Roselle School District
Mathematics Curriculum
Grade 8 Unit 7: Proportional Relationships, Lines, and Linear equations
Essential Question(s)
What is the difference between a proportional and a nonproportional relationship?
How are linear relationships related to consistent rates of change?
What would a graph look like for a linear relationship?
How are proportions and similarity used in the real world?
Enduring Understanding(s)
Proportional relationships have equivalent ratios and nonproportional relationships do not have equivalent ratios.
Constant rates of change when graphed will form a line just as linear
relationships when graphed form a line.
Proportions and similarity are often utilized in real-world situations.
Summative Assessment Task
See attached document
Common Core Standards, 2010
Understand the connections between proportional relationships, lines, and linear equations.

8. EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships
represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving
objects has greater speed.

8. EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate
plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8. F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function
from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change
and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8. F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or
decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

W8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts and information through the selection, organization, and
analysis of relevant content.
Learning
Expectations
TLWBAT…
Activities/Resources
Student Strategies
Formative Assessments
Technology/Resources
Find proportional
relationships using
a graph,
interpreting the
unit rate as the
slope of the graph
while comparing
two different
proportional
relationships
represented in two
different ways:
graph and
equation.
Introduction:
Students will be given a scenario on the Smart
board: “The more groceries I buy, the more
money I spend,” or “The less sleep I get, the
less energy I have.” Allow students to analyze
if two variables are in direct variation, as one
gets larger, the others get proportionally
larger, or as one gets smaller, the other gets
proportionally smaller.
Small group
instruction
Introduction
conducted on smart
board in groups of two
with white erase
boards
Exit ticket
Mrs. Perez has $4000 in a cd
and $4000 in a money market
account. The amount of
interest she has earned since
the beginning of the year is
organized in the following table
(display it on page 656).
Determine whether there is a
direct variation between either
data set and time. If so, find
the equation and graph it.
Video tutorial:
http://www.onlinemathlea
rning.com/direct-variationalgebra.html
Interpret two
different
proportional
relationships by
comparing the
slopes.
Guided Instruction:
Based on the real world scenario given,
students will complete a data chart based on
money spent in groceries (no money spent as
well) and the number of hours a student
sleeps on a nightly basis.
Students will determine the direct variation
(linear function) and the constant of variation.
More so, they will graph the data displayed
and compare ratios. Since the rate of change
k is constant for any direct variation, the graph
of a direct variation is always linear. Finally,
the graph of any direct variation always
contains the point (0,0) because for any value
of k, 0 = 0 x k.
Individualized
instruction
Independent practice
Peer tutoring
Allow students to
work together
Use of manipulatives
Smart board
White erase boards
Choice activities
Independent practice:
math stations
Chunking information
Guided reference
sheet created by
Journal entry
Compare and contrast
proportional and nonproportional linear
relationships
Do now
POD from LOTI
Quiz
Direct variation quiz created by
teacher
Test
Battleship for advance
learners:
http://www.quia.com/ba/
30197.html
Independent practice:
Physical science application: “When a driver
applies the brakes, a car’s total stopping
distance is the sum of the reaction distance
and the breaking distance. The reaction
distance is the distance the car travels before
the drivers presses the brake pedal. The
braking distance is the distance the car travels
after the brakes have been applied.”
Determine whether there is a direct variation
between both data set and speed. If so, find
the equation of the direct variation and graph
it. (page 656)
Use similar right
triangles (rise/run)
to explain why the
slope is the same
between any two
distinct points on a
non-vertical line in
the coordinate
plane.
Compare the lines
of equations with
same slope but
different yintercept by
graphing.
Find slope from a
line given on a
coordinate plane.
Math stations to follow: taken from textbook
guided practice problems on page 657.
Introduction:
Review of slope of a line. Allow students to
