MTH 6030 ........................................................................................................................ Bryan Phillips
Geometry Lesson Plan ..................................................................................................June 28, 2011
Common Core Practices
The Common Core Practices that are evident throughout this lesson are:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Content Area
Topics to be covered during this five-class lesson (80 minute class periods) are Special
Right Triangles, Angles of Elevation and Depression, and Volume of Cylinders and Cones.
These lessons are not taught sequentially in our curriculum by the math department at
Plano High School, therefore will be completed over the course of 4th quarter. Since this is a
lower level geometry course guided notes will be provided for the students to ensure that
drawings in the examples are accurate.
Objectives
By the end of this five-day lesson, students will be able to:
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Use the sine, cosine, and tangent functions in order to determine missing side
lengths in a triangle
Use the angles of elevation and depression in a real world setting to solve problems
Apply the formula for volume of a cylinder and a cone to use in real world situations
Sequence of Activities
Day one
 Hook: Youtube video on How Louisville Slugger Started
(http://www.youtube.com/watch?v=jroExgSSjzo)
 Present Students with Task #1 – Discussion
 Allow Students to investigate on Louisville Website Pros/Cons of Ash and Maple
Wood
 Have students complete Task #1
 Introduction of the Sine, Cosine, and Tangent Functions and Their Inverses (Guided
Notes: Sine, Cosine, Tangent and the Inverses)
 Homework: Kuta Software Worksheet: Right Triangle Trig. #2-24 evens
Day two
 Questions on Homework
 Hook: Youtube video of Ziplining
(http://www.youtube.com/watch?v=I9RfT1yBw6s&feature=related)
 Discussion about height from which they started. Lead to finding heights using trig.
 Introduction to Angles of Elevation and Depression (Guided Notes)
 Youtube video of How to Make a Clinometer
(http://www.youtube.com/watch?v=GMLcU1Qknts)
 Create Clinometers in class
 Homework: Angles of Elevation and Depression Worksheet #1-9 all
Day three
 Questions on Homework
 Hook: Youtube video of How to use a clinometer with example problem
(http://www.youtube.com/watch?v=LiNUI1R2gmI)
 Hand out Task #2 worksheet
 Go outside to the trees just off the faculty parking lot to take measurements (done in
pairs)
 Come back inside and perform calculations on Task #2 worksheet
 Homework: Complete Task #2 Worksheet (on an individual basis)
Day four
 Questions on Homework
 Present students with Task #3
 Introduction to Volumes of Cylinders (Guided Notes)
 Demonstrate how volume of a cylinder is similar to volume of a rectangular prism
 Youtube video on Deriving the Volume Formula of a Cone
(http://www.youtube.com/watch?v=QnVr_x7c79w)
 Introduction to Volume of Cones (Guided Notes)
 Homework: Volumes of Cylinders and Cones Worksheet #1-7 all
Day five
 Questions on Homework
 Hook: Youtube video on How Wood Baseball Bats are Made
(http://www.youtube.com/watch?v=ptyIxhiMvtM&feature=related)
 Have students Task #3 worksheet
 Students will be working in pairs to complete Task #3
 Once completed, students will grab laptops to start working on their summary using
Microsoft Word
 Homework: Complete Task #3 Worksheet (if needed) and finish summary
Anticipatory
My previous Geometry courses have been conducted by doing a lot of modeling. I am trying
a new approach during this lesson in presenting my students with the problems first and
then talking about the ideas and concepts needed to complete the task. Since, I anticipate
that there will be frustration from the students as this is a new approach, I will try hooking
them each day with a Youtube video showing them what we are learning is used outside of
the class.
Resource/Materials
The resources that will be used during this lesson are:

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White Board and Markers for classroom notes
LCD Projector and Computer (Microsoft Word) for guided notes
Calculators for use in approximating answers
Prentice Hall Mathematics Geometry Book for extra practice
Guided notes worksheets for accurate drawings
Real World Problem Solving Worksheet
Outside activity handout
5 – 10 foot tape measures with centimeters on one side
5 – 100 foot tape measures
5 homemade clinometers (string, protractor, straw, 3x5 index card, paper clip, tape)
Laptops with access to Microsoft Word
Assessment
The students will be assessed in the following ways:
 Homework
 Through completion of their Tasks (3)
 Summary of written report
 Informally: independent work during notes
Conclusions
I am excited to try this new approach in my Geometry classroom. I wanted to tie in real
world substance to what we were learning in class to make it real to them and also allow
the students to see what type of work is available to them. Throughout my lesson I tried to
incorporate as many of the Common Core Practices as possible. In a lot of my notes,
homework, and tasks I tried to give my students real world problems for them to solve. Not
all of the problems had a straightforward answer and I believe this ties directly to students
making sense of problems and persevering in solving them. Task #3 shows evidence of
students having to reason quantitatively in having to determine the maximum profit for the
bat company in producing each type of bat. Although my students are not critiquing one
another’s arguments, they do have to construct an argument in their summary as to their
findings through the three tasks. This whole lesson was designed to model a real world
situation where the students had to be precise in their calculations in order to accurately
report their findings. I feel this lesson does a good job of meeting six of the eight common
core practices. The only two that I did not see fit into this lesson were looking for and
making use of structure, as well as, looking for and expressing regularity in repeated
reasoning.
Sine, Cosine, and Tangent
* sine:
A
* cosine:
* tangent:
C
SOH
Writing Ratios
Write the ratio for each trigonometric function.
(1)
2
W
Z
1
1
4
2
6
Y
M
(2)
3 5

