Introduction to modulo seven

This week I introduced the students to the finite field of seven elements via the following puzzle found at http://mathfair.com/puzzles.html:

Circle Jump image found on http://mathfair.com/puzzles.html

Redraw the figure so that each of the seven circles is big enough to hold a penny. The problem is to shade each of the shaded circles. However, there’s a catch. Here’s the rules that you have to follow.

Starting with any circle, count clockwise three circles and shade the third circle. Continue in this way, each time beginning at an empty circle and counting clockwise three circles and then shading.

As there are seven circles, the students where able to change the problem from counting over three spaces to counting over n spaces.  They where able to figure out that multiples of seven will not work and that 10 is congruent to 3 modulo 7.

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About Branden

As a GK-12 Fellow, I meet with a group of middle school students at Rosedale Middle School in Kansas City, Kansas. There I talk to them about what a mathematician does and teach them ways of thinking about problems. I am a student of Craig Huneke at the University of Kansas. As a far as my research is concerned, I am currently studying the theory of maximal Cohen-Macaulay modules. In particular, I am interested in determining if countable Cohen-Macaulay type implies finite Cohen-Macaulay type over a complete local Cohen-Macaulay ring with an isolated singularity. I also enjoy working with Macaulay2 .
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