3a Completing the Square Lesson Plan

Length: one day
Subject: Algebra I/Algebra I Part 2
Topic: Completing the Square
Action –
Objectives- Clearly state broad goals and specific objectives for learning (e.g., concepts, procedures, skills, etc., you want students to learn).
 Students will understand why completing the square helps to solve quadratics equations and will be able to solve quadratics equations by
completing the square.
 Students will understand when it is appropriate to use the completing the square method.
Connections- Explain how objectives relate to Kentucky Learner Goals and standards for learning content established by professional organizations. (Do not simply list the
related goals, expectations, and or standards.)
MA-H-4.3.2 Students will understand how formulas, tables, graphs, and equations of functions relate to each other.
 M-H-A-8 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically, or symbolically non-linear equations such as
quadratic and exponential equations.
 MA-H-4.1.6 Students will recognize, give examples of, and apply the laws of exponents.
 Academic Expectations 1.5 - 1.9 Students use mathematical ideas and procedures to communicate, reason, and solve problems.
Core Content NSES=National Science Education Standards NCTM Standards NCSS Standards Nat’l Arts Standards
Context-Clearly describe how objectives and lesson relate to broad goals for teaching about the topic. Explain what has been done previously as it relates to this lesson.
Students will have been introduced to quadratic equations and have just completed a section on solving quadratic equations with perfect squares and
factoring. Students will learn how the a, b, and c of the quadratic equation relate and will gain a better understanding of solving before learning how
to use the quadratic formula.
Materials/Technology-List materials and technology which will be used during the lesson. Attach print material to be used with students.
 Classroom set of algebra tiles
 Overhead algebra tiles or
 Use a projector and use virtual algebra tiles from the website, http://nlvm.usu.edu/en/nav/frames_asid_189_g_4_t_2.html?open=activities
 Chart, sample below
Procedures-Describe strategies and activities to be used to involve students and accomplish objectives including how to trigger prior knowledge and adapt strategies to meet
individual student needs and the diversity in your classroom.
Warm Up
1. Solve for x
( x  3)2  4
2. Rewrite the quadratic equation in standard form.
8  x2  2x
3. Factor x  2 x  8
First explain to the students that a general equation for a quadratic is ax  bx  c  0 . In order to solve some quadratics we may need to rewrite ax  bx  c  ( x  d )
Have the students make a chart on their paper or supply them with the chart below.
( x  d )2
Have the students fill in the chart for each equation you give them. Ask them to begin to look for patterns between the b and d term and the c and d term.
Using algebra tiles have the students model the equation x  2 x  1 . Make sure the students fill in the chart for the first equation. Ask the students, using all the tiles,
rearrange the tiles in the shape of a square. Have the students give you the area of the square, i.e.
Use the following equations and continue the process above:
( x  1)2 .
x2  4x  4
x2  6x  9
x 2  8 x  16
Once the students discover that d 
and c  d begin going through the steps for completing the square for any quadratic equation.
 Steps for completing the square and an example to guide you through it.
1. Move the c term to the right side of the equal sign so it is alone.
x2  6 x  3  0
x2  6 x  3
2. Check the coefficient of a. If a is not one, then divide both sides by a.
2. a is one so we are
3. A. Take b and divide it by 2 (this gives you your d term)
B. Take that answer and square it (new c term)
 3
B.(-3) =9
C. Add this number (from B) to both sides of the equation
4. Rewrite the left side as the square of a binomial  x  d  . (We know d
from 3A
At this point, walk the students through solving for x.
Other examples to use,
x2  5x  3  0
2 x 2  17 x  15  0
x2  6 x  9  3  9
x 2  6 x  9  12
4.  x  3  12
Student Assessment- Clearly state how you will assess student progress including performance criteria. Attach written assessment measures used in relation to the lesson
Students will be assessed through homework assignments, quiz and test.
Impact - Reflection/Analysis of Teaching and LearningDiscuss student progress in relation to the stated objectives (i.e., what they learned with indicators of achievement). Discuss success of instruction as it relates to assessment of
student progress
Refinement - Lesson Extension/Follow-up -
Document created by Joy Lynn Cox Buckingham July, 1999