Andrea Palmer PROSPECT HILL ACADEMY CHARTER SCHOOL, SOMERVILLE, MA
6th Grade Math : Unit #3 - Integers and Rational Numbers : Lesson #15

Inequalities

Objective: SWBAT: • Define inequality • Write an inequality to represent a given situation • Create a graph for a given inequality
Standards: 6.NS.C.6a 6.NS.C.7 6.NS.C.7a 6.NS.C.7b MP2 MP3 MP4 MP7
Subject(s): Math
60 minutes
1 Do Now - 10 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 apply what they know about inequalities to the Log Peeler ride.  How can we show that the minimum height is 32 and the maximum height is 48?  Students may struggle to represent this with an inequality and that is okay.  I tell students to write something they think might work.  It might be easier for students to start by creating the graph and then move to writing the inequality.

I present “h is greater than or equal to 32 inches” as the inequality.  I ask students to share their opinion of my inequality.  I argue that the minimum height is 32 inches, so you have to be 32 inches tall or taller.  I want students to argue that the maximum height is 48, so you cannot be taller than 48 inches.  Then I follow their lead and declare the inequality must be “h is less than or equal to 48 inches”.  Again I ask for student input.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.  Finally I move to the graph and ask students how we would show the height requirements on the graph.  The graph should have a closed dot at 32 and at 48.  You can ride the ride if you are 32 inches, 48 inches, or any height in between those two measurements.  If students do not come up with it, I show them that we can represent that with an inequality of 32 is less than or equal to h is less than or equal to 48.  

2 Inequalities Review - 10 minutes

Note:

  • Before the lesson I use the ticket to go data from the previous lesson (What Rides Can You Go On?) to Create Homogeneous Groups of 3-4. 

I have students move into their groups. We work on problem 1 together.  I ask students to raise their hands and share out ideas.  For 1e, student participate in a Think Write Pair Share.  I want students to realize that the temperature could not be -2.5 degrees, because that is colder than -2 degrees.  I plot -2.5 degrees on the number line.

Students work on problem 2 by themselves.  After a couple minutes we come together and share ideas.  For the graph, I ask students whether the circle should be open or closed.  A common mistake is students confuse what to do with the circle.  If this occurs, I reread the problem and ask students, “Can the elevator have 999.5 pounds on it?  Why or why not?”  

3 Inequalities Practice - 30 minutes

I review expectations and pass out a Group Work Rubric for each group.  Students are engaging in MP2: Reason abstractly and quantitatively and MP4: Model with mathematics.  I walk around and monitor student progress and behavior.  I Post A Key, so that one representative of each group can check their work on a page before moving on. 

Some students may struggle with translating a situation into an inequality or a graph.  Phrases like “at least” and “no more than” can be confusing.  If a group is struggling with this, I will give them a different situation using the same phrase.  For example, I may say, “I need at least 3 pencils.”  I have the students give me a number of pencils that they think will work.  “Can you give me 4 pencils?  3 pencils?  2 pencils? Why or why not?”  Then we go back to the situation in the problem and I ask similar questions.

In problems 5 and 6 I want students to use the context of the problem to consider their inequality and graph.  For instance, in problem 5 it says that Alex can spend at most $50.25.  Students will likely come up with d is less than or equal to $50.25.  But can Alex really go to the store and spend -$5.19?  I want students to think about what can actually happen at the store and create a new inequality and graph.

If a group successfully completes their work, I ask them to explain their work for problem 5 and 6.  Then they can choose to work on the Inequality Puzzles or to create Inequality Posters.

4 Closure and Ticket to Go - 10 minutes

 For Closure I show students the number line with the letters.  I ask students to jot down what they know from looking at the number line.  Students participate in a Think Write Pair Share.  Some students may create inequalities that involve two or three letters.  Other students may share that “a” is the smallest value on the number line or that “e” is the greatest value on the number line.

Then I ask:

  • If “a” and “e” are opposites, what do you know about “c”?  How do you know?
  • If “a” and “d” are opposites, is “c” positive or negative?  How do you know?

Students are engaging in MP7: Look for and make use of structure.  I pass out the Ticket to Go and students complete it independently.  Then I pass out the HW Inequalities.

Progress with Inequalities
Exit Tickets

In the previous lesson, What Rides Can You Go On?, I included a reflection with student work for the ticket to go.  Here are the tickets to go from this lesson for the students whose work I included for the “Novice” and  “Approaching Mastery” categories in the previous lesson.

 

Unit 3.14 Novice to Approaching Mastery.jpeg

This student was struggling reading and representing inequalities on the previous lesson’s ticket to go.  By looking at his work on this ticket to go, he has made progress but he still has areas of improvement.  He is able to possible and impossible temperatures that fit the given situation.  He is also able to explain that the temperature cannot be -3 degrees because “-3 is not as cold as -3.5”.  He understands the situation and what it means.  He is still struggling to represent it symbolically and graphically.  For his inequality he fails to put a symbol in between T and -3.5.  For his graph, he fails to recognize that T cannot equal -3.5.  He is now approaching mastery for this topic.  I will check in with him and other students that are still struggling during the next lesson, Review Stations, so that they can progress with writing and graphing inequalities.

 

Unit 3.14 Approaching Mastery to Proficient.jpg

This student was struggling with writing an inequality that matched the situation and her graph on the previous lesson’s ticket to go.  By looking at her work on this ticket to go, she has made progress in these areas.  She is able to create an inequality that matches her graph and the situation.  She is also able to explain why -3 degrees would not be a possible temperature.  She is now proficient for this topic.