Lesson Video: Comparing Three-Digit Numbers Using Number Lines Mathematics • 2nd Grade

In this video, we will learn how to use a number line to compare three-digit numbers.

13:01

Video Transcript

Comparing Three-Digit Numbers Using Number Lines

In this video, we will learn how to use number lines to compare three-digit numbers.

The number 675 is a three-digit number. We use the position of each digit to tell us its value. The six digit in the number 675 is worth six 100s. The seven digit is worth seven 10s. And the five digit is worth five ones. We use the value of each digit in a three-digit number to help us compare three-digit numbers.

These monsters are going to have a race. Each monster has been given a three-digit number for the race. But the monsters have lined up in the wrong order. 156, 153, 154, 159, 150, 151, 158, 160, 152, 155, 157. Let’s help the monsters line up in the correct order. When we count on a number line, we start with the smallest number. And we read from left to right. As we count from left to right, the numbers should increase by one each time.

Which of the monsters is wearing the shirt with the smallest three-digit number? The first number is 156. If we write this number into our place value chart, we can see it has one hundred, five tens, and six ones. The number 153 also has one hundred and five tens but only three ones. Did you notice that, so far, all of our three-digit numbers have had one hundred and five tens? 154 has four ones. The only digit that’s changing is the ones digit. 159 has one hundred, five tens, and nine ones. The number 150 has no ones. So far, this is the smallest number because all of the three-digit numbers have had one hundred, five tens, and some ones.

151 has one in the ones place. The number 160 has one hundred and six tens. This is the greatest number so far. Now we know that number 150 is the smallest, we can place it at the beginning of our number line. And we know that the number 160 is the largest number because it has six tens and all the other numbers only have five tens. Now we know that all of the monsters need to line up between the numbers 150 and 160.

Did you notice that both of these numbers end in a zero? They’re both multiples of 10. This is the halfway mark on the number line. Which number comes halfway between 150 and 160? It’s the number 155. Which number comes after 150? It’s the number 151, 152, 153. The number which comes after 153 but before 155 is the number 154. Which number comes after 155? 156, 157, 158, and the number which comes after 158 but before 160 is 159. We placed the monsters in the correct position on the number line. 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160.

To help us order the numbers, we used our place value chart to help. We compared the value of the digits in the three-digit numbers, and we placed the smallest and the largest numbers on the number line. We placed the number which is halfway between the smallest and largest numbers next on the number line. Then we counted forward in ones to place the other monsters on the number line. In this video, we’re going to use our knowledge of place value to help us compare three-digit numbers. Let’s try some practice questions.

Olivia and Amelia are comparing numbers to the right and to the left of 322 on a number line. Who is correct? The numbers to the right of 322 are greater than 322 or the numbers to the left of 322 are greater than 322.

Here’s the number 322 on both of the number lines we’re given. On the first number line, the numbers to the right of 322 have been circled orange. And the girl says that these numbers are greater than 322. Is she correct? The first number to the right of 322 is 323. Is 323 less than or greater than 322? Let’s compare the ones digits. 322 has two ones. 323 has three ones. And we know that three is greater than two. 324 is greater than 323. 325 is greater than 324. 326, 327. When we count to the right on the number line, the numbers increase by one each time. So the numbers to the right of 322 are greater than 322.

The numbers to the left of the number 322 are less than 322. 321, 320, 319, 318, 317. The numbers are decreasing by one each time. Each time we count to the left, we’re taking away one. The numbers to the right of 322 are greater than 322.

Which number sentence is correct? 225 is equal to 240. 225 is less than 240. 225 is greater than 240.

We need to use the number line to help us decide which number sentence is correct. We’re being asked to compare the numbers 225 and 240. We know that 225 is not equal to 240 because the numbers are in different places on the number line. If they were equal, the numbers would be in the same position on the number line. Is 225 less than 240? The number 225 is to the left of 240 on the number line. Let’s start at 240 and count back to 225. Watch what happens to the numbers as we count back. 240, 235, 230, 225. The numbers were going down by five each time. We’re taking away five each time we count to the left. If the numbers are getting smaller, that means that 225 is less than 240.

We know that 225 is not greater than 240. The numbers to the right of 240 are greater than 240. And 225 is to the left. The number sentence which is correct is 225 is less than 240.

Compare the two numbers. 836 what 843. Which symbol should go between them? Hint: Use the number line to help you.

We’re being asked to use the correct symbol to compare these two numbers. Is 836 less than 843? Are the two numbers equal? Or is 836 greater than 843? In this question, we’re told to use the number line to help. Where would we place the number 836? We know it comes after 830 but before the number 840. 836 only has three tens not four. The number 835 is halfway between 830 and 840. And we know that 836 is one more than 835. So the number 836 would go around here on the number line.

Where should we place 843? The four digit is worth four 10s in 843. So 843 comes between 840 and 850. It’s after 840 but before 850. The halfway mark would be 845. We know that three is less than five, so 843 would come before 845. Now we can see that 843 is greater than 836, so 836 is less than 843. The symbol which should go between the two numbers is “less than” because 836 is less than 843.

What have we learned in this video? We’ve learned how to compare three-digit numbers using a number line. We’ve learned that when we count on or count forwards, the numbers increase. And when we count to the left or we count back on a number line, the numbers get smaller or decrease.

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