I remember when I was a kid, it would take me FOREVER to solve a page of 10 long division problems. I was one of the last ones done, sitting off to the side to finish up. I'd stare blankly at 658 divided by 7 and try multiplying every number by 7 in the attempt to get 65. I felt so frustrated that I had to do all those "extra" math problems and hope that they were right too.
So when it comes time every year to teach my students long division, I've tried lots of ways. I had them make their own mnemonic devices to remember the steps (similar to the Do My Scissors Cut Bricks type acronym for Divide, Multiply, Subtract, Check, Bring Down). I've tried partial quotient. But for me it always comes back to practicing the physical process of dividing. Base ten blocks are a great way to do it, but my favorite manipulative when it comes to math is money. There's just something about counting money that makes people happy!
Last week I described how I introduce the concept of dividing hundred dollar bills, ten dollar bills, and one dollar bills into "wallets" over on Shut the Door and Teach. This activity helps get the kids used to the manipulatives involved and has a high success rate; with numbers that are carefully chosen to be evenly divisable (such as 486 divided by 2) the kids are able to compute in their heads before long. So to up the ante the next day, I give the kids numbers that are not as simple to divide.
Of course this does not complete the problem, but he is learning that 20 is a reasonable answer to 100 divided by 4, which is pretty powerful! I'm much happier with him knowing this than memorizing DMSCB and not understanding what numbers to compute at each step.
The child in the MIDDLE PHOTO is working on the same problem. She also knows that the answer to 100 divided by 4 will be about $20. However she is developing her understanding of the regrouping process. She is trading in those 2 ten dollar bills for one dollar bills. Although she has written a bunch of zeroes in the ones place on her place value mat, she will soon be able to refine her answer to include the ones place.
The child who completed the problem on the BOTTOM PHOTO has completed the process of dividing 100 by 4. She is also able to accurately record the steps she has taken to arrive at an answer. She regrouped the one hundred to become ten tens (although she forgot to erase the hundred). She also knew she could tally up the 4 twos in the tens place when writing out the long division algorithm. She used the difference (10 - 8 = 2) to find how many tens to regroup into ones, and she divided the twenty ones by 4 to get 5. Although the photo does not show her paper, she transferred the process she used with the manipulatives to the traditional long division algorithm.
If you need more examples of numbers that increase in difficulty when it comes to long division, I have 3 different levels of long division task cards with numbers similar to these two examples available as a bundle (they will be 28% off on Cyber Monday and Tuesday, 12/2 and 12/3 with promo code CYBER). I use the cards as review throughout the year because long division is one of those concepts that kids need to see many times before they can master it. I never feel guilty leaving these in my sub plans because the kids know what to do and actually enjoy long division when they get to use the money.