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Montessori Binomial Cube: A Visual for Math and Problem-Solving

What's really cool about this activity is that my students enjoy it simply as a puzzle, but it's actually a visual representation of the binomial equation in algebra. I've heard from people who went to Montessori schools and did this activity in early childhood that it helped them visualize the binomial equation when they learned it much later in school. Regardless of its benefits for math, the binomial cube is a great puzzle and problem-solving activity for even young children (starting at about 5 years old). I love that it makes my students think, and many of them actually enjoy it. I have one student who requests to do this activity during breaks! To teach a child to use this activity, I demonstrate putting together the first layer (see the video below to see how it's done). I build it directly on the lid of the box (on the right in the photo above). I then remove all the blocks, and have the student do the first layer (with any prompting needed) and then the second layer. Once the student knows how to do it, the binomial cube is a great activity for independent work. Here's a video of how to put together the puzzle. The difference between this video and how I use the cube is that I have the students build the cube on the lid of the box. This allows the student to match the colors for the first layer directly, which provides more visual support for the activity.

If you're interested in the binomial cube and/or a more advanced version, the trinomial cube, you can find them on Amazon:


Meet Dr. Caldwell

Hi! I'm Dr. Nicole Caldwell and I've been working with students on the autism spectrum for about 12 years. My background is in Applied Behavior Analysis (ABA) and Montessori. I have a Master's degree and PhD in special education with an emphasis in autism, and I love what I do! I currently work with children with autism in their homes on social, communication, and academic skills. I specialize in:

•Teaching math to students with math difficulties or math anxiety,

•Teaching science and coding to children with autism, and

•Working on language and communication by embedding learning opportunities into your child’s favorite activities. I think of this as “play to learn.”

If you’re in the Dallas/Rockwall, Texas area and would like to learn more about working with me, please send me an e-mail to and we’ll set up a free initial consultation.

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