Download Geometry

Standards – Based Instructional Unit
Subject: Mathematics
February 4, 2010
COURSE: Geometry
Topic: Numbers and Operations
GRADE/LEVEL: 10
Lesson Objective(s):
Identify and demonstrate conceptual understanding of real numbers
 Accurately solves mathematical and contextual problems involving proportions
 Use mental arithmetic to calculate perfect square, percentages, and fractions
 Use estimation to determine accurate results
 Apply and understand properties of numbers to solve 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
3.1 Making informed life and career decisions
3.2 Recognizing and respecting the diversity and individuality of students
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:
 understand numbers, ways of representing
numbers, relationships among numbers, and
number systems;
 understand meanings of operations and how
they relate to one another
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 2 Vocabulary Strategies
R 3 Breadth of Vocabulary Knowledge
R 7 Analyzing Informational Text
R 8 Analysis of Informational Text
R 11 Fluency and Accuracy
R 12 and R 13 Reading Strategies
R 15 Breadth of Reading
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 formulate responses based on properties of numbers.
Problem Solving
 Students will use the “guess and check” method for solving variables.
 Students will use a model.
 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, can one utilize and apply basic number and operations properties to
draw logical conclusions.

How can one draw a logical conclusion using basic number and operations properties?
Content Topics:
 Percents
 Ratios
 Proportions
 Logical Reasoning
 Prime
 Fractional Operations
 Divisibility
 Even/Odd
 Classifications (counting, whole, integers, etc.)
 Elements
 Union
 Intersection
 Patterns
 Counting Techniques
Student-Centered Instructional Strategies:
 Technology
 Differentiated instruction
 Pre and Post Assessment
Student-Centered Learning Tasks and Opportunities:
 Cooperative learning
 Models and Manipulative
 Peer editing
Instructional Resources and Equipment:
 Computers (Sketchpad on mobile Laptops)
 Rulers, protractors, compasses
 Calculators
 Text Books
Assessment Task(s):
 Quarterly Portfolio Assessments
 Tests/Quizzes
 Class discussions
 Homework problems
 Pre-Assessment
Rubric(s) for Assessment:
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
February 4, 2010
COURSE: Geometry
Topic: Geometry and Measurements
GRADE/LEVEL: 10
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
Properties of circles
Proving triangles congruent
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:
 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,
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
surface area, and volume of geometric figures,
including cones, spheres, and cylinders
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
 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 using deductive and inductive reasoning.
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, can one utilize and apply basic geometry and measurement properties to
draw logical conclusions.

How can one draw a logical conclusion using basic geometry and measurement properties?
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
 Manipulatives
 Peer editing
Instructional Resources and Equipment:
 Compasses
 Computers
 Rulers
 Calculators
Assessment Task(s):
 Quarterly Portfolio Assessments
 Tests/Quizzes
 Class discussions
 Homework problems
 Pre-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
February 04, 2010
COURSE: Geometry
Topic: Functions and Algebra
GRADE/LEVEL: 10
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
Algebraic proofs
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(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
 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 give detailed step by step analysis using algebraic properties.
Problem Solving
 Students will use the “guess and check” method for solving variables.
 Students will use a model.
 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, can one utilize and apply basic algebraic properties to draw logical
conclusions.
 How can one draw a logical conclusion using basic properties of functions and Algebra?
Content Topics:
 Simplification of Algebraic Expressions
 Substitution of Algebraic Expressions
 Properties of Exponents
 Solving Multi-Step Equations
 Algebraic proofs
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
 Graphic Organizers
 Compass
 Protractors
Assessment Task(s):
 Quarterly Portfolio Assessments
 Tests/Quizzes
 Class discussions
 Homework problems
 Pre-Assessment
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: Geometry
Topic: Data, Statistics, and Probability
February 4, 2010
GRADE/LEVEL: 10
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 formulate responses based on data and statistics.
Problem Solving
 Students will use the “guess and check” method for solving variables.
 Students will use a model.
 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, can one utilize and apply basic data, statistic and probability
standards to draw logical conclusions.
 How can one draw logical conclusions using basic data, statistic and probability methods?
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 Task(s):
 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 Data,
Statistics, and Probability.