Yesterday was a wonderful day & today I'm still riding a bit on that "high," so here's a Waldorf math ride for you. What you see here is work that was done by 2nd graders after they had been introduced to these forms in the spirit of "beautiful numbers make beautiful forms." Have you ever experienced math like this? Buckle up and get ready for the ride!
Take a paper, make a circle & divide the circle into 10 equal parts. (You may cheat with a compass if you are older than a 6th grader, but free-handing a circle is a nice exercise in itself.)
Going clockwise, place numbers from zero to nine. (Our number system really goes from zero to nine, not from one to ten.) Then, say a times table in your head and "connect the dots," ignoring the tens in the process. For example: The fours table goes 4, 8, 12, 16, 20, 24, 28, 32, 36, 40. You will then start with number 4 & draw a line to 8, from 8 to 2, from 2 to 6 and so on.
You will end up with something that looks like this...

Isn't that just awesome?
In this manner all times tables make different forms & some numbers do similar things.
You will see that 1s create a 10-sides polygon & that 9s do the same thing, just in reverse order. 2s make a pentagon, and 8s do the same thing, just in reverse order. 3s make a 10-pointed star & 7s do that, too, but in reverse order. 4s make a pentagram, and 6s do the same thing, just - yeap, you guessed right - in reverse order. 5s are rather boring, but they make a straight line.


It was so exciting for my 2nd graders to learn the - usually dreaded - times tables this way. I don't believe that education needs to be entertaining, but when something like this unfolds in front of you, it's just amazing! Beautiful numbers do make beautiful forms. We did a lot of jump roping, too. Try it! We had some visitors in our class during the math block and even these adults had never seen this before. They were quite amazed. There's enough meat (or tofu) here for an entire 2nd grade math block!