Brett
Penza
Math
in Technology
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. 020% 

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.
5421
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 







