This is a story about the second meeting of a Calculus for Kids math circle. The math circle started off with the class attentively watching the trailer of Flatland. The movie itself is shown on a 2D screen, but it talks about journeys from 0 to 4 dimensions.
Download the Math Spark that invites you to travel to Flatland with us.
Today’s challenge is making 2D, flat shapes out of other shapes. Maddie and Sydney are discussing and examining how to transform Sydney’s green playdough shape into “what it is about to become” (they don’t know yet).
Sometimes, you just have to build something without even naming what it is. Yash built “something” imaginary out of LEGO blocks.
Maddie is making a 2D pair of glasses by coiling 1D pipe cleaners. She also created a 2D half-circle that transformed into a 3D sphere.
“Would you look at this!”
That flat object…
…Transforms into a sphere!
A triangle is not just a triangle, but a slice of pizza (as well as a 2D object).
If you make several such shapes, you can arrange them into a whole pizza. Note how the children are building while listening. Doing something with your hands often helps to listen, even if it looks like children’s undivided attention is on their own project.
How do you know they are listening? Try asking a question: “What kind of shape would the slices of pizza make in a row instead of a circle?”
Hmm … let’s see!
(Spoiler: it makes a rectangle.)
Yash meanwhile finished creating another “something” – many sticky notes reminded grown-ups of the field of math called Chaos Theory. Maria asked him to write out his thoughts on the paper. In return he wrote: “I think it’s a bunch of sticky notes.”
Mark made a rectangle out of six smaller rectangle – order in contrast to chaos.
This rectangle, just like the chaotic 2D object Yash made, is abstract (not representing anything). The same technique can be used to model objects. On the other side of the table, Emma is discussing with Maria how to integrate a Minecraft sword out of sticky notes.
Mark is holding an imaginative 3D bow and arrow he made from LEGO blocks. It’s a flat shape that we can use as a 2D model.
Sydney is making an unknown shape. From blocks and imagination, she bravely creates something totally new. Older children and adults often lose that bravery and become hesitant to build things that don’t look like things. For Sydney, it’s the process of building that matters – and if the end product turns out interesting enough, like this tower, it’s good too, but not a requirement.
Eli just finished making a church. First, he integrated flat squares out of “dots” (LEGO blocks) and then he made the 3D building out of squares, one on top the other.
But instead, you can integrate “dots” into a 1D line – a really tall one, taller than you. But what if you got up on the chair?
Allison is making a 2D pattern inspired by a doll’s dress. Sydney is getting up to go make her own version of a sword (not shown), using a different grid layout. When children make objects out of rectangles (like sticky notes), different types of grids come up a lot.
We are about to watch and play with the String Spin interactive, and pose for a picture! “Make very silly faces for the New York Times!”
Mark is experimenting, drawing on the pad to see what kind of shape his string will create.
Sydney is predicting what will come of drawings.
There is a temptation to say everything looks like “a weird shape” – children use a generic word, maybe “alien” or “spaceship” for everything, instead of specifying a cone, a cylinder, or a sphere. But they are not wrong, they are just expressing the fact there are similarities in all the different shapes the toy makes. It’s a mathematical value to see similarities over differences.
You can use the “Yes, and…” improv technique here: “Yes, all these shape look like spaceships. And that’s because they are all figures of revolution, so they all are similar to one another!”
Photos by Erin Song, captions by Erin Song and Maria Droujkova, Math Spark by Kalid Azad, Shelley Nash, and Maria Droujkova, edited by Ray Droujkov.