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- Combinatorics Topics for K-8 Teachers - Roger Day
Notes from fifteen sessions of a 1996 course for professional development. Includes a link to the home page for the course, where you can see problem sets, quizzes, tests, and the syllabus. Note topics include: Perfect Covers of Chess Boards, the Pigeonhole Principle, Summation and Product Notation, Combinations, Circular Permutations, Arranging Items When Repetition is Allowed, Pascal's Formula, Binomial and Multinomial Expansion, Pascal's Triangle, Number of Subsets of a Set, Fibonacci's Sequence in Pascal's Triangle, Solving sigma(i,1,n;a(i))=K Over Nonnegative Integers, Induction, Recursion, Finite Differences, the Inclusion/Exclusion Principle, and Derangements.
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- Games on Graphs (MegaMath) - Nancy Casey; Los Alamos National Laboratory
Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems. Graphs, stories and games provide scenarios for games that student can play on graphs. Also Three for the Money: The Degree/Diameter Problem, an unsolved problem for students to work on, and other games that can help students increase the range of possibility for games that they can invent on graphs. Big Ideas and Key Concepts include pages on Graphs; Properties of mathematical objects; Modeling; and Abstraction.
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- How Many Different Paths - Karen Wheeler; SCORE Mathematics
A discrete mathematics lesson for working on addition and multiplication skills, with connections to counting, adding, multiplying, and Pascal's triangle. Aligned to the California State Standards. From the Schools of California Online Resources for Educators SCORE Mathematics Lessons.
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- How Many Ways Can a Team Win a 7-Game Series? - Kent Anderson; SCORE Mathematics
Students discover how many ways a team can win a 7-game series (NBA Finals, World Series, Stanley Cup) by accessing the Internet and then systematically constructing a sample space that lists all the possible ways. Aligned to the California State Standards. From the Schools of California Online Resources for Educators SCORE Mathematics Lessons.
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- The Most Colorful Math of All (MegaMath) - Nancy Casey; Los Alamos National Laboratory
Coloring is a profound mathematical topic with multi-million-dollar industrial applications. The problem presented here has been of interest to mathematicians for over a hundred years. With a few crayons or markers and some hand-drawn maps, children can quickly find themselves grappling with the four-color map problem. Activities, Background Information, Evaluation.
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- Three for the Money: The Degree/Diameter Problem (MegaMath) - Nancy Casey; Los Alamos National Laboratory
Students can understand and work on an unsolved problem in mathematics. There is a good chance that this problem can be solved by someone who spends enough time experimenting with it. The only skills required to work on it are the ability to draw dots and connect them with lines, and the understanding of four ideas related to graphs: degree, diameter, planarity, and size. With ideas for discussion.
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The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies.