Long Division...any helpful tips out there?

[Wee Pip]

Long division seems to be Math's dirty little secret. When people talk about "making math fun!", I'm certain they aren't talking about long division. So....any helpful tips to making long division fun? Or at least tolerable? Or at least accurate?

 

Any tips to actually GETTING THE RIGHT ANSWER more than once in awhile? :banghead: We're understanding the concept and procedures (heck, I've even taught about 4 different procedures, for good measure). But it's the little things that are throwing off the number, like: we multiplied wrong somewhere in one problem, and we subtracted wrong in another problem. Or we misread our number and that led to a whole downward spiral into wrongness.

 

BTW, I'm mostly referring to big ugly numbers like 17,657 / 54. Yuck.

[thundersweet]

OMG.....

Same thing here! One thing that helps a little is to write on dd's paper the 4 steps. Divide, multiply, subtract, and bring down. Other than that, I just watch and wait and stop her when she makes a mistake. I think I need a buzzer.:lol:

I will also make her slow down and rework the problem. Fast sloppy work usually results in an error. Someone gave me the idea to use graph paper so each number fits into a square. I'm going to get some at my homeschool store as soon as I can. They have some with larger squares.

 

Sandy

[Shannanlee]

I am dreading when we come to that. I still have nightmares from elementary school with that one.

[EKS]

Not that this is going to help, but this is a very common problem. Just some perspective--in the problem you gave as an example (17,657/54), when I did it, I counted 9 separate calculations and that doesn't even include the bringing down properly. That's a lot to hold it together for.

 

It will come with practice and maturity. And there is a reason that adults routinely use calculators for these things!

[GingerPoppy]

Have you spent a lot of time on mental math? I would recommend it. That way, the poor kid isn't writing out the multiplication the long way for each and every step. For example, first estimate how many times 50 (54 rounded) would go into 176 (first three digits). The child should quickly be able to count up by 50s (50, 100, 150, 200) to realize that four 50s is too far, so it's likely three 50s. Then (doing this mentally) they should say, "Well, if three 50s is 150, there were still 4 left from the 54 that I haven't dealt with yet... so three times that 4 is 12... and I'll add it onto the original 150 in my head to get 162."

 

Write the 162 underneath, and the 3 above. Then mentally count up in chunks (like they show in Math Mammoth for example)... so say, "We were aiming to get our number to fit into 176. We got close, but not quite there. How close did we get? Hmmm, from 162 up to 170 is 8, and from 170 continuing up to 176 is 6... that makes 14." Or, of course, you can simply subtract, but I find the mental version shaves off a bit of time once they get good at it.

 

And so on. The goal, I think, to make it engaging, efficient, and less painful is to try to shorten the process and not have to do much writing of additional steps in the margins.

 

I hope this made some sense. It's difficult to explain without a pencil in my hand, and with no morning tea yet!

[foxbridgeacademy]

My very "mathy" son even struggled with long div. Here's what worked for him: First he remembers his "family" D=Dad/Divide, M=Mom/Multiply, B=Brother/Bring-down, S=Sister/subtract. I also gave him a calculator. After each problem he did on paper he checked them on his calc. If he got it wrong then using the calc. he went back through step by step until he figured out his mistake. It also helped to do the problems on a big whiteboard. On paper all those #'s get jummbled up, but on a board he could space them all out.

[thundersweet]

My very "mathy" son even struggled with long div. Here's what worked for him: First he remembers his "family" D=Dad/Divide, M=Mom/Multiply, B=Brother/Bring-down, S=Sister/subtract. I also gave him a calculator. After each problem he did on paper he checked them on his calc. If he got it wrong then using the calc. he went back through step by step until he figured out his mistake. It also helped to do the problems on a big whiteboard. On paper all those #'s get jummbled up, but on a board he could space them all out.

 

Very good idea!

 

Sandy

[christine in al]

And basic facts. We are stopping forward motion with my dd until she can NAIL facts. She now has to spend an hour a day on MM and RS games with me.

 

And turn lined paper side-ways to create columns to keep numbers lined up.

