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 example, x <

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

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?"
A sking 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
Rides
What are the height conditions/restrictions for each ride?
What Hershey Candy Categories would be allowed to ride this ride?
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
Graph the inequality that represents the height restrictions for each ride.
Graph the inequality that represents the heights that cannot ride the rides.
Sooperdooperlooper
60" & taller
54"to60" less than 42 inches Can Ride: x>42
Cannot Ride: x<42
48"to54"
Trailblazer
42" to
48"
Must be accompanied by a responsible rider.
60"
& taller
54" to
60" less than 36 inches Can Ride: x>36
Cannot Ride: x<36

Skyrush
Bizzy Bees
Dizzy Drums
48" to
54"
42" to
48"
36" to
42"
48" to
54"
42" to
48"
36" to
42"
Must be accompanied by a responsible rider.
Must be accompanied by a responsible rider.
60"
& taller
54" to
60"
48" to
54"
42" to
48"
36" to
42"
Under
36" less than 54 inches Can Ride: x>54 greater than 54 inches
Cannot Ride: x<54
Can Ride: x<54
Cannot Ride: x>54 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
54" to
60"
48" to
54"
42" to
48"
Must be
36" to accompanied by a
42" responsible rider.
Must be
Under accompanied by a
36" responsible rider. everyone can ride the ride

Can Ride: all
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?
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
Graph the inequality that represents the height restrictions for each ride.
Graph the inequality that represents the heights that cannot ride the rides.
Sooperdooperlooper
What Hershey Candy Categories would be allowed to ride this ride?
Can Ride:
Cannot Ride:
Trailblazer Can Ride:
Cannot Ride:

Skyrush
Bizzy Bees
Dizzy Drums
Dry Gulch Railroad
Can Ride:
Cannot Ride:
Can Ride:
Cannot Ride:
Can Ride:
Cannot Ride:
Can Ride:
Cannot Ride: