Summary
In this lesson, students explore the relationship between a set of numbers and the constraints of an inequality. They will write, graph, and identify solutions to inequalities and connect these 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 identify possible solutions to inequalities using a t-chart and number lines.
Explain
Students discuss their solution methods and clarify misconceptions about solving inequalities.
Extend
Students match scenarios with inequalities and find corresponding algebraic and graphical solutions.
Evaluate
Students demonstrate understanding by identifying and correcting a mistake in a solved inequality.
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)
Sweet Inequalities Signs (attached; one per classroom; printed one-sided)
Sweet Inequalities handout (attached; one per group; printed two-sided)
Sweet 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, introduce 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 pair up and distribute one set of Linear Inequalities Cards to each pair. 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 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 will 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 from the What Numbers Work handout 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
15 Minute(s)
Move to slide 8 and ask the class, How can you solve x – 3 < 15 without making a table? Guide students through isolating x to solve the inequality, emphasizing each step. Ensure that students understand the process, checking for comprehension by asking them to explain each step back to you.
Once students are comfortable, display slide 9. Instruct students try to solve the inequality: x + 2 ≥ 11. Have students also graph the solution on a number line. Use this time to make sure there are not any misunderstandings about graphing on a number line.
Display slide 10 and ask students to solve this challenge question: 19 < x + 6. Use this question to deepen understanding. As students are solving algebraically and graphing the inequality, address any lingering misconceptions.
Extend
30 Minute(s)
Organize students into groups of 2-3 and give each group a Sweet Inequalities handout. Display slide 11 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 Sweet Inequalities (Teacher Guide) document to quickly check their results and give feedback.
Evaluate
5 Minute(s)
Display slide 12 and 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.). Google docs. Tech Tools. https://learn.k20center.ou.edu/tech-tool/2327
K20 Center. (n.d.). Quizlet. Tech Tools. https://learn.k20center.ou.edu/tech-tool/666
