Title of Book:
Title of Book: The Number DevilAuthor: Hans Magnus EnzenshergerPublisher/Date: Henry Holt Books/2000ISBN: 0805062998Grade Level for recommended use: Texas Remedial College Math: 0370-0371-0373 Standards IX: Communication and Representation A. Language, terms, and symbols of mathematics1. 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 work1. 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 work1. 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-PermutationB-CombinationC-Factorial What is Permutation?What is Combination? 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, SuSoAThe number of ways to arrange three students three at a time is: 3! = (3)(2)(1) = 6 waysExample 2: What is the general formula? What is the total number of possible 4-letter arrangements of the lettersm, 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 permutationExample 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 principleLet's look at which is which:Permutation versus Combination1. Picking a team captain, pitcher, and shortstop from a group.1. Picking three team members from a group.2. Picking your favorite two colors, in order, from a color brochure.2. Picking two colors from a 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). CombinationA 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: Adapted by: Emmanuel Atangana (2012) ................
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