Secondary Mathematics
Material Type:
Activity/Lab, Assessment, Lesson Plan
Middle School, High School
  • Linear Inequalities
  • Systems
    Creative Commons Attribution

    Systems of Linear Inequalities

    Systems of Linear Inequalities


    This is a lesson plan about solving systems of linear inequalities. Students will be creating a digital story to answer the question.


    This lesson is to finalize student thinking about systems of linear inequalities. We are using the task 5.5: All For One, One for All from the Mathematics Vision Project. Students will tell a digital story at the conclusion of this lesson.

    This lesson is designed to be an 80 minute peiod. 

    This lesson is for a whole class, split into groups of 2 or 3. 



    Background for Teachers

    Teacher should be very familiar with the Mathematics Vision Project tasks 5.1 - 5.4. Click here for a link to those tasks. 

    Teahcers should have an understanding of systems of linear inequalities. If you don't have an understanding of this topic, I strongly encourage you to not teach this course as you may be harming students with incorrect thinking. I would encourage you to collaborate with your team about this concept if you have any questions or concerns. 

    If you want to learn more about this topic, you can check out this article. 


    Student Prior Knowledge

    Students should have completed tasks 5.1 - 5.4 in Mathematics Vision Project before this lesson. They will need to have an understanding of:

    • How to graph one linear inequality on a coordinate graph
    • How and why we shade as we do
    • There are an infinite number of solutions to a system of linear inequalities
    • A solid line means coordinate points that lie on the solid lie are solutions to the inequality. 
    • A dotted line means coordinate points that lie on the dotted lie are NOT solutions to the inequality.


    Student Learning Intentions & Success Criteria

    Learning Intentions:

    • Students will be able to graph a system of linear inequalities
    • Students will be able to understand why solutions lie in the multiple-shaded area of the graph.

    Success Criteria:

    • Students will be able to graph a system of linear inequalities correctly
    • Students will identify coordinate points that are solutions to the system.


    Instructional Procedures


    Say, "Carlos and Clarity are about ready to start their business, but they realize that they have four constraints that they need to pay attention to when trying to decie the number of cats and dogs they should prepare for.

    • Cost
    • Space
    • Feeding Time
    • Pampering Time

    "They need to determine how many cats and how many dogs they could prepare for given all of these constraints. Go back in your notebooks and write the equations for each constraint we found.

    • Cost: 32c+80d≤1280
    • Space: 6c+24s≤360
    • Feeding Time: 12c+20d≤480
    • Pampering: 16c+20d≤480

    Graph each constraint on the coordinate graph given to show the combinations of dogs and cats they could prepare for while staying within each constraint. The cats will be on the x-axis, and the dogs will be on the y-axis. When you are finished, you will be creating a digital story to explain how many cats and dogs Carlos and Clarita could plan for."

    Give studnets about 10 minutes to graph each inequality on the coordinate grid, then give then the following instructions:

    "We are now going to prepare for your story. Your digital story needs to be between 1 and 2 minutes. 

    Your story should be about Carlos and Clarita. You are recommending to them a number of cats and dogs that would fit in all four constraints. You are going to recommend this to them by telling a story. 

    1. Brainstorm: What could your story be about? Come up with an idea of what you want your story to be.
    2. Talk with your partner and look in your past notes to research the validity of the number of cats and dogs you are recommending. 
    3. Using this storyboard, write out what you will say in your movie. Remember, it needs to be at 1 - 2 minutes long.
    4. Go to adobe spark and begin to create your video. Use images from adobe spark to help tell your story.
    5. Record your story using adobe spark. 
    6. Get together with two other groups and share your story. 
    7. Discuss the validity of your story with the other groups. Do your recommendations make sense in this context? How do you know that Carlos and Clarita could plan on the number of cats and dogs you recommended?


    Strategies for Diverse Learners

    All students will be able to access this task because they all will have different recommendations. Even if a student proposes two cats and two dogs, that is a correct solution. For studnets who need an extension, teachers can ask them to maximize the profit as much as possible, adding another level of complexity to the task.