My child has been playing with Perler beads for a while now making all sorts of things, including a map of Minecraft. So when I suggested making a multiplication table, the kid was very interested. Except a) I didn’t have a clear idea of how to make multiplication tables out of multi-colored beads and b) my child didn’t know what multiplication was.

No worries, I figured we would both learn by doing. Pretty soon we figured out that we wanted to use the large beads, not the little ones, and that making the entire tables would be too boring and time-consuming. So we decided to concentrate our efforts on square numbers.

After we put the cornerstone 1×1=1 round bead in the top left corner, the kid asked why do we call these square numbers if 1 didn’t look like a square. “Let’s make some more and see what happens, shall we?” Sure thing, 2×2=4 looked like a square and so did 3×3=9. But would 7×7 be a square? How do you know?

At first we made each square filled in with beads of the same color. So our 2×2 was all orange and 3×3 was all blue and 4×4 was all green and so on. It was pretty, but pretty boring. Then we started experimenting, taking out the inside beads so that only a square frame was left. So we decided to fill this frame with different colored beads. As we were discussing which colors to use for the 4×4 square, we noticed something:

*2×2 square frame had no opening*

*3×3 square frame had a 1×1 opening*

*4×4 square frame had a 2×2 opening*

What opening would a 5×5 frame have? Turns out:

*5×5 square frame had a 3×3 opening, which had a 1×1 opening!*

“Mom, it’s a fractal of square numbers!”

Let’s see what other patterns we noticed. Even squares (4×4, 6×6, 8×8 and 10×10) had even openings in them. And odd ones had odd openings. Why? Hint: it had a lot to do with the beads themselves and with how we chose to nestle the frames.

Then it was time to fuse the beads together and then to admire them. I set them out on a diagonal, as they would be in a 10×10 multiplication grid. The kid made another discovery of his own:

“We can integrate a pyramid with the squares!” and “This is like a mandala for Minecraft!”

My child played a very active role in the process, from choosing colors to noticing patterns to coming up with the unexpected connections to other ideas, like fractals and integration. What was my job? First, I helped keep the patterns consistent, especially when we did the frames. Second, I shared what I knew – the multiplication grid, square numbers. Third, I documented the experience. Later, as we looked through the pictures and went through my notes, it gave us both a chance to reflect on the math we found.

Together, we had a great time exploring and discovering patterns. Perhaps we’ll try the rest of the tables another time. Do you see bridges to even more ideas we can explore?

Posted in Make

This is truly fabulous! Thank you or sharing! What a great way to get connections flowing! Out of curiosity, how hold is your kiddo?

Rachel, I’m glad you like this idea. My kid is 7, but I think this activity can be done with much younger kids as well. If you or anyone you know tries it with kids younger or older, I would love to know how it went, how they chose to explore it and also how the adults had to adjust their role to better fit the needs of different age/stage kids.

Love this–

“My child played a very active role in the process, from choosing colors to noticing patterns to coming up with the unexpected connections to other ideas, like fractals and integration. What was my job?

First, I helped keep the patterns consistent, especially when we did the frames. Second, I shared what I knew – the multiplication grid, square numbers.

Third, I documented the experience.

Later, as we looked through the pictures and went through my notes, it gave us both a chance to reflect on the math we found.”

Wishing I could post a photo here of Montessori’s bead squares in pyramid form.

Curious Montessorians would like seeing all this done in her color scheme. Since they’re practiced at associating a different set of colors for the numbers one to ten their own neurons would fire and connect more rapidly with the play, discovery, and anticipation.

This is a great idea and it seems that you and your child learned a lot. I am going to try it with my kids (6 and 8). Thanks.

Thank you, Stephen. It would be great to see what you and your kids come up with since there are so many patterns hidden in the multiplication tables.

Can’t wait to try this with my six-year-old. Where can you get large, interlocking perler beads?

Thanks for sharing such a great idea.

MamieJane, I bought our Perler Beads at Michael’s, but they are also available on Amazon.com as Perler BIGGIE Fusion Beads. They don’t interlock, but get fused together with an iron. If you get a bucket of Perlers, you will also need clear square pegboards. They are sold separately from the beads or you can buy a kit that includes everything – the beads and the pegboard.

Yelena, I’m in love with this post. I’ve made a decanomial set out of felt, and my daughter and I are embarking on fusable beads. How to handle the color scheme is a question we’re fiddling with. I want to make the entire decanomial, and the 10s alone requires 1000 beads. Your pattern of 2×2=orange, 3×3=blue is brilliant, for the squares at least. I’m probably going to buy a package of solid color beads for the largest few, and then do colorways for the smaller ones where I lack enough – orange can be oranges, golds, yellows, etc. Fun stuff. Thanks for sharing all your activities on Moebius Noodles.

Did this with my 11 and 9 year olds and it was FUN — We are discussing square numbers and trying to work on memorization of the multiplication table as well. I wish I had the biggie beads template, because nothing above a 6×6 grid stayed together long enough to fuse them together. They built all of it but some could not be ironed. Overall, it was worth it and they also colored in the square numbers (1, 2, 4 ,9, 16 etc) on a blank multiplication chart with colored pencils. TY for this idea!

Glad to hear it was joyful for you, Lisa! For a variation, you can try other shape numbers too – they have their own fun patterns in the number theory (like triangular or pentagon numbers).