An old-fashioned way to divide

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Home : 2007 : December : 21

An old-fashioned way to divide
By jeanmarie

I've been teaching a very long time. We're using EM and some of the ways they attempt to teach kids end up confusing them PLUS they have too many methods to choose from and master none of them. All of mine learn to long
divide like this: (if they can't master it THEN I try another method)

We set the problem up and first discuss that when we say 1349 divided by 62, the 62 goes OUTSIDE the bracket (yep - gotta start small) We proceed one digit at a time - I even cover them as we go)

We ask ourselves - will 62 go into 1 - no- so we put a small X above that place to show that we won't have

a 4 digit answer. (My kids don't line things up well so sometimes we turn the notebook paper sideways so they have columns)

Then we move over and ask ourselves if 62 will go into 13 - no - so we put another small x above the 3.

Then we move over and ask ourselves if 62 will go into 134 -yes - so we put a small line above the 4 and the 9 to let us know we will have a 2 digit answer. (and no more!) We also estimate at this point. We ask ourselves how many times a 6 will go into a 13 (or 60 into 134). That would be twice so we put a 2 on the line above the 4 and stick a zero on the line above the 9. Our estimate is 20. This estimate is written at least 1 finger's space above where we will put the answer, NOT right on top of the problem (Heaven knows we wouldn't want to have to rewrite the things)

Now we are ready to solve the problem. We go back to our estimate of 2 and take 2 times 62 to get 124. This goes under the 134 (We do NOT put a zero under that 9. In fact, I even hold a finger over the nine or use a sticky note to cover it for now. 134 divided by 62 looks so much easier, don't you think?) We then subtract 124 from 134 to get 10.

Now we draw an arrow to bring the 9 down so it lines up to make 109. Our established rule is that if we draw an arrow, we have to put a number in the answer. Otherwise, mine forget to put zeroes in.

Now we go thru our steps again. How many times will 6 go into 10 (or 62 into 109) and the answer is 1. The 1 goes in our answer above the 9 which fills our 2-digit answer spaces. We multiply 1 times 62. Put that under 109 and subtract to get 47.

We double check. Is 47 smaller than 62? If so, do we have any more numbers to bring down? If not, are all of our answer spaces filled? If so, we are done. Any remainder is then brought up to the answer. We look up at our original estimate to see if we're close.

Then we check our problem by multiplying which reinforces multiplication skills AND means they never have to miss a division problem. My kids pretty much ace division tests. They can also do huge numbers if we go one digit at a time.

When we divide decimal numbers, we follow the exact same procedure and then move the decimal up. Mine do not generally divide BY a decimal - we just can't get everything in 1 year.

We've had major discussions as teachers on all the whys and whatfors of the process, but when mine need to perform on those tests, they'll nail division. What they miss is the multiplication - go figure.

Hope this is sort of clear, but if you work it thru as I presented it, I think you'll see it. When we do these, I draw student teacher's to go to the board to model and "talk" us thru the process. I also have a large chart on the wall of the steps: determine digits in the answer; estimate; 1. divide, 2. multiply, 3. subtract, 4. bring down the next number - repeat from divide step.