THE OTHER LONG DIVISION
Posted by: HEIDI
My kids loved the division rap... because I tried to sing it and really hammed it up for them with one kid making rap sounds. Then they practiced it several times. Now out of the blue if I ask the steps of division, they sing me the chorus... even though we did it weeks ago!
Are you teaching long division the old way we all learned? There is another newer way that seems to provide that AHA! moment for kids who just don't grasp the other method. I'll try to explain but you can e-mail me for a MS Word document that will probably convey it better!
For example 234 divided by 8. Get students to use the math facts they know. Their goal is simply to use up "chunks" of the 234 until there are no chunks left. They must record each thing they do. Read on to see... I know 8 x 10 is 80, so I can subtract 80 under the dividing problem to show that I've used up 80. I don't write an answer on top yet, but I do put (8 x 10) in brackets over to the right beside my problem to keep track of it. This will be important later on.
Now I have just 154 left to "use up". So I know I can do 8 x 10 again and subtract another 80. That leaves me with just 74 now to use up. Well, I'll do 8 x 5 and subtract 40. So now I have just 34 of the original 234 to figure out. I know that 8x3 is 24 so I can subtract that from the 34. Now I just have 10 remaining. So I will say 8x1 and subtract 8 from the 10. Now I only have 2 remaining and that can't be divided by 8 so it must be a remainder. But I still don't have an answer. Did you notice that every times question I used started with 8? That's becuase the divisor was 8, so I have to use that all the way through. Look at the list of multiplying I did. Ignore the 8 number but use the other number from each question. Add them up and that is your answer that you write on top of the problem. Placement doesn't matter using this method because puttin it in the wrong spot won't mess up your work. So I figure 10+10+5+3+1=29 Check my math the old way... I hope it matches up!
Kids understand this method and it is just as valid as our other method. In fact, in my province, I have to teach both!
Posted by: sandy
I don't know if these ideas will help, but they worked for me in the past...I try to get the kids to think of expanded form when we're doing division. Ex. 358=300+50+8 Then we talk about how we are going to deal with one part at a time, so if I have 358 div. by 3, first I'm going to look at how many 3s are in the 3 hundreds, then in the tens, then in the ones. Sometimes I've even used graph paper to help them keep everything lined up.
Also, to get them to remember and apply the steps of division (div. mult. subt. check, bring down) I teach them a mnemonic to help them. We use "Does McDonalds Sell Cheese Burgers?" It's something they'll remember, and it has worked pretty well.
I don't know what I'll be doing to teach division this year, since we've moved into Saxon.
Posted by: kat
This is so hard, but once they get it the expressions on their faces is worth every painful hour you've spent working on it. I too was feeling overwhelmed with this, but just kept doing it over and over again. Finally they got it and I give them a few problems every day to keep practicing. It's a great settling activity as we switch classes.
The one thing I did that really helped was I put the letters DMSCB on the board with the phrase "does McDonalds Serve Cheese Burgers", so they would remember it. I explained what each letter stood for and MADE them write it on every paper with long division. It really helped too to have them use this and go back and find where they got lost. Oh! This is what the letters stood for:
D--Divide, M--multiply, S--subtract, C--compare(is answer after subtraction smaller than the dividend?) B--bring down the next digit. Repeat steps until all numbers have been brought down. By having them check for the mistakes it reinforced the order of the steps and soon the trips to my desk or the hands going up ceased! Keep working hard, they will get it!
Long Division Cheer/Chant
Posted by: luv2learn
I actually taught the students a cheer/chant for long division. We all stand up and using our hands chant, "Divide, Multiply, Subtract, Bring it Down". We use our hands to make a divide symbol with our fists being on either side of our head making the dots... then our hands with an X shape....then hands togeher to show subtract (-)....finally we make a jazzy bring it down motion. We would chant this a few times before each math lesson and while we worked on any long division math problems. I would see the kids teaching the chant to other classes during recess and chanting it during down time.
Hope this all makes sense...my kids loved it and I would see them making the motions and mouthing the words to this chant during tests and worksheets.
