Advanced Algebra Days 15-27

59

STRUCTURED CURRICULUM LESSON PLAN

Day: 015 Subject: Advanced Algebra Grade Level: High School

Correlations (SG,CAS,CFS): 6A1

TAP:Perform arithmetic operations involving

integers, fractions, decimals and percents,explicitly stated or within context

Choose and apply appropriate operationalprocedures and problem-solving strategies toreal-world situations

Understand number systemsUse variables, number sentences, and equations

to represent solutions and solve problems

ISAT:Solve problems requiring computations with

whole numbers, fractions, decimals, ratios,percents, and proportions

Use mathematical skills to estimate,approximate, and predict outcomes, and tojudge reasonableness of results

Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs

Unit Focus/Foci

Properties and Operations of Real Numbers and Functions

Instructional Focus/Foci

Comparing and Identifying Number Systems

Materials

Grid paper

Educational Strategies/Instructional Procedures

Opener: Have students complete the following in five minutes or less:

a b c= = =1

24 0 04.

Compute:

1. abc 2. a+b+c 3. a b c

4. 1

ab5.

a b

c

+6. ab + c

60

Real Numbers Venn Diagram

Remind students that they will always encounter numbers of different types, such as:

Natural Numbers (N) = {1, 2, 3, 4, } counting numbers Whole Numbers (W) ={0, 1, 2, 3, 4, } numbers used to answer how many

Rational Numbers (Q) = any number that can be written as a

b (a quotient) where a and b are

integers; b 0

Integers (I) = {, -4, -3, -2, -1, 0, 1, 2, 3, 4, }positive and negative whole numbers.

Irrational Numbers = any number that cannot be written asa

b where a and b are integers; b 0 .

Real Numbers (R) = combination of all rational and irrational numbers

Have the students place each number in the proper place in a Venn diagram:

0, -4, 3, 5, 12, 3 , 14

6,

100

4, 0.3.

Real Numbers

Rational Irrational

Natural

Whole

Integers

61

Solution:

3 -4

0.3

Have the students work in groups of four to complete the following explorations of addition andmultiplication of rational numbers.

Exploration 1:

Let a = -3 b = -1

2 c = 5 d = -

3

4 e =

2

3 f = 1

Substitute the given values for the variables.

Which statements are true?

1

2

3

4

5

6

7

8

9

10

.

.

. ( ) ( )

. ( ) ( )

. ( )

. ( )

.

. ( )

. ( )

. ( )

a c c a

b d d b

d a f d a f

b c e b c e

c f a c f a

e d d e

f c f c

b e f b e f

b e b e

d c d c

+ = +

=

=

+ + = + +

= +

+ =

+ = +

+ = +

= +

+ = +

160

4 3

5

0

12

62

Solutions to Exploration 1:

1 3 5 5 3 2 2

2 12

34

34

12

14

14

3 3 14

1 14

456789

. ; ; ;

. ; ; ;

. ( ) ( ) ; ;

. ( ) ) ;. ( ) ;....

a c c a

b d d b

d a f d a f

b c e b c ec f a c f a

+ = + + = + =

= = =

= =

+ = = + + = +

True

False

False

TrueTrue

TrueTrueFalseTrue

10. False

Exploration 2

Use the values for the variables used in Exploration 1.

Which statements are true?

1. a c c a =

2. b d d b =

3. d

a e =

d a

e

4. 1

b e =

e

b

5. 1 1 1

f e f c =

6. c d

bc d b

= ( )

7. d

c

c

d

=

1

8. e dd

e

=

1

9. b c e b c e = ( ) ( )

10. d

f ad f a

=

63

Exploration 3:

Repeat the process of Explorations 1and 2 for the following equations:

11 1 1

2

3

4

5

6

7

8

.

. ( )

. ( )

. ( )

. ( )

. ( )

. ( )( )

. ( )( )

d c d ca e f ae af

a e a e

b c d bd cd

e b a eb ea

f d e fd fe

d a e b de db ae ab

f b a c fa ba fc bc

+= +

+ = +

=

=

=

+ =

+ = +

= +

Solutions to Explorations 2 3:

Exploration 2:

1. True2. False3. False4. True5. False6. True7. False8. True9. True10. False

Exploration 3:

1. False2. True3. False4. True5. False6. True7. True8. False

Have each group review the properties of real numbers: closure, associative, commutative,identity, inverse, and distributive.

Randomly select a member from each group to explain a property and give examples.

64

Integration with Core Subject(s)

LA: Understand meaning of key words and phrases in text

Connections

Enrichment: Have students write a paragraph describing each property. The paragraph shoulddiscuss the propertys name and applications.

Fine Arts:

Home: Have students keep a record of all assignments. (The homework record will be signedby a parent on a weekly basis.)

Remediation: Provide each student with a piece of grid paper. Have the students create a largegrid of 12 squares (4 squares by 3 squares), and randomly write one of the properties oneach square. One square will be a free square. Write an example of each of the propertiesmentioned above [such as 3(x + 2) = 3x + 6]. Have students cross out the corresponding square.The first student to cross out a row or column is the winner.

Technology:

AssessmentTeacher observation

Homework

Assign appropriate problems from your text.

65

Teacher Notes

Solutions to Opener:

1. abc

(1

2)(-4)(0.04) = -0.08

2. a + b + c1

2 + -4 + 0.04 = -3.46

3.a b c

(1

2) (-4) 0.04 = 4.46

4.1

ab1

1

24

1

2( )( )=

5.a b

c

+

1

24

0 04

35

0 0487 5

+ =

=

.

.

..

6.ab + c

1

2( 4) .04 2 .04 1.96 + = + =

66













Unit Focus/Foci



Performing Operations and Evaluating Expressions Using the Laws of Exponents

Materials

Copies of Exploring Exponents Worksheet


Review the homework and answer students questions. Introduce the students to exponents.Define exponent as the number of times the base is used as a factor. Stress the fact that the basecan be a variable or a constant.

Exponent Exponent Exponent

1. bm 2. 52 3. (4ab)4

Base Base Base

67

Remind students that power and exponent have the same connotation.

Guide the students to discover the basic rules involving exponents.1

2

31

4

2 3 5

4 5

2 2 2 4

3 4

5

32

6

4

4

44 4 0

. ( ) ( )

. .

. ( ) ( ) ( ) ( )

( ) . ( ) .

.

. .

.

a a a a a a a a

a a a a

a a a a a a a

a a

a

a

a a a a a

a a a

a aa

a

a

a

a

a

aa a

m n

m n

m

n

= =

= = =

=

=

=

= =

Have students try Ask the class to make a conjecture about

Have the students try Ask the class to make a conjecture about

Have students try Ask the class to make a conjecture about

and using the property of one we know that ; therefore,a

aa

4

401 1= = .

The remaining two rules are definitions.

11 1

21

.

. ( )

aa a

a

a a a

nn n

n

m

n m n mn

= =

= =

or

Have students complete the Exploring Exponents worksheet.



Connection(s)

Enrichment: Use the library or Internet to find real-world applications of exponents. Gatherpictures, diagrams or articles and make a report for class.

Fine Arts:

Home: Have parents sign homework and record weekly.

68

Remediation: Have students simplify an expression that uses the rules of exponents,writing out each step. In addition to simplifying, have students explain which rule was applied ineach step.

Technology: See Enrichment.Assessment

Evaluate Exploring Exponents.

Homework


Teacher Notes

Solutions to Exploring Exponents worksheet:

1.X X X 2 X

1

22 4 1

42

3 9 1

93

4 16 1

164 = 2

5 25 125

5

6 36 1

366

7 49 1

497

8. 64 164

8 2 2=

9 81 1

819 = 3

10 100 1100 10

2. (3a)= 1

3

1

3

1

92 2 2 4 4( )a a a= =

3. ( )( )6 612

2 =6 5 =88.2

4. ( ) ( )x

xx x

5

233 3 9

= = 5. 15

3

153

2 4

5 6

2

5

4

63 105a b

a b

a

a

b

ba b

= =

69

6. ( ).2 547 2 0 1x =7. [ ] [ ]( )( )4 4 1

2162 6 8

1

2 8 416 4k k k k k= = =

8. 7 9 7 81 5672 2 2 8 104k k k k k( ) = = 9. ( )m m =3 3 9

10. (5 )( )a b ab

a b

2 3 4

7 36

3 = 30

3

101 7

7 3

4

6

a b

a b

b

a

=

70

Exploring Exponents

1. Complete the following table.

X X X 2X

1

2

2 4 14 2

3 94 25 1

25

6 367 78 1

64

9 8110 1

100

Simplify:

2. (3a) 2 3. ( )( )6 6122 4. ( )x

x

5

2

3

5. 1532 4

5 6a ba b

6. (2.574x) 7. [( )( )]4 42 61

2k k

8. 7k(9k 4 ) 9. (m 3 ) 3 10. ( )( )5 63

2 3 4

7 3a b ab

a b

71


Day: 017 018 Subject: Advanced Algebra Grade Level: High School









Unit Focus/Foci



Identifying and Comparing Relations and Functions

Materials

Graph paperClassroom set of graphing calculatorsOverhead graphing calculatorOverhead projectorCopies of Function or Relation activities


Review homework and answer students questions.

Define and discuss domain, range, relation, and function.

Relation: any set of ordered pairs Domain: the set of possible values for the first coordinates of a relation Range: the set of possible values for the second coordinates in a relation

72

Function: a set of ordered pairs such that for each first coordinate, there is exactly one corresponding second coordinate

Have students note that a function is always a relation, but a relation is not always a function.

Present and discuss the vertical line test. Emphasize that if any vertical line passes through thegraph more than once, the graph is not a function.

Draw the following on the chalkboard and discuss with the students which relation is a function.Explain why each relation is or is not a function.

a. b.

Solutions: Solutions:Does not pass the verticle line test. Passes the verticle line test (a function)(not a function)

Have the students work in-groups of four to complete the Function or Relation activities.



Connection(s)

Enrichment: Create pictures of functions and relations and exchange them with your classmatesto see if they can determine which are functions and which are relations.

Fine Arts:


Remediation: Work with students individually on their areas of deficiency.

Technology:

Assessment

Evaluate Function or Relation activities using the Structured Curriculum Scoring Rubric.

73

Homework


Teacher Notes

Solutions to Function or Relation Activity 1:

1. Function - 1-1 Correspondence 2. Not a function not a 1-1 Correspondence3. Not a function not a 1-1 Correspondence 4. Not a function - not a 1-1 correspondence5. Function - -1-1 Correspondence 6. Not a function - not a 1-1 Correspondence

7. Function - Passes the vertical line test 8. Not a function Does not pass the vertical line test

Solutions to Function or Relation Activity 2:

1. Domain - (0,3,5)Range - (-2,-1,0)

Not a function not a 1-1 correspondence

2. Domain ( -7, -2, 0 )Range - (1, 3, 4, 7)

Not a function Not a 1-1 correspondence3. Domain (2, 9)

Range (-5, -4, 4, 5)Not a function not a 1-1 correspondence

4. {x | x -2}

5. {x | x > 0} 6. {x | 0 x 3}7. {x | -4 x 5}

8. a. See student workb. Domain {x |x R} Range {y| -1}c. Function

9. a. See student workb. Domain {x|x R} Range {y|y -1}c. Function

10. a. See student workb. Domain {x |x > 0} Range {y|y 0}c. Function

75

Function or Relation Activity 2

Determine whether each relation is a function. Identify the domain and range.

1. {(5, 0),(3, -1), (0,0), (5, -1),(3, -2)}

2. {(-7,3), (-2,1), (-2,4), (0,7) }

3. {(9,-5), (9,5), (2,4), (2,-4)

Find the domain of the following functions.

4. f(x) = 1

2x +5. g(x) = x

6.

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5

7.

5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5

(0,3)

(3,0)

(5,5)

(-4,-4)

76

Use a graphing calculator to graph each relation.

a) sketch the graphb) find the domain and the rangec) determine whether the relation is a function

8. y x x= +2 34 3 9. yx

=

1

52

10. yx

=

12

77



Correlations (SG,CAS,CFS): 6A1; 8B1; 8D2




Use variables, number sentences, and equationsto represent solutions and solve problems

Analyze and interpret data presented in charts,graphs, tables, and other displays





Unit Focus

Exploring Properties of Real Numbers

Instructional Focus

Mid-Unit Assessment

Materials

Copies of the Mid-Unit Assessment


Review homework from the previous day and answer students questions.

Administer the Mid-Unit Assessment.


LA: Understand explicit, factual informationSC: Apply scientific method to solve problems

78

Connections

Enrichment:

Fine Arts:



Technology:

Assessment

Evaluate the Mid-Unit Assessment using the Structured Curriculum Scoring Rubric.

Homework

Have students review class notes.

Teacher Notes

Solutions to the Unit Two Mid-Unit Assessment:

1. x 3 2. 2x +4

3. 4 3

2

x

x

+4.

5

12

2x

5. 3 27

8 3x

x

6. 1

27. a. Domain {x|-6

79

Unit Two Mid-Unit Assessment

Simplify.

