# Casa di Mir Summer Mathematics: Adventure #8

###### The Magic and Mathematics of Bubbles

No summer is complete without at least one afternoon spent on the magic of bubbles. The small, classic spherical bubbles that are made using a plastic wand and a bottle of bubble solution are just the beginning of what is possible.

Bubble Solution. You can make your own bubble solution, scaling the recipe up or down, depending on what kind of bubbles you want to make.  The recipe below is enough for giant bubbles. (It’s worth the trouble to get the glycerin, as this helps the bubbles last longer.)

• 6 cups water (distilled is ideal, but tap water works)
• ½ cup dishwashing liquid (original Dawn or Joy works best)
• ½ cup cornstarch
• 1 Tbsp baking powder (not baking soda)
• 1 Tbsp glycerine (usually available at drugstores and some craft stores)

Mix this up, put it in a large plastic bin or bowl, and let it sit for a bit of time. Meanwhile, you can make some bubble wands.

Small Bubbles. You can use pipe cleaners (available in most craft stores) to make small bubble wands of different shapes and sizes. Try a circle, square, and triangle. Do differently shaped bubble wands make differently shaped bubbles? Do differently sized bubble wands make differently sized bubbles? Can you make a double bubble? (Blow a bubble, catch it on a wand, blow another bubble, catch it on another wand, and then bring the two bubbles together.) What do you notice about your double bubble? What do you wonder?

Giant Bubbles. You can make bubble wands that will make giant bubbles.

• One very easy model uses just two straws and a length of cotton string that is about 8 times the length of a straw. Thread the string through the straws, tie a knot in the string, and you’ll have a loop of string with the straws as the handles.
• A different model uses two 24-inch dowels (3/8-inch works well); two screw eyes – one for each dowel, screwed into an end; a 40-inch length of cotton string with ends fastened to the two screw eyes, and an 80-inch length of cotton string with one or two washers placed in to middle and then the ends fastened to the two screw eyes. Laid out on the ground, this wand looks like a triangle with two handles.

To make bubbles using these wands, the entire loop of each wand needs to be dipped in the solution. Then, holding the loop out, you slowly walk backwards and gently move the loop in the air. What shapes do these bubbles turn out to be?

Zometool Bubbles. If your kids have a Zometool set, they can make some three-dimensional shapes with the pieces and dip these shapes in the bubble solution. The “bubbles” that are formed are entirely on the interior of the frame, and the geometry of the bubble solution on such a structure is truly a marvel to observe. Try building a tetrahedron or a cube with the Zometool pieces and dip these in the bubble solution. What do you notice and what do you wonder? What might happen with more complex three-dimensional shapes?

Explore, experiment, and have fun with your bubbles. Here’s hoping that your magical bubble experience is just a bit mathematical too.

About the author: Trisha Bergthold has been the middle school math teacher at Casa di Mir Montessori School since 2014. She holds a PhD in mathematics with emphases in curriculum and pedagogy. Prior to her work at Casa di Mir, she designed curriculum for kindergarten through college level. She also taught university-level mathematics courses for sixteen years.

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