 

And maybe do just a few and concentrate on doing them not only correctly, but beautifully. ( this is a total pipe dream for me regarding my ds. he keeps trying to get things done an hour ago, rather then do them well.)

 

chrisitne ( still playing math games ) in al

 

~c.

[jjins]

My favorite tip for long division and multiplication:

 

Use regular lined paper, but use it so that the lines run VERTICALLY. Then you have place value lines. This helps keep things orderly.

 

Also, I draw an arrow in long division from the digit in the dividend being brought down, to just above its place.

 

This does not make it "fun" but it does make it easier to manage. Also, I completely believe in, Understand it, Can do it when needed... good- done.

 

We do not normally have to carry out long division without a calculator. So as long as the process is clear, do able and understood, then I move on. Mind you these problems pop up in daily math problems (random problems from mom and dad) for years... those are done without calculators and from real life situations.

[jjins]

I also gave him a calculator. After each problem he did on paper he checked them on his calc. If he got it wrong then using the calc. he went back through step by step until he figured out his mistake. It also helped to do the problems on a big whiteboard..

 

 

Love this idea! Calculator added to our plan... Then you can quickly check your work and resolve to get the correct answer.

[Dana]

The graph paper or lined paper for place value is really good.

 

We have only worked with single digit division but when we were getting started, I used base 10 blocks for the first couple of days. First just working the problem with the blocks, then working the problem and writing the steps. Finally, we'd just write the steps... although getting a problem wrong resulted in going back to the manipulatives.

[Tam101]

Have you spent a lot of time on mental math? I would recommend it. That way, the poor kid isn't writing out the multiplication the long way for each and every step. For example, first estimate how many times 50 (54 rounded) would go into 176 (first three digits). The child should quickly be able to count up by 50s (50, 100, 150, 200) to realize that four 50s is too far, so it's likely three 50s. Then (doing this mentally) they should say, "Well, if three 50s is 150, there were still 4 left from the 54 that I haven't dealt with yet... so three times that 4 is 12... and I'll add it onto the original 150 in my head to get 162."

 

Write the 162 underneath, and the 3 above. Then mentally count up in chunks (like they show in Math Mammoth for example)... so say, "We were aiming to get our number to fit into 176. We got close, but not quite there. How close did we get? Hmmm, from 162 up to 170 is 8, and from 170 continuing up to 176 is 6... that makes 14." Or, of course, you can simply subtract, but I find the mental version shaves off a bit of time once they get good at it.

 

And so on. The goal, I think, to make it engaging, efficient, and less painful is to try to shorten the process and not have to do much writing of additional steps in the margins.

 

I hope this made some sense. It's difficult to explain without a pencil in my hand, and with no morning tea yet!

 

:iagree:

 

Exactly! Thank you for taking the time to write out what I was thinking. ;)

 

You really need to be strong in mental math and know your math facts forwards and backwards, then long division isn't difficult.

[OK Family]

I haven't read all the posts, but when I taught fourth grade I modeled the same examples everyday until they got the procedure down. That tends to be the hardest thing, unless they don't know their math facts then it's really difficult. Hope this helps.

[Wee Pip]

Thanks for the tips! We spent last year learning multiplication/division facts. She knows the procedure (we started with the family - Daddy divides, Mom multiplies, etc - love that!) I think making her use separate paper is a must (she tries to do it in the sidelines of the workbook, and I think that is where the error is coming in). We also went back to using Partial Product Division, but took our time with it, and weren't in a hurry to get to the answer. Viola! Right answers every time today!

 

We've used the rounding method before, but I just lost her there. Our lessons sounded a bit like this -

"Round 54 so that it's 50. How many times does 50 go into 176? No? Ok, so look at the 5. How many times would 5 go into 17? 3? Ok, good. So you have 3, and now your 5 is no longer a 5, and its not 50 anymore either; it's back to 54. So now multiply 54 by 3..."

I might as well turn green and sprout antennae.

Our math uses a lot of rounding, so she might get there, eventually.

She does use a lot of mental math tactics, so she gets pretty close to a good guess. But I think the Partial Product Division method (for now) is what works for her. I just need to stay with her while she's doing the math (and pay no attention to that 2yo with the permanent marker in her hand...)