Linear Equations and
Inequalities
7.EE.4b Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and inequalities
to solve problems by reasoning about the quantities.
Think Pair Share
Explain the difference between these symbols.
How does it change the meaning of each
mathematical statement?
3+p>7
3+p>7
3+p<7
3+p<7
3+p=7
Scenario
Grant is trying to make money to help pay for
college by taking a job with Brian’s Bike Taxis of
Baltimore. He has an agreement with Brian that
he will rent the bike for $35.00 a night. He
charges $3.75 for every mile he is transporting
people.
Task
Work with your group to determine how many miles he needs to ride
with customers in order to make a profit. You will have 15 min.

Each group member must record all problem-solving strategies in the
class work section of their notebook.

Record ALL attempts that your group explored; please don’t erase
any even if they turn out to be wrong.

As a group, choose one strategy that you used to solve the problem and
post it on chart paper to share with the class.
GALLERY WALK

You will have the opportunity to view all of the different ways
that your classmates have solved the problem.

It is your job to comment on their work.

You need to make one accolade. They may have thought of
something you did not, they may have explained something
really clearly, or some other positive thing you noticed.

You also need to make a suggestion of one thing the group
might want to consider. Maybe something is not very clear or
you thought of something that they could add that would
strengthen the explanation of their strategy.
Time For Adjustments

Read through all of the accolades and
suggestions. Make any changes or additions that
you think are appropriate.

Re-Post your work for all to see.
Share Out

You have 2-3 min to explain your strategy and the
suggestions that others made for your group.
Summarize
 Which
strategies did you like?
 Which
would you choose to use in the
future? Why?
 Which
you?
strategy makes the most sense to
Consider the Context
 Is
it possible for Grant to make exactly 16
dollars? Why or why not?
 Use
whatever strategy you would like to
solve this problem.
Share Your Understanding
 Now
that you‘ve had some time to
consider the context, share your
understanding with your group.
Enough with the Hotdogs
A
car rental agency charges Shae’s family
$25.00 plus $0.10 per mile that the car is
driven. Shae wants to spend less than $35.00
on the car rental. How many miles can she
drive the rental car?
Exit Ticket

If Grant made $15 profit, how many miles did
he ride?

How would your equation change if I said Grant
needed to make at least $15 a day, how many
miles would he need to ride?
Day 3 Objective
 Students
will use the graphing
calculator to graph linear functions in
order to determine how much money
Grant will make transporting people
around Baltimore.
Warm-up

Pete was completing a science project about the life-cycle.
In 6th grade he was 51 inches and grows 2 inches each
year. How tall will he be by the time he graduates high
school?

Write an equation that represents his growth.
 x represents his grade.
 y represents his height in 12th grade.
 Graph your findings
Yesterday

We determined that the linear equation for the money
Grant makes transporting people was

y = 3.75x – 35

Use the table we created yesterday to graph his data.
Interpreting our Graph
In your groups answer the following questions:
 What do you notice about the shape of the graph?

At what point does the line intersect the x-axis?

At what point does the line intersect the y-axis?

What do these intersections represent?
Closure
Identify
the x- and y-intercepts of
Pete’s growth from 6th grade to his
graduation (warm-up)