number sets: infinity is only the beginning
Number sets are one of my favorite mathematical topics. I find that my students, however, greet the concept with a yawn and an 'okay, whatever'. I fail to inspire them with Venn diagrams illustrating the relationships among the Counting, Whole, Integer, Rational, Irrational and Real number sets. What can I do to bring this topic to life?
An idea struck. I needed a story. I also needed a powerful metaphor, something better than a hook, to harness and hang onto students' attention. This would be a children's story that my 9th graders could appreciate and understand. The metaphor evolved into a house. The Counting, Whole, Integer and Rational sets created the house; the Irrationals were embedded within a cloud. With a focus on storytelling, mathematical precision, and subtle humor, I penned the story below.
An idea struck. I needed a story. I also needed a powerful metaphor, something better than a hook, to harness and hang onto students' attention. This would be a children's story that my 9th graders could appreciate and understand. The metaphor evolved into a house. The Counting, Whole, Integer and Rational sets created the house; the Irrationals were embedded within a cloud. With a focus on storytelling, mathematical precision, and subtle humor, I penned the story below.
Tech note - these were the steps to create the video:
1. I wrote the story, edited it, and read it a few times.
2. I recorded myself reading the script using my i-Phone. This took several takes.
3. I practiced playing the audio while writing on a whiteboard. My hand (and brain) had a tough time keeping up with the audio.
4. Once I felt comfortable with the pacing of the audio, my wife recorded my hand drawing the house and cloud. Fortunately, this only took one take.
5. I uploaded the video to my YouTube channel and embedded the code onto this webpage.
1. I wrote the story, edited it, and read it a few times.
2. I recorded myself reading the script using my i-Phone. This took several takes.
3. I practiced playing the audio while writing on a whiteboard. My hand (and brain) had a tough time keeping up with the audio.
4. Once I felt comfortable with the pacing of the audio, my wife recorded my hand drawing the house and cloud. Fortunately, this only took one take.
5. I uploaded the video to my YouTube channel and embedded the code onto this webpage.
A Number Story
Once upon a time, in a land far, far away, there was a structure named Counting. Counting housed close friends named 1, 2, 3, 4, 5, 6, 7, 8 and 9. As time went on, Counting grew larger and larger: 29 entered the picture; 113 landed from outer space and decided to stay; 1,000 married 1,000,000 and they had a gigantic child named 1,000,000,000. A few years later, Counting welcomed a new element: 0. The head of Counting, 1, decided to rename the structure based on this historic move: with the addition of 0, Counting became known as Whole. Things in the Whole structure stayed the same for many years until more elements joined the Whole. The Integers added an entirely new dimension to the structure. Soon, the Integers found new partners: 1 paired with -1, 2 linked with -2, 3 buddied with -3, and so on. As 1 aged, 0 took charge of the new Integers household. Decades upon decades passed until the greatest addition finally occurred: the Rationals. The Rationals were very reasonable and got along well with the Integers. In fact, the Integers saw that, with a little effort, they could see themselves in the mirror as Rationals. Now the structure, known as the Rational House, was complete. To celebrate, the Rationals (which kindly included the Integers, Whole and Counting groups), threw a party, ate tons of cake, and tied balloons to the house. Lots of balloons. Infinitely many balloons. These balloons made the Rational House rise high into the air. It was at this moment that a curious cloud named the Irrationals floated into the picture. The Irrational Cloud, which comprised of fascinatingly foreign objects like the square root of 2, pi, the number e, and many, many others – in fact, many more than the Rationals could imagine – the Irrational Cloud floated alongside the Rational House. The Rationals and Irrationals stared at each other for a long while. There was some confusion and disagreement at first. Name calling ensued. ‘You’re being irrational,’ the Rationals said. ‘But we want you to think big: don’t ever stop growing,’ the Irrationals replied. These two groups didn’t join each other, but they learned to coexist. They became what we now know as the Reals and they lived affably ever after. To be continued…
Once upon a time, in a land far, far away, there was a structure named Counting. Counting housed close friends named 1, 2, 3, 4, 5, 6, 7, 8 and 9. As time went on, Counting grew larger and larger: 29 entered the picture; 113 landed from outer space and decided to stay; 1,000 married 1,000,000 and they had a gigantic child named 1,000,000,000. A few years later, Counting welcomed a new element: 0. The head of Counting, 1, decided to rename the structure based on this historic move: with the addition of 0, Counting became known as Whole. Things in the Whole structure stayed the same for many years until more elements joined the Whole. The Integers added an entirely new dimension to the structure. Soon, the Integers found new partners: 1 paired with -1, 2 linked with -2, 3 buddied with -3, and so on. As 1 aged, 0 took charge of the new Integers household. Decades upon decades passed until the greatest addition finally occurred: the Rationals. The Rationals were very reasonable and got along well with the Integers. In fact, the Integers saw that, with a little effort, they could see themselves in the mirror as Rationals. Now the structure, known as the Rational House, was complete. To celebrate, the Rationals (which kindly included the Integers, Whole and Counting groups), threw a party, ate tons of cake, and tied balloons to the house. Lots of balloons. Infinitely many balloons. These balloons made the Rational House rise high into the air. It was at this moment that a curious cloud named the Irrationals floated into the picture. The Irrational Cloud, which comprised of fascinatingly foreign objects like the square root of 2, pi, the number e, and many, many others – in fact, many more than the Rationals could imagine – the Irrational Cloud floated alongside the Rational House. The Rationals and Irrationals stared at each other for a long while. There was some confusion and disagreement at first. Name calling ensued. ‘You’re being irrational,’ the Rationals said. ‘But we want you to think big: don’t ever stop growing,’ the Irrationals replied. These two groups didn’t join each other, but they learned to coexist. They became what we now know as the Reals and they lived affably ever after. To be continued…
