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Geometry and Its Real World Applications

Geometry and Its Real World Applications. Bryan Phillips Aurora University Summer 2011. Background Information. High School Geometry Course Students 10 th – 12 th Grades (predominately 10 th ) Come from Lower Level Algebra Course Done Over 5 Class Periods (80 min in length)

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Geometry and Its Real World Applications

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  1. Geometry and Its Real World Applications Bryan Phillips Aurora University Summer 2011

  2. Background Information • High 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 Periods • Year Long Block (A/B Days) • Takes Place During 4th Quarter • Already Know Pythagorean Theorem • Already Know Area/Circumference of Circles • Already Know Area of Regular Polygons • Already Know Volume of Prisms

  3. Day 1 • Hook: 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

  4. 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 theprosand 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.

  5. Task #1 Cost of Ash per Ounce: Cost of Maple per Ounce:

  6. Day 2 • Questions 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 Clinometerhttp://www.youtube.com/watch?v=GMLcU1Qknts • Create Clinometers • Homework: Angles of Elevation and Depression Worksheet #1 – 9 all

  7. Day 3 Questions on Homework Hook: Youtube Video of How to Use a Clinometerhttp://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)

  8. 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.)

  9. Task #2 Your 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.

  10. 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

  11. Day 5 Questions 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

  12. 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.

  13. Task #3 What 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.

  14. Task #3 If 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:

  15. Task #3 If 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: 32” bat? Ash: Maple: 33” bat? Ash: Maple: 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?

  16. Task #3 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 fromthe 3 Tasks you completed. Remember, this is a sales pitch to them so they will want to know details about the bat you selectedand how much money they could make. Your summary should be no more than one page, double-spaced.

  17. 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

  18. 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

  19. 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

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