Download Law of Sines Lesson Plan

Law of Sines
Candidate Name:
On my honor as a University of South Carolina Aiken student, I have completed
my work according to the principle of Academic Integrity. I have neither given
nor received any unauthorized aid on the assignment/examination.
Signature: Amanda Joyce
Date: 4/14/2014
Subject Area:
Mathematics
Grade Level:
10
Date Being Taught:
April 16, 2014 2:30 pm and April 21, 2014 2:24 pm
Time Frame/Duration: This lesson will last 2 days.
Standard:
HSG-SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines to
find unknown measurements in right and non-right triangles (e.g. surveying
problems, resultant forces).
Learning Objective:
The learning objective that this lesson will use is how the students will find the
missing angles and sides of a right or non-right triangle.
Essential Question:
How do you find the missing angles and side measurements of a right or nonright triangle with more than one number missing?
Number of Students:
This lesson is for a class with 26 students.
Grouping:
The students will start out as a whole class and will then work individually or in
groups of two.
Accommodations:
I will accommodate the students that are visual learners by doing examples on
the board showing them step by step on how to do the problems. I will
accommodate the students that work at a slower pace by allowing them to
work individually and at their own pace. For students that are auditory learners,
I will explain each step as in much detail as possible and will continue to explain
until the students understand. For students that are kinesthetic learners, I will
have them do multiple problems until they understand the problems.
Materials/Resources:
The materials needed for this lesson will consist of two different worksheets.
On April 16th, the students will complete the Law of Sines worksheet and on
April 21st, the students will complete the Law of Sines Ambiguous Case
worksheet.
Educational Technology:
Technology will not be used in this lesson because having students work
out problems on their own will help them understand the material easier than
having a PowerPoint.
Safety Issues/Concerns:
There are no safety issues/concerns inherent in executing this lesson.
Lesson Procedures:
Step-By-Step Outline of the Lesson:
1. Students will begin the class period by completing the problem that is in the “Prior to Lesson”
section.
2. After the students complete the problem, the teacher will ask a student to come to the board
and complete the problem for the class.
3. After the student completes the problem on the board, the teacher will ask the rest of the class
if they got the same answer. If not, the teacher will ask what answer they got.
4. After completing the pre-assessment problem, the teacher will begin her lesson by explaining to
the students what exactly Law of Sines is and how Law of Sines could benefit them in the real
world. For example, the teacher will explain that you could figure out how tall a building or pole
is based on the shadow that the sun produces.
5. After explaining how it will benefit the students, the teacher will begin by explaining that an
oblique triangle is a triangle that does not have a right triangle.
6. After explaining what an oblique triangle is, the teacher will tell the students that in order to
solve an oblique triangle you must know the measure of at least one side and the measures of
any two other parts of the triangle – two sides, two angles, or one angle and one side.
7. The teacher will then explain that when you have two angles and any side or two sides and an
angle opposite on of the sides, you have to use Law of Sines. The other two cases – three sides
and two sides and their included angle – are solved using Law of Cosines. The teacher will draw
these cases on the board to allow those students who need to see them be able to see them.
8. The teacher will supply the students with the equation a/sinA = b/sinB = c/sinC. They will use
this equation to solve multiple problems later.
9. The teacher will also explain that this equation can also be flipped and that when solving for a
missing variable, you want that missing variable in the numerator.
10. The teacher will then go step by step of Example 1 page 405 of the students textbook.
11. The teacher will start by drawing the triangle based on the information given – angle C = 102.3o;
angle B = 28.7o; and b = 27.4 feet. The problem asks to find the remaining angle and sides.
12. After the triangle is drawn, the teacher will start with finding the missing angle because two
angles are already given. We know that the total measurement of a triangle is 180o. Because
we are given two angles, the teacher will subtract the two angles from 180o. The answer will be
the measure of angle A.
13. Now we have to find the two missing sides. Because we have angle B and side b, we will use
those numbers to find side a and side c.
14. Begin with side a: the equation that the teacher will use is a/sinA = b/sinB. The teacher will then
manipulate the equation to get the missing variable on the left side. The equation will then look
like this: a = (b/sinB)(sinA).
15. After getting the equation manipulated, the teacher will then plug in the numbers that were
given in the problem. The equation will look like this: a = (27.4/sin28.7o)(sin49o). The answer is
43.06 feet.
16. After finding side a, the teacher will then find side c the same way. The equation will be
manipulated to look like c = (b/sinB)(sinC). The teacher will then plug in the numbers given. The
equation will look like c = (27.4/sin28.7o)(sin102.3o). The answer 55.75 feet.
17. After the teacher finishes example 1, example 2 will be completed.
18. Example 2 (page 405) will not be as easy as the first example. The teacher will first ask the
students if they have an idea of how to solve for angle B because the actual angle is not given
but information is given to help find the angle.
19. After the teacher makes sure that the students understood how angle B was found, the teacher
will complete the rest of the example the same way the first example was solved.
20. After the teacher completes the two examples, the Law of Sines worksheet will be handed out
to the students row by row.
21. The teacher will walk around the classroom while the students complete the worksheet.
22. The students will turn in their worksheet, finished or not, at the end of the class period.
23. The teacher will look over the worksheets to assess the students on the material.
Suggested Assessments:
Prior to Lesson: Students will complete the problem: angle A – 56o, angle B – 72o, and side a =
1o inches. Once the students complete this problem, I will go over the problem
with the students and answer any questions that the students may have. I will
be able to see how many students might already know how to do Law of Sines
after going over this problem.
During the Lesson: Students will be asked a series of questions like “How do you find the total
angle measurement of a triangle?” and “How do you know which side goes with
which angle?” by first asking the whole class and calling on a student who has
their hand raised. If no students raise their hand, I will call on a student and ask
if they know the answer. If that student does not know, I will walk through the
question with that student. While the students are working individually, I will
walk around the classroom and help any student that might need help with a
problem.
After the Lesson: I will be able to see if the students mastered the material by looking at their
worksheet that they will turn in at the end of the class period.
Follow-up:
After looking at the worksheets and seeing if the students understand the
material that was taught, I will be able to move on to the next part of the
section. If the students do not understand the previous material taught, I will
do a review with the students and help them to master the material.
References:
Additional Topics in Trigonometry. (2014). In PreCalculus Mathematics for
Calculus(6th ed., pp. 404-408).