Writing Simple Inequalities

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SWBAT represent a real world or mathematical context using a simple inequality and describe the solution set.

Big Idea

Real-word contexts can be represented by algebraic inequalities when there is a comparison of two unequal quantities, or when there are a range of possible solutions.

Think About It

5 minutes

Students work alone on the Think About It problem.  After a few minutes, I pull popscicle sticks to cold-call students for possible costs of Beyonce's ring.  I ask for an example or two of a number that could not be the cost of the ring.  I then have a student define our inequality.  

This Think About It is a quick one, and it is designed to be an engaging way to connect the work we've done so far with inequalities to real-world scenarios.  We've had practice creating expressions and equations to represent real-world scenarios and this lesson provides students the opportunity to do the same with inequalities.  

Intro to New Material

15 minutes

To begin the new material for this lesson, we review how to read each of the inequality symbols.  In the table in the INM materials, we translate the inequalities into words and then also re-write the inequality in the opposite direction (so, x > 12 becomes 12 < x).

It's important that students continue to define their variables as they create inequalities.  This is a habit we build with our expressions and equations work.

If students are having a hard time deciding which symbol to use in the inequality, I coach them to use a number line.  They are able to pick a number smaller than what we have in the scenario and a number larger than what we have in the scenario.  They can use the number line as a way to 'test out' if we need greater than or less than.  

In this lesson, students have trouble with 'at least' and 'at most.'  To help them remember, I make a bold statement and say 'I am at least 16 years old.'  They get a good giggle, but then also remember that 'at least' means that we have a minimum value.  

Partner Practice

20 minutes

Students work together on the Partner Practice problems.  As they work, I am circulating around the room.  

I am looking for:

  • Are students making inequalities that match verbal descriptions?
  • Are students using substitution to check that their inequality is correct?
  • Are students choosing an appropriate variable?

 I'm asking pairs:

  • How did you know the inequality was greater than/less than?
  • How can you test your inequality to make sure it accurately portrays your description?


After 15 minutes of work time, the class comes back together.  I have students share out the work they did in the matching portion of the partner practice.  Students then work independently on the Final CFU problem.  I have them put fingers in the air to represent the inequality they picked to go along with this problem (1st, 2nd, 3rd, 4th).  I then ask students to explain to the class why it could not be each of the other inequalities.


Independent Practice

15 minutes

Students work on the Independent Practice problem set.  As they work, I am looking for and asking the same questions as from the partner practice section.


Closing and Exit Ticket

10 minutes

After independent work time, we discuss problems 9 and 10 from the independent work problem set. First, I ask for a student to share out the inequality (s)he wrote for this problem.  Then, I ask for that student's paper to show on the document camera.  Question 10 asks students to agree or disagree with the given inequality. As a class, we give feedback to the written response for question number 10.

In exemplar written responses, we are looking for:  1) the question to be answered ("Yes, I agree" or "No, I do not agree"), 2) the reason for the agreement/disagreement, and 3) a counterexample, if appropriate. 

After the conversation, students work independently on their Exit Ticket.