Why do kids hit a wall with division?

[Alana in Canada]

We were going along tickety-boo (Singapore 3A) and then BAM.

 

He can divide in his head--but get him to do something like 46 divided by 3. I can put the 1 on top of the line, but he cries out "I'm confused" right when I start writing a 3 under the 4.

 

What are we missing?

 

 

I hope that made sense?

TIA

[Beth in Central TX]

Division requires a lot of coordination, and you have to know all of the math facts because it involves multiplication and subtraction. You have to line up numbers above the line and below the line properly. You have to mutliple, then subtract, and then bring down the correct number before you multiple again. There's a lot going on that requires great focus. Division was by far the hardest math skill for my older boys to learn. Graph paper definitely helps.

 

For your son, just keep modeling the division process and tell him what you are doing. We did a lot of whiteboard work on division. I even had them mirror what I was writing as we worked through long division problems. I would write the problem on one side of the board and talk through what I was doing. My son would copy what I was writing on the other side of the board and repeat what I said. This process was more difficult for my middle son, and it took a long time for it to finally sink in.

[BusyBee]

My oldest child's favorite subject was Math until he hit division. All of a sudden we had tears and confusion and at times Mommy lost her patience. We stopped math for a while to work on Multiplication Facts workbooks and Division workbooks (which we bought at our local Wal-Mart and K-Mart). I also made up division and multiplication card games. He loved this. This worked well and he was soon back to Math as usual.

[Tammyla]

Both my kids were stressed the first day or two with long division. Once they memorize the steps, it becomes simple according to my two. I do remember seeing a few tears. It just takes time to pull all those skills together.

[Mom2boys]

My ds10 recently hit the same wall with long division. I had to set it aside and move on to fractions. I think it is because he is still a very concrete thinker. We'll revisit division in a few months, and keep trying every few months, until he is able to handle it. Other moms of boys have told me their sons made the leap to more abstract thinking at age 11.

[Alana in Canada]

Thank you all.

 

Last week he was calling himself a "math genius"--today he's hitting his head against the wall.

 

I "made up" some simple problems and gave them to him on graph paper.

He's doing well, but it really is a stretch for him.

 

We really do have to get those multiplication tables down!

[LisaKinVA]

There are a lot of steps... and for the first REAL time, showing all of their work is very important.

 

Pull out the grid paper (graph paper) and go slow. This one takes repetition -- and make sure they check their work. This reinforces those multiplication steps...

 

Take comfort and know that it's normal! And don't be afraid to take multiple days on one lesson.

[Cherrie]

using dona young websit you can download free paper I used the guitar / bass one and played with the numbers so I had boxes separted for each question and a square for each number I only put 4 to 6 questions on a page to start. My dd had a difficult time keeping her number in a row and keeping enough of a distance from one question to another. This may help

 

http://www.incompetech.com/graphpaper/fretboard/;)

[Alana in Canada]

Cadam--How could I have forgotten?

 

My son had "mid-line" crossing problems as a youngster. In addition to everything else suggested, I'll start having him do some physical excercises beforehand. Thanks!

[Kathie in VA]

When I followed our text and taught division as the opposite of mult. my dd didn't get it. She didn't get WHY she had to suddenly do math backwards! So I told her not to worry about division, it is really only a short cut anyway. All division problems can be done by repeated subtraction. We did it with a few small problems to prove it. (I also related all the problems to a word problem that she understood... something to do with ordering hot wings). I let her go on some problems with the requirement that everything gets written down. It didn't take too long for her to ask me to show her the shorter way. Then I just circled the number of times she subtracted a specific number... and wow just the number we need for the division part! Showing her the relationship between the repeated subtraction and the division is the only thing that made it click for her!!

 

hth

[Guest Lorna]

Squared paper helps. We also found that it helps to just write the multiplication facts that they are going to need at the top of the page so that they only need to worry about one aspect at a time (you can work on these facts at a different point in the day).

[Kim in SouthGa]

We switched from Saxon 2 years ago, using 5/4 while he was in 4th grade. I started him all the way back at Gamma, which would typically be a 3rd grade book, even though he was in 5th grade, because he didn't have his multiplication facts down. He worked through it fairly quickly, then on to Delta and division. Long division gave him a bit of a hard time, but is was more like a bump in the road, not the tears and drama we had with Saxon. I hate for him to be so "behind", but I know I did what was best for him. He started Epsilon after Christmas break (6th grade), so I am hoping if we work through the summer he should be caught up to grade level by the end of 7th grade. KNowing those multiplication facts and easily doing simple division is key.

HTH

Kim

[Myrtle]

We were going along tickety-boo (Singapore 3A) and then BAM.

 

He can divide in his head--but get him to do something like 46 divided by 3. I can put the 1 on top of the line, but he cries out "I'm confused" right when I start writing a 3 under the 4.

 

What are we missing?

