Standards – Based Instructional Unit
Subject: Mathematics
COURSE: Honors Calculus
Topic: Numbers and Operations
April 28, 2010
GRADE/LEVEL: 12
Lesson Objective(s):
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Identify a real number
Solve problems that involve ordering and comparing subsets
Solve problems that involve proportional relationships, ratios and rates
Use mental arithmetic to calculate perfect square, and fractions
Use estimation to determine level of accuracy needed and analyzing the accuracy of results
Simplify computations
Apply the concepts of congruency by solving problems on or off a coordinate plane involving
transformations
Uses ratio of the sides of special right triangles and uses similarity of right triangles with trigonometric
functions
Makes conversions, uses successive approximations, decides appropriate degree of accuracy
Calculates distance, midpoint, and slope of perpendicular and parallel lines
Identifies a variety of patterns and generalizes a linear and non-linear relationships to find a specific
case
Demonstrates conceptual understanding of algebraic expressions by solving problems involving
algebraic expressions and by translating problem situations into algebraic expressions
Solve problems involving algebraic reasoning
Translate problem situations into equations; solving problems and expressing the solution set
graphically
Interprets and analyzes differences and similarities between data sets to make observations, to answer
questions, to analyze the data to formulate or justify conclusions, or critique conclusions to make
predictions, or to solve problems within mathematics and across disciplines and contexts
21st Century Graduation Expectation(s):
1.1 Acquiring and applying knowledge and skills within and across the curriculum
1.2 Analyzing and evaluating information
1.3 Applying Technology as a learning tool across all disciplines
2.1 Working cooperatively and/or independently
2.2 Applying problem solving strategies
2.3 Utilizing resources and time effectively
2.4 Accessing, compiling, interpreting and presenting data and information
3.1 Making informed life and career decisions
3.2 Recognizing and respecting the diversity and individuality of others
3.3 Understanding and accepting the benefits and consequences of his/her behavior
4.1 Reading widely and critically
4.2 Writing clearly, concisely and persuasively
4.3 Speaking, listening and interpreting effectively
4.4 Mastering technology as a means of communication
Standards:
Students should:
 develop a deeper understanding of very large
and very small numbers and of various
representations of them;
 compare and contrast the properties of
numbers and number systems, including the
rational and real numbers, and understand
complex numbers as solutions to quadratic
equations that do not have real solutions;
 judge the effects of such operations as
multiplication, division, and computing
powers and roots on the magnitudes of
quantities;
 develop fluency in operations with real
numbers;
 judge the reasonableness o f numerical
computations and their results
GSES:
M(N&O)4 Solving Problems
M(N&O)6 Mental Computation
M(N&O)7 Estimation
M(N&O)8 Properties of Numbers
M(G&M)4 Concepts of Congruency
M(G&M)5 Concepts of Similarity
M(G&M)7 Uses Units of Measure
M(F&A)1 Patterns
M(F&A)2 Linear & Nonlinear Functions
M(F&A)3 Algebraic Equations
M(F&A)4 Equality
R 10-3 Breadth of Vocabulary Knowledge
R 10-7 Analyzing Informational Text
W-10-1 Structures of Language
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
*Calculus is an advanced mathematics course that
exceeds the mathematics covered in the GSEs.
Reading
 Students will use vocabulary strategies to identify context data.
 Students will read the text for understanding.
 Students will organize information to show understanding.
Writing
 Students will summarize responses.
 Students will demonstrate informational writing.
Problem Solving
 Students will compare and contrast graphs.
 Students will work backwards.
 Students will write a number sentence/formula.
 Students will use a model.
 Students will look for a pattern.
 Students will make and test conjectures.
 Students will construct and present valid arguments.
Essential Question(s):

Using a mathematical model, calculate the Instantaneous rate of change as the limit of average rate
of change.

Using a mathematical model, calculate the Approximate rate of change from graphs and tables of
values.

