Long division woes!

Join Teachers.Net

Chatboards

Recent Groups

Upper Elementary

MEMBERS

0 Members

+ Join Group

Pinned Posts

ALLAll Teachers

Teachers.Net LIVE CHAT Support group - Tues eve!

Featured Jobs

Full-timeMontessori Teacher

Maple Ridge, British Columbia, Canada

TemporaryTeachers, rural schools

Peace River North School District

Full-timeHead Teacher: 2nd/3rd Grades – Mills College Children’s School

Mills College

Teaching Jobs on Teachers.Net

Featured Job special only $39!

https://teachers.net/jobs

Become a Teachers.Net sponsor!

Upper Elementary Teachers Chatboard

Long division woes!

by Cheryl

Mar 24, 2009

Help! I am a 5th grade teacher and need help reaching one of my students in the area of long division. He cannot complete a long division problem. He forgets the steps (even when there is a list of steps right beside him). He gets multiplication and division confused, doesn't know his multiplication facts, so I have resorted to a multiplication chart which is successful for multiplication, but not with division. His subtraction is weak and often doesn't realize when he needs to borrow. I have tried color coding each step for him, but it's more work for him to remember colors and remember when to switch them. He was getting special services, but mom pulled the plug and now the little guy has nothing to fall back on. He is a very visual learner. Does anyone have any tricks different from conventional methods of teaching long division? Cheryl

Comment

(8)

report post

view previous comments

from Cheryl to Donna Unfortunately, mom is in complete denial. He is supposed to have a tutor, but mom uses excuses of why he does not see the tutor (I think there really isn't one). He also needs help clear across the board...math is just the tip of the iceberg. I send home extra work, and it comes back done, but I can tell that someone fed him the answers at home bec...See More

Mar 26, 2009

report post

Adrienne This student is certainly in trouble! The best thing would be to back up and get him solid on the prerequisite skills for division. If you can't and you must teach him division now, then let's dissect the problem and look at it one step at a time.

1. The student doesn't understand the difference between multiplication and division. This i...See MoreThis student is certainly in trouble! The best thing would be to back up and get him solid on the prerequisite skills for division. If you can't and you must teach him division now, then let's dissect the problem and look at it one step at a time.

1. The student doesn't understand the difference between multiplication and division. This is the root of the problem. Work with manipulatives and the same fact family (6x2, 2x6, 12/6 (of course use other symbol for division), 12/2.) to help him practice and understand the relationship. Although students may not be able to choose the correct operation for a situation/word problem, they should be able to use manipulatives to show division and multiplication. In addition, have him manipulate post-it notes with 2, 6, and 12 each written on one post-it note and symbols in between to show the relationship between mult. and division.

2. The student doesn't know facts. The multiplication chart can actually be used for division. The student just has to understand how it is organized so he can quickly find the dividend and work from there. You could start a math fact program to help him learn his math facts. Until he knows them, he can use the chart. Introduce one fact family at a time and build on that one, keeping all math fact family cards in the review pile so he doesn't forget them. I usually start teaching a fact family by using the What's Missing Game. Use post it notes 2, 6, 12 to show him that math facts are just like phone numbers, they are numbers that go together. (Don't include symbols at this point.) Have him close his eyes and take one post-it note away. Ask him to tell you which one is missing and why (The 2 is missing because 2 times 6 equals 12 or a student could say because 12 divided by 6 equals 2.) Switch the order of the post-it notes some of the time, so that he sees the bigger number first. Then I write the math fact very large on the board, in shaving cream etc. and have the student trace over it several times while saying the entire fact. (The speaking while tracing is critical.) Then I create a flashcard for each of the facts, writing the math fact one one side of an index card and the math fact including the answer on the other side of the card. The student practices the cards each day, saying the entire math fact before stating the answer. I explain why saying the entire math fact is important by asking the student to tell me the last four digits of his phone number. After the student tells me, I ask the student how they figured it out. The student usually says that he started from the beginning of the phone number. I explain that he has memorized the phone number as a chunk and that is exactly what I what him to do with the math facts.

3. The student doesn't know how to borrow. Until the student does know how to borrow, he/she is going to either have to use a calculator or you can only give him problems that don't require borrowing. (I actually prefer the latter, even though it will be more work for you.) Teaching when to borrow is sometimes easier for the student if the student says "I have" before subtracting.

