Title of Book:
Author:
Publisher/Date:
ISBN:
The Number Devil
Hans Magnus Enzensherger
Henry Holt Books/2000
0805062998
Grade Level for recommended use: Texas Remedial College Math: 0370-0371-0373
Standards IX: Communication and Representation
A. Language, terms, and symbols of mathematics
1. Use mathematical symbols, terminology, and notation to represent given and
unknown information in a problem.
2. Use mathematical language to represent and communicate the mathematical
concepts in a problem.
3. Use mathematics as a language for reasoning, problem solving, making
connections, and generalizing.
B. Interpretation of mathematical work
1. Model and interpret mathematical ideas and concepts using multiple
representations.
2. Summarize and interpret mathematical information provided orally, visually, or
in written form within the given context.
C. Presentation and representation of mathematical work
1. Communicate mathematical ideas, reasoning, and their implications using
symbols, diagrams, graphs, and words.
2. Create and use representations to organize, record, and communicate
mathematical ideas.
3. Explain display, or justify mathematical ideas and arguments using precise
mathematical language in written or oral communications.
Brief Summary and reading (5 minutes): Night 8: Summary of the story. This night during the
dream Robert stands in front of the white board. The Number Devil teaches Robert about
combination and number of cases. If there are 2 kids in class, there are 2 possible ways for
them to line up. If there are 3 kids, then 6 possible ways. As more and more students enter the
room, Robert and the Number Devil try to figure out the number of possible ways to line up, but
eventually everyone goes back to their home. Then, he tells Robert that he will be on vacation
for few moments.
Materials needed: Handout, 3 different pictures of different colors: The 8th Night.
Teacher will give the following vocabulary bank and 3 full sheets of paper to each student for a
Suggested Activity and three words: (10 minutes)
A-Permutation
B-Combination
C-Factorial
What is Permutation?
What is Combination?
1- When order matters AB
BA. True or False (Expected answer is True!)
Ask three volunteer students (Angie, Sophie and Sue) to come up front and have them
change the position according to the following: Angie, Sophie and Sue
How many different ways can these three students be arranged where order matters?
Answer:
Let ASoSu stand for the order of Angie on the left, Sophie in the middle and Sue on the right.
Since order matters, a different arrangement is SoASu. Where Sophie is on the left, Angie is in
the middle and Sue is on the right.
If we find all possible arrangements of Angie, Sophie and Sue where order matters, we
have the following:
ASoSu, ASuSo, SoASu, SoSuA, SuASo, SuSoA
The number of ways to arrange three students three at a time is:
3! = (3)(2)(1) = 6 ways
2- Example 2: What is the general formula? What is the total number of possible 4-letter
arrangements of the letters
m, a, t, h, if each letter is used only once in each arrangement?
or
or simply 4!
Write down your own definition of Permutation, try to represent a permutation
3- Example 3:
What about having 12 boys and 14 girls in Mr. A's math class. Could you help Robert
and Number Devil to figure out the number of ways Mr. A can select a team of 3 students
from the class to work on a group project. The team is to consist of 1 girl and 2 boys.
It’s important here to know that Order, or position, is not important. Using the
multiplication counting principle
Let's look at which is which:
Permutation versus Combination
1. Picking a team captain, pitcher, and shortstop from 1. Picking three team members from a group.
a group.
2. Picking your favorite two colors, in order, from a 2. Picking two colors from a color brochure.
color brochure.
3. Picking first, second and third place winners.
3. Picking three winners.
Answers and activities (5 minutes):
Permutation:
A set of objects in which position (or order) is important. To a permutation, the trio of Brittany,
Alan and Greg is DIFFERENT from Greg, Brittany and Alan. Permutations are persnickety
(picky).
Combination
A set of objects in which position (or order) is NOT important. To a combination, the trio of
Brittany, Alan and Greg is THE SAME AS Greg, Brittany and Alan.
Source for lesson and extended work:
http://www.regentsprep.org/Regents/math/algtrig/ATS5/Lcomb.htm
http://www.omegamath.com/Data/d2.2.html
Adapted by: Emmanuel Atangana (2012)