# Three digit Addition with Regrouping - Base Ten Blocks

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## 3 Digit Addition with Regrouping and Base Ten Blocks

Displaying addition with base ten blocks is a useful method to simplify the addition of three-digit numbers. In this text, we will teach the use of place value charts to represent three digit number addition.

## Addition with Regrouping and Base Ten Blocks – Using Place Value Charts

We can use place value charts and base ten blocks to help model column addition using base 10 with regrouping. Ones are represented with single squares, tens with columns of ten, and hundreds as squares of one hundred ones. In a place value chart, we build the addends in blocks to add and regroup, or move the blocks from one place value to another. This helps us to solve equations more easily.

To begin addition with base 10 blocks, model your addends with base ten blocks in a place value chart. Add up the ones place. If the sum in the ones place is ten or greater, regroup as needed to the tens place and write the remaining total below. Next, add the tens place.If the sum in the tens place is ten or greater, regroup as needed to the hundreds place and write the remaining total below. Finally, count all of the squares in the hundreds column and write the total below.

## 3 Digit Addition with Regrouping and Base Ten Blocks – Example

Let’s use two hundred and sixty-five plus four hundred and thirty-seven as an example to model three digit addition using base ten blocks and regrouping.

Begin by modelling the equation with base ten blocks. Put the first addend’s blocks in the place value chart. Then, put the second addend’s blocks below it.

Start counting all of the blocks in the ones column. There are twelve ones. Twelve is made up of one ten and two ones, so we need to regroup the set of ten. This set moves to the tens place. Two blocks are left in the ones column, so we write two below.

Now, move on to counting in the tens place. There are ten columns of ten which means we have one hundred in the TENS place. We need to regroup the one hundred from the tens place to the hundreds place. After we do this, the tens column is empty. We write a ZERO here to show there are no tens here anymore.

Finally, count the hundreds in the hundreds place. There are seven hundreds, so we write seven below the hundreds place.

## 3 Digit Addition with Regrouping (Base 10 Addition) – Summary of Steps

Here you can revise the necessary steps for three digit addition with regrouping and base ten blocks:

Steps What to do
1 Model your addends with base ten blocks in a place value chart.
2 Add up the ones place. If the sum in the ones place is ten or greater, regroup as needed to the tens place and write the remaining total below.
3 Add the tens place. If the sum in the tens place is ten or greater, regroup as needed to the hundreds place and write the remaining total below.
4 Count all the squares in the hundreds column and write the total below.

## 3 Digit Addition with Regrouping and Base Ten Blocks – Exercises

Have you practised yet? On this website, you can also find addition with regrouping using base 10 blocks worksheets as well as addition base 10 interactive exercises and activities.

### TranscriptThree digit Addition with Regrouping - Base Ten Blocks

Mr. Squeaks and Imani successfully built a time machine to go dino gazing!

On their two hundred million year journey back home, they are trying to add up all of the amazing things they saw, but they are having trouble regrouping their three-digit numbers! Let's help them by modeling "Three-digit Addition with Regrouping - Base Ten Blocks" Remember, we can use place value charts and base ten blocks to help model addition with regrouping. When we draw base 10 blocks, ones are represented with single squares, tens with columns of ten, and hundreds as squares made up of one hundred ones. In a place value chart, we build the addends, or numbers we are going to add, in blocks. We use these to add and REGROUP, or move the blocks from one place value to another. This helps us to solve equations more easily. First, Mr. Squeaks and Imani saw a herd of Diplodocus. There were one hundred and forty-seven on the ridge and six more eating leaves in the valley. How many were there altogether? We can model one hundred and forty-seven plus six using base ten blocks in a place value chart. First, we represent each of our addends using base ten blocks.

We put the FIRST addend in the place value chart. Then, we put our SECOND addend beneath it. Next, we begin to add by counting up all of the blocks in the ones column. There are thirteen ones. Thirteen is made up of one ten and three ones, so we need to REGROUP.

