This lesson plan aims to teach students how to use trigonometric ratios to solve problems. Students will first review trigonometric ratios, then practice solving application problems in groups. Examples include finding missing side lengths and angles of triangles. Teachers will monitor student progress and provide help as needed. To assess understanding, students will complete sample problems and discuss their work. The goal is for students to learn how to approach word problems using trigonometric concepts.

1. Course: Analytic Geometry
Title of Lesson: Trigonometric Ratios (Lesson Plan 1)
Date: October 7th, 2014
Learning Objectives:
By the end of the lesson, students should be able to know the definitions of sine
cosine and tangent. This includes knowing what each trig ratio means (e.g. 𝑠𝑖𝑛𝑒 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
, 𝑐𝑜𝑠𝑖𝑛𝑒 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
, 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
) and also knowing how to
calculate them.
Essential Question: How are trigonometric ratios related to one another?
Standards:
MM2G2 Students will define and apply sine, cosine, and tangent ratios of
complementary angles.
Practice Standards:
(1) Make sense of problems and persevere in solving them
(2) Reason abstractly and quantitatively
(5) Use tools appropriately
(6) Attend to precision
(7) Look for and make use of structure
Materials:
 Pencil or Pen
 Ruler
 Trig Ratios Learning Task worksheet
Vocabulary:
 Adjacent Side
 Angle
 Cosine
 Hypotenuse
 Complementary Angles
 Opposite Side
 Ratio
 Right Triangle

2.  Sine
 Special Right Triangles
 Tangent
 Theta (𝜃)
 Trigonometric Ratios
Learning Task:
The activity will be completed in one 70-minute class period depending on how long
the students spend on the lesson. For this lesson we will spend 10 minutes the
introduction where students will work on the warm-up. For the warm-up, students
are provided with cut outs of various similar triangles on them where they need to
measure certain sides of the triangles that will be specified via the SMART board.
We did this so that later on in the lesson (the closer) they will be able to quickly
calculate the sine, cosine, and tangent values. All in all this should take about 10
minutes to complete. After this, we will dive right into the main activity. With this
students will be exploring the trigonometric ratios. They will have to first measure
the sides of a group of triangles; then they will have to categorize them as either the
opposite side, adjacent side, or the hypotenuse; then they will have to calculate the
trigonometric ratios; then lastly they will need to investigate if these values will be
the same for all right triangles with congruent angles. This activity will take about
30 to 40 minutes to complete. Basically it will last the rest of the class period. During
this time, we will move around each table monitoring and helping in what ever way
we can. For the closing part of the classroom, if time permits, they will have to
answer the wrap-up problem. Hopefully students will realize that the wrap-up looks
familiar since it is exactly the same as the warm-up. The only difference is that
instead of measuring the lengths of the triangles form the warm-up, they will now
use those measurements to calculate the sine, cosine, and tangent values. We did
this to gauge if students learned the main topics of the lesson. With this, we will
have them write their answer on a separate sheet of paper, which we will take up as
a quick classwork grade. Again if time permits, this should take around 10 minutes.
While they are completing the wrap-up, we will discuss what the homework will be
for the night and make any announcements that are needed in order to prepare for
the next class.

3. Handouts for students:

4. Extensions of task/lesson:
Some extensions of this task could be to add some application problems. This will
include calculating the sine, cosine, and tangent values of triangles. Since this is an
introductory lesson, I do not want to go to crazy on extensions since students will
already be struggling with the new concept. These extensions will be provided to
the students if needed.
Instructional Strategies:
Since this is an introductory lesson into the trigonometric ratios, the only thing I can
think about as a way to differentiate the task is through the use of technology. Since
this task touches on how the trigonometric ratios change over an interval, this
applet will mainly be used for trying to make comparisons between the sine, cosine,
and tangent measures of similar triangles. Through the use of the applet, we can
have the calculations for each trigonometric ratio shown on screen and from there
we can have a slider that controls the size of the triangle. This will allow the
students to see that now matter what the size of the triangle, as long as the triangles
are similar the sine, cosine, and tangent values amongst them will be the same.
Ways to assess student progress:
Since there are three of us in the classroom, we will each monitor two to three
groups during the activity. With this, we are able to go back and forth between each
group and help them with any questions/concerns they may have with the activity.
If we see that some groups are not completing the activity with the time we allotted,
we can either add more time or decrease the amount of time needed for this
investigation. Also by monitoring the progress of each group we will have a better
understanding of where the students are struggling with the most while working on
this assignment. This will allow us to get a better idea of the questions they may ask
at the end of the class during the full class discussion.

