NCDJJDP Lesson Plan

NCDJJDP Lesson Plan

Main Street ACADEMY LESSON PLAN 2011-2012

Teacher: Clark / Period(s):4th / Start date: 2/13/12 / End date:
State competency goal and objective:2.03 Model and solve problems involving fair outcomes:
c) Voting Power
EQ: Section 2.3: What is a Banzhaf Power Index and which players are important?
  • Objective: Calculate the Banzhaf and Shapley-Shubik power distribution in a weighted voting system

Literacy enhancements/Key Vocabulary:
•WEIGHTED VOTING SYSTEM •PLAYERS • PIVOTAL PLAYER •CRITICAL PLAYER •WEIGHTS •QUOTA •BANZHAF POWER INDEX •BANZHAF POWER DISTRIBUTION •COALITION •GRAND COALITION •DUMMY •DICTATOR •VETO POWER •SHAPLEY-SHUBIK POWER INDEX •SHAPLEY-SHUBIK POWER DISTRIBUTION
Adaptations/Differentiation:
Lesson steps:
1. Start the lesson
Warm-ups:
1) [35: 12, 7, 3, 8, 9, 6, 1]Identify the quota, # of players, and weight of the 4th player.
2)[35: 12, 7, 3, 8, 9, 6, 1] Write out 3 winning coalitions.
3) How many total possible different coalitions exist from problem #2?
4) Perform the Banzhaf power distribution on [19: 9, 8, 5, 3].
2. Presentation
2.4Shapley-Shubik Power Index – PowerPoint
2.5 Shapley-Shubik Power Index Applications – PowerPoint
3. Guided practice
2.4 and 2.5 Guided notes
Guided notes handout/ with examples
  • Practice with factorials
  • Finding sequential coalitions
4. Independent practice
Pg. 68-69 # (25-33) odd
Interact math exercises (online) – student completes on the “mini” and prints
5. Evaluation/Summarizing strategies:
Pg. 71 # 51 (b) - A professional basketball team has four coaches, a head coach (H), and three assistant coaches (A, A, A). Player personnel decisions require at least three yes votes, one of which must be H’s. (b) Find the Shapley- Shubik power distribution of the weighted voting system.
6. Closure
In underlying the Shapely-Shubik interpretation of power, what are players doing and what are player’s committing to?

Main Street ACADEMY LESSON PLAN 2011-2012

Teacher: Clark / Period(s):4th / Start date: 2/14/12 / End date: 2/14/12
State competency goal and objective:2.03 Model and solve problems involving fair outcomes:
c) Voting Power
EQ:Section 2.4: What is a Shapley-Shubik Power Index and which players are important?
Objective: Calculate the Banzhaf and Shapley-Shubik power distribution in a weighted voting system.
Literacy enhancements/Key Vocabulary:
•WEIGHTED VOTING SYSTEM •PLAYERS • PIVOTAL PLAYER •CRITICAL PLAYER •WEIGHTS •QUOTA •BANZHAF POWER INDEX •BANZHAF POWER DISTRIBUTION •COALITION •GRAND COALITION •DUMMY •DICTATOR •VETO POWER •SHAPLEY-SHUBIK POWER INDEX •SHAPLEY-SHUBIK POWER DISTRIBUTION
Adaptations/Differentiation:
Lesson steps:
1. Start the lesson
Indicator 2.03cA. Find the Shapley-Shubik power index for each voter. [q: A, B, C] 10: 3, 7, 9]
B. Consider [20: 12, 6, 5, 3, 2]. What is the weight of P1 and P3 if they form a coalition?
C. Find 15!/13!
D. Given that 10! = 3,628,800, find 9!
2. Presentation
Review Chapter 2: Weighted voting practice problems- mult. choice
3. Guided practice
Chapter 2 review materials handout
Test Review Guide handout
Interactive Exercises (optional)
4. Independent practice
Chapter 2 Test 1
5. Evaluation/Summarizing strategies:
Chapter 2 Test 1
6. Closure
n/a

Main Street ACADEMY LESSON PLAN 2011-2012

Teacher: Clark / Period(s):4th / Start date: 2/15/12 / End date: 2/15/12
State competency goal and objective:2.03 Model and solve problems involving fair outcomes:
c) Voting Power and d) Fair Division.
EQ:
Objective: Calculate the Banzhaf and Shapley-Shubik power distribution in a weighted voting system.
State the fair-division problem and identify assumptions used in developing solution methods.
Literacy enhancements/Key Vocabulary:
Adaptations/Differentiation:
Lesson steps:
1. Start the lesson
Review problems from chpt 1 and 2

1. In the weighted voting system [q: 10, 8, 5], the smallest possible value that the quota q can take is: a. 14 b. 11 c. 13 d. 12 e. None of the above

2. In the weighted voting system [12: 13, 7, 2]
  1. P1 has veto power but is not a dictator b. there are no dictators c. P1 is a dictator. D. every player is a dictatore. None of the above
2. Presentation
  • Discussion of the Elections coming in 2012 and its relevance to discrete mathematics.
3. Guided practice
  • Discussion of Chpt 2 Test
  • Venn Diagram- compare and contrast Electoral College
4. Independent practice
Voting Power:
Project/ Papers pg. 74 – C. Mathematical Arguments in Favor of the Electoral College: Summarize and Analyze Natapoff’s mathematical arguments in support of the Electoral College. (reference 6)
5. Evaluation/Summarizing strategies:
Rubric for paper
6. Closure
Chapter 2 conclusion power point

Main Street ACADEMY LESSON PLAN 2011-2012

Teacher: Clark / Period(s):4th / Startdate: 2/16/12 / Enddate: 2/16/12
State competency goal and objective:2.03 Model and solve problems involving fair outcomes:
d) Fair Division.
EQ:Section3.1: What are the basic elements of the Fair-Division game and what methods can you use to divide the shares?
Objectives:
  • State the fair-division problem and identify assumptions used in developing solution methods.
  • Recognize the differences between continuous and discrete fair-division problems.

Literacy enhancements/Key Vocabulary:
•Goods/ “Booty”, S •players • value system • fair share • division methods • continuous • discrete
• mixed
Adaptations/Differentiation:
Lesson steps:
1. Start the lesson
Review problems from Chapters 1 and 2
2. Presentation
3-1 :Fair-Division Games PowerPoint
3-1 Student notes handout
3. Guided practice
3-1 Student notes handout:
  • Buy Cake
  • Have to split a pizza
4. Independent practice
  • Pg. 103-106 Exercises. 2-10,14 even
  • Work on Paper- Math and the Electoral College
5. Evaluation/Summarizing strategies:
Pg. 103 #12
6. Closure
What problems may arise when dividing objects among members? How can mathematics provide a solution that guarantees each player will always receive a fair share?

Main Street ACADEMY LESSON PLAN 2011-2012

Teacher: Clark / Period(s): 4th / Startdate: 2/17/12 / Enddate: 2/17/12
State competency goal and objective:2.03 Model and solve problems involving fair outcomes:
d) Fair Division.
EQ:Section 3-2: In your opinion, who gets the better end of the deal with the Divider-Chooser method? What are the pros and cons to the divider-chooser method?
  • Apply the divider-chooser, lone-divider, lone-chooser, and last-diminisher methods to continuous fair-division problems.

Literacy enhancements/Key Vocabulary:
• Divider/Chooser •Lone- Divider method
Adaptations/Differentiation:
Lesson steps:
1. Start the lesson
Warm ups – Review problems from previous lesson
2. Presentation
  1. 3-2 PowerPoint lesson
  2. Chapter 3 PowerPoint (6th edi.)
  3. 3-3PowerPoint lesson (after lesson 3-2)
3. Guided practice
3-2 student lab/notes
3-3 student lab/notes
4. Independent practice
Pg. 106 Exercises 16-20 even
Interactive Exercises: done on the mini from website :
5. Evaluation/Summarizing strategies:
Check student examples
Levels of Comprehension: Hot mess, Stuntiń, Gucci – student assessment
6. Closure
Answer the essential questions.
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