Modeling Compound Inequalities

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Students will be able model and solve compound inequalities.

Big Idea

Model and solve inequalities both algebraically and graphically as well as introduce interval notation.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Compound Inequalities which asks students to analyze the accuracy of a solved inequality.

I also use this time to correct and record the previous day's Homework.  


20 minutes

We are going to start today's lesson with a statement to model:  I can work no more than 15 hours per week making cake pops. This problem seems simple at the onset but has a trick.  My students work on this problem and then check with their partner.   If this were just a regular inequality, its interval would extend to negative infinity but since we don't have negative hours, this is actually the conjunction [0, 15].  I don't warn them of this in advance  If no one brings up the issue, I ask a question like “ Do all the numbers from (-∞, 15] fit our statement?” (Math Practice 2)  I then have them re-discuss this with their partner and modify their solution

We classify this and define the term conjunction and talk about all of its representation including three “sided” conjunctions like -7 < 4x + 5 < 3.  I have included a quadratic inequality.  Many will not remember how to solve these so we will solve this one graphically.   I have them graph both sides and then do a think-pair-share on the interval solution.  Here is a good place to teach CALC, intersect if using a TI-84 calculator as the intersections aren’t at easy integers.  

Finally they will solve a conjunction modeling problem.

My lesson PowerPoint includes detailed presentation notes.


17 minutes

We begin disjunctions with a real life problem.  Water is a liquid between 32of and 212of.  Write an inequality that represents when water is NOT liquid. With a problem like this, I often let my students know that there is a sneaky part to this problem.  Then I l go around checking on their solutions and calling out recognition (sometimes with names and sometime just generally) when students get the right solution which we then discuss as a class.

At this point, we define and look at the representations of disjunctions.

The remainder of the lesson involves some practice problems located in second section of the lesson PowerPoint- Compound Inequalities.  This includes another modeling problem (Math Practice 4) and an ordinary two inequality disjunction to solve and graph.  The final two problems are polynomial inequalities that need to be solved graphically. 

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

This exit ticket asks students to solve the conjunction -4 < 3x – 2 < 10. 


This Homework provides a range of standard compound inequalities and modeling problems as well as a polynomial inequality to be solved graphically.  Problem #9 is an extension problem that gives the students a three way conjunction that must be solved by splitting it into two separate inequalities or solved graphically (Math Practice 1). 

One homework modeling problem was adapted from here

The assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.