# Bigger Bottom? How NOT to teach to subtract with regrouping!

Last week I had my first private tutoring session with an adorable 3rd-grade boy. You should know that I’m not a real structured tutor–I kinda like to find a starting point and just dive in. My questions and the tutee’s answers guide our path. The starting point for my young friend was how to subtract with regrouping. I gave him the problem 53 – 16 to solve. He looked at it and proudly announced (so fast that I couldn’t even understand without having him repeat it 3 or 4 times…) Bigger Bottom Better Borrow. WHAT?!ย  t became obvious very quickly through questioning that he had NO idea what it meant to regroup and had very little understanding of place value in general.

Let me be clear–it is NOT okay to teach kids tricks or shortcuts such as this. It is a huge disservice to them and to their future teachers.

So I pulled out my trusty base-ten blocks and explained to him about trading tens for ones when we subtract with regrouping. We practiced with the blocks and the algorithm side-by-side. Last week we worked on two-digit minus two-digit, and today I extended it to 3-digit numbers with regrouping across a zero. After just two sessions, he totally gets it. He understands more about place value, and he understands why he does the steps in the standard algorithm. Which brings me to another point. If you have not structured your classroom to be able to work with small groups, you’re not meeting all your kiddos at their level. ย Whole group instruction addresses the needs of only about 1/3 of your students. There’s no better way to get inside the mathematical mind of a child than to work with them one-on-one or in a small group.

Unfortunately, there are way too many math skills that are taught using tricks. Check out this blog post for an amazing FREE resource to help you Nix the Tricks!

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1. Heather says:

I totally agree. We work and work with place value and teaching the “why” when teaching this most difficult skill. I only teach them that saying AFTER we know why and how. The only reason I teach them the saying at all is so that they have a little something to make them stop, think, check the numbers before they begin solving.
Heather
Kickin’ It With Class

1. Donna Boucher says:

The why is so important, Heather! Glad to hear that you’re giving you kiddos a strong foundation with place value. ๐

2. TheElementary MathManiac says:

As a K-6 math specialist who spends a lot of time with kids like this, I have to say that teaching kids tricks like bigger bottom better borrow (which is one I haven’t heard) is completely detrimental to their long term ability to learn and do mathematics. Kids need time to develop strategies for multi-digit computation and need a chance to develop their place value understanding while doing this. I totally agree with Donna that if you are not structuring your classroom for some small group work than there is no way you are meeting the needs of all your students. ESPECIALLY with regards to topics such as multi-digit subtraction. Side note: If you are giving all problems with no regrouping required before they ever see one where regrouping is required, you are leading them to over-generalize the ability to add tens and ones. Another side note: try writing a subtraction problem on the board when kids don’t have pencil and paper in front of them and give them some think time to figure out the answer. You will be surprised by the many different ways students invent strategies and are successful with these types of problems, especially if they have never been “taught how to do it.”

Another great post!
Tara
The Math Maniac

1. Donna Boucher says:

Great point about mental strategies, Tara! Our second grade teachers teach addition and subtraction using a variety of strategies, including the hundreds chart, open number lines, splitting, etc., before they ever introduce the standard algorithm. You are absolutely right about the amazing strategies they come up with! If I work with this little fellow long enough, I hope to build his overall number sense and help him develop mental strategies. For right now, I’m just trying to help him understand the method he’s already been “taught”. ๐

2. Anonymous says:

Had to comment…yrs it is paramount that kids UNDERSTAND math strategies….however showing them and teaching them mnemonic devices if they struggle is just fine. Not all kids learn the same.Kids that don’t need them won’t use them…and yes I base this on 46 years of teaching 40 of which were with students with disabilities including 4 years with gifted kids.BTW…one of the best ways to determine students level of understanding is to have them do questions at a board (smart board or chalk) and explain what they did and why they did it!

