable) with content
knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the
workplace.
Prior to this unit, in Grade 7, students represented constant rates of change in mathematical and realworld problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations.
Students determined the constant of proportionality within mathematical and real-world problems.
Additionally, students represented linear relationships using verbal descriptions, tables, graphs, and
equations that simplify to the form y = mx + b. Although students were formally introduced to the slope
intercept form of y = mx + b, students did not explicitly study slope or y-intercept.
During this unit, students use similar right triangles to develop an understanding of slope. This approach
lends itself to the development of the formula for slope by determining the ratio of the change in y- values
and x-values is the same for any two points on the same line. Students use data from a table or graph to
determine the rate of change or slope and the y-intercept.
Unit Objectives:
Students will…
-Use similar right triangles to develop an understanding that slope, m, given as the rate comparing the
change in y-values to the change in x-values, (𝑦2 − 𝑦1)/ (𝑥2 − 𝑥1 ), is the same for any two points (𝑥1 ,𝑦1 )
and (𝑥2 ,𝑦2 ) on the same line.
-Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical
and real-world problems.
Standards addressed:
TEKS:
8.1A: Apply mathematics to problems arising in everyday life, society, and the workplace.
8.1B: Use a problem-solving model that incorporates analyzing given information, formulating a plan or
strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and
the reasonableness of the solution.
8.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate,
and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
8.1D: Communicate mathematical ideas, reasoning, and their implications using multiple representations,
including symbols, diagrams, graphs, and language as appropriate.
8.1E: Create and use representations to organize, record, and communicate mathematical ideas.
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Unit #4
Developing and Understanding of Slope & Y-Intercept
Grade 8
8.1F: Analyze mathematical relationships to connect and communicate mathematical ideas.
8.1G: Display, explain, and justify mathematical ideas and arguments using precise mathematical
language in written or oral communication.
8.4A: Use similar right triangles to develop an understanding that slope, m, given as the rate comparing
the change in y-values to the change in x-values, (𝑦2 − 𝑦1 )/ (𝑥2 − 𝑥1 ), is the same for any two points
(𝑥1 ,𝑦1 ) and (𝑥2 ,𝑦2 ) on the same line.
8.4C: Use data from a table or graph to determine the rate of change or slope and y-intercept in
mathematical and real-world problems
ELPS:
ELPS.c.1A: use prior knowledge and experiences to understand meanings in English
ELPS.c.1B: monitor oral and written language production and employ self-corrective techniques or other
resources
ELPS.c.1C: use strategic learning techniques such as concept mapping, drawing, memorizing,
comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1E: internalize new basic and academic language by using and reusing it in meaningful ways in
speaking and writing activities that build concept and language attainment
ELPS.c.1F: use accessible language and learn new and essential language in the process
ELPS.c.1G: demonstrate an increasing ability to distinguish between formal and informal English and an
increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.2D: monitor understanding of spoken language during classroom instruction and interactions and
seek clarification as needed
ELPS.c.2F: listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD
ROM to build and reinforce concept and language attainment
ELPS.c.2H: understand implicit ideas and information in increasingly complex spoken language
commensurate with grade-level learning expectations
ELPS.c.3D: speak using grade-level content area vocabulary in context to internalize new English words
and build academic language proficiency
ELPS.c.3E: share information in cooperative learning interactions adapt spoken language appropriately
for formal and informal purposes
ELPS.c.3J: respond orally to information presented in a wide variety of print, electronic, audio, and visual
media to build and reinforce concept and language attainment.
ELPS.c.4A: learn relationships between sounds and letters of the English language and decode (sound
out) words using a combination of skills such as recognizing sound-letter relationships and identifying
cognates, affixes, roots, and base words
ELPS.c.4D: use prereading supports such as graphic organizers, illustrations, and pretaught topic-related
vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.5B: write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5G: narrate, describe, and explain with increasing specificity and detail to fulfill content area
writing needs as more English is acquired.
Misconceptions:
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Some students may think that the slope in a linear relationship is m =
, since the xcoordinate (horizontal) always comes before the y-coordinate (vertical) in an ordered pair, instead
of the correct representation that slope in a linear relationship is m =
.
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Unit #4

Developing and Understanding of Slope & Y-Intercept
Grade 8
Some students may think that the intercept coordinate is the zero term instead of the non-zero
term, since intercepts are associated with zeros. In other words, students may think (0, 4) would
be the x-intercept because the 0 is in the x coordinate.
Underdeveloped Concepts:
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Some students may confuse corresponding sides of similar triangles.
