Download Lesson Plan on Introduction to Trigonometry

Lesson Plan on Introduction to Trigonometry
University of Scranton
Education Department
Teacher – Shannon Robinson
School – ABC High School
Co-Operating Teacher – Dr. Scott Riley
Date – 1-22-13
Grade – 11th Grade
Class – Algebra II
Unit Title – “Introduction to Trigonometry: Sine, Cosine, Tangent”
Lesson Plan Title – “Sine and Cosine: The Beginning”
Unit Objectives – Students will learn about sine, cosine and tangent curves. Using this newly learned
information, students will be able to solve problems involving the sine, cosine and tangent curves.
Lesson Objectives – Using direct instruction lesson model, students will learn about the basic principles
of the sine and cosine curves.
State Standard(s) met – F-TF - Extend the domain of trigonometric functions using the unit circle
- Prove and apply trigonometric identities
Sequence of Planning Strategies
Procedures, Directions, Notes and
Questions
At the Bell: Students are given a
review previously taught principles
and definitions on angles. Key terms
(This lesson should take about
will be addressed.
forty-five minutes to one hour. The - Acute Angle
students in a Algebra class will
- Right Angle
review angle principles and will be - Obtuse Angle
introduced to the properties of the
- Straight Angle
trigonometric functions sine and
cosine. Direct Instruction will be Numerous examples of each will be
used)
given such as what type of angle is an
angle that measures 60 degrees
Introduction, Set Induction or
Anticipatory Set
Lesson Content, Procedures
and Body
After the review, students will learn
how to convert degrees into radians
and radians into degrees which will
come in handy when looking at sine
and cosine curves.
Students will practice by converting
270 degrees into radians and (5Pi)/6
radians to degrees.
Then students will be introduced to the
Examples, Illustrations and
Resources
Powerpoint Presentation
Blackboard if computer is not
working
Printed out copy of powerpoint
presentation for the teacher only
Protractors for the students
Handouts with these examples on
them. Students can also review how
to use a protractor
Degrees to Radians: Convert from
degrees to radians by multiplying
the number of degrees by Pi/180.
Radians to Degrees: Convert from
radians to degrees by multiplying
the number of radians by 180/Pi.
sine and cosine curve (see powerpoint)
Being able to recognize radians will
help students to understand from the
pictures given that Pi/6 = 30 degrees
and Pi = 180 degrees for example.
Students will then be shown a right
triangle, the next step in trigonometry
(see powerpoint).
The students will then be reminded
that in a right triangle, there is a right
angle and a hypotenuse opposite the
right angle.
With this in mind, students will then
Sin(x) = Opposite (O)
be taught the formula for the sine of an
Hypotenuse (H)
angle using the given picture as
reference.
Students will then be taught the
formula for the cosine of an angle
using the given picture as reference.
Cos(x) = Adjacent (A)
Hypotenuse (H)
Using that triangle, values will be
Blackboard
substitute in for the hypotenuse,
adjacent side and opposite side of
1. H = 60, A = 15, O = 30
angle x. Students will then be asked to 2. H = 150, A = 75, O = 25
solve them at their desks individually.
Performance/Behavior
Standards
Students are expected to obey all
classroom rules including listening to
the teacher and not exhibiting
disruptive classroom behavior.
Students are expected to work quietly
at their desk when doing individual
work.
Students are expected to participate in
discussion as a class by asking
questions and actively listening and
responding to others.
Closure
At the end of class, students will be
asked to give the answers that they
received for the sine and cosine by
using the given numbers.
1. Sin(x) = 30/60 = ½,
Cos(x) = 15/60 = ¼
2. Sin(x) = 25/150 = 1/6,
Cos(x) = 75/150 = ½
Assessment
The students will not be graded on a
strict point based scale or rubric.
Instead, the students' work will be
assessed on whether they show clear
understanding of the topics discussed
and whether they put the needed time
and effort into their work as the these
questions above will not be handed in.
Differentiation
Adaptions and modifications to the
lesson will be made as needed.
Lesson Plan on Introduction to Trigonometry
University of Scranton
Education Department
Teacher – Shannon Robinson
School – ABC High School
Co-Operating Teacher – Dr. Scott Riley
Date – 1-22-13
Grade – 11th Grade
Class – Algebra II
Unit Title – “Introduction to Trigonometry: Sine, Cosine, Tangent”
Lesson Plan Title – “Sine and Cosine: Problem Solving”
Unit Objectives – Students will learn about sine, cosine and tangent curves. Using this newly learned
information, students will be able to solve problems involving the sine, cosine and tangent curves.
Lesson Objectives – Through cooperative learning, students will be able to use use their newly acquired
knowledge on sine and cosine curves to solve problems involving these curves.
