Long Division Troubles?

christmastreelouisaSome children are stumped by long division. They can be progressing along just fine, learning their times tables and doing well on their math lessons, when suddenly long division enters the picture and math becomes a tearful subject. When I taught Emily (9) how to do long division, we encountered some problems. In explaining it to her, I realized that I was using an old tried-and-true, failproof method that I’d learned somewhere that seems to help every child along in learning long division. Here it is, just in case you ever need it!

Before learning long division, a child must have mastered his multiplication facts. He must also be able to do short division, one step answers such as: 45 divided by 9 = 5, 15 divided by 3 = 5, etc.

To begin your long division lesson, prepare stacks of ten- and one-dollar bills. You can use real or play money. (I like real.) Draw this on a piece of paper: a column for tens and a column for ones, labeled. Have the child count the money and lay it in stacks under the tens place and the ones place (A). long division

Draw three little children, boys and girls, depending on your family configuration (B). Now, say this:

Emily, Ammon and Louisa (use your children’s names) are going to share 47 dollars.  Count out the bills (set the rest aside) and help your children stack the ten dollar bills in the tens column and the one dollar bills go in the ones column on your paper.

Look at the first number in the division box (C). It is a 4 in the tens place. That means 4 ten-dollar bills. Ask your children to pick up the ten dollar bills in the tens place and pass them out to the three kids in the drawing.  How many ten-dollar bills can each child have to share it fairly?  (one ten-dollar bill, with one ten dollar bill left over.)

On the division problem (D), write a dark 1 in the ten’s place and a light tracing of an 0 in the ones place. Explain that this means each of the 3 children (point to the divisor “3”) gets one ten-dollar bill (point to the quotient 10, in figure D).

long division

Ask: How much money did you spend?
(3 x $10 bill = $30.) Write 30 below the 47. (figure D)
How many ten dollar bills do you have leftover now?

Point to the stack of ten-dollar bills in the ten’s place (figure A).
(one ten-dollar bill and seven ones)
Perform the subtraction to show how much money is leftover.

Ask: Can 3 children evenly share one ten-dollar bill that is left in
our tens column without cutting it in pieces?

Can they trade it into the bank for 10 one-dollar bills?

If they trade in their $10 bill for one-dollar bills, how many
one-dollar bills will they have altogether? (10 ones plus 7 ones = 17
ones.) Put the ten ones into the ones stack with the seven ones.

Can 3 children share 17 one-dollar bills evenly?
(Encourage your child to deal out the dollar bills evenly to each
drawing of a child.)

Now count up the dollar bills. How much does each
child get? What number times the 3 children is close to 17?
(five one dollar bills)

Write the number five in the ones place. (figure F)
How much money did you spend to divide the one dollars evenly?
(15 one dollar bills)

How many one dollar bills are leftover?
(2 one dollar bills).
Since the children can’t share these evenly, there are leftovers. We
call them “remainders,” and we write them after our answer like this:
r. 2. The “r” stands for remainder (see figure G).

Go through this process several times, using different numbers but the
same story of children sharing ten- and one-dollar bills. Begin by
asking, “How can ___children share ___dollars?”

Here are some good problems to do:

43 divided by 2
85 divided by 3
74 divided by 5

After your child has learned how to do long division using the $10 and
$1 bills, you can introduce harder problems by adding $100 dollar
bills to your game. Have fun with it!


May I recommend:

Indispensable Math Facts

Division Wrap-ups

Division Placemat

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