3 Digit Addition Break Apart Method with Regrouping
The 3 digit addition break apart method can be challenging for students if they don’t know their basic facts.
This strategy works best when students know their basic facts and can easily regroup numbers. You might hear this strategy referred to as the partial sums strategy.
Introduce this strategy after students master the non-regrouping strategies and addition with regrouping using base ten blocks. This strategy gives students practice visualizing place value, but without using base ten blocks. The standard 2.NBT.7 uses many different strategies to master 3-digit addition and subtraction. I take it very slowly to help with mastery of this standard.
Keep reading to learn more about the break apart or partial sums strategy and to find a resource you can use right in your classroom to teach 3-digit addition with regrouping using the break apart strategy.
Break Apart to Add 3-Digit Numbers with Regrouping Example
What do you think you would do to start solving 349 + 473 using the break apart strategy?
You would break apart the numbers into hundreds, tens and ones just like you would when writing numbers in expanded form.
In this example, 349 would be 300, 40 and 6. 473 would be 400, 70 and 3. To help the students visualize, they will write the numbers in boxes below the problem. It’s important to set up the problems for the students from the beginning.
Once the students start to feel comfortable with the strategy, you can have them draw their own boxes to show their thinking.
Be careful with this step! Many students will want to write 3 instead of 300, 4 instead of 40, 4 instead of 400, and 7 instead of 70. This will impact their thinking later on, so be sure to correct that misconception as soon as you notice it.
Once the numbers are broken apart correctly into their place values, students are ready to add. Start with adding the ones. Have students show their thinking by writing the number sentences below the boxes.
9 + 3 = 12
Note: Some students will want to keep the numbers in their heads instead of writing on paper. Encourage students to show their work throughout every step. Since this type of problem requires regrouping, it will be easier to make mistakes if they don’t show their work.
Then add the tens. Again, write this number sentence below the boxes.
40 + 70 = 110
Finally, add the hundreds. Again, write this number sentence below the boxes.
300 + 400 = 700
You are ready to add all the sums together.
700 + 110 + 12 = 822
Note: Some students are able to solve the last step as is. Other students need an additional step. Both are OK!
For the students that need an additional step, they can break apart the new number sentence to add.
700 + 100 = 800
10 + 10 = 20
2
800 + 20 + 2 = 822
Write the final answer in the circle. I encourage my students to always write the final answer in the circle so I know they have completed every step.
This strategy is called break apart since you are breaking apart the numbers into their place value to add.
It can also be called partial sums because you are getting part of the sum each time you add the numbers in different place values.
You can use both names to reference this strategy. In fact, it is important to share this with students so you don’t hear them tell you they don’t know what the strategy means if it is referenced on a standardized test! They do know what to do!
Break Apart to Add 3-Digit Numbers with Regrouping Practice
Do you need some practice pages for your students to use with this strategy?
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Comment below with any questions you have about 3-digit addition with regrouping using break apart or partial sums.
