Download Modified Algebra A, Algebra/Geometry B, Geometry C - Grades 9-12

CURRICULUM
FOR
SPECIAL EDUCATION
ALGEBRA A
ALGEBRA/GEOMETRY B
GEOMETRY C
GRADES 9-12
This curriculum is part of the Educational Program of Studies of the Rahway Public Schools.
ACKNOWLEDGMENTS
Christine H. Salcito, Director of Curriculum and Instruction
Barbara Pyne, Program Supervisor of Special Education
The Board acknowledges the following who contributed to the preparation of this curriculum.
Subject/Course Title:
Date of Board Adoptions:
Special Education
Algebra a, Algebra/Geometry B, Geometry C
Grades 9-12
June 27, 2013
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra
Unit Title : Unit One - Expressions, Equations, and Inequalities
Targe t Course /Grade Le ve l: Algebra 1/Grade 9
Unit Summary:
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•
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Using the distributive property
Interpret parts of an expression
Solving one, two, and multi-step equations
Solving literal equations
Solving one, two, and multi-step inequalities
Graphing inequalities
Approximate Le ngth of Unit: 14 weeks
Primary interdisciplinary connections: Science and Language Arts
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Expressions
Seeing Structure in Expressions
A-SSE.1, A-SSE.1a
Equations
Creating Equations
A-CED.1, A-CED.4
Equations
Reasoning with Equations and Inequalities
A-REI.1
Unit Unde rstandings
Students will understand that…
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You can solve equations and inequalities using the algebraic properties of equality.
•
Equations can represent real world situations.
•
Properties are used in solving equations and inequalities.
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Real world problems can be solved using equations and inequalities.
Unit Esse ntial Q uestions
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Identify the coefficient, variable, and constant in the expression 4x + 2.
Simplify the expressions:
o 2x – 6 +3x
o -4(5x – 2)
o 3(x – 1) + 2(x + 2) – 6
Solve varying types of equations.
How can real world situations be represented as equations?
Create an equation for the given situation and solve: Jenna buys 2 sodas and spends $3.10. How much did each soda cost?
Solve a literal equation for a given variable. Example: Solve A = ½bh, for h.
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•
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Solve and graph an inequality.
Create an inequality for the given situation and solve: Mike buys a sandwich for $4.50, a soda for $1.89, and wants to buy a
snack. He cannot spend more than $7.00 for his lunch. How much can mike spend on his snack?
Identify the properties used to solve an equation.
Knowle dge and Skills
Students will know…
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Vocabulary –
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o
o
o
o
o
o
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Students will
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•
•
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•
•
•
•
•
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•
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Formulas –
o
o
o
Real numbers
Expressions, coefficient, constant, variable, like terms, simplify, order of operations
Real numbers, positive, negative, integers, irrational numbers, absolute value,
Equations, solutions, evaluate
Algebraic properties of equality, distributive property, substitution property
Literal equations, formulas
Proportion, ratio, probability
Fahrenheit to Celsius
Simple Interest Formula
Density Formula
be able to…
use mathematical vocabulary fluently
use appropriate vocabulary to describe expressions
interpret expressions that represent a quantity in terms of its context
interpret parts of an expression, such as terms, factors, and coefficients
use order of operations to simplify expressions
evaluate expressions
solve one, two, and multi-step equations
use the distributive property
create equations and inequalities in one variable and use them to solve problems
explain each step in solving a simple equation from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution
construct a viable argument to justify a solution
rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
attend to precision
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes,
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Mathematical investigations
•
Fundraising activity pg. 154 (algebra text).
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Study Island assignments
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Create real world situations in a word problem format and solve each other’s problems (Language Arts).
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Use real-world literal equations and solve them for a variable different than the one given (science formulas: density,
Fahrenheit to Celsius, etc.)
RESOURCES
Te ache r Re sources:
•
•
•
Algebra 1 T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites
Equipme nt Ne e ded:
•
•
•
Calculators
Computers
Projectors
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra 1
Unit Title : Unit One - Linear Functions
Targe t Course /Grade Le ve l: Algebra 1/Grade 9
Unit Summary:
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•
•
•
•
Understand the concept of a function and use function notation
Identify the domain and range of linear functions
Graph linear functions
Relate the domain of a linear function to its graph.
Write a linear function that describes a relationship between two quantities
Approximate Le ngth of Unit: 8 weeks
Primary interdisciplinary connections: Language Arts and Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Interpreting Functions
Understand the concept of a function and use function notation
F-IF.1, F-IF.2, F-IF.4, F-IF.5, F-IF.6
Interpreting Functions
Analyze functions using different representations
F-IF.7, F-IF.7a, F-IF.8
Building Functions
Build a function that models a relationship between two quantities
F-BF.1
Unit Unde rstandings
Students will
•
•
•
•
understand that…
Equations and graphs are alternative (and often equivalent) ways of depicting and analyzing data and patterns of change.
Functional relationships can be expressed in a variety of ways: real contexts, graphs, algebraic equations, tables, and words.
Functions can be analyzed using different representations.
A variety of families of functions can be used to model and solve real world problems.
Unit Esse ntial Q uestions
•
•
•
•
•
•
How can change be best represented mathematically?
How can we use mathematical language to describe change?
How can we use mathematical models to describe change or change over time?
How can patterns, relations, and functions be used as tools to best describe and explain real-life situations?
How are functions and their graphs related?
How can technology be used to investigate properties of linear functions and their graphs?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Relation, domain, range, function, correlation, ordered pair
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•
•
•
•
•
•
•
•
Students will
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•
•
•
•
•
•
•
•
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•
•
•
•
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o Rise, run, slope, rate of change, x-coordinate, y-coordinate, y-intercept
o Slope-intercept form, standard form, and point slope form
o Parallel and perpendicular lines
Formulas –
o Slope intercept form - y = mx + b
o Standard form - Ax + By = C
o Point slope form
How to write linear equations and functions
How to graph linear equations
Whether a relation is a function
T he domain and range of a function
How to use slope intercept form, standard form, and point slope form
How to find and identify the slope and y-intercept of a linear function
How to identify and graph horizontal and vertical lines
How to identify parallel and perpendicular lines
be able to…
Define relations, functions, domain, range, correlation, slope, and y-intercepts
Calculate the slope of a line
Find the rate of change from a graph
Use slope intercept form, standard form, and point slope form
Write linear equations in all forms and graph them
Graph horizontal and vertical lines
Write linear equations in function notation
Describe and identify parallel and perpendicular lines
make sense of problems and persevere in solving them
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes,
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Linear function video at http//www.khanacademy.org/video/basic-linear-function
•
Study Island assignments
•
Portfolio Activity pg. 233
•
Graphing calculators
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites (Khan Academy).
Equipme nt Ne e ded:
•
•
•
•
•
Graphing calculators
Projector and computers
Graph paper
Rulers
T ape measures and spheres (portfolio activity)
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra 1
Unit Title : Unit T hree - Systems of Equations and Inequalities
Targe t Course /Grade Le ve l: Algebra 1/Grade 9
Unit Summary:
•
•
Understand, explain, and solve systems of equations using three methods.
Understand, explain, and solve systems of inequalities.
Approximate Le ngth of Unit: 8 weeks
Primary interdisciplinary connections: Science and Business
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Creating Equations
Create equations that describe numbers or relationships
A-CED.3
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the
A-REI.5, A-REI.6, A-REI.10
reasoning
Unit Unde rstandings
Students will understand that…
•
A system of equations/inequalities includes two or more equations/inequalities in the same variables
•
A system of equations can be solved using three methods: graphing, substitution, and elimination
•
A system of equations may have one, none, or infinite solutions
Unit Esse ntial Q uestions
•
•
•
Given a system of equations, which method would best be used to solve the system?
Will you get the same solution set if you solve a system using different methods?
How can real world situations be modeled using systems of equations/inequalities?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Systems of equations/inequalities
o Classifying systems: Consistent dependent system, consistent independent system, inconsistent system
o Graphing method, substitution method, and elimination method
•
How to classify systems of equations
•
How to solve systems of equations/inequalities
Students will
•
•
•
•
•
•
•
•
•
•
•
•
•
be able to…
Classify systems of equations
Graph systems of equations/inequalities
Solve systems of equations using the three methods: graphing, substitution, and elimination
Choose an appropriate method for solving a system of equations
Solve real world problems using systems of equations/inequalities
make sense of problems and persevere in solving them
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Study Island assignments
•
Chapter Project pg. 360 (Minimum Cost Maximum Profit)
•
Portfolio Activity pg. 325 (Salaries)
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites
Equipme nt Ne e ded:
•
•
•
•
Graph paper
Colored pencils
Graphing calculators
Computers
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/Geometry B
Unit Title : Linear Functions
Targe t Course /Grade Le ve l: Algebra/Geometry B/Grade 10
Unit Summary:
•
•
•
•
•
Understand the concept of a function and use function notation
Identify the domain and range of linear functions
Graph linear functions
Relate the domain of a linear function to its graph.
Write a linear function that describes a relationship between two quantities
Approximate Le ngth of Unit: 4 weeks
Primary interdisciplinary connections: Language Arts and Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Interpreting Functions
Understand the concept of a function and use function notation
F-IF.1, F-IF.2, F-IF.4, F-IF.5, F-IF.6
Interpreting Functions
Analyze functions using different representations
F-IF.7, F-IF.7a, F-IF.8
Building Functions
Build a function that models a relationship between two quantities
F-BF.1
Unit Unde rstandings
Students will
•
•
•
•
understand that…
Equations and graphs are alternative (and often equivalent) ways of depicting and analyzing data and patterns of change.
Functional relationships can be expressed in a variety of ways: real contexts, graphs, algebraic equations, tables, and words.
Functions can be analyzed using different representations.
