Warm Up – 3/13 - Thursday Apportion the classes using Adams Method

Slides:



Advertisements
Similar presentations
Agenda Goals Info sheet Overview Begin Lesson 9.1- Apportionment
Advertisements

Mathematics of Congressional Apportionment David Housman Goshen College.
How are the number of seats per state assigned by the Constitution?
The Mathematics of Elections
Chapter 15: Apportionment Part 4: Apportionment History.
Appendix 1 The Huntington - Hill Method. The Huntington-Hill method is easily compared to Webster’s method, although the way we round up or down is quite.
+ Apportionment Ch. 14 Finite Math. + The Apportionment Problem An apportionment problem is to round a set of fractions so that their sum is maintained.
1 How the Founding Fathers designed algorithms for assigning fair representation for the new United States of America How Will the Next Congress Look?
4.1 Apportionment Problems
Other Paradoxes and Apportionment Methods
Chapter 14: Apportionment Lesson Plan
Fairness in Apportionment How do you decide whether a method for apportioning representatives is fair?
Chapter 15 Section 4 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Chapter 15: Apportionment
Math for Liberal Studies.  The US Senate has 100 members: two for each state  In the US House of Representatives, states are represented based on population.
Discrete Math CHAPTER FOUR 4.1
Copyright © 2009 Pearson Education, Inc. Chapter 15 Section 3 - Slide Election Theory Apportionment Methods.
Chapter 14: Apportionment Lesson Plan
§ Adams’ Method; Webster’s Method Adams’ Method  The Idea: We will use the Jefferson’s concept of modified divisors, but instead of rounding.
Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 15.3 Apportionment Methods.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 14 Voting and Apportionment.
Chapter 15: Apportionment
Slide 15-1 Copyright © 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION.
Agenda Goals Info sheet Overview Apportionment Activity Begin Lesson 9.1- Apportionment  Hamilton Method  Adjusting a list HW Guide.
Other Apportionment Algorithms and Paradoxes. NC Standard Course of Study Competency Goal 2: The learner will analyze data and apply probability concepts.
The Webster and Hill Method for Apportionment Both are like the Jefferson method.
Chapter 15: Apportionment Part 7: Which Method is Best? Paradoxes of Apportionment and Balinski & Young’s Impossibility Theorem.
Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 4 The Mathematics of Apportionment 4.1Apportionment Problems 4.2Hamilton’s.
1 CS110: Introduction to Computer Science Homework Project #1 Due to Blackboard Dropbox on October 18 11:59PM For this Homework you will implement the.
Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 4 The Mathematics of Apportionment 4.1Apportionment Problems 4.2Hamilton’s.
Classwork: Please read p in text p. 144 (1, 11, 19a, 23) Homework (Day 14): p. 144 (2, 12, 20b, 24)
Webster and Huntington – Hill Methods (Txt: 4.6, p. 152 & SOL: DM.9) Classwork: p. 147 (43) and p. 161 (15) Homework (day 15): p. 147 (44) and p. 161 (16)
1 Message to the user... The most effective way to use a PowerPoint slide show is to go to “SLIDE SHOW” on the top of the toolbar, and choose “VIEW SHOW”
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 14 Voting and Apportionment.
§ The Population and New-States Paradoxes; Jefferson’s Method.
Chapter 15: Apportionment Part 5: Webster’s Method.
Apportionment There are two critical elements in the dictionary definition of the word apportion : (1) We are dividing and assigning things, and (2) we.
Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 4 The Mathematics of Apportionment 4.1Apportionment Problems 4.2Hamilton’s.
2.4 More Apportionment Algorithms and Paradoxes Ms. Magné Discrete Math.
1 Excursions in Modern Mathematics Sixth Edition Peter Tannenbaum.
Chapter 4: The Mathematics of Apportionment. "Representatives...shall be apportioned among the several States, which may be included within this Union,
Independent Practice Problem There are 15 scholarships to be apportioned among 231 English majors, 502 History majors, and 355 Psychology majors. How would.
1 How our Founding Father’s designed algorithms for assigning fair representation for the new United States of America How Will the Next Election Be Decided?
Apportionment Apportionment means distribution or allotment in proper shares. (related to “Fair Division”)
Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 4 The Mathematics of Apportionment 4.1Apportionment Problems 4.2Hamilton’s.
Apportionment So now you are beginning to see why the method of apportionment was so concerning to the founding fathers……it begs to question, why not just.
Paradoxes of Apportionment
AND.
Excursions in Modern Mathematics Sixth Edition
Hamilton’s Method of Apportionment -- A bundle of contradictions??
What is Fair? 1.) Martha and Ray want to divide the last piece of cake their mother baked last night. Propose a method for dividing the piece of cake.
APPORTIONMENT An APPORTIONMENT PROBLEM:
Chapter 14: Apportionment Lesson Plan
Chapter 14: Apportionment Lesson Plan
Math 132: Foundations of Mathematics
Chapter 15: Apportionment
Chapter 15: Apportionment
Section 15.4 Flaws of the Apportionment Methods
Section 15.3 Apportionment Methods
What is Fair? 1.) Martha and Ray want to divide the last piece of cake their mother baked last night. Propose a method for dividing the piece of cake.
Warm Up – 3/3 - Monday Describe in your own words the steps to each of the following fair division processes and when to use each process. Divider-Chooser.
HAMILTON – JEFFERSON - WEBSTER
Warm Up – 3/7 - Friday Find the Hamilton Apportionment for 200 seats.
Chapter 4—The Mathematics of Apportionment
Excursions in Modern Mathematics Sixth Edition
4 The Mathematics of Apportionment
Warm Up – 3/10 - Monday State A B C D E Population (millions)
Quiz.
Warm Up – 3/14 - Friday 100 seats are to be apportioned.
Flaws of the Apportionment Methods
Presentation transcript:

Warm Up – 3/13 - Thursday Apportion the classes using Adams Method A local gym instructor has a course load that allows her to teach Eight classes. At an interest meeting, 8 people wanted high-impact Aerobics, 64 wanted low-impact aerobics, 11 wanted jazzercise, and 31 wanted step exercise. Apportion the classes using Adams Method B) Apportion the classes using Webster’s Method.

Test Tomorrow Things to know: Five methods of apportionment; Hamilton, Jefferson, Adams, Webster, Huntington Hill. Paradoxes and rules; Alabama Paradox, Population Paradox, Quota Violations, know which methods violate which.

Test Tomorrow Hamilton Method: Lower Quotas, extra seats apportioned by highest residues (decimals). Jefferson Method: Lower Quotas, find a modified divisor that perfectly apportions the seats. Adams Method: Upper Quotas, find a modified divisor that perfectly apportions the seats. Webster Method: Normal Rounding, find a modified divisor. Huntington-Hill: Rounding by Geometric Means, find a modified divisor.