Clark University
Amazing Profit Problem-January 14th-January 24th
Lesson Activity Plan
I. Content: Describe what it is you will teach. What is the content?
For this lesson, students will use their prior knowledge of using linear equations from a coordinate graph
to determine eBay profit on new technology. The Lesson will last for a consecutive week two weeks due
to the amount of school students will be missing. The purpose of the lesson is provide students with
real-world application of identifying relationships and trends, and creating linear equations. Students
are back in school from February vacation, and we are continuing on to a new unit after having learned
about linear relationships and their components.
Students will apply their knowledge to a real-world application problem, titled the Amazing Profit
Problem. Students will use the knowledge of building linear equations, analyzing data, and graphing that
data on coordinate plane to interpret the relationship that is there. After students were able to brush up
on their skills, as a class we will have an introduction to a new set of data that is increasing and
intersects the lines created by the data. This will introduce the students to identifying the solution
graphically.
II. Learning Goal(s): Describe what specifically students will know and be able to do after the
experience of this class.
As a result of this lesson, students will know:
 How to apply their knowledge of linear
equations in different context other
than the classroom
 How to identify the “solution”, or,
“equilibrium” between two
relationships a point where the two
lines intersect each other.
And, Students will be able to:
 Interpret a graph to find the solution
to simultaneous linear equations.
 Construct and graph a linear equation
from data in table
 Identify the selling price of an item on
eBay
 Identify the profit from the sales of an
item off eBay.
III. Rationale: Explain how the content and learning goal(s) relate to your Curriculum Unit Plan
learning goals.
This will be the first time students encounter two linear relationships on the same plane (one increasing,
one decreasing). Students will then be prompted to discover how those two simultaneous relationships
can be balanced. They will look at the intersection of the two relationships and identify this point where
both the y (US Dollars) and x (Days after Release) are the same.
IV. Assessment: Describe how you and your students will know they have reached your learning
goals.
Afterwards, students will have an understanding of how to find the equilibrium between two lines and
know what that intersection represents. Students will then visually practice finding the intersection on a
graph of simultaneous equations.
V. Personalization and Equity: Describe how you will provide for individual student strengths and
needs. How will you and your lesson consider the needs of each student and scaffold learning? How
specifically will ELL students and students with learning disabilities gain access and are supported?
For the beginning of the lesson, I plan to provide students with an introduction to eBay, where we will
discuss what happens when people buy or sell things online. We will talk about the vocabulary of bid,
profit, and practice using those words in that context. Students will be able to work with a partner in
case they get stuck. Students developed a new rule for the classroom; a student cannot move on or
make a discovery without telling the other student a student that is lost must ask questions
continuously.
VI. Activity description and agenda (1 Day): 45 Min
Materials: Markers or Colored Pencils (4 boxes markers, 2 boxes colored pencils, Rulers (4), Amazing
Profit Overhead (teacher), Amazing Profit Activity Sheet (4)
a. Describe the activities that will help your students understand the content of your class
lesson by creating an agenda with time frames for your class. Be prepared to explain why you think
each activity will help students on the path toward understanding.
Time
Day 1
11:04-11:19
Starter Question
(15 Min)
11:19-11:29
Silent-Thinking
Time (5 Min)
Classroom
Discussion
Linear
Relationship
Building (10
Min)
What the student will do
What the Teacher will do
Rationale
Tuesday, January 14, 2014
Students will routinely enter the
classroom and get “on their Marks” for
their starter activity. The starter will be an
article describing a bid, an auction. It will
speak about people who buy (demand),
people who sell (supply), and where eBay
falls into that. Prompt questions will
include:
What is eBay? What do people do on
eBay?
1. Students will take time to read the
scenario and think silently about what
information is available to us and what we
need to find. After 5 minutes the class will
rejoin
2. LINEAR RELATIONSHIP BUILDING: After
having silent thinking time, the class will
come together and identify what we need
to find. Students will then build the
equation for the dependent variable
(profit).
Students will receive the article
and the questions for the
starter. As a class, students will
discuss what those key terms
mean and they will be
introduced to the problem.
The activity’s language
may be too advanced
for the kids. There will
be technical language
and this helps builds
students knowledge of
the technical language
before venturing into
the problem.
1. Direct students to read the
problem carefully and think
about what we know, and what
do we need to find. After those
five minutes direct the class to
rejoin and share their answers.
Prompt students to realize that
we have to find the seller’s profit
by creating a linear equation.
Also, what does the closing bid
on eBay represent?
Have the students work in
partner’s to generate this
relationship.
Students will be told to
use their knowledge of
constructing linear
equations. Students will
have to recognize that
5500 is their y-intercept
because at day 0, the
closing bid is a $5500.
Also, will know how to
find the slope and
identify that as -500
dollars per day that the
seller loses on profit.
They will know how to
graph this a decreasing
line starting at $5500.
11:35-11:49
Students will come together as a class and
solve and we will answer the questions as
a group. I will portray the graph in the
front of the room.
Day 2
11:04-11:09
Starter: Finish
graphing your
line on the
worksheet. How
do we know that
the slope is
negative? (5
Min)
11:09-11:29
(20 Min)
Construct
Equations for
questions 3 & 4
11:29-11:44
(10 Min)
As a class, go
over questions 3
and 4
11:44-11:49
(5 Min)
Day 3
11:04-11:34
(30 Min)
No Starter
Answering the
Students will partake in the
creation of the graphs and the
labeling of the poster for the
classroom. Students will be
called on to create the poster for
future reference
During this time, I plan
to create a reference
point in the classroom
for students to refer
back to on challenging
questions or for some
information on linear
questions.
Wednesday, January 15, 2014
Students won’t have a traditional starter
problem today. They will finish
constructing the line from yesterday.
Mention to students that they
won’t have a traditional starter
question today. Make sure
students are aware by pointing
to their starter on the board.
Students didn’t have
evening study last night,
so homework would be
much since they get out
a 5pm and had to
attend a program. So I
made it the starter in
the morning.
Students will continue to answer the
questions on the back of the paper with a
partner. Students will spend most time on
questions 3 and 4.
Students should answer
questions 3 and 4 and tell you
when they are finished. Students
should not move on without
your approval.
Students will share their answers to
questions 3 and 4.
The teacher will ask prompting
questions and generate a class
consensus of what the equations
should be.
This is where students
started building
equations. I wanted to
make sure they were ok
with doing that before
moving on.
This will allow me to
assess what students
need extra help. Then
we can go through a
review if necessary.
Students will have 5 min to make their
folders are put away neatly, markers are
back in the cases, and their stations are
clean and neat like they found them.
Remind students of the one hour
time limit. Collect markers and
other materials allow other class
to come in and get settled.
We share a classroom
with the sixth grade.
Therefore, students
have to make sure it is
clean so that they can
come in comfortably.
Thursday, January 16, 2014
Today, students are answering the rest of
the questions on the worksheet and are
now analyzing their graph to do so. This
should take them 30 Minutes to complete,
if done correctly and with great effort.
Walk around and answer any
questions students may have.
Any misconceptions should be
cleared up now before students
start to get the extension data.
Students will finish
answering the
questions today, so as a
class we could move on
and continue onto our
rest of the
questions on the
worksheet
11:34-11:40
(10 Min)
Don’t answer too much, because
it would be great for their
classmates to help clear any
misconceptions students may
have.
Make sure to call on each
student to help get a different
set of answers to clear any
misconceptions.
As a class, students will share their
answers with the whole class instead of
the partners.
Share Out
(11:44-11:49)
(5 Min)
Clean-Up
Students will have 5 min to make their
folders are put away neatly, markers are
back in the cases, and their stations are
clean and neat like they found them.
Day 4
(11:04-11:14)
(10 Min)
Starter: 5 Min
Remind students of the five
minute time limit. Collect
markers and other materials
allow other class to come in and
get settled.
extension, which
introduces the system
of linear equations.
Students will have
misconceptions about
something, and this is
the time to clear it up
so students will be able
to add on new content
without a problem.
The principal made it
mandatory that
students have the last
five minutes to write
homework and
straighten up before the
next class.
Friday, January 17, 2014
Students will answer the question below:
What was the relationship between the
days of the PS3 release and the profit at
Wal-Mart? What do you think happened
to the profit as the sale days increased?
Explain
Afterwards, students will share their
answers with each other. We will come to
a class agreement.
Students will construct a table of the same
amount of days as the eBay problem, with
the profit per day. Students will calculate
the profit for each day, and then graph the
line.
Write the question on the board.
Read it aloud. Add prompting
questions to students while they
are writing.
Students will now
construct a system of
linear equations on the
graph. This relationship
is positive and the line is
increasing, intersecting
the others on its path.
Ask prompting questions about
what the line is doing, what
doesn’t Wal-Mart have a Bid
column in it’s table, etc.
11:34-11:44
(10 Min)
Students will answer the Closing: Why
didn’t Wal-Mart’s line have a y-intercept.
Explain in your Starter notebooks.
Ask questions like, What was the
profit on day zero? What is the
slope of the line? What does
that tell you?
11:44-11:49
(5 Min)
Clean-Up
Students will have 5 min to make their
folders are put away neatly, markers are
back in the cases, and their stations are
clean and neat like they found them.
Remind students of the five
minute time limit. Collect
markers and other materials
allow other class to come in and
get settled.
Students will see that
the profit increases with
every sale of a PS3 by
Wal-Mart. Walmart
doesn’t accept Bids, but
you have to pay the
market price. So this is
an equation without a
y-intercept.
Students will end with a
question that will help
me assess their
knowledge of a
proportional
relationship.
The principal made it
mandatory that
students have the last
five minutes to write
homework and
straighten up before the
next class.
Share Out: 5
Min
11:14-11:34
(20 Min)
LINE BUILDING:
Day 5
Tuesday, January 21, 2014
11:04-11:14
(10 Min)
Starter: Start
graphing the
Wal-Mart line
on your papers.
Students will graph the Wal-Mart line on
their papers and label the line with the
equation.
Walk around the room and
provide students with any
assistance that they might need.
11:14-11:24
(10 Min)
Pair and Share: Students will work with a
partner to make sure their work is correct.
(5 Min)
Make sure students are
comparing and talking about
their lines. Start putting a grid
on the board for the students to
see.
11:24-11:39
(15 Min)
11:39-11:44
(5 Min)
5-Min Free
Write
Day 6
11:04-11:49
Students will give Mr. Stewart instructions
to write it on the board. (5 Min)
EQUILIBRIUM MINI-LESSON: Students will
receive a lesson on how to spot the
equilibrium between two lines. The key
notes would be that at this point, the x
and y of each relationship are equal.
Close: What does each line represent?
When they intersect at a point, what is
that point telling us? Free write for 5
Minutes.
Direct a mini-lesson about
finding the equilibrium on the
line. Incorporate key words as
equilibrium, point, and the
phrase “at this point x and y are
the same”.
Make sure students are writing
for the whole five minutes.
Allow them to draw diagrams if
they need to help explain.
Students will start to
graph the line and get a
visual representation of
the relationship that
Wal-Mart’s profit off
PS3’s has with the
number of days it has
been sold. This will help
lead us into our
discussion about the
intersections.
Students made sure
that their line was
correct, now they will
tell me how to draw it
on the board.
Students will now have
an understanding of
what the equilibrium is
for our next lesson. I
will refer back to the
problem when we start
our next one.
Friday, Friday January 22, 2014
Students will work on a worksheet while I
am away. Students should continue to
point out the intersection of each line on
the graph.
Substitute Teacher: Provide any
help they may need.
I will out this day, but
the students continued
working on a working
on a worksheet to help
them visually see the
intersection between
two linear equations.
b. What particular challenges, in terms of student learning or implementing planned activity, do you
anticipate and how will you address them?
Some challenges I anticipate in the classroom are some challenges with the vocabulary. I am thinking to
incorporate a vocabulary lesson the day before so students could be better acquainted with the
language. I may provide students with a glossary sheet for the lesson, where they will be able to refer
back and use them terms efficiently.
VII. List the Common Core Mathematical Practices and content standards this lesson addresses.
This Lesson will be taught in my 8th grade math class (Pre-algebra)
Analyze and Solve Linear equations and pairs of simultaneous linear equations
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to
points of intersection of their graphs, because points of intersection satisfy both equations
simultaneously
The practices to be explicitly emphasized are:
1. Make sense of problems and persevere in solving them.
2. Reason Abstractly and Quantiviley.
3. Construct Viable Arguments and Critique the Reasoning of Others.
4. Use appropriate tools accordingly.
VIII. Reflection: This was a great problem to start with. Students really took to the lesson. They were
extremely interested in eBay after the fact. The lesson was successful, in terms of introducing my next
unit. I like to quietly venture into another unit because the students can feel when we are starting
something new. It allowed me to do that and get students comfortable with having two lines on a plane
that are intersecting. Students have that visual of an intersection as the place where two lines meet.
If I use this lesson again, I will emphasize the vocabulary a little stronger. That hindered our progress in
the beginning. I plan to have more extensions available for the students to use and allow them to
continue learning for homework or the problem of the week. These last two weeks, the students and I
only saw each other for 5 days. However, I checked their last assignment and they did well. So I think we
are ready to move on.