1. Maggy Mathe Teacher says:

Thank you! My thoughts exactly! Plus, they will not be able to use base ten blocks on any kind of standardized testing! Using blocks and other strategies is a good place to start, but this has to transition to the algorithm. Absolutely, mnemonic devices are fine. (ROY G. BIV, Never Eat Soggy Waffles) These are not tricks, they are reminders. What a shame that we seemed to have lost the ability to relate to the students who do understand numbers in the traditional ways. I think the problem lies more in the todayโs young teachers and parents not understanding the algorithm, than with student ability to learn to use it. The group of students who historically presented low test scores, and caused the nation’s frenzy over โNo child left behindโ and standardized testing are now becoming teachers and having children, many of whom lack the depth of understanding to adequately present the subject matter to their students and children. Why is it that students even 6 years ago could understand and use the algorithm but todayโs kids cannot? Yet another example of the dumbing down of our society!

1. Donna Boucher says:

Of course the base ten blocks are a stepping stone! They help students understand the place value that is happening behind the standard algorithm. The problem with mnemonic devices is that it’s more stuff that students need to memorize without understanding. Understanding helps students make connections that allow them to retain what they learn more easily. Many students learned well when math was focused completely on memorizing procedures, but others didn’t. And research shows that students who learn through memorization score more poorly on international tests, because they can’t transfer that knowledge to new situations. It’s a balancing act for sure! It’s not one or the other, but a little of both. For more on the progression for learning multi-digit addition and subtraction, check out this post.

3. B3achHouse says:

I totally agree with you about grouping children for a deeper understanding of their knowledge but I’m having as lot of difficulty actually implementing this strategy. I have 33 children in my class this year. 1 of my boys is severely disabled and has a large wheelchair and a large desk for him to use. The classroom I have is wall-to-wall children! My wheelchair-bound child can only access a very limited area of the classroom and I am finding it extremely difficult to include him in any group activities. [I sometimes do some group activities when my boy is at our special ed block doing some intensive work but I feel quite guilty for not including him in all aspects of the class!] I don’t have anywhere in my room to accommodate a group which can include him! My take on group work at the moment is to allocate activities to the children simply sitting at their desks and race around seeing as many as I can. I use a checklist so I’m seeing a different group each time but I’m not really happy with this arrangement. Any suggestions please?? Jenny

1. TheElementary MathManiac says:

Hi Jenny,
It sounds like you have your hands full! I have never had 33 children in a classroom at once and can’t even begin to imagine what that is like. I think doing what you can to target small groups is the best you can do. Good luck!

Tara
The Math Maniac

4. Mrs. Labrum says:

I find I need to spend a lot of time teaching, or re teaching place value and number sense each year. As a third grade teacher for 28 years, I know how important this is for children to really understand the whys of math. My students work a long time on different ways to make a number, especially renaming a number. We learn that 300 is also 30 tens, so 305 has 30 tens and 5 ones, which makes it easy to change to 29 tens and 15 ones. After lots of hands-one with place value cubs, sticks, etc., it is so much easier to teach subtraction across a zero. I love the look on parents’ faces when they finally realize how easy it is with so much ” crossing out, make this a 10, cross it out make it a nine, ” etc. What a shocking revelation to them! Thanks for validating my thoughts.

5. Mrs. Aldred says:

I’ve struggled with small groups since I became a teacher four years ago. It was never taught in my program how to actually manage groups and there is always the question of “What is everyone else doing?” I imagine kids would be working on practice problems from the day’s lesson, but if I’m pulling small groups to work on other skills, they are never getting to practice the skills from that day. Does that make sense? Any thoughts?

1. Donna Boucher says:

Small group instruction is so powerful, but you’re not the first teacher (or the last!) to struggle with how to manage it. There are a couple of great resources for implementing a workshop type approach. The first is Guided Math: A Framework for Mathematics Instruction, by Laney Sammons. Another great one that has ideas for setting up and managing workstations as well as ideas for what to put in the workstations is Math Work Stations: Independent Learning You Can Count On, K-2 by Debbie Diller. Hope that helps some!

2. Valerie Baxter says:

The books that were mentioned in Math Coach’s reply are my staple! I also use a structure called BUILD that I found.

