Ahhhh, subtraction with regrouping. I can feel the confusion in the air just talking about it. I may have a little PTSD from my first year of teaching it actually. Ok, that may be a touch dramatic but if ya know, ya know. It seems that no matter what strategy you use, there are confusing parts to each one. Typically, it’s the concept of “borrowing.” Subtraction with regrouping is one of those skills that requires several prerequisite skills. I always like to start at the bottom and work my way up to make sure students have a solid foundation. So this blog will be a mixture of how to build the foundation up to the skill and how to teach the skill itself. Ready? Here we go!
Building the place value foundation before teaching subtraction with regrouping is essential. Sometimes the concept of “borrowing” is so foreign to students because they don’t have a good understanding of place value and how those values can be manipulated. I always like to put place value activities like this one in centers as a refresher before teaching subtraction with regrouping. Keep your eyes on students who seem to be struggling with the center work and hopefully you can catch their place value problems before subtraction hits.
This is another pre-req skill that is essential to subtraction with regrouping. A lot of times in the classroom, we are so busy composing tens and hundreds that we forget to decompose them. Students need to know that if needed, one hundred can be decomposed into ten tens and one ten can be decomposed into ten ones. If students have had ample practice decomposing tens and hundreds, this makes the “borrowing” concept a bazillion times easier for students. And for you too, honestly. Just like the above mentioned tip, I like to put this in for center work before subtraction hits.
This may seem like a no-brainer, but when I tell you I have place value PTSD, I may not exactly be kidding. I, personally, don’t remember learning subtraction with regrouping using manipulatives. I think I was thrown directly into naked number equations and asked to cross out numbers and borrow. I definitely felt the confusion in the air as a student. Hence, why I was a much better math teacher than math student. When teaching subtraction regrouping, use a place value chart so students can physically see the values being broken down and moved to other areas of the chart. Each time, associate the equation with the model and show students where the movement is happening within the equation.
Starting with place value blocks is helpful in the fact that sometimes these manipulatives can be physically broken down. Once students have a good grasp on place value blocks, move to place value chips. For some reason, the light bulb moment usually starts to happen with the transition of place value chips. Always associate the expanded form of numbers with the place value chips. The chips, however, can be a little abstract for primary students, so use your judgement on ability level when it comes to which manipulative to use.
Once students have been successful with showing the regrouping with manipulatives, move on to drawings. Now is the gradual release from manipulatives and bridging to the equations. Model how to do the math using a drawing. We all know those kiddos that are going to try to draw 35 circles and cross out 19. Remind students to use place value in their drawings. This can be tricky to show the decomposing of tens, moving into ones so model, model, model.
This was a complete game changer my first year teaching. Instead of immediately asking students to stack numbers and borrow, decompose and expand the number first. Even though you’re essentially still asking students to stack the numbers and borrow, they can visually see that a TEN is moving into the ones column, not just a “one.” For example, if you have 432-229, expand it into 400 30 2 – 200 20 9 and then allow students to borrow. I know it’s something so small but I promise, it’s a little magic trick for subtraction. From this point, you can move into the standard algorithm if you feel like students are ready.
Now that the teaching part is done, it’s time to hand the reigns over to the students for ample amounts of practice. Play games, put out activities in centers, send work home and see if mom and dad can help. Incorporate subtraction into a number of the day or a math routine.
Ok, the air is a little less tense now and the feeling of confusion in the room has calmed down some. Take a deep breath and go print those place value charts!
Looking for a fun and easy way to incorporate these skills in everyday activities? Check out these resources below:
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