Brett Penza

Math in Technology

September 17,2006

Instructor: Mary Ellen DuBois

 

Lesson Plan: The Secret of Nim!

 

A Technology Plan with elements of Mathematical, Logical thinking.

Designed for a High School classroom.

 

The NCTM Framework Standards employed:

· Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

· Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;

· Draw reasonable conclusions about a situation being modeled.

 

Websites to be used:

www.2020tech.com/fruit/index.html The Fruit Game

 

 

Lesson Objective: To SPARK THE STUDENT MIND. Give them an opportunity to creatively unlock the secret of the game of NIM (The fruit game). Then, give them a research tool to analyze and deepen their understanding of the mathematical concept of the game. Finally, they will use this “greater understanding” to improve their skills and compete against the computer to win the game.

 

Tasks:

1. Explain the basic rules of “The Fruit Game”. A player can pick any number from only one row at a time. The winner is the last player to pick fruit.

2. Tell the students to go to “The Fruit Game” web site. Have them play 10 games and try to defeat the FruitMaster. They must play the game only. They must not surf the site!

3. The students will keep score on the Handout. Allow 15 minutes.

4. Now present the Binary Sum Concept to the students using the PowerPoint Presentation. (10 Minutes)

5. Give the students time to digest and allow them to further surf the site to gather other game pointers. (10 Minutes)

6. Now, have the students play the game again. They will keep track of their wins and losses. Have them play 10 games.

7. Students perform analysis. Fill out questionnaire.

 

RUBRIC – 20 POSSIBLE POINTS

SCORE

ROUND ONE

RESEARCH

ROUND TWO

WORKSHEET

COMMENTS

5

Consistent Performance 80%

Outstanding effort on task.

Analyzes Binary Logic.

Consistent Performance

80%, or high improvement.

Answers all questions using acquired knowledge.

 

4

60% with improvement

Learns from research, uses combinations.

Improves into the 60% range.

Answers most questions. 80%

 

3

40% with slight improvement

Mild effort, more concerned with play.

40% range

Answers correct for 60%

 

2

20% with no improvement

Surfing site, but not focused.

20% range

Answers are very brief, show limited learning. 40%

 

1

0% No sign of effort

Does not take part.

0% No sign

No evidence of learning. 0-20%

 

TOTALS

 

 

 

 

 

 


 

 

“The Secret of Nim                                                       NAME: ______________________

Student WorkSheet

 

I. Initial Game Log. Computer vs. You

I

II

III

IV

V

VI

VII

VIII

IX

X

 

 

 

 

 

 

 

 

 

 

Total Wins: ____________

 

II. Game Log. (After Research)

I

II

III

IV

V

VI

VII

VIII

IX

X

 

 

 

 

 

 

 

 

 

 

Total Wins: _____________

 

III. Final Analysis

 

1. Did you Improve your score? ___________________________

 

2. What technique did you use to Improve your game?

(Combination Memorization, Sum Binary, Other)

________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

3. What is the reasoning behind going first or second in the game?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

4. Using the Sum Binary Technique, what would the next move be in these situations?

JJJJJJJ                          JJJJJJ                          JJJJJ

JJJ                                JJJJJ                JJJ

    JJ                                  J                                 J

______________                  _______________            _______________

 

5. When using the Sum Binary Process, your objective is to: _____________________________________________________________________

_____________________________________________________________________

 


 

Sum Binary Worksheet - For optional use while playing second round games.

5-4-2-1

Row

Open

I

II

III

IV

V

VI

VII

VIII

1

101

 

 

 

 

 

 

 

 

2

100

 

 

 

 

 

 

 

 

3

10

 

 

 

 

 

 

 

 

4

1

 

 

 

 

 

 

 

 

Sum

010

 

 

 

 

 

 

 

 

 

Row

Open

I

II

III

IV

V

VI

VII

VIII

1

101

 

 

 

 

 

 

 

 

2

100

 

 

 

 

 

 

 

 

3

10

 

 

 

 

 

 

 

 

4

1

 

 

 

 

 

 

 

 

Sum

010

 

 

 

 

 

 

 

 

 

Row

Open

I

II

III

IV

V

VI

VII

VIII

1

101

 

 

 

 

 

 

 

 

2

100

 

 

 

 

 

 

 

 

3

10

 

 

 

 

 

 

 

 

4

1

 

 

 

 

 

 

 

 

Sum

010

 

 

 

 

 

 

 

 

 

Row

Open

I

II

III

IV

V

VI

VII

VIII

1

101

 

 

 

 

 

 

 

 

2

100

 

 

 

 

 

 

 

 

3

10

 

 

 

 

 

 

 

 

4

1

 

 

 

 

 

 

 

 

Sum

010

 

 

 

 

 

 

 

 

 

Row

Open

I

II

III

IV

V

VI

VII

VIII

1

101

 

 

 

 

 

 

 

 

2

100

 

 

 

 

 

 

 

 

3

10

 

 

 

 

 

 

 

 

4

1

 

 

 

 

 

 

 

 

Sum

010