Title: Solving Linear Equations

Grade Level: 9th-10th grade

Objective: - Students will understand the concept of linear equations and how to solve them. - Students will be able to solve linear equations using various methods, including the addition/subtraction method and the multiplication/division method. - Students will apply their knowledge of linear equations to solve real-world problems.

Materials: - Whiteboard or chalkboard - Markers or chalk - Handouts with practice problems - Calculators (optional)

Procedure:

1. Introduction (10 minutes) a. Begin the lesson by asking students if they have heard of linear equations before. Write the term “linear equation” on the board and ask for any initial definitions or ideas from the students. b. Explain that a linear equation is an equation that represents a straight line on a graph. It contains variables, constants, and coefficients. c. Provide examples of linear equations, such as “2x + 3 = 7” or “4y - 5 = 3y + 2.” Explain that the goal is to find the value of the variable that makes the equation true.

2. Solving Linear Equations using Addition/Subtraction Method (15 minutes) a. Write a simple linear equation on the board, such as “3x + 4 = 10.” Explain that the addition/subtraction method involves isolating the variable on one side of the equation. b. Demonstrate the steps to solve the equation:
   • Subtract 4 from both sides: 3x = 6
   • Divide both sides by 3: x = 2 c. Provide a few more examples on the board and solve them together as a class. d. Distribute handouts with practice problems for students to solve individually or in pairs.
3. Solving Linear Equations using Multiplication/Division Method (15 minutes) a. Write a linear equation on the board that requires the multiplication/division method, such as “2y/3 = 8.” Explain that this method involves isolating the variable by multiplying or dividing both sides of the equation. b. Demonstrate the steps to solve the equation:
   • Multiply both sides by 3: 2y = 24
   • Divide both sides by 2: y = 12 c. Provide additional examples on the board and solve them together as a class. d. Allow students to practice solving equations using the multiplication/division method with the provided handouts.

4. Real-World Application (15 minutes) a. Explain to students that linear equations can be used to solve real-world problems. Provide examples such as calculating the cost of items, determining the time it takes to complete a task, or finding the distance traveled. b. Present a real-world problem on the board, such as “A store sells shirts for $15 each. If a customer buys 4 shirts, how much will they spend?” Guide students through the process of setting up and solving the equation. c. Provide additional real-world problems for students to solve individually or in pairs using linear equations.

5. Conclusion and Recap (5 minutes) a. Review the main concepts covered in the lesson, including the definition of linear equations and the methods used to solve them. b. Ask students if they have any questions or if there are any topics they would like to review further. c. Assign homework that includes solving linear equations and solving real-world problems using linear equations.

Note: Adjust the duration of each section based on the pace and needs of your students.