Casa di Mir Summer Mathematics: Adventure #5

A Day at the Beach             

Has your family been to the beach yet this summer? Many elements of the beach experience are surprisingly mathematical.

Sea Level. The beach is a place where your kids can get first-hand experience walking back and forth between elevations above sea level (which we measure with positive integers) and below sea level (which we measure with negative integers). Of course identifying a spot to stand that represents exactly “sea level” at a particular place and time is a bit tricky, since waves are continually coming in and going out.

  • Ask your youngest child to observe the waves for a few minutes, and then stand about halfway between the highest flow and the lowest ebb – this is good enough.
  • Slightly older kids can play the game Simon Says, with the directions such as, “Move so that the soles of your feet are about 6 inches below sea level,” or, “Move so that the soles of your feet gain 12 inches of elevation.”
  • The oldest kids can check out the tide tables online before the trip to the beach to see the times and elevations for high tide and low tide – this involves greater understanding of sea level and positive and negative integers.

For more about the physics of determining sea level, see this short video, “What is Sea Level?” from Minute Physics: https://www.youtube.com/watch?v=q65O3qA0-n4

Sand Castles. It wouldn’t be a day at the beach without building a sand castle. Basic supplies include a large bucket, a smaller bucket, a spade, and empty cans of different sizes and heights with both ends removed. There is much debate about the best ratio of sand to water in the making of large, sturdy sand castles.

By experimenting and tinkering with different ratios of sand to water (bring a measuring cup), your kids will gain skills in measuring volume, comparing ratios, and tracking data.

(It turns out that you need much less water that you might expect. See the article titled, Secret to Perfect Sand Castles from Live Science to learn more: https://www.livescience.com/22083-secret-to-perfect-sandcastle-revealed.html.)

Sea Shells.  Many kids love to hunt for sea shells. You can make a scavenger hunt (bring small tape measures and buckets) that focuses on counting, measuring, identifying, and sorting activities. There are many different levels of mathematical ideas that could be incorporated into such a scavenger hunt.

  • The littlest kids can be asked to find three shells of the same type or all different sizes; to find a shell that is smaller than 1 inch across; and to find a shell that is larger than 2 inches across.
  • Slightly older kids can be asked to find a shell with mirror symmetry; to find a spiral shaped shell; and collect enough shells that, laid end -to-end, they measure at least 12 inches.
  • The oldest kids can be asked to gather a collection of shells with an average distance across of 2 inches.

Here’s hoping your day at the beach is as mathematical as it is sunny.

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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