Posted by: BN
I show the students compatible numbers for division. I also show them a simple rounding/estimating process.Which is basically the same thing you are doing but it may be a little easier for the students to see the estimated number.
Round one place.
(I tell them to cover one place number in the divisor and one in the dividend.)
362/51 Simple round to 36/5
What number multiplied by 5 will give you a number close to 36? 7 5x7=35
Multiply 7 times the divisor 7x51=357.
(The answer may be too small in that case go up one number or too big go down one number.)
It's easier for the students because they can see the basic multiplication facts.
I know this is basically the same process you are showing them but for some 360/50 is difficult. 36/5 is easier.
I do this on the overhead and put my fingers over the numbers.I have the students put their fingers over the numbers in the divisor and dividend on their papers.
I also put up a big grid with the multipication facts. Even though most students know the facts it helps them during this process.There are many steps in the long division process and they get confused.Looking at the facts charts helps them estimate the right number. After we have practiced for a few days I put the grid away.
Ms. Math's way
Posted by: kiasun711
A few years ago we had an in-service with Ms. Math. At first I thought it was hard, but when I tried it I found out I liked it a lot more! I know it is hard to understand without seeing it done, but here is what I send home to explain to parents:
This year my math class is learning an alternate way to do long division. This is different then the divide, multiply, subtract, bring down, repeat sequence that you and I most likely learned. I refer to that way as the traditional method. This alternative way, when understood, helps students master place value, and number sense, as well as what division actually is.
1- Ask how many groups of 4 can be pulled out of 573?
(Students should try to start with the largest place value
and multiples of 10, but they do not have to)
I know that 100 groups of 4 can be taken out of 573.
2- Ask how many did I actually take out?
100 groups of 4 means 100 x 4 which equals 400.
3- Subtract the removed amount from the whole group.
4- Since the difference is still more then the divisor the pattern continues
5- Ask how many groups of 4 can be pulled out of 173?
I know that 40 groups of 4 is equal to 160 so I will take that out next.
6- Subtract the removed amount from the whole group.
7- The difference is still more then the divisor so we keep going.
8- How many groups of 4 can be taken out of 13?
I know that 3 groups of 4 is 12 and that is very close to 13
9- Subtract the removed amount from the whole group.
10-The difference is now less then the divisor so I circle it because it is my remainder
11- Add up all the groups that I took out
100+40+3= 143 with my remainder of 1, so my final quotient is 143R1.
12-Check by multiplying.
143 x 4= 572 + 1= 573
Posted by: Karen
We use an acronym, but we also use graph paper to keep our digits straight. The students take a piece of white paper and cover all digits "inside the house" except the 1 or 2 digits that they are dividing into. We draw an arrow to pull down the number we are bringing down so they can actually follow where it is being brought down to. This seems to help. Hope I've made sense.
Get out the manipulatives!
Posted by: lv2read
My students struggled with this as well. I used base ten blocks, tiles, coins and cookies. (Yeah, I broke down to the food element.) Ask the students to help you figure out how many containers, boxes, etc you will need for x amount of cookies. Tell the students that 4, 6 or 8 will fit in one container. The students will more than likely begin creating groups of 4, 6 or 8 until all the cookies are in a group. This lesson was one of our grades' concept lessons. The students loved it. The cookies were an incentive but they grasped the concept. This lesson also works well with remainders too and long division.
Be sure that the students know that each group has to have equal amounts.
Does McDonald's Serve Cheese Burgers?
Posted by: jph
I have a small banner with the question: "Does McDonald's Serve Cheese Burgers?" (Divide, Multiply, Subtract, Check, Bring down)
It's easy to remember and the kids love shouting it out when we have a division problem. If they know their multiplication facts and know the steps above, maybe division will be easier for them. Good luck!
Posted by: Jump4Joy
We always use "Dad, Mom, Sis and Brother" to teach the process for long division. If you want to add "cousin" after sis you could do that to remind them to compare their subtraction answer with the divisor. I also recommend using graph paper as a way to help them line up the digits properly. Sometimes it helps to show them what happens when you line up the digits incorrectly so you can show them the absudity of the answer. Otherwise, it takes a lot of practice and reinforcement. After you move on to some other skill, revisit division on a regular basis, even if it's just a few problems per week. It's amazing how fast they forget when they don't really learn it well. Be patient!!
