Download Math Topics

Standards – Based Instructional Unit
Subject: Mathematics
June 2010
COURSE: Topics in Mathematics
Topic: Numbers and Operations
GRADE/LEVEL: 11-12
Lesson Objective(s):
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Identify a real number
Solve problems that involve proportional relationships, percents, ratios and rates
Determine the level of accuracy needed and analyze the accuracy of results.
Compare and contrast the number systems.
21st Century Graduation Expectation(s):
1.1 Acquiring and applying knowledge and skills within and across the curriculum
1.2 Analyzing and evaluating information
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.
4.3 Speaking, listening and interpreting effectively.
Standards:
Students should:
 develop a deeper understanding of very large
and very small numbers and of various
reputations 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;

understand matrices as systems that have
some of the properties of the real-number
system;
GSES:
M(N&O)1 Rational Numbers
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 Writing Conventions
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
Reading
 The 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 formulate responses based on research. (Such as “The Hallway of Lights” common
assessment)
Problem Solving
 Students will utilize a chart/Venn diagram
 Students will write a number sentence/formula
 Students will use a model
 Students will work backwards
Essential Question(s):
 Using a mathematical model, how can one analyze and synthesize information from multiple sources,
such as in “The Hallway of Lights?”

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Percents
 Ratios
 Proportions
 Logical Reasoning
 Prime
 Fractional Operations
 Divisibility
 Even/Odd
 Classifications (counting, whole, integers, etc.)
 Elements
 Patterns
 Counting Techniques
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Informal Peer editing
Instructional Resources and Equipment:
 Computers
 Rulers
 Calculators
 Assessment Booklets
 Performance-based real-world applications
Assessment Task(s):
 Common Tasks
 Pre-Assessments
 Tests
 Class Discussion
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Students should be able to summarize the graduation expectations and the GSEs utilized throughout Number
and Operations.
Standards – Based Instructional Unit
Subject: Mathematics
COURSE: Topics in Mathematics
Topic: Geometry and Measurements
March 2010
GRADE/LEVEL: 11-12
Lesson Objective(s):
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Utilize geometric properties or theorems involving angles, lines, and polygons.
Utilize distance formula.
Solve problems on and off the coordinate plane.
Determine the effect of changing a scale factor on similar figures.
Calculate perimeter, circumference, area, volume, and/or surface 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
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.
4.2 Writing clearly, concisely and persuasively.
Standards:
Students should:
 analyze properties and determine attributes of
two and three dimensional objects;
 use Cartesian coordinates to analyze
geometric situations;
 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,
surface area, and volume of geometric figures,
including cones, spheres, and cylinders;
GSES:
M(G&M)2 Uses Geometric Properties
M(G&M)4 Concepts of Congruency
M(G&M)5 Concepts of Similarity
M(G&M)6 Two-dimensional Figures
M(G&M)7 Uses Units of Measure
M(G&M)9 On and off coordinate plane
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 Writing Conventions
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
Reading
 The 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 “A WWI Biplane, A pack mule, and your
own two feet…”
Problem Solving
 Students will compare and contrast appropriate units of measure
 Students will apply the distance formula
 Students will use a model
 Students will work backwards
 Students will observe patterns
Essential Question(s):
 Using a mathematical model, how can one analyze and synthesize information from multiple sources,
such as in “A WWI Biplane, A pack mule, and your own two feet…”

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Perimeter
 Area
 Properties
 Circumference
 Lateral Area
 Surface Area
 Volume
 Isosceles
 Equilateral
 Right
 Pythagorean Theorem
 Similarity
 Transformations
 Parallel Lines
 Perpendicular lines
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Peer editing
Instructional Resources and Equipment:
 Compasses
 Computers
 Rulers
 Calculators
 Assessment Booklets
 Web based performance assessments
Assessment Task(s):
 Common Tasks
 Pre-Assessments
 Tests
 Class Discussion
 Web Based Assessments
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 Measurements.
Standards – Based Instructional Unit
Subject: Mathematics
June 2010
COURSE: Topics in Mathematics
Topic: Functions and Algebra
GRADE/LEVEL: 11-12
Lesson Objective(s):
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Solve problems utilizing pattern
Simplify expressions
Evaluate expressions
Translate problem situations into algebraic expressions
Solve problems involving algebraic reasoning
Translate problem situations into equations
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:
 generalize patterns;
 use symbolic algebra to represent and explain
mathematical relationships;
 draw reasonable conclusions about a situation
being modeled;
GSES:
M(F&A)1 Patterns
M(F&A)3 Algebraic Equations
M(F&A)4 Equality
M(F&A) 1 Rational Numbers
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 Writing Conventions
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
Reading
 The 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 “The Hungry Hobo…”
Problem Solving
 Students will use the “guess and check” method for solving variables
 Students will work backwards
 Students will observe patterns
 Students will formulate a number sentence from a given situation
Essential Question(s):
 Using a mathematical model, how can one analyze and synthesize information from multiple sources,
such as in “The Hungry Hobo.”

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Simplification of Algebraic Expressions
 Substitution of Algebraic Expressions
 Positive/Negative Exponents
 Properties of Exponents
 Solving Multi-Step Equations
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Peer editing
Instructional Resources and Equipment:
 Computers
 Rulers
 Calculators
 Assessment Booklets
 Web based performance assessments
Assessment Task(s):
 Common Tasks
 Pre-Assessments
 Tests
 Class Discussion
 Web Based Assessments
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
COURSE: Topics in Mathematics
Topic: Data, Statistics, and Probability
June 2010
GRADE/LEVEL: 11-12
Lesson Objective(s):
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Interpret data from a variety of sources, such as, graphs, tables, charts, bar graphs, pie graphs, etc.
Analyze data using measures of central tendency.
Represent data using a variety of methods.
Utilize counting techniques to determine combinations or permutations.
Predict the probability of an event.
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;
 understand the concepts of conditional
probability and independent events;
 understand how to compute the probability of
a compound event;
GSES:
M(DSP)1 Interpretation of Data
M(DSP)2 Linear and Nonlinear Functions
M(DSP)3 Representation of Data
M(DSP)4 Using Counting Techniques
M(DSP)5 Solving Problems
M(DSP)6 Response to Question
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 Writing Conventions
W-10-2 Response to Text
W-10-8 Informational Writing
W-10-9 Writing Conventions
Reading
 The 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 “Who Makes More.”
Problem Solving
 Students will compare and contrast data
 Students will apply the permutation and combination formulas
 Students will use a model
 Students will observe patterns
Essential Question(s):
 Using a mathematical model, how can one analyze and synthesize information from multiple sources,
such as in “Who Makes More?”

How can one design a mathematical model to inform and solve a practical or abstract situation?
Content Topics:
 Mean
 Median
 Mode
 Range
 Probability
 Independent/Dependent Events
 Permutations/Combinations
 Circle graphs, Bar Graphs, Venn Diagrams, etc.
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre-Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Manipulatives
 Peer editing
Instructional Resources and Equipment:
 Computers
 Rulers
 Calculators
 Assessment Booklets
 Web based performance assessments
Assessment Task(s):
 Common Tasks
 Pre-Assessments
 Tests
 Class Discussion
 Web Based Assessments
Rubric(s) for Assessment:
 See attached rubrics
Reflection/Comments:
Students should be able to summarize the graduation expectations and the GSEs utilized throughout Data,
Statistics, and Probability.