1. ((x))1

2 2. 2 4

2 320

x

x x

+

+c h

3. 3 4

2x x+ 4.

5

3 4

xy

z

xz

y

5. 3 27

24 2

x

xx

6. x x+

+2

3

2 1

6

For each graphed relation:a. Find the domain and rangeb. Determine whether the relation is a function

7. 10 8 6 4 2

-10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10

8. 10 8 6 4 2

-10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10

80


Day: 020-021 Subject: Advanced Algebra Grade Level: High School


TAP:Perform arithmetic operations involving integers, fractions, decimals and percents, explicitly stated or within contextChoose and apply appropriate operational procedures and problem-solving strategies to real -world situations

ISAT:Solve problems requiring computations with whole numbers, fractions, decimals, ratios, percents, and proportionsIdentify, analyze, and solve problems using equations, inequalities, functions, and their graphs

Unit Focus/Foci



Using the Slope Formula to Write and Identify Increasing and Decreasing Linear Functions

Materials

Graph paperClassroom set of graphing calculatorsOverhead graphing calculatorOverhead projector


Review previous days homework and answer students questions.

Return and review the Mid-Unit Assessment.

Remind students that f(x) = a and y = a have the same meaning. Traditionally, y = mx + bdescribes a linear equation. Ask the students: What does f(x) = mx + b describe? (A linearformation function) Ask the students to write the formula for the slope of a linear function.

Solution: mf x f x

x xf x y f x y=

= =2 1

2 12 2 1 1

b g b g b g b gwhere and .

The slope of a line describes how quickly a line is rising or falling as we look from left to right.Illustrate increasing and decreasing linear functions.

81

Increasing function Positive slope

Decreasing function Negative slope

Neither

Zero

A horizontal line is not rising or falling at all, so its slope = 0.

Undefined slope

A vertical line rises so quickly that we cant describe it, so its slope is undefined or infinite.

Have students find the slope and determine whether the graph is an increasing or decreasingfunction.

1 3 2 8

2 4 3

3 3 0

4 5 5 5

.

.

.

.

x y

x y

x y

x y

+ =

=

+ =

+ =

Review the solutions with the class.

82

Solutions:

1. Slope = - 3

2 decreasing function

2. Slope = -4 decreasing function




LA: Understand explicit, factual informationUnderstand the meaning of words in context

Connection(s)

Enrichment: Find the value of x:

Solutions: 6(x + 6) = 8(12) 6x + 36 =9 6 6x = 60

x = 10

Fine Arts:



Technology: Have students use a graphing calculator to graph a series of linear equations anddetermine the relation between the value for m and the direction of the slant.

Assessment

Teacher observation

Homework


6x

8

4

83

Teacher Notes

Create a transparency to illustrate increasing and decreasing functions.This is a two-day lesson. The second day (Day 021) should be used to review homework,remediation exercises, or for extra practice as necessary.

84



Correlations (SG,CAS,CFS): 6A; 8A1; 8C1




Understand number systems




Unit Focus/Foci



Identifying and Using Properties of Functions

Materials



Explain to students that functions can be combined to create new functions by the operations ofaddition, subtraction, multiplication, and division.

Demonstrate by using the following example: f(x) = x + 3 g(x) = x2 + 1

ADDITION f(x) + g(x) = x + 3 + x2 + 1 = x2 + x + 4

SUBTRACTION f(x) g(x) = x + 3 (x2 + 1) = - x2 + x + 2

85

MULTIPLICATIONf(x) g(x) = (x + 3)(x2 + 1) = x3 + 3x2 + x + 3

DIVISIONf xg x

xx

( )( )

=+

+

312

Have the students note that:

f(x) + g(x) = (f + g) (x)f(x) - g(x) = (f - g) (x)f(x) g(x) = (f g) (x)

f x

g x

f

gx g x

( )

( ),=

FHGIKJ b g b g 0

Assign the following to be completed in class.

Find the sum, difference, product, and quotient for each. State the domain of the quotient.

1. f(x) = x + 1 g(x) = x - 1

2. f(x) = 2x g(x) = 12x

3. f(x) = x g(x) = x2 - 14. f(x) = x2 g(x) 5



Connection(s)

Enrichment: Have students create additional problems using the sum, difference, product, andquotient properties of functions.

Fine Arts:


Remediation: Review function notation and have students explain examples of evaluatingfunctions.