A variety of families of functions can be used to model and solve real world problems.
Unit Esse ntial Q uestions
•
•
•
•
•
•
How can change be best represented mathematically?
How can we use mathematical language to describe change?
How can we use mathematical models to describe change or change over time?
How can patterns, relations, and functions be used as tools to best describe and explain real-life situations?
How are functions and their graphs related?
How can technology be used to investigate properties of linear functions and their graphs?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Relation, domain, range, function, correlation, ordered pair
o Rise, run, slope, rate of change, x-coordinate, y-coordinate, y-intercept
o Slope-intercept form, standard form, and point slope form
o Parallel and perpendicular lines
•
Formulas –
o Slope intercept form - y = mx + b
o Standard form - Ax + By = C
o Point slope form
•
How to write linear equations and functions
•
How to graph linear equations
•
Whether a relation is a function
•
T he domain and range of a function
•
How to use slope intercept form, standard form, and point slope form
•
How to find and identify the slope and y-intercept of a linear function
•
How to identify and graph horizontal and vertical lines
•
How to identify parallel and perpendicular lines
Students will be able to…
•
Define relations, functions, domain, range, correlation, slope, and y-intercepts
•
Calculate the slope of a line
•
Find the rate of change from a graph
•
Use slope intercept form, standard form, and point slope form
•
Write linear equations in all forms and graph them
•
Graph horizontal and vertical lines
•
Write linear equations in function notation
•
Describe and identify parallel and perpendicular lines
•
make sense of problems and persevere in solving them
•
reason abstractly and quantitatively
•
construct viable arguments and critique the reasoning of others
•
model with mathematics
•
use appropriate tools strategically
•
attend to precision
•
look for and make use of structure
•
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes,
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Linear function video at http//www.khanacademy.org/video/basic-linear-function
•
Study Island assignments
•
Portfolio Activity pg. 233
•
Graphing calculators
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites (Khan Academy).
Equipme nt Ne e ded:
•
•
•
•
•
Graphing calculators
Projector and computers
Graph paper
Rulers
T ape measures and spheres (portfolio activity)
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/ Geometry B
Unit Title : Unit T wo - Systems of Equations and Inequalities
Targe t Course /Grade Le ve l: Algebra/ Geometry B /Grade 10
Unit Summary:
•
•
Understand, explain, and solve systems of equations using three methods.
Understand, explain, and solve systems of inequalities.
Approximate Le ngth of Unit: 4 weeks
Primary interdisciplinary connections: Science and Business
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Creating Equations
Create equations that describe numbers or relationships
A-CED.3
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the
A-REI.5, A-REI.6, A-REI.10
reasoning
Unit Unde rstandings
Students will
•
•
•
understand that…
A system of equations/inequalities includes two or more equations/inequalities in the same variables
A system of equations can be solved using three methods: graphing, substitution, and elimination
A system of equations may have one, none, or infinite solutions
Unit Esse ntial Q uestions
•
Given a system of equations, which method would best be used to solve the system?
•
Will you get the same solution set if you solve a system using different methods?
•
How can real world situations be modeled using systems of equations/inequalities?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Systems of equations/inequalities
o Classifying systems: Consistent dependent system, consistent independent system, inconsistent system
o Graphing method, substitution method, and elimination method
•
How to classify systems of equations
•
How to solve systems of equations/inequalities
Students will
•
•
•
•
•
•
•
•
•
•
•
•
•
be able to…
Classify systems of equations
Graph systems of equations/inequalities
Solve systems of equations using the three methods: graphing, substitution, and elimination
Choose an appropriate method for solving a system of equations
Solve real world problems using systems of equations/inequalities
make sense of problems and persevere in solving them
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Study Island assignments
•
Chapter Project pg. 360 (Minimum Cost Maximum Profit)
•
Portfolio Activity pg. 325 (Salaries)
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites
Equipme nt Ne e ded:
•
•
•
•
Graph paper
Colored pencils
Graphing calculators
Computers
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/ Geometry B
Unit Title : Unit T hree - Exponents and Exponential Functions
Targe t Course /Grade Le ve l: Algebra/ Geometry B/Grade 10
Unit Summary:
•
•
•
Understand and use the laws of exponents to simplify and evaluate expressions
Graph exponential functions
Apply exponential functions to real world situations
Approximate Le ngth of Unit: 6 weeks
Primary interdisciplinary connections: Science, history, and economics
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Interpreting Functions
Analyze functions using different representations
F-IF.7. F-IF.8
Linear and Exponential Models
Construct and compare linear and exponential models and solve problems
F-LE.1, F-LE.1a, F-LE.1b, F-
The Real Number System
Extend the properties of exponents to rational exponents
LE.1c
Unit Unde rstandings
Students will
•
•
•
•
understand that…
T he laws of exponents can be used to simplify expressions
Exponential growth and decay can represent real world problems
A comparison can be made between linear and exponential functions
Scientific notation can be used to express large and small numbers
Unit Esse ntial Q uestions
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•
•
How do you simplify an expression involving exponents?
