Anna Weltman’s Loop-de-loops part 2

Earlier in the week I did a short project on Anna Weltman’s loop-de-loops with my younger son:

Anna Weltman’s Loop-de-loops

He’s been doodling and coloring loop-de-loops since we did this project 🙂

His enthusiasm for the project made me want to revisit the idea again this morning since my older son missed it the first time because of an early morning school event.

We started by introducing my older son to the loop-de-loop idea and then we talked about some of the pictures that my younger son made during the week:

For our first exploration today, my younger son wanted to see if he could make a shape with really big “arms.” He tried to draw a 1,2,15 loop-de-loop. Unfortunately he accidentally made a little error while he was drawing the shape – that small mistake gave us an extra chance to talk through the ideas of turning left and right.

After revisiting the left / right rules at the end of the last video, we returned to draw a 1, 2, 15 loop-de-loop. He’d hope to make a shape that had big arms, but we got a surprise – this one had small arms. Why did that happen?

Next we decided to take a look at my older son’s idea: whether or not the arms ever “double split.” It seemed that the arms with 3 numbers never really double split, so he thought we’d need more numbers. He that we’d need 5 numbers for a really interesting reason – he thought ones with 4 numbers would always “spiral to infinity” rather than having arms that split. We decided to explore that idea with a 1, 3, 5, 7 loop-de-loop out of our Zometool set in the living room:

Here is that build as well as a few of their ideas about what they think is going to happen (and what is happening).

After they finished the loop-de-loop with 4 numbers, they built one with 5 numbers while I was publishing the first set of videos:

So, a super fun project – on so many levels – for kids, and an amazing way to get kids talking about and thinking about mathematical ideas!

One way to extend this project that I’m pondering is to talk about a relatively new (for math) idea – Langton’s Ant – that was invented / discovered in 1986. The concepts you need to talk about Langton’s Ant are pretty similar to the ones you talk about in these loop-de-loops. Here’s a short video by Katie Steckles and Numberphile about the ant which hopefully shows why I’m thinking of extending the project in this direction: