So, this week, I’d like to share with you one of my past lessons about Type of Numbers. Who knew numbers had types, right? LOL! :) Well, you teachers did, but for the kids we teach, this concept can be confusing.
There are two main types of numbers I talked about in my lesson, but all of these numbers are part of the real numbers. Incorporating math into everyday things kids love is a great way to keep their attention and interest. The goal here is to change the “I stink at math” mindset that discourages and sets back so many bright students.
In the real numbers, you have rational numbers, and you have irrational numbers. I represented the rational numbers by using Iron Man, and I represented the irrational numbers by usng Captain America. There were some cool superhero nesting dolls that I used as a fun way to get the kids engaged. I have provided a link at the bottom of this blog if you’d like to purchase them for your classroom. Also, if you’re not familiar with the Marvel Universe characters, here’s a quick cheat sheet you might find helpful.
The reason I chose Iron Man is not just because I am a Marvel fan, but because after watching the movie, Captain America Civil War, I personally believed that Iron Man was rational in his decisions and Captain America was irrational in his decisions. A discussion on the definitions of “rational” and “irrational” would be a great start here for kids who aren’t yet familiar with these words.
Let's start with the rational Iron Man. So, rational numbers contain integers, represented by War Machine, and the whole numbers, represented by Black Panther. The counting numbers, or natural numbers, represented by Black Widow, and my example number was the number 1 represented by Vision.
I chose the number 1 as it is has positive connotations for most kids. Everybody wants to be number 1! All of these dolls fit inside of the other, which visually demonstrated how each set of numbers were connected together.
The counting numbers start with 1. Remind your students that when they’re counting, they don't usually start with zero. If they’re playing hide and seek, they don't count “0, 1, 2…” They start at 1. But if you want to include 0, it now becomes a whole number. Inside of the whole numbers doll are the counting numbers and zero. So, counting numbers do not have zero but the whole numbers do.
The whole numbers are zero plus the counting numbers. Next, we have the integers. The integers are the positive numbers, like the counting numbers, and they’re the negative numbers and zero. The whole numbers doll fits inside of the integers doll but it also includes the negative numbers. So, inside of the integers doll are the whole numbers plus the negative numbers.
Finally, we're dealing with rational numbers as an entire group. The integers doll fits inside of the rational numbers doll. All of these numbers are rational, but they also include fractions and decimals that end and repeat. Your kids will likely ask “what do you mean by that?” and sort of glaze over.
Here’s how I explained it:
The integers do fit inside the rational numbers, but they also include fractions like 4/5 or 1/3. All those fractions are considered to be rational because those fractions end or they also might repeat.
The next likely question might be “what do we mean by end? Well 3/4 is .75 and it's done! it ends. But, 1/3 is .333333 (forever!). It doesn't end, but the same number repeats over and over again. But, that's still okay to be a rational number. Any number that can be written as a fraction is rational and is part of Iron Man's team!
Next, I talked about the irrational people. Captain America - he's an irrational number in this example. These dolls stay separate from each other and do not nest together. They're not a part of the same team as Iron Man (so sad!). Instead, the dolls illustrate examples of irrational numbers.
This is a great place to introduce pi. I like to start with the fact that the most famous irrational number is pi (not pie - although that would be awesome too!) represented here by the Winter Soldier. So, pi would be considered to be irrational because it never ends. In fact, it's famous for never ending. All the numbers are different and they do not repeat. They are non-terminating because they don’t end.
Next, non-terminating decimals, represented by The Falcon, show numbers that do not end or repeat are irrational. Other examples I used for irrational numbers were the square root of 3 (or Hawkeye) and the square root of 2 (Ant Man). You can have your students put them in a calculator to see that they never end and they also never repeat! If you notice in my video below, I made sure our irrational superheroes were all separated from each other. They were not nested because one doesn’t fit into the other like our Iron Man rational number team does. It’s kind of irrational, just like they are! But, rational numbers and irrational numbers all make up the Real Number Universe just like the superheroes make up the Marvel Universe!
Check out these notes that one of my students created based on the video: