Algebra 2 Goal IV: To Use Polynomials, Polynomial Equations, and Polynomial Functions
Learning Outcomes
Differentiated Instructional Activities
4.1 Simplify expressions
involving powers by
using the properties of
exponents
Use the Developing Concepts Activity to introduce
Lesson 6.1. An alternative way to approach
Lesson 6.1 is to use the Application Lesson
Opener. Have students copy the properties of
exponents on a 3X5 index card. The names for the
properties of exponents are very similar. Mention
to students that in English, word order is often
important in determining meaning. Then talk
about how words in each name relate to the
property. Continue vocabulary file or algebra
glossary. Ask students where numbers with
exponents are used in real life. If students are
using graphing calculators, remind them to use
parentheses when they enter and evaluate the given
expressions. Be aware that many students have
difficulty understanding that a number with a
negative exponent does not necessarily represent a
negative number. Evaluate some expressions that
use positive bases and negative exponents to show
that the results are always positive. Ask students
which properties of exponents require them to
check that two or more bases are the same before
applying the property. Writing Activity: Have
students explain how the power of a power
property of exponents differs from the product of
powers property.
Chapter Reference 6.1
*
^
#
Text Book
References*
Developing
Concepts: p. 323
Chapter Resource Book
References
Warm-Up Exercises:
p. 11
Assessments#
Examples: 1-4,
pp. 324-325
Lesson Opener (Application):
p. 12
Guided Practice:
p. 326, #’s 1-15
Practice A, B, & C:
pp. 13-15
HQ: p. 42^
Practice:
pp. 326-328,
#’s 16-83
(See Assignment
Guide, p. 326)
Reteaching with Practice:
pp. 16-17
Quiz 1: p. 344, #’s 1-12, 27
RS: Quiz 1: p. 48, #’s 1-8^
WT: p. 40^ Prerequisite
Skills Review
WT: p. 41^
Checkpoint Exercises:
pp. 324-325
Real Life Application:
p. 19
Challenge: p. 20
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
Learning Outcomes
Differentiated Instructional Activities
Text Book
Chapter Resource Book
Assessments#
References*
References
0
4.2 Evaluate and graph a
polynomial function
Chapter Reference 6.2
4.3 Add, subtract, and
multiply
polynomials
An alternative way to approach Lesson 6.2 is to
use the Application Lesson Opener. Use the
Developing Concepts Activity that uses the
graphing calculator to investigate end behavior.
Have students copy the end behavior for
polynomial functions on a 3X5 index card.
Continue vocabulary file or algebra glossary. Try
the Using Technology Activity on setting a good
viewing window. Ask students which term of a
polynomial function is most important in
determining the end behavior of the function.
Have students give an example of a function that is
a polynomial function and an example of a
function that is not a polynomial function. Writing
Activity: Have students explain the meaning of
the following notation in terms of the size of the
values of x and f(x): For a particular function,
f(x)  +  as x - 
An alternative way to approach Lesson 6.3 is to
use the Activity Lesson Opener. Use the Graphing
Calculator Activity to explore operations
performed on polynomials. Ask students to
explain how to add or subtract polynomials.
Writing Activity: Have students explain how to
cube a binomial.
Chapter Reference 6.3
*
^
#
Developing
Concepts: p. 331
Examples: 1-5,
pp. 329-332
Warm-Up Exercises: p. 23
WT: p. 42^
Lesson Opener (Visual
Approach): p. 24
Checkpoint Exercises:
pp. 330-332
Practice A, B, & C: pp. 26-28
Guided Practice:
p. 333, #’s 1-14
Reteaching with Practice:
pp. 29-30
Practice:
pp. 333-336,
#’s 15-110
(See Assignment
Guide, p. 333)
Interdisciplinary Application:
p. 32
Using Technology:
p. 337
Examples: 1-8,
pp. 338-340
Guided Practice:
p. 341, #’s 1-12
Practice:
pp. 341-344,
#’s 13-88
(See Assignment
Guide, p. 341)
HQ: p. 43^
Quiz 1: p. 344, #’s 13-18
RS: Quiz 1: p. 48, #’s 9-10^
Challenge: p. 33
Graphing Calculator Activity:
p. 25
Warm-Up Exercises: p. 36
WT: p. 43^
Lesson Opener (Activity):
p. 37
Checkpoint Exercises:
pp. 339-340
Practice A, B, & C: pp. 40-42
Reteaching with Practice:
pp. 43-44
HQ: p. 44^
Quiz 1: p. 344, #’s 19-26
RS: Quiz 1: p. 48, #’s 11-14^
Real Life Application: p. 46
Challenge: p. 47
Graphing Calculator Activity:
pp. 38-39
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
Chapter Resource Book References
Differentiated Instructional Activities
Text Book
Assessments#
Learning Outcomes
References*
1
4.4 Factor polynomial
expressions and solve
polynomial equations:
Sum or difference of cubes
Grouping
Quadratic form
Polynomial equations
Chapter Reference 6.4
4.5 Divide polynomials
An alternative way to approach Lesson 6.4 is to
use the Application Lesson Opener. Use the
Developing Concepts Activity on the difference of
two cubes. Have students copy the special
factoring patterns on a 3X5 index card. Continue
vocabulary file or algebra glossary. Use an activity
that pairs students. One student evaluates a3– b3
and, the other student evaluates the factored form
of the expression for the same chosen values of a
and b. The results should be equal. Have students
give an example and show the complete
factorization of a binomial that can be factored
either as the difference of two squares or as the
difference of two cubes. Encourage students to be
on the lookout for polynomials that can be factored
by grouping in more than one way. Ask students
to explain how to use the zero product property to
solve polynomial equations of degree 3 or more.
An alternative way to approach Lesson 6.5 is to
use the Activity Lesson Opener. Use the
Developing Concepts Activity to investigate
polynomial division. Have students copy the
remainder and factor theorems on a 3X5 index
card. Continue vocabulary file or algebra
glossary. Ask students if f(x) is a polynomial that
has x – a as a factor, what do you know about the
value of f(a)? Have students give an example of a
polynomial division that can and cannot be
performed using synthetic division.
Chapter Reference 6.5
*
^
#
Developing
Concepts: p. 345
Examples: 1-5,
pp. 346-347
Guided Practice:
p. 348, #’s 1-17
Practice:
pp. 348-351,
#’s 18-104
(See Assignment
Guide, p. 348)
Developing
Concepts: p. 353
Warm-Up Exercises: p. 51
WT: p. 44^
Lesson Opener (Application): p. 52
Checkpoint Exercises:
pp. 346-347
Practice A, B, & C: pp. 53-55
Reteaching with Practice:
pp. 56-57
Cooperative Learning Activity:
p. 59
HQ: p. 45^
Quiz 2: p. 365, #’s 1-8
RS: Quiz 2: p. 87, #’s 1-4^
Interdisciplinary & Math and
History Applications: pp. 60-61
Challenge: p. 62
Warm-Up Exercises: p. 65
WT: p. 45^
Lesson Opener (Activity): p. 66
Checkpoint Exercises:
pp. 353-355
Examples: 1-5,
pp. 352-355
Practice A, B, & C: pp. 67-69
Guided Practice:
p. 356, #’s 1-14
Reteaching with Practice:
pp. 70-71
Practice:
pp. 356-358,
#’s 15-83
(See Assignment
Guide, p. 356)
Real Life Application: p. 73
HQ: p. 46^
Quiz 2: p. 365, #’s 9-14
RS: Quiz 2: p. 87, #’s 5-7^
Challenge: p. 74
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
2