Three digit Addition on a Number Line  Number Line
 3 Digit Addition with Regrouping on Number Lines
 Three Digit Addition with Regrouping on a Number Line – Explanation
 Three Digit Addition with Regrouping on a Number Line – Practice Example
 Three Digit Addition with Regrouping on Number Lines – Summary
 Frequently Asked Questions about Equivalent Fractions
Basics on the topic Three digit Addition on a Number Line  Number Line
3 Digit Addition with Regrouping on Number Lines
Addition and subtraction are taught in maths in the early stages. We are familiar with the addition or subtraction process from real life examples. Also, we do some mathematical operations like addition or subtraction at least a couple of times a day. In this learning text, we will show addition using the number line to add 3digit numbers. This text will explain how number lines can visualise threedigit addition with regrouping. You can refresh your memory on how to create number lines for additions.
Three Digit Addition with Regrouping on a Number Line – Explanation
The number line can help us to model an equation. In our examples, we use an open number line to show the movement while adding different amounts.
We are going to add two numbers: 306 and 262.
 Firstly, draw a number line and plot the larger number on the lefthand side of the drawn number line.
 Secondly, write the amount you are adding in expanded form.
Then, start adding starting with hundreds, jump by hundreds twice and plot the answer.
Now move to the tens and start jumping by tens six times and write the answer.
Finally, move to the ones and skip forwards twice and put the final answer.
Our solution from the addition of adding 306 to 262 is 568.
Three Digit Addition with Regrouping on a Number Line – Practice Example
We are going to show another example of 3digit addition with a regrouping of the open number line. This time we are going to add 568 and 143. We are going to follow the same steps:
 Firstly, draw a number line and plot the larger number on the lefthand side of the drawn number line.
 Secondly, write the amount you are adding in expanded form
 Then, start adding beginning with hundreds and jump by hundreds once and plot the answer.
 Then, move to the tens and start jumping by tens four times and write the answer.
 Finally, move to the ones and jump forward three times and put the final answer.
Our solution from the addition of 568 and 143 is 711.
Three Digit Addition with Regrouping on Number Lines – Summary
To solve addition equations with regrouping we can model with an open number line and follow the steps:
Step #  What to Do 

1  Draw a number line and plot the larger lumber on the lefthand side. 
2  Write the amount you are adding in expanded form. 
3  Count forwards by the hundreds, tens and ones, plotting the number as you go. 
4  The final number is the solution. 
Now you should be able to show addition using the number line to add 3digit numbers. Feel free to watch the video explaining the addition using an open number line to add 3digit numbers, or complete the worksheet.
Frequently Asked Questions about Equivalent Fractions
Three digit Addition on a Number Line  Number Line exercise

What is the expanded form of the number 555?
HintsLook at the number 555.
 How many hundreds are in this number?
 How many tens are in this number?
 How many ones are in this number?
There are 5 hundreds in 555, which is 500.
As an example, 262 in expanded form is 200 + 60 + 2.
SolutionThe expanded form of 555 is: 500 + 50 + 5.
There are:
 5 hundreds or 500
 5 tens or 50
 5 ones or 5
 500 + 50 + 5 = 555

How do you use a number line for three digit addition with regrouping?
Hints200 + 30 + 2 is the expanded form of 232.
 How many hundreds are in 232?
 Count forwards by two hundreds. One hundred has already been done for you.
200 + 30 + 2 is the expanded form of 232.
 How many tens are in 232?
 Count forwards by three tens.
200 + 30 + 2 is the expanded form of 232.
 How many ones are in 232?
 Count forwards by two ones.
In each box you should fill in either 100, 10 or 1.
SolutionFirst, write the number you are adding in expanded form. Then, count forwards on the number line in intervals.
Here we can see that 232 = 200 + 30 + 2.
 There are 2 hundreds so we count forwards by 100 twice.
 There are 3 tens so we count forwards by 10 three times.
 There are 2 ones so we count forwards by 1 twice.
347 + 232 = 579

What is 443 + 321?
Hints First, write the number you are adding in expanded form.
 341 in expanded form is 300 + 40 + 1.
Then, count forwards in steps of 100, 10 and 1.
Solution443 + 321 = 764
321 = 300 + 20 + 1
 443 + 300 = 743
 743 + 20 = 763
 763 + 1 = 764

Solve 643 + 143.
Hints First, write the number you are adding in expanded form.
 How many tens do you need to add?
How many ones in 143?
Then, count forwards in steps of 100, 10 and 1.
Solution643 + 143 = 786
143 = 100 + 40 + 3
 643 + 100 = 743
 743 + 40 = 783
 783 + 3 = 786
Therefore 643 + 143 = 786.

Which number line shows 333 + 222?
HintsHow many hundreds are in this number? There are two hundreds, so this choice is incorrect.
How many tens are in this number? There are two tens, so this choice is incorrect.
SolutionThis number line shows 333 + 222.

Find the solution for each addition problem.
Hints First, write the number you are adding in expanded form.
 The expanded form of 120 is: 100 + 20 + 0.
 Then, count forwards in steps on the number line.
 First, write the number you are adding in expanded form.
 The expanded form of 154 is: 100 + 50 + 4.
 Then, count forwards in steps on the number line.
Solution 242 + 120 = 362
 172 + 154 = 326