complete a minute paper of 20 slope problems
to determine the number of slopes each
student can calculate. Students should be
timed using the smart board timer or Google
timer.
Given a line displayed on smart board, allow
students to complete the following as an
introduction:
 Find the slope of a line
 What geometric figure is formed by
connecting vertices (0, 2), (0,4), and
(3,4)?
 What geometric figure is formed by
connecting vertices (6,6), (6,8), and
(9,8)?
 How do two figures identified in
exercise 3 and 4 relate to each other?
 What geometric figure is formed by
teacher
Summative assessment
Video tutorials from
textbook
Homework
Handout from textbook
Rephrasing of
questions:
What is direct
variation?
Describe the slope and
the y-intercept of a
direct variation
equation.
Small group
instruction
Introduction with class
activity
Individualized
instruction
Independent practice
work displayed on
class pages
Peer tutoring
One on one
instruction with
various examples
Use of manipulatives
Smart board
White erase boards
Calculators
Diagrams given
Exit ticket
Which of the following
statement is not true
concerning the graph below?
(display graph from pdf file)
 A simplified ratio of
the vertical side length
to the horizontal side
length of each triangle
is 1
 Slope of the line is 1
 Slope of the line is -1
 Smaller triangle and
larger triangle are
similar
Do now
POD from LOTI
Quiz
Formative assessment on
similar right triangles
Cockroach game:
Slope of a line interactive
game:http://hotmath.com
/hotmath_help/games/kp/
kp_hotmath_sound.swf
Jeopardy game created by
teacher.
connecting the vertices (0,2), (0,6),
and (6,6)?
 How do the two figures you identified
in exercise 3 and 5 relate to each
other?
Triangles identified are congruent triangles.
Ratio of the slope of the line of the vertical
side length to the horizontal side length of
each triangle. Therefore, the ratio of side
length is vertical side length/horizontal side
length.
Independent practice:
Analyze congruent triangles (examples
displayed on Smart board).
Challenge work:
The slope of the line is -3.5. What is the
simplified ratio of the vertical side length to
the horizontal side length of each triangle
formed? Justify your response.
Construct a
function to
model a linear
relationship
between two
quantities.
Choice activities
Display examples
given for review and
practice
Chunking information
Reference sheet given
created by teacher
with notes
Rephrasing of
questions
Give steps and allow
students to recite
each step before
completing it
Working with partner
Work in pairs on
examples
Video tutorials from
textbook
Small group
instruction
Individualized
instruction
Peer tutoring
Use of manipulatives
Computer activities
for remediation
Choice activities
Chunking information
Rephrasing of
questions
Working with partner
Video tutorials from
textbook
Test
Summative Assessment
Oral questioning
IEP recommendation
Minute paper
20 slopes in one minute
Directed paraphrasing
Rephrasing steps needed to
complete assignment
Transfer and apply
Steps for finding slopes of a
line
Homework
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work
Determine the
rate of change
and initial value
of the function
from a
description of a
relationship or
from two (x, y)
values, including
reading these
from a table or
from a graph.
Interpret the rate
of change and
initial value of a
linear function in
terms of the
situation it
models, and in
terms of its graph
or a table of
values.
Describe
qualitatively the
functional
relationship
between two
quantities by
analyzing a
Small group
instruction
Individualized
instruction
Peer tutoring
Use of manipulatives
Computer activities
for remediation
Choice activities
Chunking information
Rephrasing of
questions
Working with partner
Video tutorials from
textbook
Small group
instruction
Individualized
instruction
Peer tutoring
Use of manipulatives
Computer activities
for remediation
Choice activities
Chunking information
Rephrasing of
questions
Working with partner
Video tutorials from
textbook
Small group
instruction
Individualized
instruction
Peer tutoring
Use of manipulatives
Computer activities
for remediation
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
graph.
Sketch a graph
that exhibits the
qualitative
features of a
function that has
been described
verbally
Choice activities
Chunking information
Rephrasing of
questions
Working with partner
Video tutorials from
textbook
Small group
instruction
Individualized
instruction
Peer tutoring
Use of manipulatives
Computer activities
for remediation
Choice activities
Chunking information
Rephrasing of
questions
Working with partner
Video tutorials from
textbook
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work
Exit ticket
Journal entry
Do now
Quiz
Test
Oral questioning
Minute paper
Muddiest point
Directed paraphrasing
One-sentence summary
Transfer and apply
Cubing Activities
Homework
Stations work