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• Exploring Different Number Systems with Younger Learners

As a mathematics educator, I always welcome any opportunities to use manipulatives in the classroom. I believe that regardless of the grade level, most students appreciate how manipulatives can help make mathematical concepts/ideas more concrete and often easier to understand. I wish secondary math teachers (myself included) got to use manipulatives as much as our elementary colleagues. My daughter for example, constantly uses them within the math topics she is learning in second grade. It’s very common for her to use number frames, number lines, blocks, pattern shapes, and dice, just to name a few.

Not too long ago, during family movie night, we watched “Black Panther: Wakanda Forever”. During the movie my daughter asked me about the Mayans, I shared they were an old civilization that had its own number system. My goal with my brief response was to spark her curiosity and it worked. The next day, while we were in the basement (aka MathPlay headquarters) my daughter and I read together about the Mayan numeral system through Wikipedia (https://en.wikipedia.org/wiki/Maya_numerals)

As we learned about the Mayan numeral system together, I explained the difference between our base-10 system and the Mayan’s base-20 system which she found interesting, however, what really caught her attention were the pictorial representations of the numbers. We both immediately knew we needed our shape sets.

Our goal was to play and explore the Mayan numeral system using the manipulatives we had available in our basement. We started by assigning some of the shapes to the different numeric values we needed. We used a big green oval to represent zero, a yellow circle for units 1-4, and a wooden bar (made of two classic “Jenga” pieces) to represent 5. At that point, we had our basic “building blocks” and were ready to explore and play.

Using our manipulatives with a degree of confidence my daughter was able to represent every number all the way up to nineteen. She then tried using four bars for twenty but because of my facial expression, she knew needed to do something different. She is familiar with ones, tens, and hundreds in the context of second grade. I told her we needed something similar to represent twenty, only that instead of adding digits to the left of the number, we would add a shape above the shapes we already had. It took some trial and error, but I’d like to say that she was able to understand these numbers behaved a little differently. She then was able to build a solid representation of twenty.

At this point, she was excited and feeling confident about Mayan numbers. She kept on going representing one number at that time until she got to 40. She then knew, without any directions, to use two yellow circles on top and the green oval on the bottom which was fun to watch. She decided to stop at 68, which I was ok with, she felt she has done enough.

I honestly don’t think we would have explored the Mayan numeral system if it wasn’t for the use of manipulatives. She was eager to try and explore because it really felt like a game. I also believe that using manipulatives came very naturally since she’s constantly using them in school. This experience really made me think about creating more opportunities for my high school students where we can use manipulatives during our lessons. Whether it’s during our activation, direct instruction, exploration, group work, and/or assessment, using manipulatives can add a different layer to our lessons.

I really hope you find these ideas helpful and can use them with your students in the near future. I would love to learn what math manipulatives you are using with your students. What was your experience like? How did your students respond?