5. Course: Analytic Geometry
Title of Lesson: Trigonometric Word Problems (Lesson Plan 3)
Date: October 14th, 2014
Learning Objectives:
By the end of the lesson, students should be able to use the definitions of the
trigonometric ratios in order to solve problems. Students will have to be able to
solve for the missing sides of a triangle, the missing angles of triangles, and also
various application/“real world” problems.
Essential Question: How can use the trigonometric functions to solve problems?
Standards:
MM2G1: Students will define and apply sine, cosine, and tangent ratios of
complementary angles.
b) Explain the relationships between the trigonometric ratios of complementary
angles.
Practice Standards:
(1) Make sense of problems and persevere in solving them
(2) Reason abstractly and quantitatively
(4) Model with mathematics
(6) Attend to precision
(7) Look for and make use of structure
Materials:
 Pencil or Pen
 Paper
 Notebook
Vocabulary:
 Adjacent Side
 Angle
 Angle of Depression
 Angle of Elevation
 Cosine
 Hypotenuse
 Complementary Angles

6.  Opposite Side
 Ratio
 Right Triangle
 Sine
 Special Right Triangles
 Tangent
 Theta (𝜃)
 Trigonometric Ratios
 Vertices
Learning Task:
The activity will be completed in one 70-minute class period depending on how long
the students spend on the lesson. For this lesson we will spend 10 minutes the
introduction where students will work on the warm-up. With this, students are to
use the knowledge that they have learned about the trigonometric functions in
order to determine how they might be able to find the missing side length of a
triangle. Since they do not yet know how to do this, this question is mainly for
discussion. We did this in order to have students start thinking about how they can
use the trigonometric ratios to solve various problems. This will help smooth out
the lesson since students will have to be able to think about the ratios and also how
to manipulate them in order to solve various application problems. All in all this
should take about 10 minutes to complete. After this, we will hold a quick lecture
that reviews the trigonometric ratios and also work some guided application
problems. Once the lecture is done, we will dive right into the main activity. With
this students will be exploring application problems of the trigonometric ratios. The
actual task will be given via the SMART board so there will not be a handout given to
the students. With this, students will have to solve various application problems
including finding missing side lengths and also finding missing angle measures.
Even though this activity is given through the SMART board this task is still group
based. The students will have to copy down the problem and in their groups they
will have to figure out first what the problem is asking, how to use the information
given, then actually solve the problem. Thus the first few problems will be guided in
order for students to see the process behind these application/word problems. All
in all, this activity will take about 30 to 40 minutes to complete. In other words, this
activity will last the rest of the class period. During this time, we will move around
each table monitoring and helping in what ever way we can. For the closing part of
the classroom, if time permits, they will have to answer the wrap-up problem. For
this portion of this class, we will come together as a class and discuss the wrap-up
problem at the end of the slides. Instead of now finding the missing side, students

7. will need to use the knowledge they learned from the activity in order to find the
missing angles of a triangle. We did this to gauge if students learned the main topics
of the lesson. Also this will give the students a foundation for them when they start
practicing more with finding the missing angles and sides of triangles by using the
trigonometric ratios. With this, we will have them write their answer on a separate
sheet of paper, which we will take up as a quick classwork grade. Again if time
permits, this should take around 10 minutes. While they are completing the wrap-
up, we will discuss what the homework will be for the night and make any
announcements that are needed in order to prepare for the next class.
Instructional Strategies:
One way to differentiate the class would be make the task a white board activity or a
stations activity. For the whiteboard activity, we would give each student a
whiteboard and a marker to write their work on. With this, we would have each
student work the problem on the whiteboard and then once tie is allotted we will
ask the class to raise up their boards. Then if we need we will go over the problem
as a class. With this, it will be a quick and easy way to gauge if the class understands
how to solve these types of problems. For the stations activity, we would use the
same problems as the slides, but instead they will be spread out across the room.
That way, students will be able to move around and have some activity rather than
sitting at their desk taking notes. This will allow us as teachers to walk around and
monitor students more one-on-one allowing for more in depth and personalized
instruction. I do believe that these methods are great for working on application
problems, but since this task is mostly used as an introductory lesson I believe
students will need guided instruction.
Handouts for students:
Since the task will be given via the SMART notebook, there will be no handouts
given to the students, but the students will have a copy of the slides in order to
complete them for homework.
Extensions of task/lesson:
Since the task is being provided via the SMART notebook file, there will be no
extensions given with this task. This is because I believe that students will struggle
enough with the problems that are provided to them. This is because the students
have a hard time looking and also utilizing information given to them whether it is
in a word problem or proof.
Ways to assess student progress:

8. Since there are three of us in the classroom, we will each monitor two to three
groups during the activity. With this, we are able to go back and forth between each
group and help them with any questions/concerns they may have with the activity.
If we see that some groups are not completing the activity with the time we allotted,
we can either add more time or decrease the amount of time needed for this
investigation. Also by monitoring the progress of each group we will have a better
understanding of where the students are struggling with the most while working on
this assignment. This will allow us to get a better idea of the questions they may ask
at the end of the class during the full class discussion.