Lesson Plan (non-inquiry)
Name: Elizabeth Berlinger
Title of
Lesson: Triangle
Simulation
Date of
Lesson: Thursday/Friday
of the 1st week of the Unit
Length
of Lesson: 50
minutes
Description
of the class:
Name
of course:
Pre-Calculus
Grade
Level: 11th
or 12th
Honors
or Regular: Regular
Source
of the lesson:
http://argyll.epsb.ca/jreed/math9/strand3/3103.htm
TEKS
addressed:
(b3B) The
student constructs and justifies statements about geometric figures and their
properties.
(c3) The
student identifies and applies patterns from right triangles to solve problems,
including special right triangles (45-45-90 and 30-60-90) and triangles whose
sides are Pythagorean triples.
(e1C) The
student develops, extends, and uses the Pythagorean Theorem.
(f3) In a
variety of ways, the student develops, applies, and justifies triangle
similarity relationships, such as right triangle ratios, trigonometric ratios,
and Pythagorean triples.
The
goal for this lesson is to give students a way to review and solidify their understanding of the use of trig to
find missing angles and sides, the use of the Pythagorean
Theorem and other basic concepts of trigonometry, with the help of a simulation.
II.
Performance or learner outcomes:
Students
will be able to:
1).
Use sine, cosine, and tangent ratios to calculate angles in a right triangle
with and without scientific calculators.
2).
Use the Pythagorean Theorem to calculate angles in right triangles.
3).
Define and explain trig vocabulary such as sine, cosine, hypotenuse,
tangent, opposite angle, ect.
III.
Resources, materials and supplies needed:
1).
Computers with internet access for each student
Five-E Organization
ENGAGEMENT:
Teacher
Does
Probing Questions
Student Does
Since
this lesson is a review of concepts learned in previous courses, I will start
the lesson with a discussion about what they should, but may not, already
know. Through this I will be assessing prior knowledge as well. |
What are
the names of the three types of triangles, and what characteristics make them
unique? How many degrees do the angles inside of any triangle sum to? How do
you know this? Is there a way to find the length of a missing side of a
triangle if you have the length of the other two sides and the angle
measures? How would you go about doing this? Can anyone tell me what the
Pythagorean Theorem says and why it is useful? Has anyone heard or seen the
acronym SOHCAHTOA? What does it stand for, and how is it used? |
Student
responses will reflect any misconceptions about how to calculate angles
measures and side lengths. It will also let me know how solid or shaky their
understanding of these concepts are. |
Briefly
discuss how these “old” concepts will be useful to them when thinking about
and answering the driving question. |
|
|
EXPLORE:
Teacher
Does
Probing Questions
Student Does
We are
going to be using the computers today to work on some simulations to see how
well you remember the concepts you learned in Geometry. This will act as a
review for most of you, but it will be helpful in the next coming weeks.
Please everyone find a computer and go to the following website: http://argyll.epsb.ca/jreed/math9/strand3/3103.htm |
|
Students
do as they are told, and use this time to ask any preliminary questions they
might have. |
There are many different links on the website that all
have different activities and games for you to play that address right
triangles and other geometry concepts you have learned. Some of your options
are: 1. Vocabulary matching game 2. Exercises utilizing SOHCAHTOA, with explanations 3. Trigonometry flash cards 4. Manipulation of triangles and use of trig to calculate
angles 5. Exploration of trig ratios and patterns I will be
walking around the room helping whoever needs it, but please use your peers
as sources of guidance first. |
|
Students
explore the website choosing activities that deal with the concepts they feel
weakest in. |
EXPLAIN:
Teacher Does
Probing Questions
Student Does
After the
students work on theses activities for a majority of the time, we will
conclude with a discussion about what they learned, how much of what they did
was a review, and did they find something out that they never knew before |
Were
there any concepts covered in the simulation that you had never seen before? If so, which ones? Did
these activities/games help solidify your understanding of triangles and the
geometry behind them? Did you find the vocabulary game helpful at all, or was
the terminology more confusing than it was beneficial? What would you guys
say was the major theme of this entire simulation, and if you had to describe
it someone else, what would you say? |
Students
respond to probing questions hopefully leading to more questions left
uncovered by the simulation. Students respond and discuss with each other as
much as with me. |
EXTEND/ELABORATE:
Teacher
Does Probing Questions Student Responses
Now that
we have done a fairly thorough review of the concepts needed to start your
projects, let’s discuss how you might apply these concepts to your sundials. |
Which
concepts do you think will be most important, and in what ways do you think
you will use them? |
Students
will respond with guesses that they will need some knowledge of circles (for the
base), isosceles triangles (for the time increments), etc. They will not know
at this point that the Law of Sines and Cosines will be needed when
constructing the gnomon. I would also like them to note that some knowledge
of latitude and longitude will be necessary. |
EVALUATE:
Teacher
Does
Probing Questions
Student Does
I will
be doing the “Misconception/Preconception Check” from our list of CAT’s as an
assessment for this lesson. I chose this one because most of the students
will be coming into this review with different Geometry backgrounds. This
will help me to gauge how far along everyone is. I will create a list of
common misconceptions that I believe the students will have, and from that I
will create a questionnaire to elicit their ideas on these concepts. |
|
Students
fill out the questionnaire to the best of their abilities and turn them into
me to evaluate. From there I can create a plan for what I should plan to
cover again or in a different way. |