How can we apply exponential functions to real world situations?
Why/how can we use scientific notation to represent numbers?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Base, exponent, degree, monomial, coefficient, laws of exponents, product, quotient
o Scientific notation
o Exponential functions, growth, decay
•
How to simplify expressions involving exponents
•
Scientific notation
N-RN.1, N-RN.2
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•
Students will
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•
•
•
•
•
•
•
•
•
•
•
How to graph exponential functions
How to describe exponential functions
be able to…
Simplify expressions involving exponents
Write numbers in scientific notation
Understand the need for scientific notation
Understand exponential functions and how they are used
Describe if an exponential functions represents growth or decay
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Study Island assignments
•
Portfolio Activity pg. 395
•
Portfolio Activity pg. 415
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Online Websites
Equipme nt Ne e ded:
•
•
•
Graphing calculators
Graph paper
Computers
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/ Geometry B
Unit Title : Unit Four - Polynomials and Factoring
Targe t Course /Grade Le ve l: Algebra/ Geometry B /Grade 10
Unit Summary:
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•
•
Perform operations on polynomials.
Solve problems involving polynomial functions.
Factor polynomials.
Approximate Le ngth of Unit: 8 weeks
Primary interdisciplinary connections: Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Seeing structure in expressions
Write expressions in equivalent forms to solve problems
A-SSE.3
Arithmetic with Polynomials and Rational
Perform arithmetic operations on polynomials
A-APR.1
Analyze functions using different representations
F-IF.7c
Expressions
Interpreting Functions
Unit Unde rstandings
Students will
•
•
•
understand that…
Operations can be performed on polynomials.
Factoring can be used to simplify polynomials.
Equations can be solved by factoring.
Unit Esse ntial Q uestions
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•
•
•
What is a polynomial?
How can factoring be used to simplify polynomials?
What are the different ways to factor polynomials and when are they used?
How can factoring be used to solve equations?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Polynomial, degree, standard form
o Polynomial functions
o Greatest Common Factor, binomial factor, perfect square trinomial, difference of two squares
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How to perform operations on polynomials
•
How to factor polynomials
•
How to find the zeros of a function
Students will
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•
•
•
•
•
•
•
•
•
be able to…
Perform operations on polynomials
Factor polynomials
Solve equations using factoring
make sense of problems and persevere in solving them
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Study Island assignments
•
Portfolio Activity pg. 457
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites
Equipme nt Ne e ded:
•
•
•
Graphing calculators
Graph paper
Computers
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/ Geometry B
Unit Title : Unit Five - Quadratic Functions
Targe t Course /Grade Le ve l: Algebra/ Geometry B / Grade 10
Unit Summary:
•
•
•
•
Understand and analyze quadratic functions
Solve problems involving quadratic functions
Using the quadratic formula to solve quadratic functions
Complex numbers
Approximate Le ngth of Unit: 5 weeks
Primary interdisciplinary connections: Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Seeing structure in expressions
Write expressions in equivalent forms to solve problems
A-SSE.3a, A-SSE.3b
Reasoning with Equations and Inequalities
Solve equations and Inequalities in one variable
A-REI.4, A-REI.4a, A-REI.4b
Interpreting Functions
Analyze functions using different representations
F-IF.7a
Unit Unde rstandings
Students will
•
•
•
understand that…
Quadratic functions form a parabola when graphed.
Quadratic functions can be solved in a variety of ways.
Quadratic functions are used to represent real world situations.
Unit Esse ntial Q uestions
•
•
•
•
What is a quadratic function?
How can a quadratic function be solved?
How can you determine the number of real solutions of a quadratic function?
What is a complex number?
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Quadratic function, parabolas, axis of symmetry, vertex form, minimum value, maximum value, zeros
o Discriminate, imaginary unit, imaginary numbers, complex numbers
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•
•
•
Students will
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•
•
•
•
•
•
•
•
•
•
•
Formulas –
o Quadratic Formula
How to graph quadratic functions
How to solve quadratic functions
How to find the zeros of a function
be able to…
Describe the graph of a quadratic function
Determine the vertex and axis of symmetry of a quadratic function
Factor and solve quadratic functions
Use the quadratic formula
Use the discriminate to determine the number of real solutions of a quadratic function
make sense of problems and persevere in solving them
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Study Island assignments
•
“ Rescue at 2000 ft.” Pg. 504-505 activity
•
Quadratic Function video at http://www.yourteacher.com/algebra2/quadraticfunction.php
RESOURCES
Te ache r Re sources:
•
•
•
Algebra T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Math websites
Equipme nt Ne e ded:
•
•
•
Graphing calculators
Graph paper
Computers
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Algebra/ Geometry B
Unit Title : Unit Six - Congruence, Proofs, and Constructions
Targe t Course /Grade Le ve l: Algebra/Geometry B/ Grade 10
Unit Summary:
•
•
•
Experiment with transformations in the plane.
Understand congruence in terms of rigid motions.
