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Introduction
Students will have
previously learned how to multiply binomials (FOIL method). They
will also have learned how to square binomials (first squared plus last
squared plus two times first times last). At the completion of this exercise
students will recognize special trinomials and understand the rules for
factoring.
Algebra
I
Factoring a Perfect-Square Trinomials
Factoring a Difference of Two Squares
Grades 9 - 12
Standards
Addressed
California's
Mathematics Standards 8-12
ALGEBRA I
11.0 Students apply basic factoring
techniques to second- and simple third degree polynomials. These techniques
include finding a common factor for all terms in a polynomial, recognizing
the difference of two squares, and recognizing perfect squares of binomials.
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Instructional
Objectives
 Students
will factor the difference of two squares.
Students
will factor perfect-square trinomials.
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Student Activities
Students will begin lesson reviewing through
the use of warm-up activity and lecture They will then complete a worksheet
in class modeling the concepts of factoring perfect squares and differences
in squares. They will finish by
Introductory Activity
Students
will complete a warm-up review activity
utilizing FOIL and squaring binomials.
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Enabling Activity
Through class
lecture:
Students will recognize patterns in a perfect-square trinomial.
example: 4x²
+ 12x + 9 = (2x + 3)²
Is the first term a perfect square? 4x² = (2x)²
Is the last term a perfect square? 9 = 3²
Is the middle term equal to2 times first times last? 12x = 2 (4x²)(9)
Students will recognize the pattern in a binomial that is the
difference of two squares.
example: 9x²
- 16 = (3x + 4) (3x - 4)
Is the first term a perfect square? 9x² = (3x)²
Is the last term a perfect square? 16 = 4²
Are they connected by subtraction? 9x² "-" 16
Students
will complete a worksheet using the
concepts learned to factor a perfect-square trinomial and the difference of
two squares.
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Culminating Activity
Students
will complete problems from the textbook.
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Assessment
Students will complete a pre-activity assessment. After they have completed the lesson activities they will
complete a post-activity assessment.
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Results
Students completed the pre-assessment, the
lesson activities and a post assessment. Here you will find comparison
charts showing their progress.
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Web Resources
& Supplementary Materials
For
additional information on factoring perfect squares refer to the following
list of web sites.
View Power Point summary presentation
Galt High School
145 N. Lincoln Ave.
Galt, CA 95632
Debra Crane
Last Revised: 05/29/01
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