Vocabulary:
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Rate – a multiplicative comparison of two different quantities where the measuring unit is different
for each quantity
Similar shapes – shapes whose angles are congruent and side lengths are proportional (equal
scale factor)
Slope – rate of change in y (vertical) compared to the rate of change
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in x (horizontal),
or
or
, denoted as m in y = mx + b
y-intercept – y-coordinate of a point at which the relationship crosses the y-axis meaning the xcoordinate is equal to zero, denoted as b in y = mx + b
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Congruent
Constant of proportionality
Corresponding angles
Corresponding sides
Horizontal
Input
Linear
Negative
Non-proportional
Origin
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Output
Positive
Proportional
Rate of change
Ratio
Right angle
Right triangle
Rise
Run
Scale factor
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Undefined
Vertical
x-axis
x-coordinate
x-value
y-axis
y-coordinate
y-value
Similarity
List of Materials:
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Slope and Intercept BrainPop video
LearnZillion Make Lines video
-https://learnzillion.com/lessons/1341-make-lines-from-right-triangles
Foldable materials- scissors, glue, paper, markers
Slope Intercept Race (from teacherspayteachers; it’s a powerpoint-Free) *game board on
poster board/butcher paper (Example at the end of the lesson)
Calculators
Interactive notebooks/Journals
Linear Equations and Data Tables Matching Activity (Included at the end of the lesson)
Linear Equations Gift Tag Activity (Recording sheet is attached at end of the lesson; answer key
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Unit #4
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
Developing and Understanding of Slope & Y-Intercept
Grade 8
is located in the adobe file) (http://www.teacherspayteachers.com/Product/Linear-Equation-GiftTag-Match-up-Matching-linear-graphs-to-their-equations-970025)
I Have Who Has Slope Looping Activity (http://www.teacherspayteachers.com/Product/IHaveWho-Has-Slope-Looping-Activity-79309) *Instruction sheet is at the end of the lesson
Slope Intercept Form Stations Activity (Attached at the end of the lesson)
INSTRUCTIONAL SEQUENCE
Phase: Engage
Day 1
Activity:
 Brain Pop Video and Quiz-Slope and Intercept
 Group Discussion on the BrainPop Quiz
 Watch video from LearnZillion on how to create a line using similar right triangles
-https://learnzillion.com/lessons/1341-make-lines-from-right-triangles
 Students write in their interactive notebook a paragraph about what they learned from the two
videos and what prior knowledge they already know about the topic.
What’s the teacher doing?
 The teacher is administering the video
and walking around the room making
sure that all students are watching.
 The teacher is also clicking the answers
on the computer as the students discuss
and decide an answer.
 Teacher asks the students:
-How did you calculate slope based off
of the videos? You calculated slope by
taking the change in y values divided by
the change in the x values.
-What is something that you saw in the
video that is something you already
knew from previous math classes?
Already know what the x-axis and y-axis
are and how to graph an ordered pair.
Answers will vary on this question.
-What was the expression used to
calculate slope (m)? The expression
used was rise/run.
 Teacher is walking around making sure
that all students are writing in their
journals about one or more things that
they have learned from the video.
What are the students doing?
 The students are engaged in watching the
video.
 The students discuss as a group each question
in the quiz and choose an answer to each
question.
 Students watch the LearnZillion video and then
have a class discussion about what they saw
new and what was information they already
knew.
 Students write a paragraph in their interactive
journals/spirals about what is new to them and
what prior knowledge they already have of the
subject.
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Unit #4
Developing and Understanding of Slope & Y-Intercept
Phase: Explore
Activity:
Grade 8
Days 2-4
Day 2 Activity:
 Students will do the Linear Equation Gift Tag Station Activity in 6 groups of 4. Laminate
each page of gifts so that the students can use dry erase markers to plot points and erase.
To incorporate similar triangles, the teacher will need to provide the ordered pairs for each
gift so that the students can plot and calculate the rise over run for each graph. The
ordered pairs for each gift are at the end of the unit. Station 1: Graph the ordered pairs
and see if the similar right triangles have the same slope. Station 2: Graph the ordered
pairs to see if the similar right triangles have the same slope. Station 3: Identify whether the
slope is positive or negative. Station 4: Give the coordinate for the y-intercept. Station 5:
Calculate the rate of change. Station 6: Calculate the rate of change and give the yintercept ordered pair.
Day 3 Activity
 Students will do the Slope Intercept Race in groups of 4-5 each.
Day 4 Activity
 Students will play the I Have Who Has Slope Looping Activity game.
 Students will do group work to do the Linear Equations and Data Table Matching
Activity.
What’s the teacher doing?
What are the student’s doing?
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Explore Day 2: The teacher will
start with a mini lesson about how
to calculate the rate of change and
how to be able to determine if the
rate of change is positive or
negative.
-Based from the videos
yesterday, how did you
calculate the rate of change also
known as slope? You calculated
rate of change by taking the yvalues of ordered pairs and
dividing them by the change in the
x-values of ordered pairs.
Also the teacher will talk about
how to determine the y-intercept
by looking at the graph.
The teacher will ask:
-Based off of the videos
yesterday, what letter
represented the y-intercept?
