Montessori Pink Tower and Cuisenaire Rod Extensions for a Sixth-Grader

When Syd's sixth-grade Math Mammoth curriculum covered exponents, she and I (and her sister, on occasion...) did a lot of hands-on sensorial work with exponents. It's easy to forget that even bigger kids benefit from hands-on math, but when you set something down in front of them and watch them become totally immersed in it, you're unlikely to forget again.

Soon after seeing how invested Syd was in working all the Montessori pink tower extensions, and how quickly she moved through them, I asked her if she wanted to join me in creating some extensions for the pink tower and Cuisenaire rods. Both sets of manipulatives are keyed to the centimeter, and so we found that they worked quite well together!

Here are some of the combinations that Syd and I found:

For some reason, Syd really enjoyed making a pattern with the pink tower, and then repeating it with the Cuisenaire rods. It's none of my business why or what she's getting out of a particular experience--the fact that she's happily engaged and invested in her work is proof enough that there's something of value in it for her.

We made a log cabin quilt block!

You can play a lot with perspective when you explore these two materials together. Each Cuisenaire rod is only one centimeter wide, so many of the patterns are best seen looking straight down from above.

I thought that this diagonal patter that Syd made was extremely clever. You can see that she doesn't have it quite worked out in this photo, but I can tell that she's noticed that two pink tower blocks can share a Cuisenaire rod. 

I think she might be exploring along the same lines here, as she's omitted the centimeter cube that she was originally using to cap all the corners of her creations.

This was just a "play" day for us, but you could make this activity more academically rigorous, and in some cases cross-curricular, by adding more investigations to it:

• Children could be the ones in charge of photographing their designs.
• Children could diagram their designs on graph paper. To continue extending it, they could add photographs of the completed designs, write a description or instructions, hand-paste or use a graphic design program to make a book, and then bind that book themselves.
• Children could use clip art versions of pink tower blocks and Cuisenaire rods in a graphic design program, designing patterns that are impossible to create in real life.
• Children can design and perform STEM challenges, such as creating the tallest free-standing tower or the longest possible bridge with supports.
• Combine these materials with the decanomial square to explore cubes, or add more pattern possibilities. Bonus points if you use foam core and/or foam sheets to make your decanomial square pieces one centimeter thick!

Most outside resources for these materials focus on extensions best suited for young children, but here are a couple that I've found that are sophisticated enough to intrigue an older child:

• Build a tower, an inverted tower, and connecting towers from Cuisenaire rods. You can challenge your fine motor skills with this one! This takes some serious problem-solving, and you'll be well-suited for architecture or engineering afterwards.
• Long division with Cuisenaire rods. This is how I modeled long division when the kids were first learning it, but it's a useful--and mind-blowing!--model to use anytime to make the connection that MATH MAKES SENSE.