Learning Targets:
 I can determine when to use an inequality symbol versus an equal sign
 I can write inequalities to represent real world and mathematical situations.
 I can use the number line to represent inequalities from various contextual and mathematical
situations.
.
Common Core State Standards:
6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely
many solutions; represent solutions of such inequalities on number line diagrams.
Which Mathematical Practices do you expect students to engage in during the lesson?
MP4: Model with mathematics.
MP7: Look for and make use of structure.
Materials: Student copy of task; Computer access for each group
Implementation:
Engage…. Students have spent time focusing on equations and situations where the variable has only one
solution. They must now realize that in some situations, there are multiple solutions.
To engage students with today’s concept of inequalities, show a portion of the following video from Hershey
Park. http://www.youtube.com/watch?v=hIvvqgb0bGA
Ask, “When you go to an amusement park or the fair, what are some of the conditions for riding rides?”
Solicit responses from students looking for height, weight, and medical condition requirements etc. Ask, “So, if a
ride says you must be at least 48 inches tall, what does that mean?” List all the possibilities of heights for students
for this questions. Discuss with students that sometimes situations are not limited to one solution. Sometimes
there are many solutions to the situation.
Explain that at Hershey Park, these conditions or restrictions are creatively described using the candy they
manufacture.
Explore…
Each student or pair of students will need a computer with Internet access for the following exploration.
http://www.hersheypark.com is filled with numerous real-world examples of inequalities being used regarding
height requirements. For example, if you are in the ‘Jolly Rancher’ category, you must be greater than 60 inches.
At this point students are reinforcing that there is more than one solution. You will work with students to develop
the correct use of the mathematical inequality symbols for > , < , >, and <. Have students complete the first two
columns of the table below on their own. Then through class discussion, help students complete the chart
At Hershey Park, let’s take a look at the creative way they describe who can ride on the rides. The word to is very
important in the description. For example, the Twizzler says 54” TO 60”. Therefore the Twizzler is x> 54” but
x<60 This is a great illustration of how careful you must be when reading. For fun, you can make a frequency
table of the categories in the class and then create a histogram (statistics standards)
Hershey Park Height
Restrictions
Categories
Describe each
restriction using
words
List the heights
described by
each restriction
Graph the heights
described by each
restriction
Describe each
restriction using
mathematical
symbols
60"
&
taller
54"
to
60"
48"
to
54"
42"
to
48"
36"
to
42"
Under
36"
.
Explain…
Show students the four inequality symbols and, together, determine examples of when each could be used. Begin
by asking which symbol they think would be appropriate for the scenario in the warm up. Using this situation,
determine when situations would require the other three symbols. Also provide an example of when an equal sign
would be appropriate so students can differentiate between the uses of an inequality symbol and an equal sign.
Begin charting key words that indicate each symbol
(Note: This section of the lesson could be completed after students have had more practice with translations and
are ready to begin graphing or immediately following the online activity to help students make the immediate
connection between their answers and the number lines.) . Say, ‘we said we would represent the height you could
be if you were in the Jolly Rancher category as x  60. How would you represent this on the number line?’
After accepting student responses, instruct students that when graphing inequalities, an open-circle is placed on
the number line if the inequality involves a greater than or less than symbol because the number in the inequality
is not included. An arrow should point in the direction of the numbers that are involved in the inequality. For
 because 40 is not included but all numbers less than 40 are included.
example, x < 40 the circle would be open
This means the arrow should point in the direction of the numbers that are less than 40. Follow the same
explanation for x  60 except remind students the circle should be filled in because the person could be 60 inches
or more than 60 inches. Since 60 is included, the circle should be filled in. Note: When creating the numbers
lines, consider having students only use three numbers. For the above example, 60 would be in the middle, 59
would be to the left, and 61 would be to the right. (Look for evidence of MP4)

Elaborate:
Ask students how this situation could be translated into a mathematical sentence using an inequality symbol. To
ride the roller coaster ‘The Comet’, your minimum height is 42 – 48 inches. Ask ‘how tall could you be to ride
this ride? If you are not allowed to ride this ride, how tall might you be?’ Using questions like this will help
students to understand the possible values for x so they are able to translate an inequality. Consider either
allowing students to explore the site by clicking on the ‘Rides’ tab at the top of the page and translating
inequalities of their choice or using the provided worksheet as a guided practice
Have students explore the website to collect data on height requirements for each ride on their handout.
If students have internet access at home, consider having them visit www.sixflags.com/america, choose 5 rides,
write the height requirement, translate it to an inequality, and then graph it. For students who do not have internet
access, create a resource sheet with the information for 7-9 rides and have students choose 5 to translate and
graph.
Evaluate:



How do you know when to use an inequality symbol and when to use an equal sign?
When graphing an inequality, when should a closed circle be used?
If someone has to be at least 42 inches tall to ride a ride, what inequality symbol would you use to define x?
Ticket out the door
Fishing Adventures rents small fishing boats to tourists for day-long fishing trips.
Each boat can hold at most eight people. Additionally, each boat can only carry
900 pounds of weight for safety reasons.
1. Let p represent the total number of people. Write an inequality to describe the number of people that a
boat can hold. Draw a number line diagram that shows all possible solutions.
2. Let w represent the total weight of a group of people wishing to rent a boat. Write an inequality that
describes all total weights allowed in a boat. Draw a number line diagram that shows all possible
solutions.
Items to Consider. The vocabulary at least and at most is difficult for all students, but especially for ESL
learners. Make sure you are consistently using the vocabulary by verbalizing it and writing it down each
time so students can hear and see it together. Using talk move during discussion to promote
mathematical discourse helps all students make better sense of the content:
Revoicing: the teacher tries to repeat what a student has said, then asks the student to respond and verify
whether or not the teacher's revoicing is correct. "So you're saying..."
Asking students to restate someone else's reasoning: the teacher asks one student to repeat or rephrase
what another student has said, then follows up with the first student. "Can you repeat what he just said in your
own words?"
Asking students to apply their reasoning to someone else's reasoning: students make their own
reasoning explicit by applying thinking to someone else's contribution. "Do you agree or disagree and why?"
Prompting students for further participation: the teacher asks for further commentary. "Would someone
like to add on?"
Using wait time: the teacher waits at least ten seconds for students to think before calling on someone for an
answer. "Take your time...we'll wait.”
This lesson was created by Christine Kreider, adapted from original idea by Dawn Perks.
ANSWER KEY
Ride Height and Weight Requirements
When designing and building a ride, the manufacturers strive to design the ride so that the most amount of people (approx. 90% of the
population) will be able to fit inside the ride vehicle (including height and weight requirements), and make certain the safety restraints
operate correctly. Unfortunately the 90% does not quite cover all the population. Due to ride restrictions, not all of our guests will be able
to ride all rides. Guests approaching 300 pounds or taller than 6’3” may have difficulty on some rides at the park. Click here to access
further information: http://www.hersheypark.com/rides/size.php
Hershey Park
What are the height
How tall would you Describe the
Graph the inequality that represents
Rides
conditions/restrictions for each
have to be to NOT
height
the height restrictions for each ride.
be allowed to ride
restrictions
ride?
on this ride?
using the correct Graph the inequality that represents
a mathematical
the heights that cannot ride the rides.
What Hershey Candy Categories
symbols
would be allowed to ride this ride?
Can Ride:
Sooperdooperlooper
less than 42 inches
60" &
x>42
taller
Cannot Ride:
x<42
54"to60"
48"to54"
42" to
48"
Trailblazer
60"
&
taller
54"
to
60"
Must be
accompanied
by a
responsible
rider.
less than 36 inches
Can Ride:
x>36
Cannot Ride:
x<36
48"
to
54"
Skyrush
42"
to
48"
Must be
accompanied
by a
responsible
rider.
36"
to
42"
Must be
accompanied
by a
responsible
rider.
60"
&
taller
less than 54 inches
Can Ride:
x>54
Cannot Ride:
x<54
greater than 54
inches
Can Ride:
x<54
54"
to
60"
Bizzy Bees
48" to
54"
42" to
48"
Cannot Ride:
x>54
36" to
42"
Under
36"
Dizzy Drums
48"
to
54"
42"
to
48"
36"
to
42"
less than 36 inches
and greater than 48
inches
Can Ride:
x<54 and x>36
Cannot Ride:
x<36 and x>54
Dry Gulch Railroad
60"
&
taller
everyone can ride
the ride 
Can Ride:
all
54" to
60"
48" to
54"
42" to
48"
Must be
accompanied
36" to
by a
42"
responsible
rider.
Must be
accompanied
Under
by a
36"
responsible
rider.
Cannot Ride:
none
Ride Height and Weight Requirements
When designing and building a ride, the manufacturers strive to design the ride so that the most amount of people (approx. 90% of the
population) will be able to fit inside the ride vehicle (including height and weight requirements), and make certain the safety restraints
operate correctly. Unfortunately the 90% does not quite cover all the population. Due to ride restrictions, not all of our guests will be able
to ride all rides. Guests approaching 300 pounds or taller than 6’3” may have difficulty on some rides at the park. Click here to access
further information: http://www.hersheypark.com/rides/size.php
Hershey Park
Rides
What are the height
conditions/restrictions for each
ride?
What Hershey Candy Categories
would be allowed to ride this ride?
Sooperdooperlooper
How tall would you
have to be to NOT
be allowed to ride
on this ride?
Describe the
height
restrictions
using the correct
a mathematical
symbols
Can Ride:
Cannot Ride:
Trailblazer
Can Ride:
Cannot Ride:
Graph the inequality that represents
the height restrictions for each ride.
Graph the inequality that represents
the heights that cannot ride the rides.
Skyrush
Can Ride:
Cannot Ride:
Bizzy Bees
Can Ride:
Cannot Ride:
Dizzy Drums
Can Ride:
Cannot Ride:
Dry Gulch Railroad
Can Ride:
Cannot Ride: