How to teach division?

When I was in elementary school we learned math using mortensen math -- which i remember used a series of booklets and concrete math supplies for 1's, 10's, 100's. We were doing algebraic long division in 2nd grade and it didn't seem too hard, so I think it worked fairly well.

break stuff! illustrate what division is about by starting with something big, like a big cookie or cake.. and say, well how can we get enough pieces for everyone? then "divide" the pieces. ooh, you could start with a hypotetical question and draw out different possibilities on the board, then bring out a cake! they'll get so excited. :) i guess that would be an easier analogy for fractions.. well, might give u ideas..

I like to demonstrate division as being about sharing (so that everybody gets the same amount). I've been thinking of bringing in a bag of some kind of candy (though something healthy would work too) and have the kids figure out how much was in the bag (using the serving size and number of servings), then figure out how much candy each person should get if they divide it. Obviously, you can scale this in different ways (i.e., use small groups to change the numbers).

Sharing is the key idea, though.

use both small and gross motor skills. divide a cake with a knife. divide a bag of marbles by "dealing" them like cards, and divide a square of space with masking tape lines. also, use sentences: 12 /3 = 4 can be stated "i have 12 marbles to give to 3 friends. each friend gets four marbles."

Check out the Marilyn Burns books on teaching math. One good one is About Teaching Mathematics. There are also books specific to each grade level (2nd Grade Math, 3rd Grade Math, etc). I have always found great hands-on lessons there.

I also like to use a game called "Leftovers" to teach about remainders. (I teach 3rd grade.) Two people play the game together. They need six small squares of construction paper, about 3x3 inches each, referred to in the game as "plates." They also need 15 manipulatives like colored tiles or buttons or whatever. Person 1 rolls a dice and puts out that number of "plates." (Eg: roll 4, lay out 4 of the squares.) Then Person 1 must divide up the colored tiles onto the plates equally. Whatever is remaining (if anything), s/he gets to keep. So if a 4 is rolled, 3 tiles go on each plate, with 3 remaining, which Person 1 gets to keep. Now there are only 12 tiles left with which to play with. Person 2 rolls and does their turn, and the game continues until there are no more tiles left. Whoever has the most "leftover" tiles at the end wins. I usually make them write down their division sentences each time and draw the picture of the plates and the tiles that goes with it. That way they are also connecting the hands-on to the paper and pencil.

BTW, toward the end of the game, if a number of plates is rolled that is greater than the number of tiles left to play with, they should just roll again.

Rubber bands also make nice little division tools. They can be laid out flat on a desk or table to form circles, into which whatever is being divided can be dealt out. So if they kids are practicing 12 divided into 3 groups, they can lay out 3 rubber bands and deal out the 12 things one by one.

these are all great ideas, thanks so much! I actually have the Burns book "About Teaching Mathematics" but have never utilized it. Thanks everyone!

To teach the commutative property, that e.g. A (10 divided by 5 and then divided by 2) = B (10 divided by 2 and then divided by 5), you can give every group m and m's or some other fun, countable thing. Then, have people guess which will be more, A or B. Then, have them actually divide up the m and m's, and write down the results. Once they realize it is all the same, then they get to eat the m and ms!