7th Grade Linear Equations Lesson Plan (Math)

Topic: Linear equations

Objectives & Outcomes

• By the end of this lesson, students will be able to solve linear equations.

Materials

• Graph paper
• Pencils
• Eraser

Warm-up

• Ask students if they have ever seen or heard the word 'equation' before. Ask them to describe what an equation is.
• Write the following equation on the board: 6x + 4 = 14

Ask students to solve this equation by substituting the number 4 for the variable 'x'. They should get the answer '10'.

• Ask students if they understand what just happened. Explain that an equation is a mathematical statement that combines an expression with a given value, which is also called the 'solution'.

Direct Instruction

• Introduce the concept of a 'linear equation'. A linear equation is an equation that involves only the operations of addition and multiplication, and the variables are only multiplied by single-digit numbers.
• Show the following equation on the board: 3x + 4y = 10

Explain that this is a linear equation because it involves only addition and multiplication, and the variables are only multiplied by single-digit numbers.

• Explain the steps for solving a linear equation.
• Step 1: Find a way to isolate the variable on one side of the equation. This means we need to get the variable all by itself on one side of the equation, without any numbers.
• Step 2: Solve the equation for the variable. This means we need to find the value of the variable that will make the equation true.
• Step 3: Check the solution by substituting the solution into the original equation. This will ensure that the solution actually works.
• Using the above example, we can see that we can isolate the variable 'x' by dividing both sides of the equation by 3.
• Now we need to solve the equation for the variable 'x'. To do this, we can use the fact that dividing by a number can be thought of as multiplying by its reciprocal. So if we multiply both sides of the equation by 4, we will get:
• 4x = 40
• 4x/4 = x
• x = 10
• The solution to the equation is 'x = 10'.
• Now we can check that this solution works by substituting it into the original equation:
• 3(10) + 4y = 10
• 30 + 4y = 10
• 34y = 10
• y = 3
• Therefore, the solution to the equation is 'x = 10, y = 3'.
• Ask students if they understand the steps for solving a linear equation. Demonstrate how to solve a few more examples on the board, using the steps listed above.

Guided Practice

• Give students a few more linear equations to solve, along with the steps for solving them. Have them work in pairs or small groups to solve the equations, with guidance from the teacher if needed.
• Have students share their solutions with the class, checking for accuracy.

Independent Practice

• Give students a worksheet with several linear equations to solve on their own. Encourage them to use the steps for solving linear equations to solve the equations.
• Have students check their answers with a partner or small group, and make any corrections necessary.

Closure

• Review the steps for solving linear equations. Ask students to share any strategies that they found helpful for solving equations.
• Remind students that they can use these same steps when solving equations in future math courses, including algebra and calculus.

Assessment

• Observe students during the guided and independent practice activities to see if they are able to solve equations accurately and efficiently.
• Collect and review their practice worksheets to assess their understanding of the steps for solving linear equations.