Mathematical Beauty on Vacation to Use in Classroom Conversation

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Laura Wagenman
MCTM Communications Chair

I stepped off the elevator at our hotel in Trinidad and the floor caught my eye. It was a beautifully patterned array so I immediately pointed it out to my 8 year old daughter. She noticed it was 7 groups of 7, counting 3 white and 4 black squares, with an AB pattern, a perfect square. “Did you know squares are a kind of rectangle?”

This interaction reminded me of a talk Christopher Danielson gave at MCTM Duluth this past spring, using photos to encourage math discussion and Malke Rosenfeld’s Instagram Page, Math Off the Page. I was inspired to find the mathematical beauty as I explored Trinidad and Tobago the next several days.

While I narrowed it down to 5 images, my camera roll is filled with images that could be used in a math classroom.

1. While in Tobago,we converted our US dollars to their TT dollars at a rate of $1 US = $6.69 TT. As we had both types of money, we were constantly converting between the two. This sign was one of the only that converted for us and led to a discussion about whether this was a fair conversion. I had hoped they would have taken the tarp off the beach chairs in the background so we could estimate how many but the chair crew wasn’t there to unveil this treasure.

2. My daughter pointed out the next image while at the resort pool, asking if it was related to the Fibonacci sequence. It led to a conversation about shapes, size, and how many smaller rectangles would fit into the larger one.

3. The next images were caught while on a run through Tobago. Each building had a structural element that made it unique. When I shared these with my daughter upon my return to the hotel, she noticed the variety of shapes and lines. When she began counting the octagons, she grouped them into 10s and shared how 40 + 16 was 56 as she added 40 + 10= 50 then 50 +6 = 56. Proud of her reply, she noticed the rhombuses and wanted me to help her recount.

4. I was admiring these flowers and noticed they each had 5 petals. When I pointed it out to my daughter, she was excited to count by 5s. Students could discuss color, petal shapes, symmetry, and notice leaf patterns as well.

5. As we walked into town, we noticed many driveways like this. My daughter loved that there were rectangles but then noticed each shape consisted of three rectangles. She estimated there must be at least 500 of the shapes, each with 12 sides. She then wondered aloud if the shapes tessellated but then lost interest and walked away.

You definitely don’t need to be in the West Indies to find beautiful photos, though it is a magical place to visit. Minnesota is abound with beautiful objects to start mathematical conversations for any classroom.