The Menger Sponge!

School has just started, and as usual we are starting with Number Knowledge.


I'm not the kind of teacher that tends to get students to number crunch. Definitely not for days (or weeks, in some teachers' cases!) at a time.


I prefer to get students having fun, thinking about the numbers, not just using them.


Bring in the Menger Sponge!


I didn't have any classes today, so I decided to build this beast for my students! It was a lot of work, with lots of breakages - not just the Sponge itself, but also some of the mini cubies (yes, I'm calling them cubies - same as what I call the parts of Rubik's cubes).


Using the good ol' 3 Acts style, I've made some videos showing the process of building the fractal. Show the first one, ensuring the students are paying attention. I ask them what they think, what's going on, what they wonder, and what they notice. We write down ALL ideas (yep, even the way left-field ones!)



After giving this to my students, here's some of the questions we came up with:

- What are you doing?

- Are those Legos?

- How big are you going to build the cube?

- Why do you have a plaster on your finger?

- Why is there holes all through it?

...and so on.


After a bit of brainstorming, I give them a bit more info to try to lead them to a bigger question...


Now we get the good questions coming up:

- How many blocks is it?

- How big is it going to get?


After a bit of mathing around, I finally reveal the answer.

Usually the answers are shown on the final video, but I like to leave it off in case others don't like it on there. Instead, I made a quick gSlides showing the answer.

Of course, this is just one way of solving it. There's many, many more ways!


Some other questions I've gotten from people on the internet are:

- What's the surface area?

- What's the volume?


As for the real Menger Sponge - a fractal that goes on infinitely large and infinitely small, the surface area of the Sponge goes to infinity, while the volume is zero! Crazy!


Want to try it out with your students? What questions do they come up with? What is the goal you want them to solve?


Is there anything you want to know about it? Let me know in the comments or Tweet or comment on the Facebook page!


Happy mathing!


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