Our founders, Pat and Bart, loved teaching math and focused on finding ways to help kids make sense of numbers. Bart especially loved using tools like graph paper, Cuisenaire rods, and money as a way to facilitate this sense making, but he wanted a model that allowed kids to compare different shapes and sizes to each other in a more flexible way and nothing out there was quite what he was looking for. As a result, he designed his own math manipulative: Bixby Tiles.

This week, 1st graders have been exploring Bixby Tiles, and a listen in on some of their questions and discoveries makes it clear why they are such a great way for kids to explore so many mathematical concepts.

After some time for free exploration with the tiles, we came together to share questions and ideas. One of the first questions was, “What is the biggest tile?” Some thought it was the long ivory tile. Others thought it was the shorter, but much wider yellow tile. In order to answer the question, students started covering multiple yellow tiles with ivory tiles. One student noticed that it took 4 long ivory tiles to cover 2 yellow tiles. She said, “If 4 ivory tiles are the same as 2 yellow tiles, then the yellow tiles have to be bigger.” Next, they noticed that ivory tiles come in different shapes. Now they wanted to compare those. One child said, “I think these two are the same because this one is twice as long, but it is only half as wide so they are actually the same.”   Bixby tiles engage students in a way that not only brings out questions, but also provides an opportunity for students to experiment and use their own logic to find answers.

Next, students were given puzzles that involved finding how many of one tile would be equal to a given number of another tile. Students developed many efficient methods to make comparisons. When finding the number of green tiles that are equal to a yellow, one student placed four green tiles across the width and six green tiles across the length. Then he said, “Each of these would be a row of four, so it is 4, 8, 12, 16, 20, 24; it is the same as 24 tiles!” Another student excitedly told me, “I counted 8 blacks on four ivory and I know that 8 + 8 = 16, so it would take 16 blacks to make 8 ivory tiles!” This type of exploration provides many opportunities for students to use fraction, multiplication, and algebraic concepts (to name just a few) in a meaningful way that builds a foundation and a context for future work in these areas.

Bixby Tiles are not the only manipulative that we use, and we are only at the beginning of what we can do with them. The sizes, shapes, and colors lend themselves to so many applications that they inspire some truly dynamic critical thinking. Yay Bixby Tiles!