My 4-year-old declares 36 the best number

My four-year-old son has declared 36 to be the best number.

His reason: 36 is the only number (he knows of) that is both a square and a staircase number AND an up-and-down-staircase number.

“Staircase numbers” are what he calls triangular numbers (numbers that are the sum of the first $n$ integers). This name comes from the blocks he has that can be arranged into a staircase. He also calls them “step squad” numbers thanks to Numberblocks.

An up-and-down-staircase number is a sum of two sequential triangular numbers, representing the up and down parts of the staircase. He also knows that all squares are up-and-down-staircase numbers, though that doesn’t make 36 any less amazing. The next square triangular number is 1225 (OEIS A001110), so I doubt he will notice 36’s non-uniqueness for some time.

The next natural question is, “What the hell is a four year old doing identifying triangular squares?”

Despite my wife and I both having math degrees, and our willingness to engage with him when he shows interest in math, we basically didn’t do anything to actively foster this behavior. We let him watch Numberblocks (30 minutes per day), I gave him two sets of MathLink cubes to play along with the characters in the show, and once he started showing interest I picked up the first four Beast Academy comic books and I read them to him (he does not have much appetite for the exercises).

Now he spends much of his free time playing with blocks as a way to explore numbers. He peppers me with arithmetic questions, and has started to wonder about other kinds of numbers (negative numbers, fractions). I explain that those kinds of numbers are a mystery for another day, while I secretly accumulate manipulatives. He has songs for different rows of the times table, and has a seriously good grasp of multiplication, as iterated addition or rearranging quantities of blocks as rectangles. He has also built strategies for doing products he doesn’t know by breaking it down into products and sums he does know. This morning he puzzled over, “how many 7’s is in 35?” by starting from 28, which he knew as 7 by 4, and then splitting 7 into 5 and 2, counting 2 up to 30 and then jumping to 35.

I am not particularly shocked how easy it was to get my kid hooked on math. Numberblocks is a fantastic starting point, with songs and stories that draw the kids in and provide mnemonics for the concepts. My kid is always saying “18 on the scene” and dares me to say “13” because that character falls into 10 and 3 every time someone says his name, which is endless fun. As I’ve written about before, if you want a typical kid to be invested in something, just present it to them as a story.

Same goes for Beast Academy. The story and characters draw him in, the funny jokes at the end of each section are a nice reward. Then, over many re-reads, he gradually grows into the joy of understanding the concept. Beast academy is also nice because it focuses on more than just numbers, including basic geometry, categories (which one doesn’t belong), and gradually introducing symbols like $+$ and $=$ and concepts like variables and equations.

This gives me hope that parents without math degrees could still foster a love of math and a fluency with numbers by just exposing their kids to the right material.