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Limits
 Differentiation
 Integration
 Logarithmic, Exponential, and Other Transcendental Functions
Student-Centered Instructional Strategies:
 Graphing Calculator
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Peer editing
Instructional Resources and Equipment:
 Computers
 Graphing Calculators
 Textbook
Assessment Task(s):
 Performance based real world applications
 Pre-Assessments
 Tests
 Class Discussions
 Portfolio
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Students should be able to summarize the graduation expectations and the GSEs utilized throughout Numbers
and Operations.
Standards – Based Instructional Unit
Subject: Mathematics
COURSE: Honors Calculus
Topic: Geometry and Measurement
April 28, 2010
GRADE/LEVEL: 12
Lesson Objective(s):
 Use trigonometric relationships to determine lengths and angle measures
 Apply the concepts of congruency by solving problems on or off a coordinate plan involving reflections
and translations
 Determine the effect of changing a scale factor on similar figures
 Demonstrate conceptual understanding of perimeter, circumference, and/or area
 Utilize units of measure appropriately and consistently when solving problems
21st Century Graduation Expectation(s):
1.1 Acquiring and applying knowledge and skills within and across the curriculum
1.2 Analyzing and evaluating information
1.3 Applying Technology as a learning tool across all disciplines
2.1 Working cooperatively and/or independently
2.2 Applying problem solving strategies
2.3 Utilizing resources and time effectively
2.4 Accessing, compiling, interpreting and presenting data and information
3.2 Recognizing and respecting the diversity and individuality of others
3.3 Understanding and accepting the benefits and consequences of his/her behavior
4.1 Reading widely and critically
4.2 Writing clearly, concisely and persuasively
4.4 Mastering technology as a means of communication
Standards:
Students should:
 analyze properties and determine attributes of
two dimensional objects;
 use Cartesian coordinates to analyze
geometric situations;
 use trigonometric relationships to determine
lengths and angle measures;
 understand and represent translations and
reflections of objects in the plane by using
sketches, function notation;
 use various representations to help understand
the effects of simple transformations and their
compositions;
 make decisions about units and scales that are
appropriate for problem situations involving
measurement;
 analyze precision, accuracy, and approximate
error in measurement situations;
 understand and use formulas for the area of
geometric figures;
 use geometric ideas to solve problems in, and
gain insights into, other disciplines and other
areas of interest such as art and architecture
GSES:
M(N&O)4 Solving Problems
M(N&O)6 Mental Computation
M(N&O)7 Estimation
M(N&O)8 Properties of Numbers
M(G&M)4 Concepts of Congruency
M(G&M)5 Concepts of Similarity
M(G&M)7 Uses Units of Measure
M(F&A)1 Patterns
M(F&A)2 Linear & Nonlinear Functions
M(F&A)3 Algebraic Equations
M(F&A)4 Equality
R 10-3 Breadth of Vocabulary Knowledge
R 10-7 Analyzing Informational Text
W-10-1 Structures of Language
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
*Calculus is an advanced mathematics course that
exceeds the mathematics covered in the GSEs.
Reading
 Students will use vocabulary strategies to identify context data.
 Students will read the text, Problem of the Week, and supplementary materials for understanding.
 Students will organize information to show understanding.
Writing
 Students will summarize responses.
 Students will reflect and support their conjectures and solutions on various types of assessments.
 Students will write portfolio reflections.
Problem Solving
 Students will compare and contrast graphs.
 Students will work backwards.
 Students will write a number sentence/formula.
 Students will use a model.
 Students will look for a pattern.
 Students will make and test conjectures.
 Students will construct and present valid arguments.
Essential Question(s):

Using a mathematical model, how can one apply geometry concepts to “Optimization” problems to
inform and solve a practical or abstract situation that involve area and volume?

