Session Style: Multiple Representations

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Mathematical Magic for Muggles

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Presented are several easy-to-perform feats that suggest supernatural powers such as telepathy, “seeing fingers,” predicting the future, photographic memory, etc. Each trick uses simple mathematical ideas that allow information to flow effortlessly and sneakily, among them simple, efficient “coding” parity and other invariants symmetry probability One can approach these activities in many ways. At first, you may want to figure out HOW to do a trick. Then, you want to know WHY it works. Finally, you should strive to understand REALLY WHY it works: is there a simple theme or principle behind your possibly complex explanation? Look for simple and...

Piece of Cake; Delectable Fractions and Decimals

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While exploring the relationship between fractions and decimals, participants will have the opportunity to practice operations with fractions, notice and explain patterns, review understandings of place value and number sense, and justify their reasoning.

You can get a taste of math research by repeating these two steps: Think about an interesting unsolved problem, and Do Something to try solving it. Now Think about what you notice, and Do Something to explore your results. Repeat.

Pick’s Theorem

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Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter pegs, and the number of interior pegs.

This session is also suitable for student circles or the classroom.

Puzzles, Bands, and Knots

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This activity packed session starts with a fun Pythagorean Puzzle Proof. Then, Knot Theory is explored while experimenting with the Mobius Band, Knots and Links; Untangling Ropes and Rings, and acting out the Human Knot Experiment. These explorations are further connected to the coiling and knotting of DNA molecules.

These activities are suitable for the classroom or student circles.

Recruiting Change for a Dollar

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How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in order to make progress.

This monetary problem is engaging, and classroom adaptable with multiple entry points.

Visualization in Algebra

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Many topics in mathematics can be made much clearer when symmetric aspects are made clear or when nice alternative visualizations are possible. When this occurs, it helps both the student and the teacher. We will examine visualization and symmetry in a very general way by means of a set of problems.

There is a large amount of potential classroom material here, and almost any small part of it could be used for an entire class session.

Game of Criss-Cross

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The purpose for having students play the game of Criss-Cross is to motivate them to explain the underlying mathematical reason governing who wins or loses. This exploration should lead the students to form, test, and ultimately prove conjectures about how to win at Criss-Cross. The game illustrates a beautiful application of the Euler characteristic and gives them practice at elementary counting techniques as well.

Getting Started with PROBLEM SOLVING: A Trio of Friendly Problems

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The three problems presented for this extended lesson have both individual and cluster appeal. Since each of these problems can be visualized or acted out quite readily, the problems can be accessible at some level for virtually every middle school student. By offering all three of the problems to your students over a period of time, there is the opportunity to draw them into the problem-solving experience at a deeper level and allow students to practice and strengthen their ability to generalize and recognize underlying themes/parallels within various contexts. The Handshake Problem is a natural opener for the beginning of...