Make it personal
Posted by: dlynneteacher
I think math should still be concrete even in the fourth grade. I am going to assume your fourth grader is not learning disabled, but instead just does not "catch on" as fast as the other students.
I think you should make it personal for him. Use lots and lots of manipulatives-no I am not telling you to run to the teacher's store and buy a bunch of expensive stuff. Use what is handy.
Have him divide pencils, utensils, paint cans for members of the family (immediate and extended for more numbers). This becomes practice when it is repeated as opposed to mindless numbers that he gets frustrated over because he can't remember how to manipulate them.
Another thing you can do to make it personal is to find out-if you don't already know-what he wants to be when he grows up or what he is interested in. There are numbers in everything.
Even if he wants to be a rock star-"make up" problems for him-your latest CD sells for $968. To make the CD, you had 8 people in total working on it, if all of you get an equal share of the money, how much does each person get?
Have him think in personal terms when he is doing homework-with each problem, that way it is not just mindless drill and kill!
I am sorry this is so long but I hope it has given you some ideas. Best of luck!
Posted by: Combow
I have my 4th graders make a multiples list on the side of the problem using the divisor. Then then can refer to it as they do the long division problem. It helps the student who doesn't have the facts down, but can work on the division process. Once upon a time I viewed a video called "Divide and Conquer" which was about teaching division using multiple intelligences and teaching it all in one day. I have tried to get my hands on it since then but apparently it's not available. If anyone knows where I can get it please let me know. Good Luck with long division.
Posted by: dryerasedusty
One of my colleagues has, for the past 2 years, done this to introduce long division -
She starts by using only one divisor each day. For instance today we are dividing only by the number 2. Tomorrow it will be by 3. The next day only by 4 and so on. She lists all the facts for that particular divisor and has the students copy them so they have them right there in black and white. She says her students have made such progress in understanding division using this simple approach. I'm going to try it this year.
Posted by: morahsharon
Have you tried using the repeated subtraction metod?
54 divided by 7
Count how many times you subtracted 7 and what is left over is the remainder.7r5
An old-fashioned way to divide
Posted by: jeanmarie
I've been teaching a very long time. We're using EM and some of the ways they attempt to teach kids end up confusing them PLUS they have too many methods to choose from and master none of them. All of mine learn to long divide like this: (if they can't master it THEN I try another method)
We set the problem up and first discuss that when we say 1349 divided by 62, the 62 goes OUTSIDE the bracket (yep - gotta start small) We proceed one digit at a time - I even cover them as we go)
We ask ourselves - will 62 go into 1 - no- so we put a small X above that place to show that we won't have a 4 digit answer. (My kids don't line things up well so sometimes we turn the notebook paper sideways so they have columns)
Then we move over and ask ourselves if 62 will go into 13 - no - so we put another small x above the 3.
Then we move over and ask ourselves if 62 will go into 134 -yes - so we put a small line above the 4 and the 9 to let us know we will have a 2 digit answer. (and no more!) We also estimate at this point. We ask ourselves how many times a 6 will go into a 13 (or 60 into 134). That would be twice so we put a 2 on the line above the 4 and stick a zero on the line above the 9. Our estimate is 20. This estimate is written at least 1 finger's space above where we will put the answer, NOT right on top of the problem (Heaven knows we wouldn't want to have to rewrite the things)
Now we are ready to solve the problem. We go back to our estimate of 2 and take 2 times 62 to get 124. This goes under the 134 (We do NOT put a zero under that 9. In fact, I even hold a finger over the nine or use a sticky note to cover it for now. 134 divided by 62 looks so much easier, don't you think?) We then subtract 124 from 134 to get 10.
Now we draw an arrow to bring the 9 down so it lines up to make 109. Our established rule is that if we draw an arrow, we have to put a number in the answer. Otherwise, mine forget to put zeroes in.