Regrouping means we will need to move a set of ten to the TENS place. Three blocks are left, so we write three in the ones place. Now we count in the tens place. There are five tens. We write five below the tens place. Finally, we count the hundreds. There is one hundred so we write one in the hundreds place. Wow, Mr. Squeaks and Imani saw one hundred and fifty-three Diplodocus! They also stumbled upon a field of Stegasaurus footprints! The first set of prints had two hundred and sixty-five footprints and the second had four hundred and thirty-seven. How many footprints were there altogether?

Model the equation with base ten blocks.

What comes next? We put the FIRST addend in the place value chart. Then, we put the SECOND addend below it. Where do we start counting? Begin by counting all the blocks in the ONES column. There are twelve ones. Twelve is made up of one ten and two ones, so we need to REGROUP the set of ten.

Where does the set of ten regroup to? It regroups to the TENS place. Two blocks are left in the ones column, so we write two below. Move on to counting in the tens place. There are ten tens. We have ten tens which means we have one hundred in the TENS place. We need to regroup ONE hundred from the TENS place to the HUNDREDS place. The tens column is now empty, so write a ZERO here. Finally, count the hundreds. There are seven. Write seven below the hundreds place. Wow! Mr. Squeaks and Imani saw seven hundred and two Stegasaurus footprints! Before we see if Mr. Squeaks and Imani made it back to the present, let's remember! Model your addends with base ten blocks in a place value chart. Add up the ones place. If the sum in the ones place is ten or greater, regroup as needed to the tens place and write the remaining total below. Next, add the tens place. If the sum in the tens place is ten or greater, regroup as needed to the hundreds place and write the remaining total below. Finally, count up the hundreds column and write the total below. "That's strange. It took us longer coming than going."

"My weight calculations for the time machine have it heavier on the way back..."

"...oh well, it's probably nothing."

## Three digit Addition with Regrouping - Base Ten Blocks exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Three digit Addition with Regrouping - Base Ten Blocks.
• ### Which number do the blocks represent?

Hints

How much is each one of these worth on their own?

If we add these base 10 blocks together, we are adding 100 + 10 + 1 which equals 111.

Solution

These base 10 blocks represent the number 204.

Remember:

• the small green cubes are worth 1
• the long blue rods are made up of ten ones so are worth 10
• the large red squares are made up of ten ten rods or 100 one cubes, so are worth 100
_______________________________________________________

20

• Two ten rods.
• 10 + 10 = 20
45
• Four ten rods and five one cubes
• 1 + 1 + 1 + 1 + 1 = 5
• 10 + 10 + 10 + 10 = 40
• 40 + 5 = 45
125
• One hundred square, two ten rods and five one cubes
• 1 + 1 + 1 + 1 + 1 = 5
• 10 + 10 = 20
• 100 + 20 + 5 = 125
130
• One hundred square and three ten rods
• 10 + 10 + 10 = 30
• 100 + 30 = 130
204
• As shown in the image
• Two hundred squares and four one cubes
• 1 + 1 + 1 + 1 = 4
• 100 + 100 = 200
• 200 + 4 = 204

• ### How many teeth did Mr. Squeaks and Imani see?

Hints

Remember to start by adding in the ones column, then move to the tens, and then the hundreds.

Don't forget to carry over if you are left with a 2-digit number.

For example, if we were adding 28 + 17 we would add 8 + 7 to get 15. We would leave 5 ones in the ones column and carry the ten across.

Solution

Mr. Squeaks and Imani saw 272 teeth.

• We start by adding the ones. 7 ones plus 5 ones equals 12 ones. We therefore re-group the ten and write 2 in the ones place.
• We then add the tens. 2 tens plus 4 tens plus the ten we re-grouped equals 7 tens, so we write 7 in the tens place.
• We then add the hundreds. 1 hundred plus 1 hundred equals 2 hundreds, so we write 2 in the hundreds place.
• 2 hundreds plus 7 tens plus 2 ones equals 272.
• ### Are these numbers correct?

