Welcome to Episode 3 of our What’s That About? series. Marco the Great and the History of Numberville contains two stories: the story of Marco and the story of Numberville. In this episode we get our first look at this crazy and entertaining new world!

### What's in this article:

### Super Quick Recap

Super Quick Recap

Ten Charmed Ones came out to play, over the hill and far away, the biggest one said, “I want more power!” so all the others followed in dismay. Till one day the Great Scale ruled, she was not so easily fooled, then the siblings understood, place value is super cool!

They used their smarts to build a village, before they waved and said farewell

Who knew 6th graders could understand, the paradox of Hilbert’s Grand Hotel?

I’m almost finished my reading today, wait… what did that last line say?! 😳

### The MATH

To understand any mathematical concept, students must first master numbers. Marco the Great and the History of Numberville takes readers as a tabula rasa, a ‘blank state’ to re-introduce students to even the most basic of ideas. This helps build a strong foundation to master some of the tricker concepts to come.

Digits are the basis of any number system. In our first look at Numberville, we see how the digits created all of Natural using only themselves. What’s fascinating is the idea that with only 10 building blocks they can create an infinite world. It is infinity that is one of the most difficult concepts to grasp; mainly because so many talk about infinity like just another number and this is not what it is at all!

When the idea of infinity is introduced, most students take away that it is “the biggest” because so much of mathematics is based in superlatives and comparing one thing to the next. Others might think of it like forever, if we keep going and going and going, we are going towards infinity – the super big.

This is impossible for the human brain to fully comprehend. Everything we experience is finite. Everything ends at some point. When presented with the idea that the universe is infinite we struggle to picture it or to even accept that it is possible. Well, this is just the conundrum that caused Euclid a headache (we’ll hear more about this in Chapter 7) and caused some mathematicians to think about infinity in a whole new way.

How? With circles. While it’s hard for humans to understand an infinite line, it is much easier to comprehend a loop. In this school of thought, infinite isn’t going on forever but rather something that has no end. Think of the song:

This is the song that never ends,

Yes, it goes on and on my friends.

Some people, started singing it not knowing what it was,

And they’ll continue singing it forever just because

This is the song that never ends…

Where does it stop? You can’t stop at ‘because’ as ‘This is the song that never ends’ is a part of that last line. And if you say ‘This is the song that never ends’ you have to keep going because that is the beginning, also not the end. This view of infinity is easier for most humans to grasp. Like a circle you can keep going and going, there isn’t any end, but we can imagine the space it takes up as finite and so it fits in our brains. This view of infinity also paved the way for the branch of mathematics named “non-Euclidean” geometry. (More on this in a future post!)

No matter how you prefer to think about the idea of infinity, it is a good idea to have your kids start thinking about it early. The longer they have to sit with it and process it, the more comfortable they will become with the idea which will be vital in higher math!

### The QUOTE

“Go down deep enough into anything and you will find mathematics”

-Dean Schlicter

As you read through Marco the Great and the History of Numberville, one clear theme will emerge: numbers are everywhere. Now, this is a tough claim to make, especially in a world where most people would argue they never use any of the math they learn in real life.

Here is a thought: the math is there, the numbers are there, you just can’t see them. We love the analogy of Plato’s cave. It goes like this (very generalized and some liberties taken):

A group of people live their life out. They see the trees, the wind, everything you’d expect them to. For them, nothing is wrong or strange, however, it turns out they all live in a cave. What they thought was a tree, was only its shadow. One day, someone is brave enough to leave the cave, they come back and tell the group of all the miraculous things they saw. They are of course labeled as crazy, and the group happily continues to live in the shadow world.

People who don’t see math everywhere are the cave people. It’s there. As Schlicter says you just have to go deep enough. It’s in everything. It’s all around us. It’s inside us. We can’t wait to share where this idea takes Marco, Maggie, and the crew in Book 2! For now, we knew we’d need some support to convince our readers that numbers really are within everything so we leaned on all the giants that came before us 😉.

### Discussion Questions

#### Reading Questions

Nava is said to have a crown like her sisters but can also split. What does this mean? Why is Nava the only charmed one with this ability?

The Mirror of Wonders tells Nava she would need a clone to gain the power she is looking for. What does the Mirror mean by this?

Why does Nava feel the way she does? Can you see any similarities to how Marco feels?

#### Math Questions

To write the number 12 in computer language (also known as binary) we have to think of the number 12 in terms of 2s. We know it is 8+4, where 8=2×2×2 and 4=2×2. We have 1 in the 8s place and 1 in the 4s place. We don’t have anything in the other places. Therefore, the number 12 to us is the number 1100 to a computer. Use this to write the following numbers in binary:

3

16

25