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After watching this video lesson, you will know how to order numbers from smallest to largest and from largest to smallest. You will also know how to compare numbers to figure out which goes first and which goes last.

(video available February 2016)

## Numbers

We use numbers all the time. **Numbers** represent an amount or value that we are talking about. For example, when we say we have 2 puppies, it means that we have not one puppy, but two puppies. When we order food at a restaurant, we may also give a number. We might say, ‘give me a number 3, please.’ This means that we are ordering the third item, or often the third combo meal, on the menu.

In this lesson, we’ll talk about ordering numbers. We’ll learn about placing them in order from least to greatest and the other way around. Yes, this is just like the numbers on the menu. They are in order from least to greatest. You first see option 1, followed by option 2, then option 3, and so on. We will see how we can do this with a random group of numbers that are given to us.

## Comparing Numbers

Say we need to organize some index cards that we found. Each index card has a small number written in the upper right corner. This number tells us in what order the index cards go. We have five index cards with these numbers: 4, 10, 8, 2, and 1.

How do we put these in order from least to greatest? This is called **ascending order**. To put these in ascending order, we need to compare the numbers to each other. We need to figure out which number is greater than another, as well as which number is smaller than another.

Let’s begin with the first two numbers, the 4 and the 10. Which one is greater? If these numbers represented the amount of candy we have in our candy drawer, which one will give us more candy? The 10 gives us more candy, so 10 is greater than 4. This means that the 4 is smaller than the 10. We know that we need to write the 4 before the 10.

Now, what about the next number, the 8? We need to compare the 8 to the 4 and the 10. Compared to the 4, the 8 is greater, but compared to the 10, it is smaller. This means that we need to write the 8 in between the 4 and the 10 like this: 4, 8, 10.

Now, what about the 2? The 2 is the smallest when compared to the 4, the 10, and the 8, so we need to write the 2 before the numbers of 4, 8, and 10.

Finally, what about the 1? When comparing the 1 to all the other numbers, we see that it is now the smallest since it is even smaller than the 2. Our index cards in proper order are now 1, 2, 4, 8, and 10.

Let’s look at a couple more examples.

## From Smallest to Largest

Order the numbers 149, 231, 85, 589, and 900 from least to greatest.

We need to compare the numbers to one another. Beginning with the first two numbers, the 149 and 231, we see that the 231 is larger, so the 149 comes before the 231.

Next, the 85. The 85 is smaller than both the 149 and the 231, so the 85 comes before both of these numbers. Now we have 85, 149, and 231.

Next, what about the 589? Comparing this number to 85, 149, and 231, it is larger than all of them. We write the 589 at the end of the list. Our list is now 85, 149, 231, and 589.

We have one more number, the 900. Where does this one go? Comparing this to all the other numbers, we see that it is the largest. This means that it goes last. Our finished list is 85, 149, 231, 589, and 900. This is our list in ascending order, from least to greatest.

## From Largest to Smallest

Now, what if we are asked to order some numbers from greatest to least? This is called **descending order**. This means that we need to write our larger numbers first and then write our smallest number at the end. Let’s look.

Order the numbers 4,000; 10,000; 230,000; 200; and 50 in descending order.

We need to write the largest number first and then work our way down to the smallest number. So, comparing the first two numbers, we see that the 10,000 is greater than the 4,000, so we write the 10,000 first. We have 10,000, then 4,000.

When comparing the next number, 230,000, to the 4,000 and the 10,000, we see that it is larger than both of them, so the 230,000 needs to be written before these two numbers. We now have 230,000; 10,000; and 4,000.

Next, we have a 200. How does the 200 compare to the 230,000, the 10,000, and the 4,000? The 200 is smaller than all of these, so we write it behind all these numbers. Our list is now 230,000; 10,000; 4,000; and 200.

Lastly, our final number, 50, is actually the smallest compared to all the other numbers, so this means that we need to write it at the very end. Our numbers written in descending order then are 230,000; 10,000; 4,000; 200; and 50.

## Lesson Summary

Let’s review what we’ve learned. **Numbers** represent an amount or value that we are talking about. To order numbers means to put them in order from least to greatest or from greatest to least.

**Ascending order** means from least to greatest, and **descending order** means from greatest to least. To place numbers in order, we need to compare them to one another. If we are ordering our numbers in ascending order, we need to write our smaller numbers before our bigger numbers. If we are ordering our numbers in descending order, we need to write our larger numbers before our smaller numbers.