Subtraction with Regrouping

I teach 2nd grade and my students also struggle with this new concept. What I have found to be successful is to tell them about "houses" and have them draw three houses in a row. We have the ones house, the tens house and the hundreds house, etc. Throughout the lesson, I refer to our "houses." I have to remind them that we always begin any math problems with the "ones" house.
The next way I help them visualize what we are doing is to think of the bottom number as the people, and the top number as the apples in a tree. This way they will be reminded to start at the bottom and look up to see the apples for correct subtraction. If there are not enough apples in the tree, they must go next door to the tens house and take one of the tens and add it to the apples to have enough for the people on the bottom. It is strange, I know, but it works for me! I hope this helps you.

Does your cooperating teacher have any connecting cubes (multi-link cubes) to use as a manipulative? Its a great way to show kids what the whole regrouping thing means. For example, build 90 (9 groups of ten) and then take away 42. The students will have to "break a ten" to get the 2 ones that they need to remove. Having a concrete example has really helped my students see the whole regrouping process. I also teach them to remember BBBB--bigger bottom (number), better borrow (from the tens). Its so hard to put this into words--if you could come to my classroom, it would be so much simpler! Good Luck!

I use a similar story to Jen's about going to your neighbor's who lives in the tens column.

We also learn this poem -

SUBTRACTION RHYME

More on top?
No need to stop!

More on the floor?
Go next door.
Get one ten.
That's ten ones more.

Numbers the same?
Zero's the game!

When we talk about whether we need to regroup or not, we refer to the poem. I also have them circle the larger number in the ones place, if they seem to have trouble knowing whether to regroup or not.

This is in resoponse to the student teacher looking for a fun way to teach subtraction and regrouping. In my classroom, I used twizlers as a ten model and mini marshmellows for the ones and demonstrated regrouping using the treats! The children loved it! They also enjoyed eating their math manipulatives at the end of the lesson! I hope this idea helps!!!

For the problem : 43-19, How much is 3-9? IMMMMMMPOSSIBLE! (The kids love shouting this, so they stay alert for times they can use it!) Go next door and take a ten (mark out the 4 and write a 3 above it), leave 3 behind. Bring home 10 to go with 3 (mark out 3, write a 13 above it)to make 13. How much is 13-9? 4 (write 4). How much is 3-1? 2

The most common mistake in regrouping in subtraction for my students are that they try to subtract the minuend from the subtrahend when the minuend is smaller (in the ones place). Amazingly, being able to shout IMMMMMMMMMPOSSIBLE! seemed to get their attention and solved the problem for most of them! (Aren't kids weird?!?!?)

One technique I have used is to have students play a game. This might be confusing so email me if I'm not clear and you are interested. I have students play a game called "In the land of ten" it's the opposite of the same game they play to "get" regrouping in addition. It's against the law of the land to have ten you must exchange.
I give the kids a mat you can make them quickly by drawing two vertical lines so have a ones, tens and hundrds column. (place value mats if you have them) Give them a green chip (bingo chip or piece of green 1 x 1 paper or a hundreds block whatever you have available. The students roll one die and need to remove that number. To remove a 6 they would need to first regroup to 10 tens and then exchange 10 ones for one of the blue chips. ( I use green for 100's like a dollar, blue for 10's like a dime and red for ones ...pennies. Students keep taking turns and removing the chips to correspond to the number that student rolls. The winner is the one that clears the mat first. Note every time a student must regroup the players say "time out". This technique sems to help kids "understand" what it means to regroup rather than just symbolic mumbo jumbo steps of crossing out and etc... You might want to play the reverse first ... start with empty mat add pennies or red chips or units for first rolls.... students first turn rolls a 6 adds 6 chips to ones, opponents turn then rolls a 5 puts 5 chips down then says time out then regroups and game continues...first to a hundred wins. Not subtraction but gets concept of regrouping down first. My kids love it hope yours will too.

