Unit Title: Algebraic Expressions and Equations

Grade Level: 8th Grade

Duration: 4 weeks

Overview: In this unit, students will learn about algebraic expressions and equations. They will learn how to write and evaluate expressions, solve equations, and graph linear equations. Students will also learn how to apply these skills to real-world situations.

New York State Next Generation Algebra Standards:

A.ASSE.1: Interpret parts of an expression, such as terms, factors, and coefficients.

A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.4: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Lesson 1: Introduction to Algebraic Expressions

Objective: Students will be able to identify the parts of an algebraic expression.

Materials: Whiteboard, markers, algebraic expression worksheets

Procedure:

1. Begin the lesson by asking students if they have ever seen or used algebraic expressions before. Write a few examples on the board.

2. Explain to students that algebraic expressions are mathematical phrases that contain variables, constants, and operations.

3. Review the parts of an expression, such as terms, factors, and coefficients.

4. Distribute algebraic expression worksheets to students and have them identify the parts of each expression.

5. Review the answers as a class and discuss any questions or concerns.

6. Assign homework that requires students to create their own algebraic expressions and identify the parts.

Lesson 2: Solving Equations

Objective: Students will be able to solve linear equations.

Materials: Whiteboard, markers, equation worksheets

Procedure:

1. Begin the lesson by reviewing the steps to solve a linear equation.

2. Explain to students that they can use inverse operations to isolate the variable and solve for its value.

3. Distribute equation worksheets to students and have them solve each equation.

4. Review the answers as a class and discuss any questions or concerns.

5. Assign homework that requires students to create their own equations and solve for the variable.

Lesson 3: Graphing Linear Equations

Objective: Students will be able to graph linear equations.

Materials: Whiteboard, markers, graph paper, linear equation worksheets

Procedure:

1. Begin the lesson by reviewing the parts of a linear equation and how to solve for the variable.

2. Explain to students that they can graph linear equations by plotting points and connecting them with a line.

3. Distribute linear equation worksheets to students and have them graph each equation.

4. Review the answers as a class and discuss any questions or concerns.

5. Assign homework that requires students to create their own linear equations and graph them.

Lesson 4: Real-World Applications

Objective: Students will be able to apply algebraic expressions and equations to real-world situations.

Materials: Whiteboard, markers, real-world application worksheets

Procedure:

1. Begin the lesson by reviewing the concepts of algebraic expressions and equations.

2. Explain to students that they can use these concepts to solve real-world problems, such as calculating the cost of a trip or determining the number of items that can be produced.

3. Distribute real-world application worksheets to students and have them solve each problem.

4. Review the answers as a class and discuss any questions or concerns.

5. Assign homework that requires students to create their own real-world problems and solve them using algebraic expressions and equations.

Assessment:

Students will be assessed on their ability to identify the parts of an algebraic expression, solve linear equations, graph linear equations, and apply algebraic expressions and equations to real-world situations. Assessment will be based on class participation, homework assignments, and a final exam.