WOODLAND HILLS SECONDARY LESSON PLAN
Name __ Steven Flanders
Date _9/29/14____
Length of Lesson __7 Periods___ Content Area _AP Calculus AB___
STAGE I – DESIRED RESULTS
LESSON TOPIC (Module, if applicable): Functions and
Properties of Functions
BIG IDEAS:
UNDERSTANDING GOALS (CONCEPTS): Algebraic
properties, processes and representations;
Exponential functions and equations;
Quadratic functions and equations;
Polynomial functions and equations;
Algebraic properties, processes and representations;
Exponential functions and equations;
Algebraic properties, processes and representations;
Quadratic functions and equations;
Algebraic properties, processes and representations;
Polynomial functions and equations
ESSENTIAL QUESTIONS: How can you extend algebraic
properties and processes to quadratic, exponential and
polynomial expressions and equations and then apply them to
solve real world problems?
What are the advantages/disadvantages of the various methods
to represent exponential functions (table, graph, equation) and
how do we choose the most appropriate representation?
How do quadratic equations and their graphs and/or tables
help us interpret events that occur in the world around us?
How do you explain the benefits of multiple methods of
representing polynomial functions (tables, graphs, equations,
and contextual situations)?
Students will understand: How to graph polynomial, exponential,
trigonometric, logarithmic and rational functions, how to find the domain and
range of each of the previously listed functions, how to evaluate each kind of
function, how to make and extend connections between algebraic, graphic
and tabular representations of each kind of function.
(Content standards, assessment anchors, eligible content) objectives, and skill
focus)
Numbers, measures, expressions, equations, and inequalities can represent
mathematical situations and structures in many equivalent forms.
Patterns exhibit relationships that can be extended, described, and
generalized.
Relations and functions are mathematical relationships that can be
represented and analyzed using words, tables, graphs, and equations.
There are some mathematical relationships that are always true and these
relationships are used as the rules of arithmetic and algebra and are useful
for writing equivalent forms of expressions and solving equations and
inequalities.
Mathematical functions are relationships that assign each member of one set
(domain) to a unique member of another set (range), and the relationship is
recognizable across representations.
Families of functions exhibit properties and behaviors that can be recognized
across representations. Functions can be transformed, combined, and
composed to create new functions in mathematical and real world situations.
Bivariate data can be modeled with mathematical functions that approximate
the data well and help us make predictions based on the data.
Degree and direction of linear association between two variables is
measurable. 2.1.A2.A, 2.1.A2.B, 2.1.A2.D, 2.1.A2.F, 2.2.A2.C, 2.3.A2.C,
2.3.A2.E, 2.5.A2.A, 2.8.A2.B, 2.8.A2.C, 2.8.A2.E, A2.1.1.1.2, A2.1.1.2.1,
A2.1.1.2.2, A2.1.2.1.1, A2.1.2.1.2, A2.1.2.1.3, A2.1.2.1.4, A2.1.2.2.1,
A2.1.2.2.2, A2.2.1.1.1, A2.2.1.1.2, A2.1.3.1.1, A2.1.3.1.2, A2.1.3.1.3,
A2.1.3.2.1, A2.1.3.2.2
2.1.A2.B, 2.3.A2.E, 2.6.A2.C, 2.8.A2.B, 2.8.A2.D, 2.8.A2.E, 2.8.A2.F,
2.11.A2.A, A2.1.2.2.1, A2.1.2.2.2, A2.2.1.1.3, A2.2.1.1.4, A2.2.2.1.3, A2.2.2.1.4,
A2.2.2.2.1, A2.1.3.1.1, A2.1.3.1.2, A2.2.3.1.1
2.1.A2.B, 2.3.A2.E, 2.6.A2.C, 2.8.A2.B, 2.8.A2.D, 2.8.A2.E, 2.8.A2.F,
2.11.A2.A, A2.1.2.2.1, A2.1.2.2.2, A2.2.1.1.3, A2.2.1.1.4, A2.2.2.1.3, A2.2.2.1.4,
A2.2.2.2.1, A2.1.3.1.1, A2.1.3.1.2, A2.2.3.1.1
VOCABULARY: function, domain, range, exponential,
logarithmic, trigonometric
STUDENT OBJECTIVES
(COMPETENCIES/OUTCOMES):
Extend algebraic properties and processes to
quadratic, exponential, and polynomial expressions
and equations and to matrices, and apply them to
solve real world problems.
Extend algebraic properties and processes to
quadratic, exponential, and polynomial expressions
and equations and to matrices, and apply them to
solve real world problems.
Extend algebraic properties and processes to
quadratic, exponential, and polynomial expressions
and equations and to matrices, and apply them to
solve real world problems.
Extend algebraic properties and processes to
quadratic, exponential, and polynomial expressions
and equations and to matrices, and apply them to
solve real world problems.
Represent exponential functions in multiple ways,
including tab les , graphs, equations, and contextual
situations, and make connections among
representations; relate the growth/decay rate of the
associated exponential equation to each
representation. Represent exponential functions in
multiple ways, including tab les , graphs, equations,
and contextual situations, and make connections
among representations; relate the growth/decay rate
of the associated exponential equation to each
representation. Represent a quadratic function in
multiple ways, including tab les , graphs, equations,
and contextual situations, and make connections
among representations; relate the solution of the
associated quadratic equation to each representation.
Represent a quadratic function in multiple ways,
including tab les , graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
quadratic equation to each representation.
Represent a quadratic function in multiple ways,
including tables , graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
quadratic equation to each representation.
Represent a polynomial function in multiple ways,
including tab les , graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
polynomial equation to each representation.
Represent a polynomial function in multiple ways,
including tab les , graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
polynomial equation to each representation.
Students will be able to:
Evaluate polynomial, exponential, trigonometric,
logarithmic and rational functions, find the domain and
range of each of the previously listed functions, evaluate
each kind of function, make and extend connections between
algebraic, graphic and tabular representations of each kind
of function.
STAGE II – ASSESSMENT EVIDENCE
PERFORMANCE TASK: Students will be given graded
homework assignments that are selectively chosen from a
bank of practice AP questions. Students will be given a
mulitple choice test and a free response test, both with
questions chosen from released AP questions and/or AP
review books to ensure validity of test questions.
FORMATIVE ASSESSMENTS:
In class observation and frequent summative assessment
throughout each class period
STAGE III: LEARNING PLAN
INSTRUCTIONAL
PROCEDURES:
Do Now; Students will solve warm-up
emphasizing multiple representations
Mini Lesson: Students and instructor
will fill-in guided notes from sections
Guided Practice: Students and
instructor will to solve examples in
the guided notes
Independent Practice: Students will
work individually on examples in
guided notes and homework
problems
Summations/Formative Assessments:
1) Summarize main ideas of
lesson
2) I will ask open-ended
questions and then discuss
thoughtful answers
Reflections:
MATERIALS AND
RESOURCES:
Typed notebook, Gaphing
Calculator, textbook
INTERVENTIONS:
Students will begin each
class asking for help on any
previous homework
questions and one question
practice quizzess will be used
intermittently to guage
mastery of individual
concepts.
ASSIGNMENTS:
Multiple Choice and OpenEnded Homework
assignments are due at the
end of the chapter. Daily
homework assignments are
included in the notebook
after each lesson.