Advanced Algebra Goal II: To Use Radicals and Rational Exponents, Expressions, and Equations
Learning Outcomes
Differentiated Instructional Activities
5.1 Evaluate nth roots of
real numbers using
radical notation and
rational exponent
notation
An alternative way to approach Lesson 7.1 is to
use the Application Lesson Opener. Have students
copy the rules for real nth roots and rational
exponents on a 3X5 index card. Continue
vocabulary file or algebra glossary. Remind
students that the denominator of the rational
exponent is the index and that a negative power
represents a reciprocal.
Ask students to describe how to solve
m = 2.175x 3 for x when m = 7.4. Writing
Activity: Have students explain why x4 = 16 has
two real solutions while x3 =8 has only one real
solution.
Chapter Resource Book
References
Warm-Up Exercises:
p. 11
Assessments#
Guided Practice:
p. 404, #’s 1-12
Lesson Opener (Application):
p. 12
Practice:
pp. 404-406,
#’s 13-89
(See Assignment
Guide, p. 404)
Practice A, B, & C:
pp. 13-15
HQ: p. 52^
Reteaching with Practice:
pp. 16-17
Quiz 1: p. 414, #’s 1-8, 21
RS: Quiz 1: p. 33, #’s 1-6^
WT: p. 50^ Prerequisite
Skills Review
WT: p. 51^
Checkpoint Exercises:
pp. 402-403
Interdisciplinary Application:
p. 19
Challenge: p. 20
Chapter Reference 7.1
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Text Book
References*
Examples: 1-6,
pp. 401-403
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.
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Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book References
Assessments#
5.2 Evaluate and simplify
expressions using properties
of rational exponents
An alternative way to approach Lesson 7.2
is to use the Activity Lesson Opener. Have
students copy the properties of rational
exponents on a 3X5 index card. Continue
vocabulary file or algebra glossary. Ask
students if they can find the quotient of two
radicals with different indices? Have
students find the ratio of the volume of a
ball packed tightly inside a cube to the
volume of the cube.
Examples: 1-9,
pp. 407-410
Warm-Up Exercises: p. 23
WT: p. 52^
Lesson Opener (Activity): p. 24
Checkpoint Exercises:
pp. 408-410
An alternative way to approach Lesson 7.6
is to use the Graphing Calculator Lesson
Opener. Draw English learners’ attention to
the use of italics. Point out that in English,
italic letters often signal that the text is
important. Mention that in algebra,
variables are also written italics. Continue
vocabulary file or algebra glossary. Use the
cooperative learning activity and /or
graphing calculator activity.
Examples: 1-6,
pp. 437-440
Guided Practice:
p. 411, #’s 1-21
Practice:
pp. 411-414,
#’s 22-113
(See Assignment
Guide, p. 411)
Chapter Reference 7.2
5.3 Solve radical equations:
Simple radicals
Rational exponents
Equations with one and two
radicals
Guided Practice:
p. 441, #’s 1-16
Practice:
pp. 441-444,
#’s 17-90
(See Assignment
Guide, p. 441)
Practice A, B, & C: pp. 25-27
Reteaching with Practice: pp. 28-29
HQ: p. 53^
Real Life Application: p. 31
Quiz 1: p. 414, #’s 9-20, 22
RS: Quiz 1: p. 33, #’s 7-15^
Challenge: p. 32
Warm-Up Exercises: p. 78
WT: p. 56^
Lesson Opener (Graphing
Calculator): p. 79
Checkpoint Exercises:
pp. 438-439
Practice A, B, & C: pp. 82-84
Reteaching with Practice: pp. 85-86
HQ: p. 57^
Quiz 3: p. 452, #’s 4-6, 10
Cooperative Learning Activity:
p. 88
Real Life & Math and History
Applications: pp. 89-90
Challenge: p. 91
Graphing Calculator Activity:
pp. 80-81
Chapter Reference 7.6
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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.
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Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book References
Assessments#
5.4 Simplify and perform
operations with rational
expressions
An alternative way to approach Lesson 9.4
is to use the Activity Lesson Opener. Have
students copy the simplifying rational
expressions property on a 3X5 index card.
Continue vocabulary file or algebra
glossary. Ask students to explain the
procedure for multiplying and dividing
rational expressions involving polynomials.
Have students do the Using Technology
Activity that uses a graphing calculator to
verify the results of these operations
numerically and graphically.
Examples: 1-8,
pp. 554-557
Warm-Up Exercises: p. 52
WT: p. 71^
Lesson Opener (Activity): p. 53
Checkpoint Exercises:
pp. 555-557
Chapter Reference 9.4
An alternative way to approach Lesson 9.5
is to use the Visual Approach Lesson
Opener. Continue vocabulary file or
algebra glossary. Use the cooperative
learning activity and /or graphing calculator
activity. Writing Activity: Have students
describe how adding rational expressions is
like adding numerical fractions.
Guided Practice:
p. 558, #’s 1-15
Practice:
pp. 558-560,
#’s 16-73
(See Assignment
Guide, p. 558)
Practice A, B, & C: pp. 55-57
Reteaching with Practice: pp. 58-59
HQ: p. 72^
Interdisciplinary Application: p. 61
Quiz 2: p. 574, #’s 1-2
RS: Quiz 2: p. 91, #’s 1-2^
Challenge: p. 62
Graphing Calculator Activity: p. 54
Using Technology:
p.561
Examples: 1-6,
pp. 562-564
Guided Practice:
p. 565, #’s 1-11
Practice:
pp. 565-567,
#’s 12-71
(See Assignment
Guide, p. 565)
Warm-Up Exercises: p. 65
WT: p. 72^
Lesson Opener (Visual Approach):
p. 66
Checkpoint Exercises:
pp. 563-564
Practice A, B, & C: pp. 69-71
Reteaching with Practice: pp. 72-73
Cooperative Learning Activity:
p. 75
HQ: p. 73^
Quiz 2: p. 574, #’s 3-8
RS: Quiz 2: p. 91, #’s 3-8^
Real Life Application: p. 76
Challenge: p. 77
Chapter Reference 9.5
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Graphing Calculator Activity:
pp. 67-68
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.
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Learning Outcomes
Differentiated Instructional Activities
5.5 Solve rational equations:
An alternative way to approach Lesson 9.6
is to use the Graphing Calculator Lesson
Opener. Continue vocabulary file or
algebra glossary. Ask students to explain
when it is appropriate to use crossmultiplying to solve a rational equation, and
have them give an example. Have students
give an example of a rational equation that
has exactly one extraneous solution.
One solution
Extraneous solution
Two solutions
Text Book
References*
Examples: 1-6,
pp. 568-570
Chapter Resource Book
References
Warm-Up Exercises:
p. 80
Guided Practice:
p. 571, #’s 1-14
Lesson Opener (Graphing
Calculator): p. 81
Practice:
pp. 571-573,
#’s 15-77
(See Assignment
Guide, p. 571)
Practice A, B, & C:
pp. 82-84
Assessments#
WT: p. 73^
Checkpoint Exercises:
pp. 569-570
HQ: p. 75^
Quiz 2: p. 574, #9
RS: Quiz 2: p. 91, #’s 9-10^
Reteaching with Practice:
pp. 85-86
Interdisciplinary, & Math and
History Applications: pp. 88-89
Challenge: p. 90
Chapter Reference 9.6
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#
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.
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