Kiss those Math Headaches GOODBYE!

Archive for the ‘Using Color in Geometry’ Category

James Bond Math Challenge


Math in the movies … if there ever was a cool way to explore math, this has to be it. And if you missed my earlier posts on this, check them out here and here.

Math is Cool!

I was looking through the links to movies with math themes, and a question came up.

On the site showing the movies, the text says that there are “mathematical themes and patterns motivated by math” in the introduction scene for the James Bond movie, Casino Royale, this clip:

I’ve watched the clip a few times, and I have my own ideas as to mathematical themes and patterns.

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Rubik’s Slide: play your way to geometric knowledge


A toy that educates … could it be a dream?

I recently found something that fits that category, educating students in concepts of GEOMETRY.

It’s called the Rubik’s Slide, created by Techno Source. I bought this Rubik’s Slide a few months ago because I needed another puzzle to keep my tutoring clients entertained while I grade their work, which I often do at the start of sessions.

Rubik's Slide Logo

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Using Color to Show Perimeter


Many things look better in color, right?

So why should that be any different  in math?

I’ve found that taking a “colorful approach” to math not only makes mathematical objects look more interesting and pleasurable, it can also make mathematical concepts more clear.

Here’s an example from something I did today — I used color to show a shortcut for finding the perimeter of rectangular-ish objects.

I was tutoring a boy who had to find the perimeter of this figure:

Right object, find perimeter

This student did not see that there is a short-cut that could help him find the perimeter. I wanted to make this clear, so I reached for my color pencils and colorized both the left vertical segment and the two right vertical segments. My goal was to help the student see that the sum of the two right vertical segments equals the long left vertical segment.

The student realized this after I colorized it. Then I used a different color, red, to show that the sum of the two horizontal segments on top equals the longer horizontal bottom segment, like this:

At this point I felt that the student was ready to see the math that relates to the whole figure, so I wrote the math, using color to relate the numbers to the colors of the sides of the figure, like this:


At this point the student was able to see the shortcut in this kind of problem, which together we wrote as follows:


This is a fairly basic example of how color can, quickly and effectively, illustrate math concepts. Feel free to share examples of how you use color in your math lessons. I’m curious to learn (and share) a variety of ways, for I see that color has great potential.

Colouring pencils

Image via Wikipedia

Tutor Tales #1: Color in Geometry


Hi,

This if the first in what I hope will be a long series of brief blogs called Tutor Tales blogs.

The idea is that while I’m tutoring I get ideas or insights on how to help students, and then I write up a short blog entry on that experience, preferably on the day that the event occurred.

I hope that these Tutor Tales will give you examples of approaches to math that help students (or that do not help, depending on what I did), and that they give you a chance to reflect on your own teaching.

For the first Tutor Tale entry, I just noticed how useful it can be to use color in geometry.

The girl I was tutoring had a problem:  Find out how many diagonals can be drawn inside a regular, convex nine-sided polygon.

I’ve already noticed that this girl likes color, and she is 17 years old. So I had a hunch that she would be open to trying a color-approach.

We created the non-agon by first drawing a circle, and then marking off nine points on the circle. Then we connected the points sequentially.

To find out how many diagonals we could draw for such a figure, we chose one color for the top point, green, and drew all of the diagonals we could for that point, in green. It turned out that there were 6 diagonals, so we put a big 6 in green at this vertex. Then we tried the next vertex, which we colored pink. We found that we could create 6 additional diagonals from this vertex, and we colored these pink. So we put a big pink 6 by this vertex. We went around the circle in a clockwise way, using a different color for each vertex. All in all we found that the pattern of diagonals was:  6, 6, 5, 4, 3, 2, 1, 0, 0, for a grand total of 27 diagonals.

Here’s the image of the figure we worked on.

non-agon-problem

One thing to consider, especially if you teach geometry, is how many opportunities there are in geometry to use color to separate different concepts and to relate similar concepts. Check it out and see what you discover.

Happy Teaching!

—  Josh