6th Grade Math : Unit #3 - Integers and Rational Numbers : Lesson #14

What Rides Can You Go On?

Objective: SWBAT: • Define inequality • Write an inequality to represent a given situation • Create a graph for a given inequality
Standards: 6.NS.C.7a 6.NS.C.7b MP1 MP3 MP4 MP5
Subject(s): Math
60 minutes
1 Do Now - 7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to start thinking about inequalities but without the math notation.  For problem 1, I am looking for students to recognize that Sebastian could have 3, 4, 5… siblings.  For impossible number of siblings for Sebastian, some students may list 0, 1, 2.  Some students may list rational numbers, like 1.25 or 2 ½.  Other students may list numbers less than 0.  For problem 2, I am interested to hear students explain their thinking for part b. For example, technically 4.5 is less than 5 but it is not possible for someone to have 0.5 of a sibling.

Students participate in a Think Pair Share.  I call on students to share out their thinking.  If students do not mention the examples from above, I present them and ask students what they think.

2 What Rides Can You Go On? - 3 minutes


  • For this lesson I put students into heterogeneous groups of 3-4.  This material is likely to be new to most students.
  • Before the lesson I gather measuring tapes (1 for each 2-3 students) and blue painter’s tape for students to help measure their height.

I have students move into their groups.  I ask students, “Who likes amusement parks?”.  Good news – you are chaperoning a field trip to an amusement park called Knott’s Berry Farm.  Bad news – you are responsible for 3 little kids.  I present the situation and ask students, “What information do you need to know to answer these questions?”  Students need to know their own height and the requirements of the rides.  I ask students, “If I give you a measuring tape, how will you measure your height?”

3 Height - 5 minutes

I have students pick up measuring tapes and painter’s tape for their group (2 measuring tapes and 2 pieces of tape per group).  A student stands straight up against the wall and a group member marks the top of his/her head with a piece of blue painter’s tape.  Then the student steps off the wall and both members work on measuring the height to the nearest inch.  Students are using MP5: Use appropriate tools strategically. Once they are finished, they return their materials and sit back down with the rest of their group.

4 Questions - 10 minutes

I review expectations and pass out a Group Work Rubric for each group.  Groups can decide on their own what order they want to answer the questions.

As students work, I walk around and monitor student progress and behavior.  Some students may struggle with particular rides and that is okay!  The height requirements were taken from the park’s website and some of them are unclear.  For instance, for the ride Woodstock’s Airmail the height requirement just says “36 inches”.  Students may wonder if that means exactly 36 inches or at least 36 inches.  I will bring up these issues later, for now I tell students to use the information they have to make a decision.

With about 5 minutes left, we come back together as a class.  I ask students what they noticed about height requirements.  I want students to share their thinking about some of the vague or unclear requirements.  We brainstorm as a class what we think the Knott’s Berry Farm people intended to say.  It would be quite interesting if you really had to be 36 inches tall to ride Woodstock’s Airmail.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.  With the rest of the time we quickly review which rides the younger kids can ride.

5 Inequality Notes - 15 minutes

I introduce the vocabulary word inequality as something that every student has already done.  Students may be less familiar with greater than or equal to and less than or equal to signs.  We read the examples and I ask for students to come up with possible and impossible values for each n and m.  I ask, “Can n be 4? Why or why not?” and “Can m be 4? Why or why not?”

I ask students to look at the inequality graphs and to think about which graph matches which equation from the examples at the top of the page (there is one extra graph).  Students participate in a Think Write Pair Share.  Rather than presenting the rules for graphing and relying on students to memorize them, I want students to make their own observations.  I hope this way they will be more likely to remember how to graph inequalities.

If students don’t mention it, I ask, “Why is there an open circle around 1? What does that mean?”  And “Why is there a closed circle around 4?  What does that mean?”  I call on students to explain their thinking.

I ask students about the one graph that doesn’t match the inequalities at the top of the page.  I ask them to independently write down an inequality that will match the graph.  I tell them to use “x” as the variable.  A common mistake is that students will confuse the greater than and less than symbols.  If I see this I ask, “Can x be 2?  How do you know?”

6 Inequality Practice - 10 minutes

Students work on filling in the chart independently.  Students are engaging with MP4: Model with mathematics.  I walk around and monitor student progress. 

If students struggle, I may ask the following questions:

  • What is the height requirement?
  • Give me a height of someone who can ride this ride.
  • Give me a height of someone who cannot ride this ride.
  • Can a person be _____ (say number mentioned in requirement) tall?  Why or why not?
  • How can we show this on a number line?
  • Should the circle be open or closed?  How do you know?

I Post A Key so students can check their work once they have finished.  If students successfully complete their work they can work on the Inequality Challenge.  They may also work on their “Tracking Your Investments” project if they have not already finished it.

7 Closure and Ticket to Go - 10 minutes

 For Closure I ask students, “What is an inequality?” and “Why do we use them?”  I want students to articulate that inequalities represent a comparison between quantities that are not necessarily equal.  They can have a range of numbers that work as answers.

I pass out the Ticket to Go and students complete it independently.  Then I pass out the HW What Rides Can You Go On

Reading and Representing Inequalities
Exit Tickets

I collected the tickets to go to see what students understood about reading and representing inequalities and what gaps in understanding they had.  I corrected the tickets to go and grouped them in the following way:

Novice:  These students struggled to read inequalities correctly and to create an inequality for a given situation.  These students were able to explain that 1a showed that c is greater than 5, but 1b confused them.  The use of the less than or equal sign was something brand new to them.  This student in particular created a graph that shows that he understood that someone’s height would have to be greater than or equal to 35 inches, but he struggled to write an inequality to represent it. Unit 3.13 Novice.jpg

Approaching Mastery: These students were able to explain what the inequalities in 1a and 1b meant.  The common struggle was creating and graphing the inequality for problem 2.  This particular student was able to create a graph that matches the situation, but she created an inequality that said that the height had to be less than or equal to 35 inches, rather than greater than or equal to 35 inches. Unit 3.13 Approaching Mastery.jpg

Proficient:  These students were able to explain what the inequalities in 1a and 1b meant.  These students were also able to write and graph an inequality to represent the situation in problem 2.  This student’s work shows that she deliberately chose a closed point on 35 inches.  Unit 3.13 Proficient.jpg

For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work.  Most students were able to write the meaning of the inequalities in problem 1, but got hung up on part of problem 2.  This is the first time many students have been asked to graph inequalities, so it makes sense that most students need more practice.  The next lesson is also practicing these skills, so we will have time to go over common mistakes and struggles.  I will also pass back these tickets to go so students can find and correct any mistakes.  For the few students who were novices, I will be checking in with them during work time to make sure they understand what the different symbols mean and how to create graphs.