Mr. L’s Math

[N.B. - This post is written by my coauthor from Teacher to Teacher Press, Brad Fulton, with some slight tweaking from me. The activity will work well for students from grades 6 - Algebra 2. This is an extension of the activity Hundreds Magic, which can be found at the end of this activity under Related Posts.]
My 8th grade students enjoy discovering the algebraic patterns hidden within the hundreds chart. They are all familiar with this chart that they have seen since Kindergarten. One of our activities involves “Algebra Man.” I display a transparency of the hundreds chart and a second transparency of Algebra Man on top of it as shown.

I move the upper transparency around until a student yells, “Stop.” Then the students race me to find the total of the numbers inside Algebra Man. The total for the placement shown is 580. I always win this contest and boast that it is because I am so talented at math. The students insist there is a trick and demand a rematch. After a few times, some of the students see a pattern and discover the trick. (Turns out I’m not a rocket scientist after all!) Once a few discover my secret, we explore the problem using algebra.
The students notice that for any number on the chart, the number to the right is one more and the number to the left is one less. Also, the number beneath the given number is ten more and the number above it is ten less. This is always true no matter where Algebra Man runs. If we think of the number in his waist as n, then the following diagram shows the values of all ten numbers inside Algebra Man:

Many of my students say that they got the answer a different way. Often they simply look two spaces to the right of his waist and put a zero after the number. I express this algebraically on the board. The number two spaces to the right of his waist would be called n+2. Putting a zero after it is the same as multiplying by ten. Thus their method is 10(n+2). I show them that these are equivalent being the distributed and factored forms of the same expression:

10n+20 = 10(n+2)

Algebra Man works on any hundreds chart, even one that begins with -49 and ends with 50. He also works on a calendar, but the formula for his sum is slightly different. Challenge your students to find the formula when Algebra Man runs around on a calendar. This is just one of many algebraic explorations that can be made on the hundreds chart. If your students are like mine, they will want to explore all the “what if’s” they suggest. One time my students wanted to find out what happens to Algebra Man’s formula when he is standing on his head. Now I was curious.
Related Posts:

Hundreds Magic - a Simple Diagram Produces Patterns, Number Sense, and Algebra Proofs

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