 

 

I hope that made sense?

TIA

 

You are missing the zeros!:D

 

You will have noticed that in your Singpore text there are many demonstrations of composing numbers by use of cards. For example, there will be a long card with 40 on it and a shorter card with 6 on it. When you line up the right edges you compose the number 46 and the child can lift up the 6 in the ones place to see the zero under it. This is used to demonstrate place value and these cards are very useful when demonstrating the long division algorithm.

 

Demonstrate your division problems by using these cards. You will need another set for recording the quotient. They are easy enough to make via magic marker and poster board.

 

So here we go,

 

You draw the long division symbol and place the 40 card and the 6 card where they belong. Now you ask the kid "how many times to 3 go into 40?" And his only options are 1,2,3,4,5,6,7,8,9, and 10, 20, 30, 40 since these are the cards available to him.

 

Since 20 x 3 is too big, try 10 x 3.

 

Place the 10 card in the quotient.

 

Now for the sake of efficiency we grown ups normally do NOT record zeros in the long division alogorithm but we want an intermediate step for a kid. Multiply the quotient "10" by the divisor "3" and subtract that. Under the 46 you will subtract 30 (this you can write with your pencil on whatever paper you have your cards on) and you will note that normally we simply subtract 3 from the 5, what we are going to do here is simply include those invisible zeros). If you need to demonstrate each problem with hundreds and tens cubes!

 

Okay, so the kid sees that 46-30 = 16. Now he has to decide how many times does 3 go into 13 ones and he decides "5" and then he places the 5 card on top of the 10 card in the quotient. The remainder of 1 can not be evenly divided by 3 so we record that as "R 1" meaning "and one was left over."

 

The benefits of this are that it demonstrates the role of place value in the long division algorithm and that since the invisible zeros are explicitly written it eliminates the step of "bring down the next number" which automatically appears in all its glory as the result of subtracting.

 

I have taught it this way once before with my older son (My son learned long division when he was six) and I'm within a week or two of teaching long division to my seven year old. I have half a mind to let him write it all out with pencil after we work with the cards and simply erase the zeros in the quotient replacing them with significant digits as he needs to. I predict after he does some 5-7 problems like this he'll appreciate me telling him that he need not write the zero to begin with and by that time he'll certainly have a little better understanding of what's going on in the long division algorithm.

[plansrme]

My 7 yo also just hit this in Singapore 3A. It seems to help when I write out the steps on a whiteboard for her: 1. Divide. 2. Multiple. 3. Subtract. 4. "Wheeee!" The "wheee" is the next number rapelling down. She knows to repeat the steps until she runs out of digits to go "whee" (her favorite part). I also drew a "Q" (for "quotient") sitting in a chair on the top line to remind her that all quotients, but only quotients, sit on the top line. She's very visual, so she does much better when she keeps a whiteboard with the 4 steps and a picture of the Q in a chair. She also does most of the actual problems on a separate small whiteboard--easier to make the numbers big enough, I suppose.

I like the repeated subtraction method someone noted above--think I'll try that also to cement in her mind what she's doing.

 

Terri

[Nan in Mass]

I think the problem is the limited choices. When you do this in your head, you break 46 into 40+6, deal with the 40 first, add whatever is left over to the 6, then deal with that. So, you ask how many 3's in 40 and the answer is (10 for 30 of the 40) + (3 for the other 10 of the 40) + 1 left over (which you add to the 6). Your partial answer is now 13 and you are working on 7. When you do long division, you can't answer 13 for how many 3's go into 40 because your answer is going into the 10's place and is reallly a kind of 10. What you are really doing is asking how many 3's multiplied by 10 will go into 40. This is really confusing until the child gets used to NOT answering 13 and leaving more to be shoved onto the next number. No wonder they get confused.

-Nan

[Suzanne in ABQ]

It took my dd about two weeks to get through that section of the book. It took my son two months! I didn't think we'd ever get through that. I was looking up private tutors. I was calling Sylvan. I was at my wits end. Then, he got it. He's now in 4A, and he actually gets excited when he realizes that a word problem will require long division.

 

What helped him with the concept was using manipulatives in creative ways. I used base-10 blocks a lot! I made paper ships and a paper dock, and stacked the blocks on the dock. I made paper men and a paper boss who had to figure out how many "boxes" needed to go on each ship. I made paper ramps for the paper men to use to carry the boxes onto the ships. We did larger units first, and worked our way down to singles. After we had done this about a gillion times, I started writing the steps down in the algorithm as we did it. Eventually, we just used the algorithm, but it still took a very long time before he could do it on his own. He still forgets to write a zero on top if he can't divide into a smaller number. That messes everything up. :o) But, he's getting it, and he doesn't hate it! :o)

 

Anyway, hang in there. Try different things. Something will click, and he'll get it.

[Alana in Canada]

Huh?