The letter “b” represents the y-
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Explore Day 2: The students will get with their
group and go to their designated station. They
will then plot their ordered pairs and calculate
the rise over run and find which equation
matches each of the gifts in their station. They
will switch stations when constructed by the
teacher.
Explore Day 3: The students will get with their
groups and will play the race game as
instructed by the teacher. The students are
supposed to work together to reach the correct
answer and claim as many boxes on the
scoreboard as possible.
Explore Day 4: The students will read the card
that the teacher passed out to them. When it is
their turn, the student will stand up and read
their card and then sit down. The class as a
whole will try to be as fast as they can to beat
the previous round time.
Explore Day 4: The students will get into
groups and will work with their group to pair the
correct equation with the corresponding data
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Unit #4
Developing and Understanding of Slope & Y-Intercept
intercept in the slope intercept
form.
-How were you able to identify
the y-intercept by looking at just
a graph? You were able to
identify the y-intercept by finding
the ordered pair that crossed the yaxis.
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Grade 8
table. Once finished, the students will raise their
hands and have the teacher check over their
work.
The teacher will have all stations
prepared in the classroom. The
teacher will pass out a Recording
Sheet to each group. The teacher
will then observe the students
around the room and make sure
each group is on task and to help if
any questions occur.
Explore Day 3: The teacher will
put the students in groups. The
teacher will then assign a student
to be the board keeper and control
the Slope Intercept game (power
point).
Explore Day 4: The teacher will
pass out I Have Who Has Slope
Looping cards to each student
and if there are extras, pass out
the extras to several students. The
teacher will administer a trial run
with the students so that the
students can get a feel for how the
game works. The teacher will then
collect the cards; scramble them
up and re-pass them out to do it
again, but this time, the teacher
will time the round and see how
fast the class can do it. Repeat it
several times to see if the class
can beat the previous time.
Explore Day 4: Then, the teacher
will put the students in groups of 4
and pass each group a set of the
Linear Equations and Data
Matching cards. The teacher will
administer the groups and make
sure they are working
collaboratively and then will check
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Unit #4
Developing and Understanding of Slope & Y-Intercept
Grade 8
answers.
Phase: Explain
Day 5-6
Activity: You need paper for the students, markers, glue/tape, and scissors.
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Vocabulary foldable including rate, similar shapes, slope, and y-intercept.
Notes on slope-intercept form (y=mx + b) and talk about what the m and the b stand for.
Notes on all types of slope including negative, positive, no slope, and undefined slope.
Discuss data tables and have students do the Linear Equations and Data Tables Matching
activity in groups of 4-5 students, to tie the tables and slope-intercept together.
What’s the teacher doing?
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Teacher is showing students how to build
the foldable and creating the foldable on
the elmo or overhead with the students.
Teacher is explaining the different
vocabulary words and giving examples of
each word.
Teacher is visually showing examples of
all types of slopes and having students
draw examples in journal.
Teacher briefly talks about data tables
and how to find slope using ordered pairs
from the table.
What are the students doing?
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Students are creating foldables based off of the
teacher.
Students are actively writing notes in their
journal and asking questions if they have any to
bring up class discussion.
Students are in groups and are actively
engaged in their matching activity and working
with their group to correctly pair the equation
with its correct table.
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Unit #4
Developing and Understanding of Slope & Y-Intercept
Grade 8
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Teacher distributes the students into
groups and let the student pair the
equation with the correct table.
 Teacher walks around the room to make
sure that students are on task and to
ensure learning and understanding and to
answer any questions
Phase: Elaborate
Day 7
Activity:
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Slope Intercept Form Stations Activity
What’s the teacher doing?
 The teacher is walking around the room
making sure each group is working
collaboratively and staying on task.
What are the students doing?
 Students are in groups and are working
together to solve each question at each station.
 Students are staying on task and are
discussing different vocabulary and using prior
knowledge and new information to solve the
questions.
Phase: Evaluate
Day 8
Activity:
Performance Assessment Activity
Analyze the problem situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each solution process.
1) Bennett noticed a beetle crawling towards him. The table below shows the distance the beetle was
from him after each second.
a) Use the data in the table to graph the relationship between the number of seconds and distance
traveled.
b) Use the table of data or graph to determine the rate of change, or slope, and y-intercept and explain
what each of them represents in the context of the problem situation.
c) Write an equation to represent the problem situation where x represents the time in seconds
and y represents the distance the beetle is from Bennett.
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Unit #4
Developing and Understanding of Slope & Y-Intercept
Grade 8
d) Use the graph to describe how similar right triangles can be used to justify how the slope of the line
representing the problem situation is the same for any two points on the line.
What’s the teacher doing?
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The teacher will pass out the assessment
to the students and walk around to make
sure students are working independently
and answer questions students might
have.
What are the students doing?
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Students are working independently on the
performance assessment.
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