L
3
6
N
B
CAH
TOA
sin W =
sin Y =
cos W =
cos Y =
tan W =
tan Y =
sin M =
sin L =
cos M =
cos L =
tan M =
tan L =
Finding a Missing Side Length
(3)
a
7
g
1
5
54
10
27
41
f
(4)
63
33
w
24
m
b
15
2.5
32
(5) To measure the height of a tree, Alma walked 125 ft from the base of the tree and measured a 32
angle from the top of the tree. About how tall is the tree?
OYO
Find the value of x.
(6)
50
(7)
x
x
41
57
14.9
(8)
(9)
22
65
x
28
x
74.5
Inverse Sine, Cosine, & Tangent
SOH
CAH
TOA
Ө
Find the value of x.
28.5
x
32°
Find the value of x.
x°
5
2
3
6
To “undo” the trig function, you must use the
sin  

O
H
cos  

A
H
.
tan  

O
A
Examples: Solve for x.
(1)
(2)
x°
(3)
x°
x°
(4)
x°
(5)
(6)
x°
x°
Angles of Elevation and Depression

Angle of Elevation:

Angle of Depression:
Ex #1
Identify the Angles of Elevation and the Angles of Depression
1.
1
2.
3.
2
3
4.
4
Ex #2
Find the value of x in each triangle.
12m
42˚
x
x
64˚
25 ft
Ex #3
An airplane approaches a run way with a steady descent of 3˚ starting from
an elevation of 2714 ft. How many horizontal miles from the runway is the
airplane at the start of the approach?
Volumes of Cylinders
Theorem 10-7: Volume of a Cylinder
Find the volume of each cylinder.
(1)
3 cm
(2)
5 in
15 in
8 cm
* composite space figure:
Find the volume of the composite space figure.
(6)
18 in
4 in
6 in
Volumes of Cones
Theorem 10-9: Volume of a Cone
Find the Volume of each figure.
(1)
(2)
16 ft
20 cm
4 ft
8 cm
V=
V=
Name:
Date:
Period:
Geometry and Its Real World Applications
Task #1
You have just been hired by Louisville Slugger to do some site testing for their new baseball
bats that they would like to manufacture. They are having difficulty deciding on which type
of lumber they would like to use in making their new bats. They have narrowed their
choices down between ash and maple. It is up to you to research the similarities and
differences between the two, and ultimately decide which route the company should go on
manufacturing their new product. To help you get started you should visit the Louisville
Slugger Website: http://www.slugger.com/technology/wood.html.
Ash
Pros
Cost of Ash per Ounce:
Maple
Cons
Pros
Cost of Maple per Ounce:
Reference: http://www.badgerwood.com/products.html
Cons
Name:
Date:
Period:
Geometry and Its Real World Applications
Task #2
Now that you have decided on which type of lumber Louisville Slugger should use, it is time
to investigate how much wood we can get out of one tree to produce the bats. In order to
do this you are going to need to go out in the field and investigate heights of trees and
determine how much “good” wood you can obtain from one tree. You will need to test three
trees and use what you know about Geometry in order to figure out how much wood you
can obtain. (Note: Make all calculations in inches.)
Tree #1
Tree #2
Distance from tree:
Distance from tree:
Angle:
Angle:
Height:
Height:
Circumference:
Circumference:
Radius:
Radius:
Area:
Area:
Tree #3
Averages
Distance from tree:
Distance from tree:
Angle:
Angle:
Height:
Height:
Circumference:
Circumference:
Radius:
Radius:
Area:
Area:
Your height at eye level is
. Remember to figure this into the height of the tree.
How can we figure out how much “good” wood is in a tree?
Think about the shape of a tree. Which formula would best depict the shape of a tree? What
is that formula?
Now calculate the amount of “good” wood we can obtain on average from all of your trees.
Name:
Date:
Period:
Geometry and Its Real World Applications
Task #3
In this task you are going to use the calculations from the previous task to determine how
many baseball bats you can create from your “good” wood. Your goal is to make as many
32” , 33” , and 34” bats as possible with your wood. In order to make a 32” in bat, you are
going to need to add 2” (i.e. a 34” bat now becomes a 38” bat) of wood to both ends to run
through the press that makes the bats. In this given situation you have 10 feet of “good”
wood to work with. Complete the questions below pertaining to your calculations from
Task #2.
radius =
diameter =
Diagram #1
Diagram #2
10 ft
Use Diagram #1 for questions 1 – 2.
1. What is the amount of “good” wood that you can use to create your Louisville Slugger
Bats?
2. Given the 10 ft of lumber that you have to work with, is it possible to create each length
of bat using the specifications stated above? Explain your reasoning.
Use Diagram #2 for questions 3 – 4.
3. If it takes 3” in diameter to create a baseball bat, how many bats could you make given
your radius of the tree?
4. If you wanted to make each size of bat, how many bats could you make from this 10 ft
section of lumber? (Hint: Think tiers.)
32” bats:
33” bats:
34” bats:
Total # of bats:
5. If it costs $1.50 per inch to produce Ash bats and $1.80 per inch to produce Maple bats,
what should Louisville Slugger Charge for a:
a. 32” bat?
Ash:
Maple:
b. 33” bat?
Ash:
Maple:
c. 34” bat?
Ash:
Maple:
6. Using the information from Questions 4 and 5, what is the maximum amount of money
Louisville Slugger could make from your 10 ft section of lumber in Ash bats? What
about Maple bats?
7. In a Word document, write your recommendations to Louisville Slugger bats about your
investigation in producing wood bats. Your report should include pieces of information
from your 3 Tasks. Remember, this is a sales pitch to them so they will want to know
details about the bat you selected and how much money they could make. Your
summary should be no more than one page, double-spaced.