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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
STRUCTURED CURRICULUM LESSON PLAN
Day: 016 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
Performing Operations and Evaluating Expressions Using the Laws of Exponents
Materials
Copies of Exploring Exponents Worksheet
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
LA: Understand meaning of key words and phrases in text
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
Assign appropriate problems from your text.
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 017 018 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
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
Identifying and Comparing Relations and Functions
Materials
Graph paperClassroom set of graphing calculatorsOverhead graphing calculatorOverhead projectorCopies of Function or Relation activities
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
LA: Understand meaning of key words and phrases in text
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:
Home: Have parents sign homework and record weekly.
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
Assign appropriate problems from your text.
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
74
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 019 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 6A1; 8B1; 8D2
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
Use variables, number sentences, and equationsto represent solutions and solve problems
Analyze and interpret data presented in charts,graphs, tables, and other displays
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
Exploring Properties of Real Numbers
Instructional Focus
Mid-Unit Assessment
Materials
Copies of the Mid-Unit Assessment
Educational Strategies/Instructional Procedures
Review homework from the previous day and answer students questions.
Administer the Mid-Unit Assessment.
Integration with Core Subject(s)
LA: Understand explicit, factual informationSC: Apply scientific method to solve problems
78
Connections
Enrichment:
Fine Arts:
Home: Have parents sign homework and record weekly.
Remediation: Work with students individually on their areas of deficiency.
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 020-021 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 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
Properties and Operations of Real Numbers and Functions
Instructional 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
Educational Strategies/Instructional Procedures
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
3. Slope = -3 decreasing function
4. Slope = -1 decreasing function
Integration with Core Subject(s)
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:
Home: Have parents sign homework and record weekly.
Remediation: Work with students individually on their areas of deficiency.
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
Assign appropriate problems from your text.
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 022 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 6A; 8A1; 8C1
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 systems
ISAT:Solve problems requiring computations with
whole numbers, fractions, decimals, ratios,percents, and proportions
Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs
Unit Focus/Foci
Properties and Operations of Real Numbers and Functions
Instructional Focus/Foci
Identifying and Using Properties of Functions
Materials
Educational Strategies/Instructional Procedures
Review previous days homework and answer students questions.
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
Integration with Core Subject(s)
LA: Understand explicit, factual informationSC: Apply scientific method to solve problems
Connection(s)
Enrichment: Have students create additional problems using the sum, difference, product, andquotient properties of functions.
Fine Arts:
Home: Have students keep a record of all assignments. (The homework record will be signedby a parent on a weekly basis.)
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
Assign appropriate problems from your text.
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 023 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 8C1
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 systems
ISAT:Solve problems requiring computations with
whole numbers, fractions, decimals, ratios,percents, and proportions
Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs
Unit Focus/Foci
Properties and Operations of Real Numbers and Functions
Instructional Focus/Foci
Performing Addition, Subtraction, Multiplication and Division of Functions
Materials
Classroom set of graphing calculatorsOverhead graphing calculatorCopies of Exploring Functions activityOverhead projector
Educational Strategies/Instructional Procedures
Review previous days homework and answer students questions.
Have students work in pairs to complete Exploring Functions activity.
Integration with Core Subject(s)
LA: Understand explicit, factual informationSC: Apply scientific method to solve problems
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 024 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 8D2
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
Use variables, number sentences, and equationsto represent solutions and solve problems
Analyze and interpret data presented in charts,graphs, tables, and other displays
Demonstrate understanding of measurementconcepts and apply measurement skills
ISAT:Solve problems requiring computations with
whole numbers, fractions, decimals, ratios,percents, and proportions
Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs
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
Instructional Focus/Foci
Investigating Bouncing Balls
Materials
Transparencies (blank)Overhead projectorGraph paperGraphing calculatorMeter sticksBouncing balls (tennis balls, racquetballs, etc.)Bouncing ball activity sheetChart paperMarkers
91
Educational Strategies/Instructional Procedures
Review previous days homework and answer students questions.
Have the students complete the Bouncing Ball Activity.
Integration with Core Subject(s)
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:
Home: Have students keep a record of all assignments. (The homework record will be signedby a parent on a weekly basis.)
Remediation: Work with students individually on their areas of deficiency.
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 025 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 8A1; 8B1; 8C1; 8D2
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
Use variables, number sentences, and equationsto represent solutions and solve problems
Analyze and interpret data presented in charts,graphs, tables, and other displays
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
Exploring Properties and Operations of Real Numbers and Functions
Instructional Focus/Foci
Reviewing Properties and Operation of Real Numbers and Functions
Materials
Educational Strategies/Instructional Procedures
Review Unit Two using a review format from the Appendix C.
Integration with Core Subject(s)
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 026 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 8A1; 8B1; 8C1; 8D2
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
Use variables, number sentences, and equationsto represent solutions and solve problems
Analyze and interpret data presented in charts,graphs, tables, and other displays
ISAT:Solve problems requiring computations with
whole numbers, fractions, decimals, ratios,percents, and proportions
Identify, analyze, and solve problems usingequations, inequalities, functions, and theirgraphs
Understand and use methods of data collectionand analysis, including tables, charts, andcomparisons
Unit Focus/Foci
Exploring Properties and Operations of Real Numbers and Functions
Instructional Focus/Foci
Assessing Property and Operations of Real Numbers and Functions
Materials
Copies of Unit Two Assessment
Educational Strategies/Instructional Procedures
Have students complete the Unit Two Assessment.
Integration with Core Subject(s)
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
STRUCTURED CURRICULUM LESSON PLAN
Day: 027 Subject: Advanced Algebra Grade Level: High School
Correlations (SG,CAS,CFS): 6A1; 8C1
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
Unit Focus/Foci
Exploring Properties of Real Numbers
Instructional Focus/Foci
Assessing Properties of Real Numbers
Materials
Unit Two Assessment (student copies)
Educational Strategies/Instructional Procedures
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.
Integration with Core Subject(s)
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