I usually start with a game. I have already played this game the opposite way for addition with regrouping.
To subtract, divide children into small groups. One is the banker. Each group has a die. I don't know what materials you use, but I use multibase tens and units to start. You could use toy money, dimes and pennies. Give each child 50 cents in dimes. The idea of the game is to be left with no money. The child throws the die. If they throw a 3 for example they can get rid of three pennies but to do this they have to exchange a dime at the bank. They then give 3 pennies to the banker. The child to get rid of all their money first is the winner. Near the end of the game it gets very exciting as they have to throw the correct number to get rid of their last few pennies.This game gives them the idea of exchanging. I always do my subtracting in a practical way first. I think it is much better that children know the real reason for exchanging rather than stories. I learnt through a story and I hadn't a clue what I was doing. You can then advance the game to hundreds or dollars when you are ready.
Give them one dollar to start. This means they have no dimes or no pennies so they would have to do a double swap to subtract what they throw on the die. I hope you can understand this. I have started with this game with able and special needs children. They always seem to understand what they are doing because they can see when they have nothing. Good luck. Grace

I know that we don't teach regrouping as "borrowing" anymore, but I still teach my students a saying I heard from another teacher. "Bigger Bottom Better Borrow" Also, when crossing out in one column and regrouping to the next, my students had trouble remembering and understanding all the steps. So my students mark through the one and instead of crossing out the three and writing a 13 above it, write the one beside it to make the number thirteen.
13
- 6

I hope you can make sense of what I wrote. Nothing amazing just tried and true techniques. Just remember to be patient and be ready to reteach over and over until your students catch on. Good luck!

During student teaching, I cut strips of material, which almost any mom has on hand

I cut one color for hundreds, one for the tens, and a different color still for the ones - all of similar size.

I laid the strips in groupings across the floor, and did a hands-on activity. When I set up a problem, I showed how many strips were needed in each column. (Of course, I had to have plenty of strips on hand for each color to accommodate regrouping efforts.)

It was easier for some visual and tactile learners to see and experience, because they were able to associate color with columns, and the regrouping took place in front of their very eyes.

This is very similar, of course, to using cubes, but just a different twist.

Hope this helps. Let me know

When I introduce subtracting with zeros, I turn it into a story. For example, with the problem 701 - 286: We begin by looking at 1-6; it can't be done. So the number 1 goes to his next door neighbor, the zero, and asks to borrow 1. But zero says, "I don't have any, but I'll check with my neighbor." Zero goes to her neighbor 7, who happily gives one to zero. 7 loses 1 and becomes 6. 0 adds one right in front, so she becomes 10. Then 1 can borrow from 0, who is now really 10. 10 becomes 9, and 1 becomes 11 after putting the borrowed 1 right in front.
Then we go to 9-8, which can be done; then 6-2, which also can be done without regrouping. So all the neighbors are happy!

It's kind of corny, but the students are able to visualize going next door and getting something, so it's another way to learn for those who are not "math smart."

The Everyday Math Program has lots of neat ways to teach kids how to subtract, other than the traditional way. They are really good, especially for those students who just can't do the regrouping way without making errors. My favorite method is what I call the Elevator Method. I begin by telling the students my "elevator story." When you go into the hospital to have some surgery, you climb into the elevator and head UP to the surgery floor. You're pretty nervous, so this is a NEGATIVE THING. GOING UP IS NEGATIVE. However, when you get out of the hospital, you climb into the elevator and head DOWN. You're happy that the surgery went well and you are feeling POSITIVE. GOING DOWN IS POSITIVE. Now let's subtract with the problem 807 - 294. Write the problem down with the 294 under the 807. Don't look at individual numbers, but look at place values. We'll start with the hundreds column. We have 8 hundreds and 2 hundreds. 800 - 200 = 600. Write that down under the problem. Put a PLUS in front of it, because we subtracted going DOWN, and GOING DOWN IS POSITIVE. Now look at the tens column. We have 0 tens and 9 tens. 90 - 0 = 90. Write that down under the 600, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at the ones column. We have 4 ones and 7 ones. 7-4=3. Write that down under the 90, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at what we wrote down: +600, -90, -3. 600-90=510 (mental math, counting by tens backward if needed). 510-3=507. 507 is the answer. No regrouping necessary, and students can learn to do this really, really quickly!
Wow! I hope that helps!

Last year when my third graders didn't understand the concept my husband suggested that I use Cheetoes (which represented 10) and soup crackers (which represented ones).

The first day we went over the pages in our book, then I passed out the food. I would ask students to show me thirty five or fourty two. After we did that for a couple of minutes I asked them to trade in a ten for ten ones...we did that for a few minutes then they would show me two numbers. We did this until we worked our way up to using the food to subtract and regroup.

It helped a great deal, but I did still have a few that "didn't get it" until later.

Hope this helped!

