## Completing the Square Lesson Plan

This lesson plan focuses on teaching students how to complete the square for quadratic equations, convert quadratic equations from standard form to vertex form, and identify the vertex of a parabola. The lesson is designed for high school students who have a basic understanding of algebraic concepts and quadratic equations.

To use this lesson plan, teachers should first review the learning target, success criteria, essential questions, and big idea. They should also review the worksheet with answers provided to ensure they have a good understanding of the content being covered in the lesson.

The lesson begins with an introduction to completing the square and a discussion of the limitations of using the quadratic formula. Teachers should model how to complete the square for a given quadratic equation and provide students with practice problems to complete on their own. They should circulate the room to assist students as needed.

Next, teachers should discuss the vertex form of a quadratic equation and how it is related to completing the square. They should provide students with practice problems to convert quadratic equations from standard form to vertex form.

Finally, teachers should explain how to use the vertex form of a quadratic equation to identify the vertex of a parabola. They should provide students with practice problems to identify the vertex of a parabola.

To conclude the lesson, teachers should review the key concepts covered in the lesson and answer any remaining questions from students.

Overall, this lesson plan provides a comprehensive introduction to completing the square, converting quadratic equations from standard form to vertex form, and identifying the vertex of a parabola. Teachers can use this lesson plan to help their students gain a deeper understanding of these important algebraic and geometric concepts.

**Learning Target:**

Students will be able to complete the square for quadratic equations by finding the value of h and k, as well as convert quadratic equations from standard form to vertex form.

**Success Criteria:**

By the end of the lesson, students will be able to:

- Complete the square for quadratic equations by finding the value of h and k.
- Convert quadratic equations from standard form to vertex form.
- Identify the vertex of a parabola from its quadratic equation.

**Essential Questions:**

- What is completing the square?
- How can completing the square help us solve quadratic equations?
- What is the vertex form of a quadratic equation and how is it related to completing the square?
- How can we use the vertex form of a quadratic equation to identify the vertex of a parabola?

**Big Idea:**

Completing the square is a powerful algebraic technique that allows us to rewrite a quadratic function in vertex form, making it easier to graph, analyze, and solve.

**Materials:**

- Whiteboard and markers
- Worksheet with quadratic equations to solve or you can use this online test: Completing the Square Test.
- Answer key to worksheet
- Real-life problem scenarios

**Procedure:**

**Introduction**:

- Introduce the topic of completing the square and explain why it is important.
- Review the quadratic formula and discuss the limitations of using it to solve quadratic equations.

**Completing the Square:**

- Model how to complete the square for a given quadratic equation.
- Provide students with practice problems to complete on their own.
- Circulate the room to assist students as needed.

**Vertex Form**:

- Discuss the vertex form of a quadratic equation and how it is related to completing the square.
- Provide students with practice problems to convert quadratic equations from standard form to vertex form.

**Identifying the Vertex:**

- Explain how to use the vertex form of a quadratic equation to identify the vertex of a parabola.
- Provide students with practice problems to identify the vertex of a parabola.

**Real-Life Application:**

- Provide students with real-life problem scenarios.
- Have students work in pairs or small groups to solve the problems and present their solutions to the class.
- Discuss the importance of being able to apply this skill to real-life situations.

**Closing:**

- Review the key concepts covered in the lesson.
- Answer any remaining questions from students.
- Collect the worksheets to assess student understanding.