COURSE: ALGEBRA II
TOPIC: Functions
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STAGE 1:
IDENTIFY DESIRED RESULTS |
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Content Standard(s) Generalizations about what students should know and be able to do |
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Established Goals: CT FRAMEWORKS: a.) Functions can be viewed as objects on which operations can be performed. b.) Algebraic concepts can be extended from real numbers to include objects such as complex numbers and matrices. NCTM FRAMEWORKS: a.) Generalize patterns using explicitly defined and recursively defined functions b.) Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior c.) Understand and perform transformations such as combining, composing and inverting commonly used functions d.) Understand
and compare classes of functions, including exponential, logarithmic and
periodic functions |
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Enduring Understandings Insights earned from exploring generalizations via the essential
questions (Students will understand THAT…) |
Essential Questions Inquiry used to explore generalizations |
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The student will understand that: 1.) There are several types of functions 2.) Operations and transformations apply to all types of functions. 3.) Geometric and analytical information can explain local and global behavior of a function. 4.) All functions have algebraic, numeric, and graphic representations. |
1.) What are the different types of functions? 2.) What are the operations that apply to all functions? 3.) How can Geometric and Analytic representations be used to describe the behavior of the function? 4.) How
are the algebraic, numeric, and graphic representations of functions related? |
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Knowledge and Skills What students are expected to know and be able to do |
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Students will know… 1.) There are several types of functions including: polynomial, logarithmic, exponential, trigonometric, inverse, absolute value and rational. 2.) The operations and transformations that apply to the different types of functions. 3.) The algebraic, numerical, and graphical representations of functions. 4.) That
functions are used to model real world behavior. |
Students will be able to… 1.) Identify several types of functions. 2.) Use operations and transformations on the different types of functions. 3.) Find the domain, range, zeros, maxima, minima and inverse of functions. 4.) Solve equations of second or higher degree using factoring. 5.) Solve linear and quadratic inequalities with one or two variables. 6.) Represent functions algebraically, numerically, and graphically. 7.) Model
and solve real life problems using functions. |
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STAGE 2:
DETERMINE ACCEPTABLE EVIDENCE |
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Performance Task(s) Authentic application in new
context to evaluate student achievement of desired results designed according
to GRASPS (Goal, Role, Audience, Setting Performance, Standards) |
Other Evidence Application that is functional in a classroom context only to
evaluate student achievement of desired results |
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Lead poisonings in Massachusetts children under the age of
6 years of age from 1985 through 1995 can be modeled by |
In addition to tests and quizzes, one or more of the following will be used: 1.) Cooperative learning activities. 2.) Graphing calculator activities. 3.) Informal
and formal check such as homework checks, problem of the day, or review
sheets. |
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STAGE 3:
DEVELOP LEARNING PLAN |
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Learning Activities: 1.) Cooperative learning activities. 2.) Graphing calculator activities 3.) Homework
and review worksheets. |
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COURSE: ALGEBRA II
TOPIC:
Polynomials and Factoring
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STAGE 1:
IDENTIFY DESIRED RESULTS |
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Content Standard(s) Generalizations about what students should know and be able to do |
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Established Goals: CT Frameworks: a.) Functions
are used in a variety of situations including to model data and to make
predictions. b.) Functions
can be viewed as objects on which operations can be performed. NCTM Standards: a.) Represent
and analyze mathematical situations and structures using algebraic symbols. b.) Use
Algebra to represent and explain mathematical relationships. c.) Understands
patterns, relations and patterns. d.) Use
the language of Algebra to express mathematical ideas precisely. e.) Select,
apply and translate among mathematical representations to solve problems. |
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Enduring Understandings Insights earned from exploring generalizations via the essential
questions (Students will understand THAT…) |
Essential Questions Inquiry used to explore generalizations |
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The student will understand: 1.) Polynomials can be added, subtracted, multiplied and divided. 2.) Polynomial equations can be factored and solved using various methods; solutions may be real or imaginary. 3.) Polynomials may be part of a system of equations or inequalities which may be solved. 4.) Factoring can be used to solve equations of the second or higher degree. 5.) Polynomials are used to analyze the graphs of parabolas, hyperbolas, circles and ellipses. |
1.) How do you add, subtract, multiply and divide polynomials? 2.) How do you factor and solve polynomials? 3.) What techniques can you use to solve a system of equations? 4.) How are polynomials and their graphs related? 5.) Will
polynomials ever be used in real life? |
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Knowledge and Skills What students are expected to know and be able to do |
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Students will know… 1.) How to perform operations on polynomials. 2.) How to factor and solve equations and systems of equations. 3.) How to solve systems of equations and inequalities 4.) How polynomials and their graphs relate. 5.) How
to use polynomials to solve real life situations. |
Students will be able to… 1.) Use the four basic operations on polynomials. 2.) Use factorization, completing the square and the quadratic formula to solve equations. 3.) Solve systems of equations and inequalities. 4.) Graph polynomials and explain how the graph relates to the polynomial. 5.) Solve a polynomial to find the answer to a real life problem. |
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STAGE 2:
DETERMINE ACCEPTABLE EVIDENCE |
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Performance Task(s) Authentic application in
new context to evaluate student achievement of desired results designed
according to GRASPS (Goal, Role, Audience, Setting Performance, Standards) |
Other Evidence Application that is functional in a classroom context only to
evaluate student achievement of desired results |
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The shape and thickness of a contact lens depends on the vision correction that is needed. The intersection of the following inequalities describes a typical contact lens cross section. (x and y are measured in millimeters) Sketch the region. How thick is it?
(Heath:Algebra II, page 279 #59) |
In addition to quizzes and tests, one or more of the following will be used : 1.) Cooperative learning activities. 2.) Graphing calculator activities 3.) Homework
and review worksheets. |
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STAGE 3:
DEVELOP LEARNING PLAN |
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Learning Activities: 1.) Cooperative learning activities. 2.) Graphing calculator activities 3.) Homework
and review worksheets. |
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