For instance: 47 -38 ___

I have 7 can I take away 8. (Or, if he could say, I have 7 balloons, can I take away 8 balloons?)If he doesn't understand this, then you will need to go way back in subtraction.

4. The student doesn't know where to put the number. He will need to go back to more simple problems. Begin with problems (with known math facts) such as 13 / 4 and have him use manipulatives as he does the problem. (The best thing to do is teach division using math facts that he already knows. It will be much less confusing to him because only one thing,the division process, will be new for him. You will have to make up your own problems, but it will pay off.) If he is still having trouble deciding where to put the numbers, have him only do the first step of the problems for a day or so.(Putting the 3 at the top of 13/4.) Have him ask aloud while pointing to the empty space, the divisor and the dividend, "What (point to blank space) times 4 (point to the divisor) is close to 13 (point to the dividend) without going over.

The next day (or after more than one day), review the first step and then add this second step, continuing to have him also use the manipulatives - He should touch the 3 and the 4 with his pencil while saying 3 times 4 equals 12 aloud. He should then write the 12 in the proper space.

The next day (or after more than one day) add one more step. Be sure that he points and talks aloud as he does each step. (He should say, "Subtract, make sure it is lower, write the remainder at the top." while doing these steps.)

On 3/25/09, Cheryl wrote: > Thanks for responding,Kat. He does know the steps of D,M,S,C,B, > but doesn't understand what to do at that step. In other words, > if we have 324/4, he doesn't understand how to transfer to the > next step. He'll divide 32/4 and get 8, but doesn't remember > whether to put it on top, or underneath and then if he puts the > answer on top, doesn't remember to "fall off the cliff and > multiply". I just don't know how to reach him. I have tried > showing him that the process goes in a circle, but nothing is > clicking with him. Even the multiplication chart is confusing to > him to use for division. His mind can't seem to flip from one > operation to another. > Cheryl

Mar 26, 2009

report post

Cheryl to Adrienne Thanks Adrienne. I'll definately try the post it notes!

Mar 26, 2009

report post

I don't see where you'd have her explain to him what is division. Determine how many groups of a number are in another number. How many groups of 4 are there in 13? Manipulatives can be used. First, make a story problem that the student understands. When subtracting, students can count up or count back. Instead of just using algorithms, students need to unders...See Morewhere you'd have her explain to him what is division. Determine how many groups of a number are in another number. How many groups of 4 are there in 13? Manipulatives can be used. First, make a story problem that the student understands. When subtracting, students can count up or count back. Instead of just using algorithms, students need to understand what they're doing. 768-47. 47+3=50, 50+50=100, 100+668=768. You've used 3=50=668=721. Or think 47 and count up to 68, which is 21, so now you have your 68 and just add 700 to it, which is 721. 1000-648. There's no need to subtract across all those zeros. Just BORROW 1 from 1000 making it 999, then subtract 648.

999 -648 = 351

Don't forget to give back the 1 you borrowed, thus, the answer is 352 instead of 351.

In your example 47 -38 Simply add 1 to the 47 making it 48, then subtract 38 from the 48, and don't forget to take back the 1, which would be 9.

497 x 36. Start by multiplying 497 x 10. Do that 3 times. then do 497 x 5 which would be half of 497 x 10. Finally, do 497 x 1. Add all the products.

497 x 10 = 4970 497 x 10 = 4970 497 x 10 = 4970 497 x 5 = 2485 497 x 1 = 497 = 17,892

Teach students to use the distributive property to break apart numbers. Children need to understand what they're doing, then they can come up with their own strategies to solve problems, afterwhich, algorithms will make more sense.