Prove geometric theorems.
Approximate Le ngth of Unit: 4 weeks
Primary interdisciplinary connections: Art, Social Studies, Language Arts, and Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Congruence
Experiment with transformations in the plane
G-CO.1, G-CO.2, G-CO.3, G-CO.4, G-CO.5
Congruence
Understand congruence in terms of rigid motion
G-CO.6, G-CO.7
Unit Unde rstandings
Students will
•
•
•
•
understand that…
Geometric properties can be used to construct geometric figures.
Geometric relationships provide a means to make sense of a variety of phenomena.
Shape and area can be conserved during mathematical transformations.
Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry.
Unit Esse ntial Q uestions
•
•
•
Describe the result of applying each rule to a figure in the coordinate plane:
o A(x,y) = ( x-6 , y+7 )
o B(x,y) = ( x , y – 14 )
o C(x,y) = ( x + 5 , y)
o D(x,y) = ( x , - y )
o E(x,y) = ( - x , y )
o F(x,y) = ( - x , - y )
Write the transformation that would translate a figure 5 units to the left and 12 units down
Identify the properties of quadrilaterals and the relationships among the properties.
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Point, line, ray, segment, plane, and angle
o
o
o
o
o
o
o
o
•
•
•
•
•
•
•
•
Students will
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
transformation, translation, reflection, axis of symmetry, rotation
congruent, congruence, corresponding parts
hypothesis, conclusion, conditional, converse, counterexample, bi-conditional, logical chain, proof, theorem
conjecture, theorem, postulate, proof, two-column proof, paragraph proof
vertical angles, adjacent angles, consecutive angles, complementary, supplementary, linear pair
right angel, acute angle, obtuse angle
transversal, alternate interior angles, alternate exterior angles, same-side interior angles, corresponding angles
parallel, perpendicular, bisect, perpendicular bisector
Segment Addition and Angle Addition postulates
Overlapping Segments and Overlapping Angles T heorems
Linear Pair property
Vertical Angles T heorem
T ransitive, Reflexive and Symmetric Properties
Corresponding Angles Postulate and it’s converse
Alternate Interior, Alternate Exterior, Same-Side Interior T heorems and their converses
T riangle Sum T heorem
be able to…
use mathematical vocabulary fluently
use appropriate vocabulary to describe rotations and reflections
interpret and perform a given sequence of transformations and draw the result
accurately use geometric vocabulary to describe the sequence of transformations that will carry a given figure onto another
use rigid motions to map one figure onto another
use the definition of congruence as a test to see if two figures are congruent
recognize why particular combinations of corresponding parts establish congruence and why others do not
prove theorems about lines and angles (e.g., vertical angles are congruent; when a transversal crosses parallel lines,
alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a
line segment are exactly those equidistant from the segment’s endpoints.)
construct proofs using a variety of methods: T wo-column, paragraph, flowchart
make sense of problems and persevere in solving them
reason abstractly and quantitatively
construct viable arguments and critique the reasoning of others
model with mathematics
use appropriate tools strategically
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
•
•
•
•
Unit tests, quizzes,
Open-ended problems that involve written responses
Daily student work
Student/group presentations
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Mathematical investigations
•
Construct and analyze geometric figures
•
Make conjectures from geometric figures and data and then prove or disprove them
•
Work with tools of geometry
•
•
•
Use geometric properties to solve real-world problems
Design a piece of art that illustrates reflectional and/or rotational symmetry. Describe the symmetries in detail.
Create a translation or rotation te ssellation. (examples by M.C. Esher)
RESOURCES
Te ache r Re sources:
•
•
•
•
•
•
Geometry T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Literature: Flatland: A Romance of Many Dimensions by E.A.Abbott
Movie: Flatland (starring Martin Sheen)
Geometers Sketchpad
Visual aids (suggestions) e.g.
o Dominos for logical chains
Equipme nt Ne e ded:
•
•
•
•
•
•
Rulers/straight edge
Protractors
Compasses
Patty paper
Graph paper
Geometers Sketchpad
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Geometry
Unit Title : Unit One - Congruence, Proofs, and Constructions
Targe t Course /Grade Le ve l: Geometry/Grade 11
Unit Summary:
•
•
•
•
•
Experiment with transformations in the plane.
Understand congruence in terms of rigid motions.
Prove geometric theorems.
Prove or disprove whether the figure is a certain type of quadrilateral or triangle*
Make geometric constructions.
Approximate Le ngth of Unit: 16 weeks
Primary interdisciplinary connections: Art, Social Studies, Language Arts, and Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Congruence
Experiment with transformations in the plane
G-CO.1, G-CO.2, G-CO.3, G-CO.4, GCO.5
Congruence
Understand congruence in terms of rigid motion
G-CO.6, G-CO.7, G-CO.8
Congruence
Prove geometric theorems
G-CO.9, G-CO.10, G-CO.11
Expressing Geometric Properties With
Use coordinates to prove simple geometric theorems algebraically
G-GPE.4, G-GPE.5
Equations
Unit Unde rstandings
Students will understand that…
•
Geometric properties can be used to construct geometric figures.
