Download Factoring Quadratics Direct Instruction

FSD Lesson Plan Template
Factoring Quadratics
Lesson Title
Algebra
Grade Lev/Course
Algebra 11.0: Students apply basic factoring
Standard Addressed
techniques to second- and simple third-degree
polynomials.
Chapter 8: Factoring Polynomials
Textbook Chapter
To factor trinomials when a > 1.
Goal
Materials for Teacher Overhead, paper, asst colored markers, OH
handouts, OH markers.
Materials for Students White boards (optional), pencil/pen, lesson
handouts.
Students will discover how to factor trinomials
Description
by using the “X-Box” Method when a > 1.
Five-question individual or cooperative/group
Assessment
assessment at end of class.
Leads students into discovering patterns such
Reflection/Looking
as difference of two squares, perfect square
Ahead
trinomials, etc.
FACTORING QUADRATICS LESSON
PART 2
Lesson Overview: This lesson is designed to allow students to factor trinomials
using the “X-Box” Method when a > 1. It is assumed that the students know the
“X” Method from the Factoring Quadratics Lesson Part 1
Suggestions for Teaching:
1. Teacher goes through the example using direct instruction.
2. This would lead into some drill in having the students solve a series of
quadratics using this factoring technique. A worksheet or selection of
problems from text would be most useful at this time.
Looking Forward: This lesson leads students into discovering patterns for
factoring such as difference of two squares, perfect square trinomials, etc.
Factoring Quadratics
Using the “X-Box” Method when a > 1
Teacher leads students through the first example:
Step Directions
1 Students need to know the standard form of a
quadratic.
2 Find a, b, and c.
3 Fill in the top and bottom numbers in the table.
The top number is the product of a times c.
The bottom number is b.
6 • 2 = 12
b=7
4
Find the side numbers.
3 • 4 = 12
3+4=7
Work
2
ax  bx  c
a = 6, b = 7, c = 2
12
7
12
4
3
7
5
Draw a 2 X 2 box and plug in the first term
into the top left box and the last term into the
bottom right box.
6
Plug in the side numbers (3 and 4) into the two
remaining boxes with the variable of the
middle term. It does not matter which order
they go in.
7
Factor out the GCF for each row and column
on the left side of the box and the top of the
box. Double check your work by multiplying
the outside terms like a multiplication table.
8
Your answer is outside the boxes.
2
Teacher leads students through the second example: 3x  10x  8
Step Directions
1 Students need to know the standard form of a
quadratic.
2 Find a, b, and c.
3 Fill in the top and bottom numbers in the table.
The top number is the product of a times c.
The bottom number is b.
3 • 8 = 24
b = -10
4
Find the side numbers.
-6 • -4 = 24
-6 + -4 = -10
Work
2
ax  bx  c
a = 3, b = -10, c = 8
24
-10
24
-4
-6
-10
5
6
Draw a 2 X 2 box and plug in the first term
into the top left box and the last term into the
bottom right box.
Plug in the side numbers (-6 and –4) into the
two remaining boxes with the variable of the
middle term. It does not matter which order
they go in.
7
Factor out the GCF for each row and column
on the left side of the box and the top of the
box. Only factor out positive numbers from the
top left box. (Note to teacher: point out why
second terms both need to be negative.)
8
Your answer is outside the boxes.
3x
2
8
3x
6x
2
4x
8
3x  4 x  2 
Factoring Quadratics using the X-Box Method
Quadratic: ______________________________
a = ________
b = ________
c = ________
Factored form: ___________________________
Quadratic: ______________________________
a = ________
b = ________
c = ________
Factored form: ___________________________
Quadratic: ______________________________
a = ________
b = ________
c = ________
Factored Form: __________________________
End of Lesson Assessment
Factor using the “X-Box” Method.
2
1) 6x  x  2
2
2) 9x  9x  2
2
3) 2x  13x  20
2
4) 8x  10x  3
2
5) 4x  x  5