The best thing is you can modify it to fit your structure and needs. “I” for me is IXL on the computer. I do two rotations each day and so the students get to each center twice in a week. I keep the buddy games the same for the week and generally do the same with the manipulatives. The “L” is the students working on differentiated practice packets and then the “D” is meeting with me. Again.. you can fit it to meet your needs. My students LOVE BUILD time.

1. Donna Boucher says:

Thanks for the details about organizing math workshop, Valerie. I think the point you make about adapting the structure to fit your own individual needs is so important!

6. Fontenot's Firebreathers says:

I heard this but never used it!!! Knowb i have to remediate every year on subtraction and addition regrouping and i know our third grade team is fantastic it just does not stick with some kids. I also pull small groups but struggle with organization of it all. The accountability, etc. I

7. Anonymous says:

Hi Donna!
I could not agree with you more about teaching for conceptual understanding and NOT just tricks. I was wondering if you have ever used Cuisenaire rods with students before? They have different sized rods representing the digits 1-9. I just returned from an incredible Math course taught by a professor in MA and he used Cuisenaire rods to model every priority skill from Kindergarten up to high school algebra. It was incredibly powerful. For years I have used base-ten blocks with my 5th grade students. Many still needed remediation on subtraction with regrouping. It took a lot of time to trade the tens into ten ones and then combine with the ones already there. Prof. Sharma says that when we then try to figure out how many are there, we are counting. If we don’t progress them into thinking of the single digits as their own entity, they will will never progress from counting. This way, when the kids see the light green rod they immediately think of 3 and aren’t counting three ones. You can also use them to see how to decompose numbers and model addition and multiplication strategies. I am going to be the Math Specialist this year at two local elementary schools which is a new position for our district. My first priority is to get the money so that every classroom K-5 (and I believe up through high school) has a class set of these Cuisenaire rods. They are particularly valuable in showing the area model for multiplication. In the past, I would have the kids get out 12 ones cubes to show a 3×4 array. This way, you can just grab three of the four-rods or four of the three-rods. You can then easily put them on top of each other to model the commutative property. So amazing!!
๐ Ann Elise

1. Donna Boucher says:

Yes, Ann Elise, Cuisenaire rods are a great manipulative. Another very common use is for developing fraction concepts.

2. LoriLabrum says:

I, myself, have tried using cuisenaire rods and wish I could more. But I keep forgetting the value of each color. If I have a hard time, how can I expect a struggling child to remember? I agree we want them to get past counting, but many are not able. Those same children struggle with any type of memorization. I still use base ten blocks after 31 years of teaching.

1. Donna Boucher says:

Base ten blocks are essential!

2. Sherry Kopecky says:

I teach sped resource and that is so true. They will not remember or understand the different colors of the rods. They need base ten blocks.

8. Kerry Marshall says:

For me, when I saw “bigger bottom better borrow” I wanted to scream! ๐ Not because of all your great reasons, but because of the word BIGGER! Bigger should be reserved for measurement in my opinion, whereas GREATER should be used to compare numbers!
With my first graders, one of the first lessons I do is draw a 2 and an 8 on the board. I draw the 2 HUGE and the 8 very tiny. Then I ask “which is bigger? 2 or 8?” The kids get into a lively discussion we learn a valuable lesson! ๐

1. Donna Boucher says:

Nice point, Kerry! Great conversation for firsties! ๐

2. Karen says:

I do this too! Every year, multiple times. Language matters!!

9. Katie says:

LOVE this. I hate when kids break out their fingers for multiplying by 9. I made them put them away and figure it out based off of what they know (like multiplying by 10 and subtracting one group) but it’s what the 3rd grade teachers teach them to use (ugh!)

10. Mark says:

Have you seen the Nix the Tricks videos?

http://youtu.be/QxKUsN3UFh0

You mentioned base 10 blocks as a way to understand “regrouping”, but sometimes students don’t really see how close or far apart numbers are without visualizing or representing things on a number line!

11. KIm says:

Thank you for these posts. I’m a math coach and see and hear this everyday and it makes me crazy!!! The latest that I heard was “more on the floor, go next door!”

1. Donna Boucher says:

I’ve heard that one, too. Keep fighting the good fight!