•
Geometric relationships provide a means to make sense of a variety of phenomena.
•
Shape and area can be conserved during mathematical transformations.
•
Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry.
•
Coordinate geometry can be used to represent and verify geometric/algebraic relationships.
Unit Esse ntial Q uestions
•
Describe
o
o
o
the result of applying each rule to a figure in the coordinate plane:
A(x,y) = ( x-6 , y+7 )
B(x,y) = ( x , y – 14 )
C(x,y) = ( x + 5 , y)
•
•
•
•
o D(x,y) = ( x , - y )
o E(x,y) = ( - x , y )
o F(x,y) = ( - x , - y )
Write the transformation that would translate a figure 5 unit to the left and 12 units down
Given four coordinates, prove mathematically which type of quadrilateral is formed.
Determine whether two given triangles are congruent and state which postulate justifies your answer.
Identify the properties of quadrilaterals and the relationships among the properties.
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Point, line, ray, segment, plane, angle, diagonal, endpoint, polygon, center of a polygon, central angle
o transformation, translation, reflection, axis of symmetry, rotation
o congruent, congruence, corresponding parts, equilateral, equiangular, regular polygon, equidistant
o hypothesis, conclusion, conditional, converse, counterexample, bi-conditional, logical chain, proof, theorem
o conjecture, theorem, postulate, proof, two-column proof, paragraph proof
o vertical angles, adjacent angles, consecutive angles, complementary, supplementary, linear pair
o right angel, acute angle, obtuse angle
o transversal, alternate interior angles, alternate exterior angles, same-side interior angles, corresponding angles
o parallel, perpendicular, bisect, perpendicular bisector
o CPCTC- Corresponding Parts of Congruent T riangles are Congruent
•
Formulas –
o distance, midpoint, slope
•
Segment Addition and Angle Addition postulates
•
Overlapping Segments and Overlapping Angles T heorems
•
Linear Pair property
•
Vertical Angles T heorem
•
T ransitive, Reflexive and Symmetric Properties
•
Corresponding Angles Postulate and it’s converse
•
Alternate Interior, Alternate Exterior, Same-Side Interior T heorems and their converses
•
T riangle Sum T heorem
•
Sum of Interior Angles of a Polygon
•
T he Measure of an Interior Angle of a regular polygon
•
Sum of Exterior Angle of a Polygon
•
the slopes of parallel and perpendicular lines are opposite reciprocals
•
the criteria for triangle congruence (ASA, SAS, SSS, and the special case of ASS (HL))
•
CPCTC- Corresponding Parts of Congruent T riangles are Congruent
Students will be able to…
•
use mathematical vocabulary fluently
•
use appropriate vocabulary to describe rotations and reflections
•
interpret and perform a given sequence of transformations and draw the result
•
accurately use geometric vocabulary to describe the sequence of transformations that will carry a given figure onto another
•
use rigid motions to map one figure onto another
•
use the definition of congruence as a test to see if two figures are congruent
•
identify the corresponding parts of two triangles
•
recognize why particular combinations of corresponding parts establish congruence and why others do not
•
prove theorems about lines and angles (e.g., vertical angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are
exactly those equidistant from the segment’s endpoints.)
•
construct proofs using a variety of methods: T wo-column, paragraph, flowchart
•
use distance, slope and midpoint formulas then use the information to solve geometric problems
•
calculate slopes of lines and use the information to determine whether two lines are parallel, perpendicular or neither
•
make sense of problems and persevere in solving them
•
reason abstractly and quantitatively
•
construct viable arguments and critique the reasoning of others
•
model with mathematics
•
use appropriate tools strategically
•
•
•
attend to precision
look for and make use of structure
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes,
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Mathematical investigations
•
Construct and analyze geometric figures
•
Make conjectures from geometric figures and data and then prove or disprove them
•
Work with tools of geometry
•
Use geometric properties to solve real-world problems
•
Design a piece of art that illustrates reflectional and/or rotational symmetry. Describe the symmetries in detail.
•
Create a translation or rotation te ssellation. (examples by M.C. Esher)
RESOURCES
Te ache r Re sources:
•
•
•
•
•
•
Geometry T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Literature: Flatland: A Romance of Many Dimensions by E.A.Abbott
Movie: Flatland (starring Martin Sheen)
Geometers Sketchpad
Visual aids (suggestions) e.g.
o Dominos for logical chains
o AngLegs for triangle congruence
Equipme nt Ne e ded:
•
•
•
•
•
•
Rulers/straight edge
Protractors
Compasses
Patty paper
Graph paper
Geometers Sketchpad
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Geometry
Unit Title : Unit T wo - Similarity, Right T riangles and T rigonometry
Targe t Course /Grade Le ve l: Geometry/Grade 11
Unit Summary:
•
•
•
•
Understand similarity in terms of similarity transformations.
