Every morning this week the Rocket Boy spent an hour online in the Natural Math‘s online summer camp. We love just about everything that comes from Natural Math (yep, that includes the Moebius Noodles book I co-authored some years back and the new one, Avoid Hard Work, that’s coming out in the Fall). But up ’til now the only online classes were for the parents and educators, although kids were always welcome to participate. But this summer Natural Math added several week-long math camps led by Shelley Nash.
Rocket Boy chose the Transformers camp (other options included Logic and Calculus). Because of his severe grapho-motor issues plotting anything or even writing is extremely difficult for the Rocket Boy. So I thought after Day 1 that he would not want to do it. But I was wrong! He absolutely loved the camp! And willingly did all the (optional) homework. So I played the role of a recorder, writing down all the numbers. But all the decision-making and calculations were his work.
He was very tired at the end of each hour. But in the evenings he was back to talking about matrices and transformations and how he wanted to transform four-dimensional objects next.
We haven’t covered graphing yet, but he was familiar with the ideas from programming in Scratch. So Day 1 was a good balance of the old (the coordinate plane, pairs of coordinates) and the new (graphing functions).
On Day 2
the kids dove right into matrices. First, they practiced on “simple” 2×1 and 3×1 matrices. But by the end of that Day’s meeting they were working with multiplying the 3×3 monsters.
started with checking whether matrix multiplication was commutative or not.
And then they drew their own little shapes, created their own 2×2 matrices and experimented with transformations. The Rocket Boy drew, what else – a rocket. After each of the three points on the rocket was multiplied by a matrix, the rocket got flipped, moved down the coordinate plane, and got stretched out. So we made up a story that the matrix was an asteroid and the pilot had to take evasive actions.
For homework that day the Rocket Boy drew a TV and came up with a different matrix for transforming it. We did this one over dinner, taking turns calculating the coordinates since there were so many points. Our transformed TV looked like it got dropped on the floor and somewhat flattened. So we decided that the matrix was really a very cute, but very mischievous pet elephant.
Day 4 was tough! The task was to draw a shape and then create a matrix that would flip the shape around the y-axis without distorting it. The next task was to create a matrix that would flip the shape around the x-axis without distorting it. Finally, the kids had to create a matrix that would flip the shape around both x- and y-axis, again without any distortions. When all was said and done, we ended up with a very pretty drawing of a shape rotated fully around the point of origin… and with several pages of calculations.
For homework, Rocket Boy had to figure out how to make a shape to double in size and how to have it shrink to half its size. We used the dog shape. After a couple of tries, Rocket Boy came up with a matrix that, when applied, did create a dog twice the size. So we figured that it was really a bag of doggy treats. After doubling the dog, Rocket Boy quickly figured out how to triple or quadruple it and how to make it “a million times bigger”. Figuring out how to shrink the dog took a bit longer, but he did it too. It felt very much like “Alice in Wonderland” – all this growing and shrinking.
Most of Day 5 was spent in GeoGebra flipping kittens. After 4 days of lots and lots of lengthy calculations it felt awesome to transform much more complicated pictures with just a few clicks of the buttons!