Subtraction with Regrouping: 2-Digit Base Ten Strategy
When students master subtraction without regrouping, they are ready for subtraction with regrouping.
Just like with addition, subtraction with regrouping is the last step to teaching students how to subtract 2-digit numbers.
There are many strategies for subtracting 2-digit numbers, but I like to start with using base ten blocks to represent the numbers. It helps students visualize the numbers. You should use the physical base ten blocks to start and then move into drawings of base ten blocks. Finally, you can teach students how to draw sticks and dots to represent the tens and ones.
I love using these magnetic base ten blocks when teaching this strategy. You can model on the board or have students show the class how they solved problems with these.
Keep reading to learn more about this strategy and to find a resource you can use right in your classroom to teach 2-digit subtraction with regrouping.
2-Digit Subtraction with Regrouping Example
What do you think you would do to start solving 42 – 14?
You should build 42. Sometimes, you might see problems that also build 14. That will just confuse some students, so you want to teach the students just to build 42 in this example.
When working with the physical base ten blocks, it is not necessary to build 14.
Once you have the number built with base ten blocks, you will need to regroup one ten into ten ones before you can subtract the ones.
Now, you can subtract the ones. Take four ones away.
Then subtract the tens. Take one ten away.
Now you have the final answer.
2-Digit Subtraction with Regrouping Using Drawings of Base Ten Blocks
Once the students master solving 2-digit subtraction problems using the physical base ten blocks, you can move to base ten blocks on paper. Let’s use the same problem again.
The students might see problems where both numbers are drawn using base ten blocks.
You can teach the students to just cross out the blocks with the whole number. It will be very confusing because they have to regroup in this problem.
Students should recognize they can’t subtract 4 ones because they only have 2. So they need to regroup. Cross out one ten and draw ten ones to replace it.
Then the students are ready to subtract 4 ones. Cross out 4 ones.
Then subtract the tens. So cross out one ten.
Important Note: Students need to cross out another ten. The one that is already crossed out is not the ten in 14. It is the ten that was regrouped into ten ones.
To get the answer, students need to count the base ten blocks that are not crossed out.
There are 2 tens and 8 ones.
Important Note: Do not forget to count the ones that are not in the circle. These are very easily missed.
Once the students master regrouping using pictures of base ten blocks, you can take it a step further.
I like this last version of solving these problems because it is less likely to confuse students this way.
2-Digit Subtraction with Regrouping Using Sticks and Dots
You can introduce sticks and dots as a simple way to draw tens and ones. When using sticks and dots, you can just give the students the problem and they can draw sticks and dots to solve. This saves you time and gives your students the opportunity to show their thinking.
When given subtraction problems, students only need to draw 42. Teach them NOT to draw 14 – that is the number they are taking away, which will be shown by crossing off.
Students should recognize they can’t subtract 4 ones because they only have 2. So they need to regroup. Cross out one ten and draw ten ones to replace it.
Then the students are ready to subtract 4 ones. Cross out 4 ones.
Then subtract the tens. So cross out one ten.
Important Note: Students need to cross out another ten. The one that is already crossed out is not the ten in 14. It is the ten that was regrouped into ten ones.
To get the answer, students need to count the base ten blocks that are not crossed out.
There are 2 tens and 8 ones.
Important Note: When students are drawing their own sticks and dots, they need to draw them neatly and far apart so they don’t get confused when crossing off the tens and ones. If the sticks and dots are drawn too close together, it may be hard to count the ones that are not crossed off.
Practice 2-Digit Subtraction with Regrouping
Do you need some practice pages for your students to use with this strategy?
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