Prove theorems involving similarity.
Define trigonometric ratios and solve problems involving right triangles
Apply geometric concepts in modeling situations.
Approximate Le ngth of Unit: 8 weeks
Primary interdisciplinary connections: Art, Social Studies, Language Arts, and Science
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Similarity, Right Triangles & Trigonometry
Understand similarity in terms of similarity transformations
G-SRT.1, G-SRT.2, G-SRT.3
Similarity, Right Triangles & Trigonometry
Prove theorems involving similarity
G-SRT.4, G-SRT.5
Similarity, Right Triangles & Trigonometry
Define trigonometric ratios and solve problems involving right triangles
G-SRT.6, G-SRT.7, G-SRT.8
Expressing Geometric Properties With Equations
Use coordinates to prove simple geometric theorems algebraically
G.GPE.6, G.GPE.7
Unit Unde rstandings
Students will understand that…
•
Geometric properties can be used to establish similarity.
•
Comparing similar figures is useful when there is a need for indirect measurement.
•
Smaller scale models can be created by using similarity
•
Geometric relationships provide a means to make sense of a variety of phenomena.
•
Measurements can be used to describe, compare, and make sense of phenomena.
Unit Esse ntial Q uestions
•
•
•
•
•
Show how to find the measure of a tree using indirect measurement.
What properties do all triangles share? How are triangles classified?
How are similarity and congruence established? Why is this important?
Prove that two given triangles are similar.
Given a side and an angle of a right triangle, use the trigonometric ratios to find the remaining angles and sides of the triangle.
Knowle dge and Skills
Students will know…
•
Vocabulary –
o
Dilation, center of dilation, contraction, expansion, scale factor, similar, proportionate, corresponding parts
o
Isosceles triangle, vertex angle, base angle, base and legs of an isosceles triangle
o
Corollary
o
Altitude, base and height of a parallelogram, trapezoid and triangle
o
Legs of a trapezoid
o
Apothem
•
Formulas –
o
T rigonometric ratios: SohCahT oa
o
Area of a triangle, parallelogram, trapezoid and a regular polygon
•
T riangle similarity theorems and postulate (ASA, SAS, SSS, the special case of ASS (HL)and AA)
•
Side-splitting theorem
•
Proportional Altitudes, Medians, Angle Bisectors and Segments T heorems
•
Polygon similarity Postulate
•
Pythagorean T heorem and it’s converse
•
Pythagorean Inequalities
•
Pythagorean triples
•
45-45-90 T riangle T heorem
•
30-60-90 T riangle T heorem
•
Isosceles T riangle T heorem and it’s converse
•
T riangle Mid-segment T heorem
•
T riangle Inequality T heorem
Students will be able to…
•
develop a hypothesis based on observations
•
make connections between the definition of similarity and the attributes of two given figures
•
set up and use appropriate ratios and proportions
•
recognize why particular combinations of corresponding parts establish similarity and why others do not
•
construct a proof using one of a variety of methods
•
use information given in verbal or pictorial form about geometric figures to set up a proportion that accurately models the
situation
•
use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems
•
apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on ratios)
•
make sense of problems and persevere in solving them
•
reason abstractly and quantitatively
•
construct viable arguments and critique the reasoning of others
•
model with mathematics
•
use appropriate tools strategically
•
attend to precision
•
look for and make use of structure
•
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes,
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Mathematical investigations
•
Construct and analyze geometric figures
•
Make conjectures from geometric figures and data and then prove or disprove them
•
Work with tools of geometry
•
Use geometric properties to solve real-world problems
•
(HRW) T ext, Pg.542 Portfolio Activity – T echniques for Indirect Measurement
Use proportions and at least two of the methods listed below to find the dimensions of a building or other structure at your school
or in your neighborhood.

Measure the shadow of the building and the shadow of a person or object with a known height

Use a mirror to create similar triangles

T ake a photograph of the building with a person or object of known height standing in front of it. Measure the building and
person in the photograph.
•
(HRW) T ext, Pg.552 Chapter Eight Project – Indirect Measurement
o Build a scale model of your school and possibly the area around it
RESOURCES
Te ache r Re sources:
•
•
•
•
•
•
Geometry T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Literature: Flatland: A Romance of Many Dimensions by E.A.Abbott
Movie: Flatland (starring Martin Sheen)
Geometers Sketchpad
Visual aids (suggestions) e.g.
o
Examples of scale models
Equipme nt Ne e ded:
•
•
•
•
•
•
•
T ape measure
Ruler
Protractor
Poster board
Scissors
T ape
Geometers Sketchpad
RAHWAY PUBLIC SCHOOLS CURRICULUM
UNIT OVERVIEW
Conte nt Are a: Geometry
Unit Title : Unit T hree - Extending to T hree Dimensions
Targe t Course /Grade Le ve l: Geometry/Grade 11
Unit Summary:
•
•
•
Explain volume formulas and use them to solve problems.
Visualize the relation between two‐dimensional and three‐dimensional objects.
Apply geometric concepts in modeling situations.
Approximate Le ngth of Unit: 8 weeks
Primary interdisciplinary connections: Art, Social Studies, Language Arts, Science and Business
LEARNING TARGETS
Content Area Domain
Content Area Cluster
Standard
Geometric Measurement & Dimension
Explain volume formulas and use them to solve problems
G-GMD.1, G-GMD.2, GGMD.3
Geometric Measurement & Dimension
Visualize relationships between two-dimensional and three-dimensional objects
G-GMD.4
Modeling With Geometry
Apply geometric concepts in modeling situations
G-MG.1, G-MG.2, G-MG.3
Expressing Geometric Properties With Equations
Use coordinates to prove simple geometric theorems algebraically
G-GPE.7
Unit Unde rstandings
Students will understand that…
•
T hree dimensional figures can be represented in two dimensions by using the orthographic projections
•
T hree dimensional figures can be drawn/created by referring to the orthographic projections of the figure.
•
Geometric properties can be used to construct geometric figures.
•
Geometric relationships provide a means to make sense of a variety of phenomena.
•
Coordinate geometry can be used to represent and verify geometric/algebraic relationships.
Unit Esse ntial Q uestions
•
•
•
Given a choice of two box designs with different dimensions, which of the two is better from the manufacturer’s point of view.
Justify your answer.
Give examples of when it is better to maximize the surface area to volume ratio and when it is better to minimize the surface area
to volume ratio. Explain what makes it better. (e.g. T ums vs. T ylenol, Plants in hot climates vs. cold climates)
Calculate the volume, surface area or specific dimensions of a variety of polyhedral.
Knowle dge and Skills
Students will know…
•
Vocabulary –
o Orthographic projection, isometric drawing, parallel planes
o Polyhedron, faces, edges, vertices, dihedral angle, cross section,
o Prism, base, height, slant height, lateral height, lateral edge, lateral face, right prism, oblique prism, altitude
o Cylinder, pyramid, cone, sphere
o Surface area, volume, density
o Surface area to volume ratio
•
•
Formulas –
o Area of a regular polygon
o Volume of prism, cylinder, pyramid, cone, sphere
o Surface Area of a right prism, right cylinder, right pyramid and right cone
o Diagonal of a right rectangular prism
o Distance Formula in T hree Dimensions
Cavalieri’s Principle
Students will be able to…
•
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and
cone.
•
Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
•
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
•
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects
generated by rotations of two-dimensional objects.
•
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a
cylinder).
•
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on ratios).
•
Make connections between two-dimensional figures such as rectangles, squares, circles, and triangles and three-dimensional
figures such as cylinders, spheres, pyramids and cones.
•
Connect experiences with this standard as it related to the two-dimensional shapes studied in Unit 2 to three-dimensional shapes.
•
make sense of problems and persevere in solving them
•
reason abstractly and quantitatively
•
construct viable arguments and critique the reasoning of others
•
model with mathematics
•
use appropriate tools strategically
•
attend to precision
•
look for and make use of structure
•
look for and express regularity in repeated reasoning
EVIDENCE OF LEARNING
Asse ssment
What evidence will be collected and deemed acceptable to show that students truly “understand”?
•
Unit tests, quizzes
•
Open-ended problems that involve written responses
•
Daily student work
•
Student/group presentations
•
Daily Homework
Le arning Activities
What differentiated learning experiences and instruction will enable all students to achieve the desired results?
•
Mathematical investigations
•
Construct and analyze geometric figures
•
Make conjectures from geometric figures and data and then prove or disprove them
•
Work with tools of geometry
•
Use geometric properties to solve real-world problems
•
(HRW) T ext, Pg.485 Portfolio Activity Creating Solids of Revolution
•
(HRW) Alternative Assessment Chapter 7 Form A – Product Packaging
•
“ Building a Castle” – Find the volume and surface area of a ‘castle’ built with a variety of children’s blocks
RESOURCES
Te ache r Re sources:
•
•
•
•
•
•
Geometry T extbook: T eachers’ Edition & accompanying resources, e.g. T ransparencies, practice worksheets, assessments,
writing assignments
T eacher developed worksheets and activities
Geometers Sketchpad
Literature: Flatland: A Romance of Many Dimensions by E.A.Abbott
Movie: Flatland (starring Martin Sheen)
Visual aids (suggestions) e.g.
o
Unit blocks, children’s blocks
o
Deck of cards to illustrate Cavalieri’s Principle
o
Set of Geometric Solids, everyday solids
o
Nets of solids
o
Real life examples of solids
o
Assortment of packaging options
o
Cutouts made from Honeycomb balls to identify three-dimensional objects generated by rotations of twodimensional objects.
Equipme nt Ne e ded:
•
•
•
•
•
•
•
•
•
•
Isometric Dot paper
Graph paper
Rulers
Calculators
Student set of Geometric Solids
Nets of solids
Poster board
Scissors
T ape/Glue
Geometers Sketchpad