Using a graph, how can one approximate the area under a curve using Riemann Sums?
Content Topics:
 Limits
 Differentiation
 Integration
 Logarithmic, Exponential, and Other Transcendental Functions
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Peer editing
 Oral Presentations
Instructional Resources and Equipment
 Computers
 Rulers
 Graphing Calculators
 Textbook
Assessment Task(s):
 Performance based real world applications
 Pre-Assessments
 Tests, Quizzes
 Class Discussion
 Portfolio
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Students should be able to summarize the graduation expectations and the GSEs utilized throughout Geometry
and Measurement.
Standards – Based Instructional Unit
Subject: Mathematics
COURSE: Honors Calculus
Topic: Functions and Algebra
April 28, 2010
GRADE/LEVEL: 12
Lesson Objective(s):
 Demonstrate how to solve absolute equations, inequalities, trigonometric, exponential and
logarithmic equations
 Identify, state the domain and range, and sketch the graph of elementary functions
 Graph and find the roots of a function utilizing a graphing calculator
 Identify the characteristics of equations and sketch their graphs
 Calculate limits using Algebra
 Estimating limits from graphs or tables of data
 Identify continuity as a property of functions
 Derive first, second, third,…functions
 Apply applications of derivatives
 Apply the Fundamental Theorem of Calculus to evaluate definite integrals
 Find the antiderivative of basic functions
 Apply the Riemann, Trapezoidal, Simpson’s sums to approximate definite integrals of
functions represented algebraically and graphically
 Simplify expressions
 Evaluate expressions
 Translate problem situations into algebraic expressions
 Solve problems involving algebraic reasoning
 Translate problem situations into equations
 Trigonometric functions and their application
 Relationships among functions
21st Century Graduation Expectation(s):
1.1 Acquiring and applying knowledge and skills within and across the curriculum
1.2 Analyzing and evaluating information
1.3 Applying Technology as a learning tool across all disciplines
2.1 Working cooperatively and/or independently
2.2 Applying problem solving strategies
2.3 Utilizing resources and time effectively
2.4 Accessing, compiling, interpreting and presenting data and information
3.3 Understanding and accepting the benefits and consequences of his/her behavior
4.1 Reading widely and critically
4.2 Writing clearly, concisely and persuasively
4.4 Mastering technology as a means of communication
Standards:
Students should:
 use symbolic algebra to represent and explain
mathematical relationships;
 draw reasonable conclusions about a situation
being modeled;
 understand functions; operations and
relationships;
 use technology such as graphing calculator to
compare and contrast functions
 understand trigonometric functions and their
applications;
 demonstrate their knowledge of algebraic
trigonometric, exponential, and logarithmic
functions;
 demonstrate their knowledge of the limits,
continuity, the derivative and problem solving
using derivative concepts;
 demonstrate their knowledge of anti-derivative
techniques and problem solving in integral
calculus
GSES:
M(N&O)4 Solving Problems
M(N&O)6 Mental Computation
M(N&O)7 Estimation
M(N&O)8 Properties of Numbers
M(G&M)4 Concepts of Congruency
M(G&M)5 Concepts of Similarity
M(G&M)7 Uses Units of Measure
M(F&A)1 Patterns
M(F&A)2 Linear & Nonlinear Functions
M(F&A)3 Algebraic Equations
M(F&A)4 Equality
R 10-3 Breadth of Vocabulary Knowledge
R 10-7 Analyzing Informational Text
W-10-1 Structures of Language
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
*Calculus is an advanced mathematics course that
exceeds the mathematics covered in the GSEs.
Reading
 Students will use vocabulary strategies to identify context data.
 Students will read the text for understanding.
 Students will organize information to show understanding.
Writing
 Students will summarize responses.
 Students will reflect and support their responses, such as in various Performance based real world
applications.
 Students will write portfolio reflections.
Problem Solving
 Students will compare and contrast graphs.
 Students will work backwards.
 Students will write a number sentence/formula.
 Students will use a model.
 Students will look for a pattern.
 Students will make and test conjectures.
 Students will construct and present valid arguments.
Essential Question(s):

Using a mathematical model, how can one analyze and synthesize information from multiple sources,
such as in real world/performance base applications?

