Summary
This lesson focuses on the relationship between a set of numbers and the constraints of an inequality. Students write, graph, and identify solutions to inequalities, connecting them back to real-world scenarios when applicable.
Essential Question(s)
How can we use inequalities to represent relationships?
Snapshot
Engage
Students match scenarios with inequalities in a Card Matching activity.
Explore
Students investigate solutions to inequalities using a T-chart and number lines.
Explain
Students formalize their understanding of solving multi-step inequalities and discover the rule for multiplying and dividing by a negative number.
Extend
Students match their given scenarios to inequalities and the corresponding algebraic and graphical solutions.
Evaluate
Students correct mistakes in solved inequalities to demonstrate understanding.
Materials
Lesson Slides (attached)
Linear Inequalities cards (attached; one set per pair; printed one-sided)
What Numbers Work handout (attached; one per pair; printed two-sided)
Pies and Inequalities Signs (attached; one per classroom; printed one-sided)
Pies and Inequalities handout (attached; one per group; printed two-sided)
Pies and Inequalities (Teacher Guide) document (attached)
Exit Ticket handout (attached; one per student; printed one-sided)
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 and share the essential question: How can inequalities represent relationships? Then move to slide 4 to outline lesson objectives.
Display slide 5 and share the Card Matching strategy with the class. Have students find a partner or assign partners. Distribute one set of Linear Inequalities cards to each pair. Remind students to be kind and careful with the printed cards. Ask pairs to complete the card matching activity that involves matching various scenarios with one-variable inequalities. Give about five minutes for them to complete the matching activity, then have each pair join another pair to discuss their choices, using guiding questions like “Why did you match those cards?” or “How do you know the inequality symbol is correct?”
Explore
20 Minute(s)
Show slide 6. With students still in pairs, distribute a copy of the attached What Numbers Work handout to each pair. Ask them to list numbers that make the given inequality true, along with those that do not. Encourage pairs to discuss their reasoning. Students are to show the numbers that work on the number line (graphing the inequality). This activity allows students to visualize the solution set of the inequality. Students then answer the question: Why do certain numbers not work?
Display slide 7 and direct students’ attention to the back side of their handout. Have students reflect on their findings and write their “rule” (an explanation) for graphing inequalities. Ask a few volunteers to share their rules, then facilitate a class discussion about the relationship between the numbers from the table that worked with the values on the number line.
Explain
25 Minute(s)
Display slide 8 and share the steps for solving multi-step inequalities.
Transition to slide 9 and solve the inequality (–3 < 2x + 15) together, keeping the variable on the right side of the inequality symbol. After finding the solution (–9 < x), ask students how they would solve the inequality if they instead moved the variable term to the left in the first step. This approach will lead students to encounter dividing both sides by a negative number. Remind them that regardless of which side the variable is on, the solution remains the same. Then ask the class which inequality symbol they should use and what rule they should use when they divide by a negative number. Use this example to facilitate a brief discussion about the reasoning behind “flipping the inequality symbol” when multiplying or dividing by a negative number.
Use hidden slide 10 as a guide for walking students through this example.
Display slide 11 and ask the class to help you list the similarities and differences between solving equations and solving inequalities on the board. You can write or type their responses directly onto/into the slide.
Display slide 12 and have students try the given problem independently.
Move to slide 13. Use this challenge question to further their understanding. Clarify misconceptions as students are solving and graphing.
Extend
30 Minute(s)
Organize students into groups of 2–3 and give each group a copy of the attached Pies and Inequalities handout. Display slide 14 and preview the activity. Inform students that they are to match their verbal descriptions of inequalities on their handout with the algebraic representations, algebraic solutions, and number line solutions that are hanging around the room. Each group is to look around the room for the inequality, solution, and number line that corresponds to the verbal description. Then they are to record the letter that is printed in the top-left corner of the sign on their handout.
Direct students’ attention to the Show Your Work side of their handout. As they complete the front side of their handout, remind them to record the letters of the corresponding signs that are hung around the room. Each problem has three corresponding signs; encourage students to not visit a sign that has another group. All signs should be used exactly once. To ensure all group members participate, consider requiring each group member’s distinct handwriting on the handout. This activity allows students to choose the order they complete their work.
Give students time to work at their own pace. Some may visit signs in order of their algebraic work; others might search for matching number lines first. Allow either approach to foster their engagement and problem-solving.
When a group finishes the Your Results side of their handout, have them bring you their handout. Use the second page of the attached Pies and Inequalities (Teacher Guide) document to quickly check their results and give feedback.
Evaluate
5 Minute(s)
Display slide 15 to introduce the Exit Ticket strategy. Distribute a copy of the attached Exit Ticket handout to each student. Here students are to analyze two solved inequalities and determine which was solved incorrectly, justifying the rationale behind their choice.
Have students correct the work and graph the solution on a number line. Collect the handouts to assess comprehension and identify any remaining misconceptions.
Resources
K20 Center. (n.d.). Bell Ringers and Exit Ticket. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Card Matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (n.d.). Desmos classroom. Tech Tools. https://learn.k20center.ou.edu/tech-tool/1081
K20 Center. (n.d.). Google classroom. Tech Tools. https://learn.k20center.ou.edu/tech-tool/628
K20 Center. (n.d.). Quizlet. Tech Tools. https://learn.k20center.ou.edu/tech-tool/666