WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name Steven Flanders Date 2/15/13
was updated this week:
Length of Lesson 15 Class PeriodsContent Area Calculus AB
Edline
My Class website was updated this week:
STAGE I – DESIRED RESULTS
LESSON TOPIC:Area under Curves and The Definite
Integral
BIG IDEAS:
(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
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
Students will understand: How to find the area under a curve byt using Riemann
Sums for estimation, infinite Riemann Sums to find exact answers, the Use of the
Fundamental Theorem as a method of evaluating Definite Integrals, the
Fundamental Theorem as a method to find the Derivative of an Integral, the
relationship between integrals and derivatives, how to estimate Areas using the
Trapezoidal approximation, how to find the average value of a function, how to
integrate using U-substitution, how to sue the Ti-83 to enhance understanding of
Areas and how to evaluate definite integrals, the difference between the definite
integral as a constant and as a function.
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)?
VOCABULARY: Area, definite integral, Riemann Sum,
Trapezoidal Rule, indefinite integral, Fundamental Theorem
of Calculus, Integration by Substitution, average value of a
function, Numerical Integration
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 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 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. v
Students will be able to:
find the area under a curve by using Riemann Sums for
estimation, infinite Riemann Sums to find exact answers,
understand the Use of the Fundamental Theorem as a method
of evaluating Definite Integrals, the Fundamental Theorem as
a method to find the Derivative of an Integral, the
relationship between integrals and derivatives, show how to
estimate Areas using the Trapezoidal approximation, how to
find the average value of a function, how to integrate using Usubstitution, how to use the Ti-83 to enhance understanding
of Areas and how to evaluate definite integrals, demonstrate
knowledge and understanding of the difference between the
definite integral as a constant and as a 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:
#1. Graphic Organizers
#2. Summarizing Main Ideas
#3. Think-Pair-Share
Others: In class observation and frequent summative
assessment throughout each class period.
STAGE III: LEARNING PLAN
INSTRUCTIONAL
PROCEDURES:
MATERIALS AND
RESOURCES:
Active Engagements used:
#1. Note-Taking
#2. Higher Level Thinking Skills
Others:
Typed notebook,
Gaphing Calculator,
textbook
Describe usage: Students will be
instructed through direct
instruction, including fill-in-theblank notes and extensive
modeling. Practice problems will
be sufficiently scaffolded in class
as to allow students to solve
problems with just enough help
from the instructor.
CONTENT AREA
READING:
Scaffolding used:
#1. Guided Notes
#2 . Build on Prior Knowledge
Others:
Describe usage: Students will be
instructed through direct
instruction, including fill-in-theblank notes and extensive
modeling. Practice problems will
be sufficiently scaffolded in class
as to allow students to solve
problems with just enough help
from the instructor.
Other techniques used:
Lesson will begin with a practice
problem from previous lesson
History of Mathematics
INTERVENTIONS:
ASSIGNMENTS:
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.
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.
(approx. 5 minutes). Students
will then ask questions from
homework (10-15 minutes). New
learning will then be presented
with several examples and
models (20-25 minutes).
MINI LESSON:
Lesson will begin with a practice
problem from previous lesson
(approx. 5 minutes). Students
will then ask questions from
homework (10-15 minutes). New
learning will then be presented
with several examples and
models (20-25 minutes).