Geometry and Its Real World Applications

Bryan PhillipsAurora University

Summer 2011

Background InformationHigh School Geometry Course

Students 10th – 12th Grades (predominately 10th)Come from Lower Level Algebra Course

Done Over 5 Class Periods (80 min in length)Not Done in Consecutive PeriodsYear Long Block (A/B Days)

Takes Place During 4th QuarterAlready Know Pythagorean TheoremAlready Know Area/Circumference of CirclesAlready Know Area of Regular PolygonsAlready Know Volume of Prisms

Day 1Hook: Youtube video on How Louisville Slugger

Started http://www.youtube.com/watch?v=jroExgSSjzo

Present Task #1

Investigate on Louisville Website Pros vs. Cons of Ash Wood vs. Maple Wood

Students Complete Task #1

Introduce Sine, Cosine, and Tangent Functions and Their Inverses

Guided Notes

Homework: Kuta Software Wkst. (Right Triangle Trig.) #2 – 24 evens

Task #1You 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 pros and cons between the two, and ultimately decide which route the company should go in manufacturing their new product. To help you get started, you should visit the Louisville Slugger Website: http://www.slugger.com/technology/wood.html.

Task #1

Ash Maple

Pros Cons Pros Cons

Cost of Ash per Ounce: Cost of Maple per Ounce:

Day 2Questions on Homework

Hook: Youtube Video of Ziplininghttp://www.youtube.com/watch?v=I9RfT1yBw6s&feature=related

Discussion About Height They Started From

Introduction to Angles of Elevation and Depression Guided Notes

Youtube Video on How to Make a Clinometer http://www.youtube.com/watch?v=GMLcU1Qknts

Create Clinometers

Homework: Angles of Elevation and Depression Worksheet #1 – 9 all

Day 3Questions on Homework

Hook: Youtube Video of How to Use a Clinometer http://www.youtube.com/watch?v=LiNUI1R2gmI

Present Task #2

Go Outside to Take Measurements (working in pairs)

Back Inside for Calculations

Homework: Complete Task #2 Wkst. (individually)

Task #2Now 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

Distance from tree:

Angle to Top:

Height of Tree:

Circumference:

Radius:

Area:

Task #2Your height at

eye level?

How can we determine 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 the formula?

Calculate the amount of “good” wood we can

obtain on average from all of your trees.

Day 4 Questions on Homework

Present Task #3

Introduction to Volumes of Cylinders Guided Notes

Demonstration of 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 Wkst. #1 – 7 all

Day 5Questions on Homework

Hook: Youtube Video on How Wood Baseball Bats are Made http://www.youtube.com/watch?v=ptyIxhiMvtM&feature=related

Students Complete Task #3 (in pairs)

Once Complete, Students Working on Laptops to Complete Summary

Homework: Complete Task #3 (if needed) and Complete Summary

Task #3In 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.

Task #3What is the amount of “good” wood that you can use to create your Louisville Slugger Bats?

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.

Task #3If it takes 3” in diameter to create a baseball bat, how many bats could you make given your radius of the tree?

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:

Task #3If it costs $1.50 per inch to produce Ash

bats and $1.80 per inch to produce Maple bats, what reasonable price should Louisville Slugger Charge for a: a. 32” bat? Ash:

Maple: b. 33” bat? Ash:

Maple: c. 34” bat? Ash:

Maple:

Explain your reasoning.

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?

Task #3In 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 the 3 Tasks you completed. 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.

Common Core Practices 1 – 3 The Common Core Practices that are evident throughout this lesson are:

1. Make sense of problems and persevere in solving them.

Task #3 – open ended questions

2. Reason abstractly and quantitatively.

Task #2 – calculations

3. Construct viable arguments and critique the reasoning of others.

Summary

Common Core Practices 4 – 6 The Common Core Practices that are evident throughout this lesson are:

4. Model with mathematics.

Task #2, Task #3, All of the Homework

5. Use appropriate tools strategically.

Task #2 – measurements

6. Attend to precision.

Task #2 – measurements, Task #3 - calculations

Common Core Practices 7 – 8 The Common Core Practices that are evident throughout this lesson are:

7. Look for and make use of structure.

Not Present

8. Look for and express regularity in repeated reasoning.

Not Present