We're actually multiplying by 10?

oh dear. Now I'm lost. That makes sense--but now I need the base ten block to figure it out.

 

Not something we have, by the way. I've managed, so far, to make every single manipulative we've needed--and I've used poker chips and the place value chart so far.

 

Any idea how I can make base 10 blocks? Legos? How many will I need?

[Alana in Canada]

Update--

I wrote out the problems on graph paper--and I pre-drew the subtraction lines. (His numbers tend to go "all over" so this kept everything neat and straight!)

 

I used Myrtle's idea of zeros--She reminded me that I'd had a teacher once who told me to put "x's" in the spots where I didn't actually have a number--just above where I was supposed to "bring it down" The x's also helped him see how many place values the answer was supposed to have. For example, for 4 into 320, we put a tiny x above the 3 to show we needed to start in the "tens" place. It also helped him figure out when he had the remainder and not yet another number we needed to divide into.

 

We also did some "cross body" excercises before we started. Lots of figure 8's with our arms. He enjoys them.

 

Then I sat down, kitty corner from him and we talked through every single step. I did the same questions on my piece of paper.

 

We did eight questions. It took us maybe 1/2 hour or 45 minutes but he got every single one of them done correctly and in the right order. He wants to write the quotient in the subtracting part. I think it's akin to a bookeeping sort of error rather than a conceptual one...but we'll do it this way for a few more days until he's feeling more confident. He may fall apart again tomorrow, so we may have to try something else.! We'll see.

 

I am so glad I can do this with him. Truly, truly grateful.

 

whew. Thank you all so much. I'm still trying to figure out base-10 blocks, though!

[ChicoryChick]

This thread is very timely as we have been going through the same struggle. We use MUS which has been great so far, but my dd has hit the division wall. We have been stuck at Lesson 19 for a couple of weeks now, first time we ever been stuck at a lesson that long. I love the "whee" idea. LOL!

[DarcyM]

Must be that time of the year, too. I decided not to fight it. We put it away for the rest of February. We'll revisit it in March. While I don't want him to learn he can avoid difficult things, this is the one time where my math confident, math-loving boy was losing self esteem. Where he was once very confident in his understanding he was starting to name-call himself. It was heartbreaking to see.

 

I told him sometimes we all just need a time out to collect ourselves. We've spent the last two weeks playing math games, doing factors, skip counting, kitchen math, yahtzee, monopoly, etc. Lots of life exposure to math, but no paper version of long division.

 

In March, I'm going to get out the RighStart place value cards and start slowly. if it takes us 3 months, so be it. He's 7. I'm not in a hurry. (although if it does take us 3 months, he'll be 8 before we're done!)

 

Oh well I remember being confused about this at first, too. Only I was in 4th grade at my school when we did long division. I wasn't 7.

 

Thank goodness for homeschool.

[Suzanne in ABQ]

Beans and popsicle sticks.

 

Individual beans are ones.

Glue ten beans to a stick to make a ten.

Glue ten sticks (each full of ten beans) together (will need a couple more sticks to support them) to make hundreds. (he won't need these right away, but will eventually)

 

Give him 9 tens and 6 ones. Get three index cards and write the word "quotient" on each of them. Lay them out in front of him. Demonstrate that three tens will go onto each quotient card; then two ones. Stress that you always start with the tens. Tell him that the number of beans on each quotient card is the quotient (might as well get him used to hearing the word). Do this problem, along with others that will divide easily (without having to break a ten), about a gillion times. When he can anticipate what you're going to do next, he's ready to move on. You could introduce the algorithm here, or do a different kind of problem.

 

Different kind of problem: give him the same 9 tens and 6 ones, but give him four quotient cards. Show him that he can put 2 tens on each quotient card, but that he'll have 1 left over. Show him that he can trade his "ten" for 10 "ones" (single beans). Then, place those 10 beans with the original 6, to make 16. Show him how he can then put 4 individual beans on each card.

 

When you're ready to introduce the algorithm, do it alongside the bean demo. After each step with the beans, write down what you did on the algorithm. Do this about a gillion times, or until he gets it. Eventually, you can skip the beans, and go straight to the algorithm.

 

I still need to bring out the manipulatives with my ds, though, 'cause he forgets if he doesn't do it regularly.

 

I hope this answers your question. I'm not sure what you meant by "multiplying by 10". Perhaps that was directed at someone else?

 

Let me knwo if there's anything I can do to help, even if it's just a virtual shoulder. I so understand your frustration.

[Alana in Canada]

Bean counting--hooray, I love beans!

We buy a bag of kidney beans JUST for math every year.:D

 

You know, that might actually be fun.

 

Yes, my multiplying by "10" comment was directed at this comment by Nan in Mass:

When you do long division, you can't answer 13 for how many 3's go into 40 because your answer is going into the 10's place and is reallly a kind of 10. What you are really doing is asking how many 3's multiplied by 10 will go into 40.