86

Technology:

Assessment

Evaluate the in-class assignment using the Structured Curriculum Scoring Rubric.

Homework


Teacher Notes

Solutions to in-class assignments:

Sum Difference Product Quotient

1. 2x 2 x-1 x

xx

+

1

11;

2. 2 13

2

x

x

+ 2 13

2

x

x

2

x2 3x ; all real numbers

3.

x x2 1+ x x +3 1 x x x2 x

xx

2 11

; ,

4. x+5 x-5 5x x 2

5; all real numbers

87



Correlations (SG,CAS,CFS): 8C1




Understand number systems




Unit Focus/Foci



Performing Addition, Subtraction, Multiplication and Division of Functions

Materials

Classroom set of graphing calculatorsOverhead graphing calculatorCopies of Exploring Functions activityOverhead projector



Have students work in pairs to complete Exploring Functions activity.



88

Connections

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Evaluate Exploring Functions activity using the Structured Curriculum Scoring Rubric.

Homework

Have students study for end-of-unit assessment and write any problems or questions they mayhave.

Teacher Notes

Soluions to Exploring Functions:

1.

2. y1 is a parabola y2 is a line

3. See studentssolutions f(x) + g(x) = x2 + 2x 5

4. See students solutionsf(x)g(x) = 2x3 4x2-2x + 4

5. See students solutions f(x) g(x) = -x2 + 2x - 3

89

Exploring Functions

Use a graphing calculator to complete the following using: f x xb g = 2 4 1)( 2 = xxg

1. Graph f(x) as y1 and g(x) as y2.

2. Describe the graphs of y1 and y2.

3. a) Make a conjecture about the graph of y1+ y2 [ f(x) + g(x)] and draw a sketch.b) Graph y1+ y2 and compare the graph to your sketch.

4. a) Make a conjecture about the graph of y y1 2 [ f x g x( ) ( ) ] and draw a sketch.b) Graph y y1 2 and compare the graph to your sketch.

5. Without graphing, sketch y y1 2 .

90



Correlations (SG,CAS,CFS): 8D2






Demonstrate understanding of measurementconcepts and apply measurement skills




Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons

Demonstrate an understanding of measurementconcepts and skills

Unit Focus/Foci

Exploring Properties and Operations of Real Numbers and Functions


Investigating Bouncing Balls

Materials

Transparencies (blank)Overhead projectorGraph paperGraphing calculatorMeter sticksBouncing balls (tennis balls, racquetballs, etc.)Bouncing ball activity sheetChart paperMarkers

91



Have the students complete the Bouncing Ball Activity.


LA: Apply information presented in the text to a new or different situationSC: Analyze and interpret data

Connections

Enrichment: Have the students sketch a graph for relationship a and b. If one variable isdependent on the other, place it on the vertical axis.

a) Your height above the ground as you ride a Ferris wheel.b) The temperature of a cup of hot chocolate sitting on your desk.

Fine Arts:



Technology:

Assessment

Teacher observation

Homework

Assign appropriate review problems from your text.

Teacher Notes

92

Bouncing Ball Activity

1. Have each member of the group assume one of the following roles:

Bouncer: drops the ball from the designated heights

Measurer: reads the initial height and rebound height

Recorder: records the data into the chart

Verifier: double-checks the measurements

2. Rotate the roles.

3. Each bouncer should complete three trials.

4. Create a scatter plot using the highest and lowest rebounds on a transparency.

5. Use the scatter plot to find the line of best fit and sketch it on the transparency.

6. Compare and discuss the results as a class, using the transparencies.

Height 1 2 3 4 5 6 7 8 9 10 11 12 Highest Lowest Rebound Rebound 100 cm 150 cm 200 cm 250 cm

93



Correlations (SG,CAS,CFS): 8A1; 8B1; 8C1; 8D2








Use mathematical skills to estimate,approximate, and predict outcomes and tojudge reasonableness of results


Unit Focus/Foci



Reviewing Properties and Operation of Real Numbers and Functions

Materials


Review Unit Two using a review format from the Appendix C.


LA: Apply information presented in the text to a new or different situationSC: Analyze and interpret data

94

Connections

Enrichment: Have the students create a story that could be represented by the graph below.

Fine Arts: See Enrichment.

Home: Students will keep a record of all assignments. The homework record will be signed by aparent on a weekly basis.

Remediation:

Technology:

Assessment

Teacher observation

Homework

Direct students to study for the Unit Two Assessment.