Now we go thru our steps again. How many times will 6 go into 10 (or 62 into 109) and the answer is 1. The 1 goes in our answer above the 9 which fills our 2-digit answer spaces. We multiply 1 times 62. Put that under 109 and subtract to get 47.
We double check. Is 47 smaller than 62? If so, do we have any more numbers to bring down? If not, are all of our answer spaces filled? If so, we are done. Any remainder is then brought up to the answer. We look up at our original estimate to see if we're close.
Then we check our problem by multiplying which reinforces multiplication skills AND means they never have to miss a division problem. My kids pretty much ace division tests. They can also do huge numbers if we go one digit at a time.
When we divide decimal numbers, we follow the exact same procedure and then move the decimal up. Mine do not generally divide BY a decimal - we just can't get everything in 1 year.
We've had major discussions as teachers on all the whys and whatfors of the process, but when mine need to perform on those tests, they'll nail division. What they miss is the multiplication - go figure.
Hope this is sort of clear, but if you work it thru as I presented it, I think you'll see it. When we do these, I draw student teacher's to go to the board to model and "talk" us thru the process. I also have a large chart on the wall of the steps: determine digits in the answer; estimate; 1. divide, 2. multiply, 3. subtract, 4. bring down the next number - repeat from divide step.
To reinforce the steps -- you can do a relay?
Posted by: Margaret916
We do this with our kids to make them focus on one step at a time, without skipping!
The kids sit in a row. Kids are in first, second, third position and so on. First kid does the "goes into" step, passes white board or paper back, second kid does the multiply, passes it back, and so on.
One thing to stress is SPEED DOESN"T COUNT. Each team that finishes with a neat, correct answer, gets a point. Usually (hopefully!) it works to a tie.
It's just a different way to do the problems....
One thing that helps is that I have the white boards with the graphing grid on the back, so the kids write a number in each box if they have writing in a line issues.
Pennies on a Plate
Posted by: Read 4 Fun
I introduce 2-3 fact families per week. I repeat the same process for introducing the different math facts so the students become very familiar with the process of multiplication and division.
I make kits for every 2 students in my class. The kit consists of 10 - 6” paper plates and 100 pennies stored in a quart plastic baggie. (Although, you can use anything that is small such as sunflower seeds, beans, etc.)
1. I give the students a problem.
2. The students take out the number of pennies to represent the dividend and take the number of plates to represent the divisor.
3. I then have them equally divide the pennies out on the plates.
4. Any pennies left over would then be the remainder (I do not begin with problems with remainders).
5. I then have them record the facts in written form.
6. After the students have explored with this activity they begin to really understand the process.
It takes 5-6 weeks to introduce all of the fact families. I focus on the same facts for the week. Although, at the end of the week I have also taught them how to multiply a two digit number by a one digit number, how to solve long division problems, how to convert a whole number into an improper fraction, convert an improper fraction to a whole number, along with the basic multiplication and division facts.
I hope you understand my explanation.
Posted by: NCteacher
The Maharaja's Tasks is a must! It is a kinisthetic way of teaching beginning division. If you google it, I am sure that you can find the program for purchase. Here is one of the initial activities:
1.) Rope off an area of your room and post a sign "Holding Pen"
2.) Give the kids one minute to think of an animal that lives in the jungle.
3.) Have them start moving silently around the room the way their animal would move.
4.) You call out, "Make groups of ___"
5.) The kids must for a group of that number, and immediately sit down.
6.)The kids who can't be in a group go into the holding pen as the "remainder"
7.) On chart paper, record the division problem as a number sentence and as ___ groups of ____ with a remainder of ____.
8.) Continue playing- it is a great time to get the kids to discover that the remainder can never be bigger than or equal to the number of "animals" in a group.
9.) As a challenge, you can tell the kids how many groups you want- they have to figure out how many kids are in each group.
I have used this for 5 years to teach division and it is fantastic. You can make it as difficult or simple as you want. It looks great for an observation, since you are addressing a couple of different learning styles and 100% of the kids will be engaged and learning. Good luck!