How can one identify the local and global behavior of a function?

How can one integrate functions to help explain the area under a curve?
Content Topics:
 Functions: Linear, quadratic, polynomial
 Limits
 Trigonometric functions
 Differentiation
 Integration
 Logarithmic, Exponential, and other Transcendental Functions
Student-Centered Instructional Strategies:
 Graphing Calculator
 Pre-Assessment
 Post Assessment and reflection
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Oral Presentations
 Peer editing
Instructional Resources and Equipment:
 Computers
 Graphing Calculators
 Textbooks
Assessment Task(s):
 Performance based real world applications
 Cooperative Learning
 Tests
 Class Discussion
 Reflections/Portfolio
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Students should be able to summarize the graduation expectations and the GSEs utilized throughout
Functions and Algebra.
Standards – Based Instructional Unit
Subject: Mathematics
May 11, 2010
COURSE: Honors Calculus
Topic: Data, Statistics, and Probability
GRADE/LEVEL: 12
Lesson Objective(s):
 Interpret data from a variety of sources, such as, graphs, tables, charts, bar graphs, pie graphs, etc.
 Represent data using a variety of methods
 Decide on most effective method to answer questions regarding data
21st Century Graduation Expectation(s):
1.1 Acquiring and applying knowledge and skills within and across the curriculum
1.2 Analyzing and evaluating information
1.3 Applying Technology as a learning tool across all disciplines
2.1 Working cooperatively and/or independently
2.2 Applying problem solving strategies
2.3 Utilizing resources and time effectively
2.4 Accessing, compiling, interpreting and presenting data and information
3.3 Understanding and accepting the benefits and consequences of his/her behavior
4.1 Reading widely and critically
4.2 Writing clearly, concisely and persuasively
4.4 Mastering technology as a means of communication
Standards:
Students should:
 understand the meaning of measurement
data;
 identify trends in data
GSES:
M(DSP)1 Interpretation of Data
M(DSP)2 Linear and Nonlinear Functions
M(N&O)2 Real Numbers
M(N&O)4 Solving Problems
M(N&O)6 Mental Computation
M(N&O)7 Estimation
M(N&O)8 Properties of Numbers
R 10-3 Breadth of Vocabulary Knowledge
R 10-7 Analyzing Informational Text
W-10-1 Structures of Language
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
*Calculus is an advanced mathematics course that
exceeds the mathematics covered in the GSEs.
Reading
 Students will use vocabulary strategies to identify context data.
 Students will read the text for understanding.
 Students will organize information to show understanding.
 Students will present information to demonstrate understanding
Writing
 Students will summarize responses.
 Students will reflect and support their responses for Performance based real world problems.
Problem Solving
 Students will compare and contrast data.
 Students will interpret graphs.
 Students will observe patterns.
 Students will use a model.
 Students will work backwards.
 Students will construct and present valid arguments.
Essential Question(s):

Using a mathematical model, how can one analyze and synthesize information from multiple sources
and/or Performance based real world problems to make conclusions/conjectures?

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Functions: Linear, quadratic, polynomial
 Limits
 Trigonometric functions
 Differentiation
 Integration
 Logarithmic, Exponential, and other Transcendental Functions
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Post Assessment and reflection
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Peer editing
Instructional Resources and Equipment:
 Computers
 Rulers
 Graphing calculators
 Supplemental materials
Assessment Task(s):
 Performance based real world applications
 Tests
 Class Discussion
 Reflections
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Calculus is an advanced mathematics course primarily focusing on Functions, Limits, and Integration. The
advanced math students take Calculus as a senior. Therefore, the coverage of Data, Statistics and Probability
GSE’s is minimal in Calculus.