State Standard(s) met – F-TF - Extend the domain of trigonometric functions using the unit circle
- Prove and apply trigonometric identities
Sequence of Planning Strategies
Procedures, Directions, Notes and
Questions
At the Bell: Students will be shown
the sine and cosine curves and asked
to determine which one is which and
(This lesson should take about
why (curves will be drawn on the
forty-five minutes to one hour. The blackboard).
students in a Algebra class will
review the properties of the
The formulas will also be written on
trigonometric functions sine and
the board.
cosine and will be asked to solve
problems involving sine and
cosine. Cooperative Learning will
be used)
Introduction, Set Induction or
Anticipatory Set
Lesson Content, Procedures
and Body
Examples, Illustrations and
Resources
Blackboard
Sin(x) = Opposite (O)
Hypotenuse (H)
Cos(x) = Adjacent (A)
Hypotenuse (H)
Students will then be shown two
examples of a trigonometric problem,
one sine and one cosine, by the
teacher.
Example problems
After this, students will be broken up
into groups to work on three problems
ranging from easiest to hardest (From
a picture of a triangle problem to a
word problem where they have to
draw, there own triangles to determine
Handouts for each student. Each
group will be given three unique
problems to work on.
Graphing calculators for the
students (just in case)
Groups will be mixed so gifted
students, average students and
the answers).
students with special needs will be
working together.
Each group of students will be visited Paper so that the teacher can
by the teacher.
acknowledge that all of the students
who are actively participating in
their groups and which students
might be having trouble with the
lesson and its material.
Performance/Behavior
Standards
Students are expected to obey all
classroom rules including listening to
the teacher and not exhibiting
disruptive classroom behavior.
Students are expected to work quietly
at their desk when doing individual
work.
Each member of the group must be
participating and contributing to the
group discussion.
While working in groups, students
may get out of their seats and move
closer to one another if needed.
Students are expected to participate in
discussion as a class and while
working in their groups by asking
questions and actively listening and
responding to others.
Closure
After checking over each others' work Blank handouts with the hardest
in the group, each group of students
problem from each group's problem
will be given a blank copy of their
sets.
hardest problem from their problem
set. One person will have to write
down their group's full solution on
how they received their final answer.
The writing should be legible and the
more work, the better.
Assessment
One at a time, each group of students Document Reader
will then be asked to come to the front
of the class to teach the class how to
Blackboard if document reader is
solve their specific problem.
not available
Students will be assessed on how they
worked together as a group and if they
contributed to their group's final work.
Differentiation
Adaptions and modifications to the
lesson will be made as needed.
Lesson Plan on Introduction to Trigonometry
University of Scranton
Education Department
Teacher – Shannon Robinson
School – ABC High School
Co-Operating Teacher – Dr. Scott Riley
Date – 1-22-13
Grade – 11th Grade
Class – Algebra II
Unit Title – “Introduction to Trigonometry: Sine, Cosine, Tangent”
Lesson Plan Title – “And We Go Off on Tangents.....”
Unit Objectives – Students will learn about sine, cosine and tangent curves. Using this newly learned
information, students will be able to solve problems involving the sine, cosine and tangent curves.
Lesson Objectives – Using guided learning, students will be able to use their knowledge of the sine and
cosine curves to learn about the properties of the tangent curve.
State Standard(s) met – F-TF - Extend the domain of trigonometric functions using the unit circle
- Prove and apply trigonometric identities
Sequence of Planning Strategies
Procedures, Directions, Notes and
Questions
Examples, Illustrations and
Resources
Introduction, Set Induction or
Anticipatory Set
At the Bell: Students will be shown
the triangle from the first lesson plan
in the unit.
Blackboard
Then students will be shown the term
SOHCAHTOA. They will be shown
that what the SOH and CAH stand.
Then using the given triangle and
context clues will have to determine a
formula for what the T stands for.
S – sine
O – opposite
H – hypotenuse
(This lesson should take two to
three days. The students in a
Algebra class will review the
properties of the trigonometric
functions sine and cosine and will
be introduced to the trigonometric
function tangent. Guided Learning
will be used)
C – cosine
A – adjacent
H – hypotenuse
T – tangent
O – opposite
A – adjacent
Lesson Content, Procedures
and Body
After discovering that the
T = O = Opposite,
A
Adjacent
students will be told that the T stands
for tangent.
Students will then be broken up into
pairs of two (groups of three if
Tangent = sin(x)
cos(x)
needed) to determine a formula for
tangent using sine and cosine.
Students will be told that there exist
reciprocal and inverse functions
functions of these trigonometric
functions
- cosecant
- secant
- cotangent
- arcsine
- arccosine
- arctangent
The class will be divided into six
groups and will have to work together
using textbooks and computers to
learn more about these functions.
The groups will have to put together
presentations to present to the class on
their findings.
During each presentation, students
should be taking notes as the students
will be teaching one another during
this lesson.
Performance/Behavior
Standards
Students are expected to obey all
classroom rules including listening to
the teacher and not exhibiting
disruptive classroom behavior.
Students are expected to work quietly
at their desk when doing individual
work.
Each member of the group must be
participating and contributing to the
group discussion.
While working in groups, students
may get out of their seats and move
closer to one another if needed.
Students are expected to participate in
discussion as a class and while
working in their groups by asking
questions and actively listening and
responding to others.
Textbooks and Computers
Closure
The groups will be asked to present
their findings to the class.
Assessment
The students will be assessed on how
much they were able to learn, how
they delivered their findings and how
they much work and effort they put in.
Differentiation
Adaptions and modifications to the
lesson will be made as needed.
Visual aids needed by the students
to present their findings.