# Three Digit Subtraction with Regrouping - Number Line

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Three Digit Subtraction with Regrouping - Number Line
CCSS.MATH.CONTENT.3.NBT.A.2

## Three Digit Subtraction with Regrouping

In this video, Sir Squeaks and Imani learn to use number line strategy with subtraction of 3-digit numbers to help calculate differences. To help solve subtraction equations with regrouping, we can model with an open number line. Open number lines are helpful because they allow us to see the movement while taking away an amount during subtraction. ## 3 Digit Subtraction using Number Lines – Example

We will use four hundred thirty two minus one hundred fifty six to illustrate how to use open number line subtraction with 3 digits. First, draw a line and plot the larger number in the equation on the right side. Then, write the second numbers in the equation, or amount we are taking away, in expanded form. One hundred fifty-six becomes one hundred plus fifty plus six. Beginning with the hundreds, count back each hundred and plot the answer, three hundred thirty two. Then, move to the tens and skip count back for each ten. Plot the answer, two hundred eighty two. Finally, move to the ones and count back for each of the ones. Two hundred seventy-six is the number we end up on, so this is our solution! ## 3 Digit Subtraction using Number Lines – Summary of Steps

These are the steps you need to keep in mind when subtracting from 3 digit numbers using number lines:

Step # What to do
1 Draw the number line and plot the larger number
in the equation on the right side.
2 Write the second number in the equation, or
the amount taken away, in expanded form.
3 Skip count back by the hundreds, tens,
then ones of the second number,
plotting the answers as you go.
4 The final number you land on is the solution.

## 3 Digit Subtraction using Number Lines – Worksheets with Friendly Numbers

Have you practiced 3 digit subtraction on number line worksheets yet? After watching the video, you can also find 3 digit subtraction open number line worksheets and exercises.

### TranscriptThree Digit Subtraction with Regrouping - Number Line

Sir Squeaks and Imani have traveled back in time to the Middle Ages where they meet King Theodore. He is extremely upset because someone has stolen from his vault! Many jewels and coins are missing. He doesn’t know how many were taken, so Sir Squeaks and Imani will help him using "Three Digit Subtraction with Regrouping- Number Line". Remember, number lines are useful tools that help us model equations. We can use an open number line to see the movement while taking away an amount during subtraction. Let's use four hundred thirty two minus one hundred fifty six as an example. First, draw a line and plot the larger number on the right side. Then, write the amount we are taking away in expanded form. One hundred fifty-six becomes one hundred plus fifty plus six. Beginning with the hundreds, count back each hundred and plot the answer, three hundred thirty two. Then, move to the tens, skip count back for each ten, and plot the answer, two hundred eighty two. Finally, move to the ones and count back for each of the ones. Two hundred seventy-six is the number we end up on so this is our solution! King Theodore knows that he had two hundred fifteen jewels now two hundred and six remain. Let's use a number line to help calculate how many were taken. Begin by drawing our number line and plotting two hundred fifteen on the right side. Next, we write two hundred and six in expanded form: two hundred plus zero plus six. Beginning with the hundreds, count back one hundred, then two hundred and plot the answer, fifteen. Move to the tens since there are no tens we have nothing to count so we move on to the ones and count back one, two, three, four, five, six! Plot nine since we finished there. Nine is our solution. Sir Squeaks reports that nine jewels were stolen from the vault. King Theodore also had five hundred twenty-five coins and now four hundred eighty-five are left. What are our steps? First draw the number line and plot five hundred twenty-five on the right side. Second, write four hundred eighty five in expanded form: four hundred plus eighty plus five. Now begin to count back for each hundred one hundred, two hundred, three hundred, four hundred and write the answer, one hundred twenty five. Where do we count next? We count the tens and count back eight tens until we reach and plot forty five! What happens next? We count back by the ones one, two, three, four, five! We finished on forty so write it here. Forty is our solution. So, Imani reports that forty coins were taken from the vault! Wait, who is this? Before we find out, let's summarize! Remember, to help solve subtraction equations with regrouping, we can model with an open number line. First, draw the number line and plot the larger number on the right side. Second, write the amount taken away in expanded form. Third, skip count back by the hundreds, tens, then ones, plotting the answers as you go. The final number is the solution. "I'm so glad you're back. There has been a theft!" "About that....you see, I was trying out a new invisibility spell this morning, when I was called away for an emergency. But I'm back now and it's as simple as..."

## Three Digit Subtraction with Regrouping - Number Line exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Three Digit Subtraction with Regrouping - Number Line.
• ### Missing golden coins.

Hints

How do we partition 137 into hundreds, tens and ones?

Look at how the number to subtract has been partitioned and written in expanded form.

Which number line counts backward by hundreds, then tens, then ones.

Solution

This is the correct solution because the number 137 has been correctly partitioned and written in its expanded form of 100 + 30 + 7.

• ### Help Imani and Mr. Squeaks.

Hints

This image shows the first and second steps when solving a subtraction using a number line.

What happens after the smaller number has been written in expanded form?

Solution

The correct order of the steps to solve a subtraction on a number line is:

• First, draw the number line and put the larger number on the right side.
• Write the amount to be taken away in expanded form.
• Count backward along the number line by hundreds, then tens, then ones, plotting the answers as you go.
• Look at the final number you plot, this is the solution.

• ### How many gems were taken?

Hints

Once you have put the larger number on the right side, partition the smaller number into expanded form and count backward.

What will 123 be when written in explanded form?

Counts backward by hundreds first, then by tens, then by ones, plotting your answers along the way.

Solution

The steps to solve this are:

• First write the larger number, 235 on the right side.
• Next partition the smaller number, 123 and write it in expanded form as 100 + 20 + 3.
• Count backward first the hundreds and plot the answer, which is 135.
• Count backward the tens and plot the answers, first 125 then 115.
• Count backward the ones, there are 3, so plot the answer of 112.
112 is the final number plotted so this is the answer.
• ### Help Mr. Squeaks and Imani.

Hints

Try drawing your own number line, putting the larger number on the right, writing the smaller number in expanded form then subtracting.

First subtract by counting backward by hundreds, then tens, then ones.

Solution
• 432 - 156 = 276
Start at 432, count backward by one hundred to reach 332, count backward by five tens to reach 282, count backward by six ones to reach 276.
• 354 - 131 = 223
Start at 354, count backward by one hundred to reach 254, count backward by three tens to reach 224, count backward by one to reach 223.
• 642 - 371 = 271
Start at 642, count backward by three hundreds to reach 342, count backward by seven tens to reach 272, then count backward by one to reach 271.
• ### Stolen crystals.

Hints

Look at how the number has been written in expanded form, first the hundreds have been subtracted. What is 350 - 100?

From 250 another 100 is subtracted, what is 250 - 100?

Count backward by ten from 250.

Make sure to count backward by ones for the last part of the subtraction problem.

Solution
• 350 - 225 = 125.
• 350 is the larger number, so is written on the right side of the number line.
• 225 is the smaller number and has been re-written in expanded form as 200 + 20 + 5.
• Count backward 100 to reach 250.
• Count backward another 100 to reach 150.
• Count backward 10 to reach 140.
• Count backward another 10 to reach 130.
• Count backward 5 ones to reach 125.
• 125 is the final number plotted so this is the answer.
• ### Solve the subtraction problems.

Hints

Make sure to partition the smaller number into hundreds, tens and ones and write it in expanded form before counting back.

Remember to plot the answers along the number line as you go.

Solution

437 - 129 = 308

464 - 283 = 181

532- 308 = 224

538 - 341 = 197