On 3/26/09, Adrienne wrote: > This student is certainly in trouble! The best thing would be to back > up and get him solid on the prerequisite skills for division. If you > can't and you must teach him division now, then let's dissect the > problem and look at it one step at a time. > > 1. The student doesn't understand the difference between > multiplication and division. This is the root of the problem. Work > with manipulatives and the same fact family (6x2, 2x6, 12/6 (of > course use other symbol for division), 12/2.) to help him practice > and understand the relationship. Although students may not be able to > choose the correct operation for a situation/word problem, they > should be able to use manipulatives to show division and > multiplication. In addition, have him manipulate post-it notes with > 2, 6, and 12 each written on one post-it note and symbols in between > to show the relationship between mult. and division. > > 2. The student doesn't know facts. The multiplication chart can > actually be used for division. The student just has to understand how > it is organized so he can quickly find the dividend and work from > there. You could start a math fact program to help him learn his math > facts. Until he knows them, he can use the chart. Introduce one fact > family at a time and build on that one, keeping all math fact family > cards in the review pile so he doesn't forget them. I usually start > teaching a fact family by using the What's Missing Game. Use post it > notes 2, 6, 12 to show him that math facts are just like phone > numbers, they are numbers that go together. (Don't include symbols at > this point.) Have him close his eyes and take one post-it note away. > Ask him to tell you which one is missing and why (The 2 is missing > because 2 times 6 equals 12 or a student could say because 12 divided > by 6 equals 2.) Switch the order of the post-it notes some of the > time, so that he sees the bigger number first. Then I write the math > fact very large on the board, in shaving cream etc. and have the > student trace over it several times while saying the entire fact. > (The speaking while tracing is critical.) Then I create a flashcard > for each of the facts, writing the math fact one one side of an index > card and the math fact including the answer on the other side of the > card. The student practices the cards each day, saying the entire > math fact before stating the answer. I explain why saying the entire > math fact is important by asking the student to tell me the last four > digits of his phone number. After the student tells me, I ask the > student how they figured it out. The student usually says that he > started from the beginning of the phone number. I explain that he has > memorized the phone number as a chunk and that is exactly what I what > him to do with the math facts. > > 3. The student doesn't know how to borrow. Until the student does > know how to borrow, he/she is going to either have to use a > calculator or you can only give him problems that don't require > borrowing. (I actually prefer the latter, even though it will be more > work for you.) Teaching when to borrow is sometimes easier for the > student if the student says "I have" before subtracting. > > For instance: > 47 > -38 > ___ > > I have 7 can I take away 8. (Or, if he could say, I have 7 balloons, > can I take away 8 balloons?)If he doesn't understand this, then you > will need to go way back in subtraction. > > 4. The student doesn't know where to put the number. He will need to > go back to more simple problems. Begin with problems (with known math > facts) such as 13 / 4 and have him use manipulatives as he does the > problem. (The best thing to do is teach division using math facts > that he already knows. It will be much less confusing to him because > only one thing,the division process, will be new for him. You will > have to make up your own problems, but it will pay off.) If he is > still having trouble deciding where to put the numbers, have him only > do the first step of the problems for a day or so.(Putting the 3 at > the top of 13/4.) Have him ask aloud while pointing to the empty > space, the divisor and the dividend, "What (point to blank space) > times 4 (point to the divisor) is close to 13 (point to the dividend) > without going over. > > The next day (or after more than one day), review the first step and > then add this second step, continuing to have him also use the > manipulatives - He should touch the 3 and the 4 with his pencil while > saying 3 times 4 equals 12 aloud. He should then write the 12 in the > proper space. > > The next day (or after more than one day) add one more step. Be sure > that he points and talks aloud as he does each step. (He should say, > "Subtract, make sure it is lower, write the remainder at the top." > while doing these steps.) > > On 3/25/09, Cheryl wrote: >> Thanks for responding,Kat. He does know the steps of D,M,S,C,B, >> but doesn't understand what to do at that step. In other words, >> if we have 324/4, he doesn't understand how to transfer to the >> next step. He'll divide 32/4 and get 8, but doesn't remember >> whether to put it on top, or underneath and then if he puts the >> answer on top, doesn't remember to "fall off the cliff and >> multiply". I just don't know how to reach him. I have tried >> showing him that the process goes in a circle, but nothing is >> clicking with him. Even the multiplication chart is confusing to >> him to use for division. His mind can't seem to flip from one >> operation to another. >> Cheryl

Mar 27, 2009

report post

Adrienne I just want to clarify something. When I mentioned in my post to break down the division steps,it's important for a child to do about 15 problems (or maybe more)doing that step so that it becomes automatic. The student may even have to spend more than one day practicing problems before you add an additional step. When you do add an additional step ...See More

Mar 28, 2009

report post