Mastering the Square: An Introduction to Completing the Square

Algebra 2 Grades High School 4:03 Video
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Lesson Description

This lesson introduces the fundamental concepts of completing the square, a crucial technique in Algebra 2. Students will learn how to manipulate quadratic expressions to a completed square form.

Video Resource

Complete Square Introduction

Kevinmathscience

Duration: 4:03
Watch on YouTube

Key Concepts

  • Standard form of a quadratic expression (ax² + bx + c)
  • The 'a' coefficient must be equal to 1 for completing the square.
  • Halving the 'b' coefficient and squaring it.

Learning Objectives

  • Students will be able to identify the 'b' coefficient in a quadratic expression.
  • Students will be able to correctly halve the 'b' coefficient and square the result.
  • Students will be able to rewrite a quadratic expression in the completed square form (x + b/2)².

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the standard form of a quadratic expression (ax² + bx + c). Emphasize that 'a' must equal 1 for the method introduced in the video. Briefly discuss the importance of completing the square in solving quadratic equations.
  • Video Presentation (10 mins)
    Play the Kevinmathscience video "Complete Square Introduction." Instruct students to take notes on the steps involved in completing the square. Pay attention to the examples provided, especially those involving fractions.
  • Guided Practice (15 mins)
    Work through several examples on the board, mirroring the examples from the video. Start with simple integer values for 'b' and then progress to fractional values. Emphasize the step-by-step process: identify 'b', halve 'b', square the result, and rewrite the expression in completed square form. Ensure all students understand the steps involved.
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to work on independently. Circulate the classroom to provide assistance and answer questions. These problems should include both integer and fractional values for 'b'.
  • Review and Wrap-up (5 mins)
    Review the key concepts and steps involved in completing the square. Answer any remaining questions. Preview the next lesson, which will build upon this foundation to solve quadratic equations by completing the square.

Interactive Exercises

  • Online Practice
    Assign online practice problems where students can receive immediate feedback on their answers. These platforms often provide step-by-step solutions to help students identify and correct their mistakes.
  • Group Work
    Divide students into small groups and give each group a different set of quadratic expressions to complete the square on. Have them work together and explain their steps to each other.

Discussion Questions

  • Why is it important for the 'a' coefficient to be 1 when completing the square using this method?
  • How does halving the 'b' coefficient and squaring it help us rewrite the expression in the form (x + b/2)²?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in completing the square for the expression x² + bx + c, according to the video?

Correct Answer: Make sure 'a' = 1

Question 2:

If the 'b' value is 10, what number do you square after halving it?

Correct Answer: 5

Question 3:

What is the completed square form of x² + 6x?

Correct Answer: (x + 3)²

Question 4:

If the 'b' value is -8, what number is inside the parenthesis when the expression is in completed square form?

Correct Answer: -4

Question 5:

What is half of -3/4?

Correct Answer: -3/8

Question 6:

What is half of -23/20?

Correct Answer: -23/40

Question 7:

If the 'b' value is 3, what number goes in the completed square form?

Correct Answer: 3/2

Question 8:

If the 'b' value is -9, what is the number that goes in the completed square form?

Correct Answer: -9/2

Question 9:

What is the purpose of 'completing the square'?

Correct Answer: To rewrite a quadratic expression in a specific form

Question 10:

In the video, what advice is given for finding half of a fraction?

Correct Answer: Multiply the denominator by 2

Fill in the Blank Questions

Question 1:

Before completing the square, the coefficient 'a' must always be equal to ____.

Correct Answer: 1

Question 2:

To find the value to square, you first need to _____ the 'b' value.

Correct Answer: halve

Question 3:

Completing the square is often used to rewrite a quadratic equation into _____ form.

Correct Answer: vertex

Question 4:

The completed square form of a quadratic equation will be of the form (x + _____)².

Correct Answer: b/2

Question 5:

Half of -11 is _____.

Correct Answer: -11/2

Question 6:

When completing the square with fractions, finding half the b value is done by multiplying the _________ by 2.

Correct Answer: denominator

Question 7:

If b is -12, the term inside the parenthesis in the completed square form is x _______ 6.

Correct Answer: -

Question 8:

After halving the 'b' value, the result is then raised to the power of _____

Correct Answer: 2

Question 9:

The video describes __________ phases of completing the square.

Correct Answer: introductory

Question 10:

Completing the square is a method for solving ________ equations.

Correct Answer: quadratic

Educational Standards

A2.A.1.1:Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

Teaching Materials

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