Do you have projects pinned that you’ve been meaning to do for years? Multiplication towers was one of mine. When I first saw them on The Map is Not the Territory I knew we’d all learn something from playing with this 3D multiplication model.

The catalyst for getting around to it was a Christmas gift. My lovely parents-in-law sent us some fine meat which arrived from Scotland packaged in polystyrene and dry ice. The steaks were delicious – but you know you’re a homeschooler (or a toddler) when you get even more excited about the packaging than the gift itself. Yes, that giant slab of polystyrene was the perfect base for our multiplication tower.

### What you need

Here’s where my learning curve began. (Skip this bit if you are an instructions-reader, you won’t get it.) You know how you sometimes start gathering materials for a project without consciously thinking it through?

So I had my polystyrene base, a pack of beads, and now I needed some skewers. How many? I thought of the multiplication grids we’ve been working on recently. Should our multiplication tower go up to 10 x 10, or all the way to 12 x 12? “Oh, why not go for it?” I thought, throwing caution to the wind and putting two 100 packs of bamboo skewers in my basket.

Back home, I used a sharpie to mark out a grid of 144 dots on the polystyrene. It wasn’t until I began inserting the skewers that I saw the flaw in my plan, and realised that (a) no skewer would be tall enough to hold 144 beads, (b) the 12 times table alone would use up almost all our 1000 beads and (c) as enthusiastic as my kids are about hands-on maths, I may not be able to persuade them to spend a week threading beads.

At this point it occurred to me to refer back to the project, where I discovered that Malke made a 5×5 multiplication tower, requiring 225 beads. Good idea.

### Bead multiplication tower

I thought about making the model myself first, to make sure I understood how it worked. But after a few beads I remembered that sometimes a student learns more if the teacher doesn’t know all the answers.

So I called C(10) and we figured it out as we went along. (See the labelled photo of our Lego multiplication tower below if you’re not sure of the reasoning behind the colour-coding.)

Of course this isn’t difficult maths – many people make multiplication towers with slightly younger kids as an introduction to the concept – but it does get you thinking logically about number patterns and the commutative property.

### Lego multiplication tower

I showed J(8) the Lego multiplication tower Frugal Fun for Boys made. He enthusiastically set about gathering 2×2 Lego bricks to make his own. He only had enough bricks to make up to 4×4, but it was enough to get the idea.

When we compared C(10)’s bead tower with J(8)’s Lego one, we noticed they were different. In our bead tower we had used the same colour beads for the “ones” on both the x and y axes, as they did at The Map is not the Territory. In the Lego tower, we had used different colours for each “one” on the y axis (as Frugal Fun for Boys did).

So in the photo above, on the x axis we have a blue Lego for “1 one”, two blues for “1 two”, three blues for “1 three” and four blues for “1 four”.

Meanwhile, on the y axis, we have one blue and one white Lego representing “2 ones”, a blue, a white and a red for “3 ones” and a blue, a white, a red and an orange for “4 ones”.

The children and I discussed the two models, and decided the Lego model made more sense to us. C(10) changed her bead tower. More great learning.

### Minecraft multiplication tower

Next, C(10) decided to make a multiplication tower on Minecraft. You can’t write numbers on Minecraft so she decided to use colours to represent the numbers (the small dark blue blocks along the axes in the picture below).

She spent some time viewing the tower from different angles in a way that made me slightly dizzy. At one point she exclaimed, “Hey, look at this pattern here, on the diagonal – 1, 4, 16, 25!” She’d discovered the squares.

C(10)’s Minecraft tower reminded me to show her the computer-generated multiplication towers at Moebius Noodles. Click over to see quite how high 12×12 multiplication towers get.

C(10) decided to save her Minecraft multiplication tower in a new “Maths World” and went on to demonstrate some maths puzzles she could play with there. {I see more fun ahead.}

### If you didn’t get polystyrene for Christmas

If you don’t have a polystyrene or foam block, you could perhaps use sand to support the skewers, or follow the example of Highhill Homeschool and use cotton. Or make a Lego tower.

Have you ever made a multiplication tower? Did you learn anything surprising?

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*I’m appreciatively linking up here:*