When I teach this to my 2nd graders, I get them all around me where they can see. I don't use the board--this is special math (little do they know it's because it's so hard for them to grasp). I use a MagnaDoodle to write on. Taking them out of their element makes them really pay attention because they aren't sure what you're up to and they don't want to miss ANYTHING! I draw boxes around each column so we make sure we line up the tens and ones. We have the Ones family and the Tens family. The number at the top of each column is how many people live in that house. I even draw a tiny roof on top of each "house". The bottom number is how many people are leaving the house to go where ever. We physically hold the numbers up with our fingers and if we don't have enough kids we go next door to the Tens house. We really knock on the door and ask if we can borrow one of the kids. We "leave them a note" (cross out and write the new number)of how many kids they have left (we wouldn't want them to worry!) We take the new kid over and put him with the Ones family. We can't add him to our family because he doesn't have the same name. He just sits beside us. Now we have enough kids to borrow.

This may sound silly, but I've done it for 3 years and the kids really relate to it. The ones who get it which is most of the class have fun working with the very few who need extra help. Good luck. This really is a hard concept.

Using MONEY, I believe, is the only way the students really comprehend regrouping. Using a pennies (ones) and dimes (tens) mat. 43-28:
They see there are only 3 pennies and can not take 8 away. They totally relate to 10 pennies being equal to 1 dime, so making this "trade" is within their realm of thinking. Now they see the 13 pennies and there are only 3 dimes left to take the two away. I taught second grade the past two years and ALL of them grasped this concept. We used the money for an entire week and VERY gradually moved to paper pencil. Good Luck!!

I play a game with my students called "sticks and stones". They each have a game mat which is a sheet of paper divided into three columns. The columns are listed (ones, tens and hundreds). They play in groups of twos. Each group has a spinner, a good supply of unifix cubes or snap together cubes and their mat. One child spins the spinner and puts that many cubes in his ones column. On his next spin, if he has enough (10 cubes) to make a stick he will snap them together and put them in the tens column with the others left over in the ones column. The winner is the child with the largest number at the end. This has really helped my students understand the concept of regrouping to make a ten.

I also use the daily straw count with my calendar. This is where you add a straw in the ones cup for each day and when you get ten straws you make a bundle of ten and that bundle goes in to the tens cup.

I bought some receipt pads like those used in diners for a dinner ticket. Then I made a menu using 2 digit numbers. One side of the menu lists sandwiches and the other side lists beverage choices. I give students a total amount of money to spend and they write their own menu ticket and then add to find their total and subtract to find their change. My studetns always enjoy this activity.

I too use houses to help the children visualize regrouping. However, I name the houses OTTO ONES, TAMMY TENS, and HARRY HUNDREDS. They know if Otto does not have enough hotdogs to feed his friends he needs to go to the house next door (Tammy's) and borrow a pack of ten. This has really helped the children to understand the idea of borrowing.

I use boxes of fruit roll-ups (ten in a box)and some individual roll-ups to show that if you don't have enough singles(ones place), you have to open a box(tens place) and take ten out. They can then see why the ones place has increased by ten and seeing the number of full boxes tells them how many groups of ten are left.

I currently teach 2nd grade bilingual and after I explained and did these examples my kids totally got it!

Let's say you have 36
- 18
______

look in the one's column. you have 6 and I want 8. can you give me 8? NO, you only have six, so you walk over to your neighbor's house (3). BUT!! your neighbor only shops at Sams club and buys things in groups of ten. he will never give you only four or six! ONLY A GROUP OF TEN!!!! so you borrow 1 group of ten from your neighbor. so now you have 16 and your neighbor only has 2 groups of 10.
Make sure when you are telling them this to tell them that your neighbor does not like to share and will not give you more than 1 group of ten.
after my kids got the concept of "walking to your neighbors" then I added in the words regrouping and borrowing.

I have another example for regrouping with 3 digits and a zero in the middle.

jen

We start off using dimes and pennies to subtract and borrow. My 2nd graders love the idea of Mr. Dime's house and Mr. Penny's house. We look at Mr. Penny's house and see that he does not have enough children to do the work at his house. With 72-48, we see that he has 2 children and needs more. We "walk over" to Mr. Dime's house and ask if we can borrow one of his kids. We have to mark out the 7 and put a 6 so he knows that we borrowed one of his kids...we wouldn't want him to worry! We put his kid in front of our 2 kids and we have 12 (we have already learned earlier in the year about adding dimes and pennies, so I don't have to say a dime = 10 pennies andd 10 +2 =12). Now we can do those 8 chores. We finish the math problem with ease. I also teach them how to add back up and check the answer to make sure it is right. That is just part of how we subtract and I expect it to be done on every problem.

I hope this is clear. My kids really like this way and I have done it for 3 years now. Of course we do TONS of problems and TONS of modeling! Good luck!