# Simulating Mixture Problems with Colored Beads

By Arthur N. DiVito, Ph.D. (copyright © 2000 by A. N. DiVito)

MATERIALS NEEDED:
• weights
• scale
• lots of beads, at least two different colors (craft stores will have them)
• containers to hold and mix beads

REMARKS:

This is an outstanding MathLab activity. As in the case of the model cars, there are many different activities these beads can be used for. Not the least of which is the simple idea of percent. That is, if a randomly mixed container of, say, red and white beads is 70% red, then smaller sizes drawn from the container will remain close to 70% red while, of course, the actual count (or weight, or volume) is quite different.

Anyone who has taught mathematics knows that students have tremendous difficulty solving “mixture” problems. One reason, of course, is that many students don’t even understand what a “70% alcohol solution” actually means! If nothing else, this activity will certainly make such notions clear to the students.

The best kind of bead is one that will not roll (e.g., craft stores will have a kind of “Y” shaped bead that works very well); otherwise, the class will soon be chasing beads all over the place. But, be sure all the beads are of the same type (i.e., you can’t have Y-shaped white beads and differently shaped or sized red beads).

These activities will result in a lot of time spent “separating the colors.” It turns out (provided you don’t use rolling beads!) that this activity is actually rather pleasant, even relaxing. Try it.

THE ACTIVITY:

Two large mixtures of red and white beads are prepared. Mixture A is 70% red and mixture B is 40% red. [This is best determined by weight. Use the scale to determine appropriate weights of red and white beads to mix (itself an elementary, but good, math problem); then, mix the beads up very thoroughly.] The problem, of course, is that someone requests a mixture of, say, 200 grams that is something between 40% and 70% red-say 60% red. How many grams of each mixture, A and B, should be combined to obtain the required 60% solution? This is the kind of problem a pharmacist might face frequently.

Of course, all different kinds of percentages, sizes, and requests can be used, so the variations are endless.

EMPIRICAL VERIFICATION:

Once the final container of 200 grams has been prepared, it is a simple matter of separating the beads into the two colors, and weighing the separate colors in order to determine the actual composition (percent red) of the container. The results should be very good.

A word of caution. It might seem that mixing water and oil should work real well (the water can be dyed blue so the mixtures can be prepared by weight, volume, or even just depth). Well it doesn’t. The two simply separate too fast while trying to pour them after they’ve been thoroughly mixed! Other liquids might work, but oil and water don’t. Stick with the beads.

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