Teacher Notes

95



Correlations (SG,CAS,CFS): 8A1; 8B1; 8C1; 8D2









Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons

Unit Focus/Foci



Assessing Property and Operations of Real Numbers and Functions

Materials

Copies of Unit Two Assessment


Have students complete the Unit Two Assessment.


LA: Draw conclusions, inferring meanings from textSC: Analyze and interpret dataSS: Read and interpret maps, charts, graphs and cartoons

96

Connections

Enrichment:

Fine Arts:

Home: Students will keep a record of all assignments. The homework record will be signed bya parent on a weekly basis.

Remediation:

Technology:

Assessment

Evaluate the Unit Two Assessment using the Structured Curriculum Scoring Rubric.

Homework

Have students select two samples of their work from Unit Two for their portfolios and explainwhy each was selected.

Teacher Notes

Solutions to the Unit Two Assessment:

1. See students work2. See students work

3. a. b. y = 1

2

1

2x +

c. The function is increasing.4. a. Function b. Function5. x xm r is a real number6. x x

RSTUVW

1

2

7. f x g x x x x x( ) ( )+ = + + + = + +3 1 4 3 3 4 42 2

8. f(x) g(x) 3x2 1 4x 3

3x2 1 4x 3

3x2 4x 2

= + +

= +

=

b g

97

9. f x g x x x x x x( ) ( ) = + + = + + +b gb g3 1 4 3 12 9 4 32 3 2

10. f x

g x

x

x

b gb ge j

=

+

+

3 1

4 3

2

11. x y

y x

x y

y x

x

y

= =

3 2 4

6 4 2

12 8

12 8

4

20

c hc h

12. FHGIKJ =

=

=

3 3

3 27

3 3

3 3

3 3

3

3 3

xy x y

x y x y

13.5a3b

8a2b22ab3

15ab 1

5a

8b

2b4

15

10ab3

120

FHGG

IKJJ FHGG

IKJJ=

FHGIKJFHGGIKJJ=

14.4x2y

xy2

1

xy2

4x2y

y

4x

FHGGIKJJ

=

=

15. x y xy3 91

3 3c h =

98

Unit Two Assessment

1. Sketch the graph of a relation that is a function.

2. Sketch the graph of a relation that is a function.

3. Determine the linear function determined by the points (3, 2) and (5, 3).

A. Sketch the graph B. Give the equation C. Is the function increasing or decreasing?

4. State whether the set of ordered pairs represents a function.

a. 2 3 2 3 4 7 51, , , , , , ,b g b g b g b g qm b. 1 3 2 5 4 0 31, , , , , , ,b g b g b g b g qm

99

For problems 5 - 6, let (x) = 4x 2 -1 and g(x) = 22 1

x

x +

5. What is the domain of ? 6. What is the domain of g?

For problems 7 10, let (x) = 3 x2 1+ and g(x) = 4x + 3.

7. Find (x) + g(x). 8. Find (x) g(x).

9. Find (x) g(x). 10. Find f xg x

( )

( ).

Simplify.

Use only positive exponents in your solution.

11. x g

g x

3 2 4

6 4 2

c hc h

12. FHGIKJ

33

xy

13. 5

8

2

15

3

2 2

3

1

a b

a b

ab

ab

FHGIKJFHG

IKJ 14.

4 2

2

1x y

xy

FHGIKJ

15. x y3 91

3c h

100



Correlations (SG,CAS,CFS): 6A1; 8C1









Identify, analyze, and solve problems usingequations

Unit Focus/Foci

Exploring Properties of Real Numbers


Assessing Properties of Real Numbers

Materials

Unit Two Assessment (student copies)


Return the Unit Two Assessment and review the solutions with the students.

Have the students write an essay reflecting on their performance in Unit Two. Invite the studentsto use the following questions as guidelines for writing their essays:

1. Did I do my best?2. What gave me the most difficulty?3. Where do I need the most help?4. What methods or recourse did I use to improve myself?5. What would I do differently next time?

101

Remind students that an essay has a minimum of three paragraphs: introduction, body, andconclusion.


LA: Understand the meaning of key words and phrases in textSC: Analyze and interpret data

Connection(s)

Enrichment:

Fine Arts:

Home:

Remediation:

Technology:

Assessment

Homework

Have students select three samples of their work to place in their portfolio; have students write anexplanation as to why each piece was selected.

Teacher Notes

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Advanced Algebra Days 15-27

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