3 Digit Break Apart Subtraction with Regrouping
Break apart subtraction with regrouping can be challenging for some students. However, this strategy is important to help students break apart numbers in order to subtract.
This strategy is perfect to introduce after students master subtraction using base ten blocks. Students still need practice visualizing place value, but no longer need to see it as base ten blocks.Â
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 differences strategy and to find a resource you can use right in your classroom to teach 3-digit subtraction with regrouping using the break apart strategy.
3 Digit Break Apart Subtraction with Regrouping Example
What do you think you would do to start solving 511 – 234 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.
Important note:Â When subtracting using the break apart method, it is important to only break apart the second number. (See the example below.) Problems with regrouping ONLY work if you break apart one number.
In this example, you do not break apart 511, so you cross out those boxes. 234 would be 200, 30 and 4. 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.Â
Be careful with this step! Many students will want to write 2 instead of 200, and 3 instead of 30. 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 subtract.Â
Start with the whole number 511 and subtract the hundreds. Have students show their thinking by writing the number sentences below the boxes.
511 – 200 = 311
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. Once they start working with larger numbers or use numbers that regroup, it will be easier to make mistakes if they don’t show their work.
Then subtract the tens from your answer in the previous step. Again, write this number sentence below the boxes.
311 – 30 = 281
Some students are able to count back 30 from 311, while others struggle. You could have the students break apart the 30 to make use of friendly numbers.
311 – 11 = 300
You’ll need to subtract 19 more in order to take away a total of 30.
300 – 19 = 281
Then subtract the ones from your answer in the previous step. Again, write this number sentence below the boxes.
281 – 4 = 277
Some students are able to count back 4 from 281, while others struggle. You could have the students break apart the 4 to make use of friendly numbers.
281 – 1 = 280
You’ll need to subtract 3 more in order to take away a total of 4.
280 – 3 = 277
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 subtract.
It can also be called partial differences because you are getting part of the difference each time you subtract 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!
3 Digit Break Apart Subtraction with Regrouping Practice
Do you need some practice pages for your students to use with this strategy?
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