Title: Solving and Graphing Inequalities

Grade Level: 7th Grade

Objective: - Students will understand the concept of inequalities and how to solve and graph them on a number line. - Students will be able to solve and graph one-step and two-step inequalities. - Students will apply their knowledge of inequalities to real-life scenarios.

Materials: - Whiteboard or blackboard - Markers or chalk - Graph paper - Worksheets with inequality problems - Number lines - Real-life scenario cards

Procedure:

1. Introduction (10 minutes) a. Begin the lesson by asking students if they have ever heard of or encountered inequalities in their daily lives. b. Discuss examples of inequalities, such as “You must be at least 12 years old to ride this roller coaster” or “You need to score at least 70% to pass the test.” c. Explain that inequalities are mathematical statements that compare two quantities using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

2. Solving One-Step Inequalities (15 minutes) a. Write a simple one-step inequality on the board, such as x + 3 > 7. b. Explain the steps to solve the inequality:
   • Subtract 3 from both sides: x > 4. c. Provide a few more examples and solve them together as a class. d. Distribute worksheets with one-step inequality problems for students to solve individually or in pairs.
3. Graphing One-Step Inequalities (15 minutes) a. Introduce the concept of graphing inequalities on a number line. b. Explain that the solution to an inequality can be represented by shading a region on the number line. c. Demonstrate how to graph a one-step inequality using the example from step 2:
   • Draw a number line and mark the point 4.
   • Since the inequality is x > 4, shade the region to the right of 4. d. Provide more examples and ask students to graph the inequalities on their own number lines.
4. Solving Two-Step Inequalities (15 minutes) a. Write a two-step inequality on the board, such as 2x + 5 ≤ 13. b. Explain the steps to solve the inequality:
   • Subtract 5 from both sides: 2x ≤ 8.
   • Divide both sides by 2: x ≤ 4. c. Solve a few more two-step inequalities together as a class. d. Distribute worksheets with two-step inequality problems for students to solve individually or in pairs.
5. Graphing Two-Step Inequalities (15 minutes) a. Review the concept of graphing inequalities on a number line. b. Demonstrate how to graph a two-step inequality using the example from step 4:
   • Draw a number line and mark the point 4.
   • Since the inequality is x ≤ 4, shade the region to the left of 4, including 4. c. Provide more examples and ask students to graph the inequalities on their own number lines.

6. Real-Life Applications (10 minutes) a. Distribute real-life scenario cards to each student or pair of students. b. Instruct students to read the scenario and write an appropriate inequality to represent the situation. c. Ask a few students to share their scenarios and inequalities with the class. d. Discuss how inequalities are used in various real-life situations, such as budgeting, sports, or age restrictions.

7. Conclusion (5 minutes) a. Recap the main concepts covered in the lesson: solving and graphing inequalities. b. Ask students if they have any questions or need clarification on any topics. c. Assign homework that includes solving and graphing inequalities. d. Encourage students to practice inequalities in their daily lives by identifying and discussing examples they encounter outside of the classroom.