1) The lesson introduces students to trigonometric ratios by having them measure angles and sides of triangles to discover relationships. 2) Working in groups, students will measure triangles, record their data, compare findings, and form hypotheses about trigonometric ratios. 3) To conclude, students will solve a problem using trigonometric ratios and describe how they could apply the ratios in real-world situations.

1. LESSON CONTENT
 Lesson Plan Template: Confirmatory or Structured Inquiry
 Formative Assessment
At the beginning of the lesson,students will discuss what
they know about triangles and why triangles areimportant.
Students will identify how they have seen triangles used in
their communities. The teacher can use questions from the
"Guided Questions"section to engage students and assess
their understandingof triangles before the lesson.
Throughout the lesson,the teacher should circulateand
observe the students. The teacher can formatively assess
the students based on student conversations aboutthe
assignment,ideas that are formed based on the assignment
and the conclusion students make.
 Feedback to Students
Students will receivefeedback from their peers when they
are workingin groups. Students will also receivefeedback
from the teacher whilethe teacher circulates around the
classroomthroughout the lesson.
 Summative Assessment
The teacher will usethe attached Trigonometric
Ratios worksheet to assess studentunderstandingof the
lesson.The teacher can choose to assign oneproblem or
several problems.The answer key is included in the
attached worksheet.
 Learning Objectives: What will students know and be able to
do as a result of this lesson?
Students will:
o understand the relationship between an identified angle
of a righttriangleand the sides of the sametriangleand
similar triangles.
o be ableto use trigonometric ratios to calculatethe
measure of the sides and angles of righttriangles.
 Guiding Questions: What are the guiding questions for this
lesson?
o What information would be useful to help us find the
missingangleor missingside?
o How do we find the information we need?
 Prior Knowledge: What prior knowledge should students
have for this lesson?
Students should know:
o how to apply the Pythagorean Theorem to find the
measure of a missingsideof a righttriangle.
o that the sum of the measure of the interior angles of a
righttriangleis 180 degrees.
o how to identify the hypotenuse and legs of a triangle.
(You can have students watch the trianglesidereview
that is partof the video Trigonometric Ratios -
SohCahToa on YouTube. The review is the first1 min 50
seconds of the video.)
o the meaning of a ratio.
 Introduction: How will the teacher introduce the lesson to
the students?
Introduce the lesson by askingthe followingquestions:
1. Where, other than in a textbook, have you seen triangles
used?
2. Why do you supposetriangles were used instead of
another shape?
3. What is the importance of triangles?
The teacher can showthe TriangleSidereview portion of the
YouTube video "Trigonometric Ratios"to refresh the
students' memories. (See Prior Knowledge for the link and
directions for this.)
 Investigate: What question(s) will students be investigating?
What process will students follow to collect information
that can be used to answer the question(s)?
Students will investigateand discover trigonometric ratios by
exploringquestions like:
o What is the relationship of a triangle's angles and their
correspondingsides?
o What happens when I have several triangles with the
same anglemeasures, but different sidemeasurements?
o How can this help me in real life?
Students will placeall measurements and calculations in a
table. They will comparetheir calculations with their peers'
and draw conclusionsbased on their findings.
 Analyze: How will students organize and interpret the data
collected during the investigation?
0. The teacher should distributethe Discover
Trig worksheet to each student. Each student should also
have a ruler, pencil,scientificor graphingcalculator and
a half sheet of paper. Students should be placed into
groups of 3 or 4 for this activity.
1. Students will complete section A on the sheet. The
teacher should circulatearound the room to ensure that
each student is correctly measuringeach triangle.
2. When students complete measuringof the triangles,
they should complete sections Band C of the handout.
3. The teacher should instructthe groups to discuss their
findings and drawa conclusion based on their
comparisons.Giveeach student 15 seconds to share.Let
the student with the earliestbirthday sharefirstand the
student on the left shares next, when the teacher calls
time. Repeat this until all students have shared.Then
give an additional minutefor students to collaborateand
summarize their findings.Students should then complete
section D on the handout. (See the Discover TrigKey for
examples of student responses.)
4. For section E, use the "Commit and Toss"strategy as
described here:
 The teacher should instructeach student to take out
a half sheet of paper.

2.  Give the students 10 seconds to think about the
group discussion and the data that they have seen
and formulate a hypothesis.
 After 10 seconds,each student will writetheir
hypothesis on a half sheet of paper.
 Students will crumpletheir papers into a ball and
stand by their desk.
 When the teacher signalsto start,each student can
throw the paper until the teacher signalsagain to
stop.
 When the teacher signalsto stop, each student
should pick up one paper ball and stand by their
desk.
 The teacher should then call on several students to
sharethe hypothesis that is on the paper and then
sitdown.
 If a student reads a hypothesis that other students
have on their papers as well,those students may sit
down. The teacher can use this strategy to
formatively assess thestudents.
5. The teacher will then introduce usingsine,cosineand
tangent on a scientific or graphingcalculator.Students
will usethe measurements from their firstchartto
complete the chartin Section F. Students can also
complete section G.
6. The teacher can use the method in step 4 to allow
students to sharewith each other and form conclusions.
Then, students should answer section H.
7. Section I: Give students think time to answer sections I
and J. For section I, students should be ableto conclude
that:
The teacher should circulatewithin the room to see if
students are drawingthe correct conclusions for this
portion. If students are struggling,the teacher can draw
the students' attention to the charts and their
correspondinganswers.Let them know that you want a
generic equation for each that you can usewith any right
triangle.Once all students get this portion,the teacher
should be sure to tell them that what they have
discovered are called Trigonometric Ratios.
 Closure: What will the teacher do to bring the lesson to a
close? How will the students make sense of the
investigation?
The teacher will assign the followingproblemto closeout
the lesson and assess studentunderstanding.
The diagrambelow shows righttriangleDPA. Angle D is 20
degrees. If the measure of segment DA is 32 meters, how
would you find the measures of the other two sides,PA and
DP? Write HOW would you solvethis problem. (Hint: Use
Section I to help you with this.)
Tell students to think of a situation where they could use
their new knowledge of right triangles and trigonometric
ratios and write it. Have students turn in their papers at the
end of class.
Answers: PA = 32(sin 20),DP = 32(cos 20)
ACCOMMODATIONS & RECOMMENDATIONS

Accommodations:
o Students will bein groups so that strugglingstudents
may be assisted by their peers.
o The teacher may model sections of the lesson to bring
clarity to students.

Extensions: Students can use their new understandingof
trigonometric ratios as a tool for indirectmeasurement. The
teacher can designatedifferent items around school campus
and have students useratios to calculatethe measurement of
the items. Example items:
o the length or height of a car
o the height of a flagpole
o height of a trash can
o length or height of a gate
o height of school building

Suggested Technology: GraphingCalculators

Special Materials Needed:
Each student will need:
o a scientific or graphingcalculator
o a copy of the Discovery TrigSheet handout and a pencil
o a half sheet of paper
o a ruler