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# Manipulatives for Division?

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My 5th grader in p.s. is struggling to remember the steps in long division. We've done mnemonic devices, which have been somewhat helpful, but we're still not there yet. I know very little about Math-U-See, but can someone tell me how exactly I could go about using manipulatives to translate this concept into tangible terms for her? (Or even if this is helpful or possible with long division?) Thanks!

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I don't know if this helps, but there are You-tube videos of the Montessori "test tube" work, which teaches long division.

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Use lined paper sideways to keep the numbers lined up. That was very helpful.

And do you mean the steps like divide, multiply, subtract, bring down? I hate to drill standard algorithms but sometimes it's just the best way. I'd have him do lots of simple problems, like 2 digits divided by 1 digit. When he gets the hang of it, then move him up to 3 digits divided by 1 digit. What kind of problems are in the book? Are the divisors in 2 or 3 digits? Is that confusing him? My kids had a hard time with moving from 1-digit divisors to 2-digit divisors.

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This is what I did with my dc...

I used paper plates and paper place value manipulatives - hundreds flats, ten sticks and ones cubes - to illustrate the thought process of long division.

The empty plates were collectively labeled "the divisor," and the paper hundreds, tens, and ones were collectively labeled "the dividend." What ended up on the plates = the quotient.

For example: 235 divided by 5

My explanation went something like this:

Me: Let's say I have 235 chocolate chips, and I want to divide the chips evenly among 5 plates. How can we to that? I have 2 bunches of 100 chips. Can I put 1 bunch of 100 chips on each plate? No. So what do we do?

We cut the bunch of 100 chips into its next smallest unit - sticks of ten chips. (at this point I used scissors to cut the paper hundreds flats into ten-sticks).

Now, I have 20 ten sticks. Lets make a pile of all the ten sticks we have, including the 3 we started with. Can we evenly distribute the 23 ten sticks amongst the 5 plates? No. Can we get close? Yes, we can put 4 ten-sticks on each plate.

Do I have any sticks left over? Yes, 3 sticks. What should we do with the unused sticks? Let's cut them into the next smallest unit - single cubes (at this point, I cut the ten-sticks into single cubes).

Now, let's make a pile of all the single cubes we have. Can I evenly distribute 35 chips amongst 5 plates? Yes, 7 on each plate.

So, how many chips did we put on each plate? Yes, 47. The quotient is 47.

We then re-worked the same problem on paper, without the manipulatives, but talking about what we had just done. My dc was able to translate what he had physically done - cutting hundreds in to tens, passing out paper tens and ones -- into the language of math.

We followed this process ("cut one, write one") for a couple of days (until I ran out of things to cut!!), and my dc understood both the how AND the why of long division...

aude sapere

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My 5th grader in p.s. is struggling to remember the steps in long division. We've done mnemonic devices, which have been somewhat helpful, but we're still not there yet. I know very little about Math-U-See, but can someone tell me how exactly I could go about using manipulatives to translate this concept into tangible terms for her? (Or even if this is helpful or possible with long division?) Thanks!

I use Base-10 blocks.

For my son, I created a scenario in which he was a worker on a loading dock, and had to load boxes onto ships. I cut some generic boat shapes out of construction paper, and made little paper workmen (you can skip the workmen, but it helped him get into the game). I told him that he was the foreman, and his job was to make sure that the "boxes" got divided evenly between the ships.

I would pick a number, say 362, and would lay out three "hundreds" flats, six "tens" rods, and two "ones" cubes on the paper dock. Then, I would place two ships on the side of the dock, and walk him through dividing up the "boxes".

I'd start with the "hundreds". I'd have him (with his paper workmen) place one "hundred" flat on each boat, then realize that the third hundred will have to be broken into smaller units (tens) in order to be divided. We'd exchange them, and he'd combine the 10 tens with the other 6 tens still on the dock, making 16.

Then, we'd divide up the 16 tens by placing 8 on each ship. Finally we'd divide up the ones, placing them evenly on the ships.

After doing this several times, using different numbers of "boxes" and "ships", I'd start writing each step in the algorithm. 2 goes into 3 hundreds 1 time > place one hundred in each "quotient boat". There's one hundred left over, so break it into tens, and combine it with the other tens to make 16. Those divide evenly, by placing 8 in each quotient boat (pause to do the subtraction and division of tens in the algorithm). Repeat for the ones.

It took my son about two weeks of using the boat game to practice before he really understood long division. We did it until he could anticipate what was going to happen next. He has never forgotten it. He forgets all sorts of things, but never forgets how to do long division!

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