[0:02]Hey everyone, it's Justin again. I am feeling super grateful today, because my cousin just gave me a ton of clothes he doesn't wear anymore. Right now the clothes are just shoved in a basket and I need to put them away. I could throw everything into one drawer, but I know I'm going to want to easily find them later. What do you think I should do? Yeah, I should probably group them together in some way that makes sense. I could group them by types of weather, by special occasion I would wear them for, or even by color. But I think it might be most useful to group them into categories that make sense and make it easy for me to find what I need. Mathematicians also find it useful to place numbers into groups that all have similar characteristics. For example, we might group even and odd numbers together, or we might group numbers based on how many digits they have. That's why today, you'll start by learning about some special groups of numbers mathematicians use all the time. By the end of this lesson, you'll be able to define and recognize natural numbers, whole numbers, and integers, and you'll be able to compare integers using a number line. Grab your guided notes and let's get into it. What are some ways you can think of to group numbers together? Maybe you thought of whole numbers, negative numbers, decimals, or fractions, and that's a great start. But let's begin with the numbers we use most, the natural numbers, or counting numbers. The natural numbers are the ones we use when we count things, like the number of t-shirts my cousin gave me. 1, 2, 3, 4, and so on. Notice that I didn't include zero in that list. That's because if there are zero of something, then I can't count it at all. Instead, zero belongs in a group called the whole numbers, which includes all of the natural numbers as well as the number zero. Okay, we've got natural numbers, like three, two, and one. Then we included zero, which got us the group called whole numbers. What if we keep going backward and look at some negative numbers? When we include negatives, we get a big group of numbers you will work with a lot, the integers. Integers include all of the whole numbers and their negative number opposites. Do you notice something about the three types of numbers we've looked at? If a number is a whole number, that means it's also an integer. And if a number is a natural number, that means it's also a whole number and an integer. Pretty cool, huh? Let's practice this together. For our first three practice problems, we want to categorize each of these numbers into all of its correct groups. So one number might fit into more than one category. Let's start with negative 10. Negative 10 isn't a natural number because we don't use it to count objects. It's also not a whole number because negatives aren't considered whole numbers. That means it's an integer. Okay, what about zero? Well, we know zero is an integer, but can zero fit into any other categories? It's not a natural number, but it is considered a whole number. So we'll put zero into the whole number box, which also places it into the integer box. That means it's both. Great work. Let's finish with 17. Where would 17 go? Okay, 17 is an integer, and 17 is also a whole number. And 17 is also a natural number. So we'll put it in the natural number box, which tells us that it actually fits into all three categories. Excellent categorization. Now, find a problem numbers four through seven on that same page in your PDF. Pause the video here to try categorizing each of those numbers. Welcome back. How'd you do? 124 and 57 should both be in the natural numbers box. Negative three and negative 21 should both be in the integers box. Great work. Our boxes can help us understand the relationship between these categories, but what if we wanted to compare numbers in these categories? That's where number lines come in. A number line is a way of visualizing positive and negative numbers in order. Here's one example of a number line. With a number line, we always place positive numbers on the right and negative numbers on the left. What's right there in the middle? Correct, it's zero. Let's try placing some integers on the number line. Six is a positive number, so it'll be six units to the right of zero. Negative one is a negative number, so it will just go one unit to the left of zero. Negative four is also negative, so it will go four units to the left of zero. And one is also positive, so it goes, you guessed it, one unit to the right of zero. Can we order these numbers from smallest to largest? You bet we can. On a number line, smaller numbers are always on the left side, and larger numbers are always on the right side. So, we list the numbers in this order, from smallest to largest: negative four, negative one, positive one, and positive six. Now it's time for you to practice. Find the page of your PDF that has a number line on it and pause the video again to practice placing numbers on the number line in your PDF. And then, ordering them from smallest to largest.
[7:09]Nice job. From smallest to largest, the numbers should be in this order: negative seven, negative three, negative two, zero, five, and seven. Now here's a tricky problem. Which one is smaller, negative 40 or negative 90? Well, we know that 40 is smaller than 90, so it might seem like negative 40 should be smaller than negative 90. What do you think we should do to know for sure? Yeah, let's put them on a number line. Negative 40 is negative, so it will be 40 units to the left of zero. And negative 90 will be 90 units to the left of zero. Which one is smaller? Which one is farther to the left? Correct. Negative 90 is farther to the left, so it's actually the smaller number. Can you think of any real life situations where we use number lines to compare integers? This makes me think of thermometers. A thermometer, like this one, has a number line right on it. This makes it easy for us to compare two temperatures, like negative 10 degrees and negative 20 degrees. We can see that negative 20 is farther below zero, which means it's a colder temperature than negative 10. Negative 20 is smaller than negative 10. Sounds like a cold day. Hope my cousin packed me something warm. Well, mathematicians, what have we learned today? First, we learned how to categorize numbers into the natural numbers, whole numbers, and integers. Second, we saw that on a number line, we place positive numbers to the right of zero and negative numbers to the left of zero. We also practiced comparing numbers using a number line since smaller numbers will always be on the left and larger numbers will always be on the right. Now it's time for me to finish sorting all these clothes. Which category should I put this in? Oh well, thanks for stopping by and I'll see you next time.
