Subtraction with Regrouping 3 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 3-digit numbers.
There are many strategies for subtracting 3-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 squares, sticks and dots to represent the hundreds, 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 3-digit subtraction with regrouping.
3-Digit Subtraction with Regrouping Example
What do you think you would do to start solving 487 – 296?
You should build 487. Sometimes, you might see problems that also build 296. That will just confuse some students, so you want to teach the students just to build 487 in this example.
When working with the physical base ten blocks, it is not necessary to build 296.
Once you have the number built with base ten blocks, you do not need to regroup the ones, so you can subtract 487 – 6.
Now you need to regroup in order to have enough tens.
Then subtract the tens. Take nine tens away.
Now you can subtract the hundreds. Take away two hundreds.
Now you have the final answer.
3-Digit Subtraction with Regrouping Using Drawings of Base Ten Blocks
Once the students master solving 3-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 start by subtracting the ones.
Now it is time to subtract the tens. The students should recognize they can’t subtract 9 tens because they only have 8. So they need to regroup. Cross out one hundred and draw ten tens to replace it.
Then the students are ready to subtract 9 tens. Cross out 9 tens.
Then subtract the hundreds. So cross out two hundreds.
Important Note: Students need to cross out two more hundreds. The one that is already crossed out is not the hundred in 296. It is the hundred that was regrouped into ten tens.
To get the answer, students need to count the base ten blocks that are not crossed out.
There are 1 hundred, 9 tens and 1 one.
3-Digit Subtraction with Regrouping Using Squares, Sticks and Dots
You can introduce sticks and dots as a simple way to draw hundreds, tens and ones.
When using squares, sticks and dots, you can just give the students the problem and they can draw squares, 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 487. Teach them NOT to draw 296 – that is the number they are taking away, which will be shown by crossing off.
Students should start by subtracting the ones.
Now it is time to subtract the tens. The students should recognize they can’t subtract 9 tens because they only have 8. So they need to regroup.
Cross out one hundred and draw ten tens to replace it.
Then the students are ready to subtract 9 tens. Cross out 9 tens.
Then subtract the hundreds. So cross out two hundreds.
Important Note: Students need to cross out two more hundreds. The one that is already crossed out is not the hundred in 296. It is the hundred that was regrouped into ten tens.
To get the answer, students need to count the base ten blocks that are not crossed out.
There are 1 hundred, 9 tens and 1 one.
Important Note: When students are drawing their own squares, sticks and dots, they need to draw them neatly and far apart so they don’t get confused when crossing off the hundreds, tens and ones.
If the squares, sticks and dots are drawn too close together, it may be hard to count the base ten blocks that are not crossed off.
Practice 3-Digit Subtraction with Regrouping
Do you need some practice pages for your students to use with this strategy?
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