Hints

Check the hundreds have been counted correctly, then the tens and then the ones.

For example, here there are 6 tens rods which equals 60.

Solution

Remember to look carefully at how many of each base 10 blocks there are.

• The first number sentence should have read 100 + 30 + 4 as there are three ten rods, not two.
• The second number sentence should have read 200 + 40 + 7 as there are seven ones cubes, not eight.
• The third number sentence should have read 100 + 40 + 3. There is only one hundred square, not two and there are four ten rods, not three.
• The fourth number sentence should have read 300 + 70 + 7. There are three hundred squares, not four. There are seven tens rods not 8 and there are seven one cubes, not eight.
• ### How many leaves have the dinosaurs eaten?

Hints

Remember to add the ones place first.

Don't forget to add anything you have carried over.

For example, if we add 13 + 8, we would add 3 + 8 which equals 11. We would leave the one in the ones column and carry a ten across.

Solution

Here is the answer for 134 + 247.

• We added 4 ones plus 7 ones which equals 11 ones. We cannot put a two-digit number into one place value so we re-group ten ones into the tens column and write 1 in the ones column.
• We now have 3 tens plus 4 tens plus 1 ten which equals 8 tens, so we write 8 in the tens column.
• 1 hundred plus 2 hundreds equals 3 hundreds, so we write 3 in the hundreds column.
• 3 hundreds plus 8 tens plus 1 one equals 381.
____________________________________________________

143 + 379

• 3 ones plus 9 ones equals 12 ones. We re-group ten and write 2 in the ones column.
• 4 tens plus 7 tens plus 1 ten equals 12 tens. We re-group a hundred and write 2 in the tens column.
• 1 hundred plus 3 hundreds plus 1 hundred equals 5 hundreds, so we write 5 in the hundreds column.
• 5 hundreds plus 2 tens plus 2 ones equals 522.
121 + 165
• 1 one plus 5 ones equals 6 ones so we write 6 in the ones column.
• 2 tens plus 6 tens equals 8 tens so we write 8 in the tens column.
• 1 hundred plus 1 hundred equals 2 hundreds, so we write 2 in the hundreds column.
• 2 hundreds plus 8 tens plus 6 ones equals 286.
248 + 332
• 8 ones plus 2 ones equals 10 ones. We re-group ten and write 0 in the ones column.
• 4 tens plus 3 tens plus 1 ten equals 8 tens so we write 8 in the tens column.
• 2 hundreds plus 3 hundreds equals 5 hundreds, so we write 5 in the hundreds column.
• 5 hundreds plus 8 tens plus 0 ones equals 580.

• ### How many dinosaur bones did Mr. Squeaks see?

Hints

Remember to start by adding the ones, then move to the tens, and then the hundreds.

Remember to check how many of each place value there are altogether and place this number at the bottom.

Solution

Mr. Squeaks saw 175 bones!

• 2 ones plus 3 ones equals 5 ones
• 1 ten plus 6 tens equals 7 tens
• 1 hundred plus 0 hundreds equals 1 hundred
• when we put these together we get a total of 175
• ### Can you find the totals?

Hints

If you don't have any of your own base 10 blocks you could draw some on a piece of paper like this.

If you are adding three numbers you still follow the pattern of adding all of the ones first, then all of the tens and then all of the hundreds. Don't forget to add any you have carried over.

Solution

Mr. Squeaks and Imani saw 353 diplodocus!

• We add 9 ones plus 4 ones which equals 13 ones. We re-group ten and write 3 in the ones column.
• We then add 2 tens plus 2 tens plus 1 ten which equals 5 tens, so we write 5 in the tens column.
• Finally, we add 1 hundred plus 2 hundreds which equals 3 hundreds, so we write 3 in the hundreds column.
• 3 hundreds + 5 tens + 3 ones equals 353.
_______________________________________________

Following the same method Mr. Squeaks and Imani saw:

• 435 bones
• 452 pterodactyls
• 406 eggs