Transcript 48x36 poster template - University of Cincinnati

Trigonometry Superbowl
Aimee
1
1
Frame ,
2
Bender
Gabrea
Department of Engineering, University of Cincinnati, Cincinnati, OH; 2 Newport High School, Newport, KY
Abstract
This lesson is intended to be a fun way to show how trigonometry can be used in a
real-world situation. The students are given a playbook in which some of the route
information is missing. They are asked to determine the missing information using
their knowledge of trigonometry and right triangles. The first play is completed as
a class with guidance from the instructor to familiarize the students with the
terminology and the idea of creating right triangles that can help solve the
problem. The class is then divided into groups to complete the rest of the
playbook. Once completed, the instructor can review the solution process as a
class, showing that there can be more than one way to solve the problem and
reach the correct answer. Afterwards, a short presentation on how this idea is
applied in other real-world applications is given.
Playbook Activity
Pos
QB
Yard Line
Field Position
Own 30 yd
line
Own 30 yd
line
WR
Prerequisite Knowledge
Pattern
45o
Pythagorean Theorem
Center
a) 30 yd pass
to his left
10 yds left of
center
a) Runs 15 yds at 0o (straight)
b) ?
Basic Trigonometric Functions (SOH-CAH-TOA)
Sine
Cosine
Tangent
a) If the pass is to be completed, at
what angle does the WR need to run
to catch the ball?
b) How far does the WR run (total
yards)?
c) Where is the pass caught?
Solving Equations
Special Right Triangles (optional)
90o-45o-45o
90o-30o-60o
Conclusions
Goals
The purpose of this lesson is to show the students how trigonometry can be
applied to real-world problems. The students are given a set of football plays
which they need to complete in order for the play to be successful. Using the
given information and the basic trigonometry functions (sine, cosine, and
tangent), the students will be able to determine the unknown values that will
make the play a success. After applying trigonometry to football, extensions to
other real-world and engineering applications will be discussed.
Pos
Yard Line
Field Position
QB
Opp 20 yd line Center
Pattern
a) At what angle does the QB need
to throw to connect with the WR?
b) How far is the ball thrown?
c) Is it a touchdown?
a) Under pressure, runs 90o left
10 yds
b) ?
Opp 20 yd line 5 yds right of center a) Runs 30 yds 40o to his right
WR
Reflections & Modifications
Objectives
Students will be able to:
Determine the right triangles in a real-world problem.
Use right triangle relationships to find the unknown length and angle
measurements.
Pre/Post Assessment
1.
Find the HEIGHT of the tree.
C las s A verag e - B ell 1
45
State Standards
o
30 feet
2.
P re-Tes t
P os t-Tes t
Find the HEIGHT of the Eiffel Tower.
8.09
650 m
Kentucky Core Content:
MA-HS-2.1.3: Students will apply definitions and properties of right triangle
relationships (right triangle trigonometry and the Pythagorean theorem) to
determine length and angle measures to solve real-world and mathematical
problems.
Ohio Standards:
Geometry and Spatial Sense Standard, Grades 8-10, I: Use right triangle
trigonometric
relationships to determine lengths and angle measures.
Geometry and Spatial Sense Standard, Grades 11-12, A: Use
trigonometric relationships to verify and determine solutions in problem
situations.
Mathematical Processes Standard, Grades 11-12, J: Apply mathematical
modeling to workplace and consumer situations, including problem
formulation, identification of a mathematical model, interpretation of solution
within the model, and validation to original problem situation.
This lesson provides an interesting application for trigonometry, encouraging the
students to apply their knowledge a different manner. Most of the students
seemed to like the real-world application of football and were engaged throughout
the activity. Although it can be challenging to those students that are struggling
with the prerequisite knowledge, the use in a different setting may help their
understanding of the basic trigonometric functions. Finally, this lesson can be
extended to the concept of vectors and vector addition for use in a physics class.
5.55
30
o
3.
Find the ANGLE the 15 ft ladder makes with the floor.
2.642.73
1
2.64
1.82
2
1.091.55
1.18
0.00
3
4
Total
4 ft
Class Average - Bell 2
C las s A verag e - B ell 2
Pre-Test
4.
Pos
Yard
Line
Field Position
Pattern
P re-Tes t
45o
QB
50 yd line
5 yds right of
center
a) Runs backward
yd line
b) Throws 15o left
WR
50 yd line
15 yds left of
center
a) Runs 0o (straight)
Post-Test
P os t-Tes t
7.26
left to the 45
7.26
4.26
4.26
2.48
2.48
1.57
1.57
1
a) How far does the WR have to run to catch the football?
b) How far is the ball thrown?
c) Is it a touchdown?
Pre-Test
The first three questions are good indicators of how well the students
understand the basic trigonometric functions
Students that did well on these questions were better able to figure out how
to apply the trigonometry functions during the activity
It may be a good idea to ensure that each group has a student that did well
on the pre-test
Playbook
Although there are five plays listed, there is not enough time in one class
period to get through all of them.
Complete the first play as a class
The terminology has to be explained well to help prevent confusion on the
remaining plays
Players face the end zone
Left/Right refer to how the players are facing
Angles are measured from “x-axis” to line
Show how to make right triangles by using the “slanted lines” as
hypotenuses
Explain that there is more than one way to solve the problems
May need to reconvene as a class periodically
For bigger classes, may not be able to get to all the groups individually
Can clarify any questions about terminology
Discuss/show different approaches to the problem
1
References & Acknowledgments
2.48
2.48
1.43
1.43
2
2
1.78
1.78
1.26
1.26
3
3
0.52 0.52
0.000.00
4
4
Total
Total
Project STEP is funded through NSF Grant # DGE058532.
http://www.eng.uc.edu/STEP/activities/
This lesson was adapted from Amy Dimmerling’s Geometry Superbowl lesson