division

Discussion in 'Elementary Education' started by Bored of Ed, Jun 4, 2008.

1. Bored of EdEnthusiast

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Jun 4, 2008

Please post your random teaching ideas for division here. I need to reinforce the basic concept and written format of division problems while some kids already get it quite nicely. I'm looking for ANY activity OTHER than just dividing random manipulatives. (You know you're in trouble when they're even tired of dividing candy...:|)

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Jun 4, 2008

I "invented" a new long division strategy. If your kids are ready for long division, I'll send you something.

4. Bored of EdEnthusiast

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Jun 4, 2008

Thanks, but I'm really still struggling with the basics. They keep mixing up their divisors and dividends or whatever they're called (I'm not working with vocabulary this year; it's too hard for them. Just the basic language of "divided by" is enough for us...)

5. MelissainGAGroupie

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Jun 4, 2008

Have you used the idea of Daddy, Mother, Sister, Brother, Rover with your kids? Mine were getting confused with it too but once we practiced a while with using D, M, S, B, R they finally got the idea.

Mother = Multiply
Sister = Subtract
Brother = Bring Down the next number

Rover = Remainder (that goes back up top)

6. EMonkeyConnoisseur

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Jun 4, 2008

Have you tried using things like stories about 24 legs how many animals are there?

7. Bored of EdEnthusiast

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Jun 4, 2008

Melissa -- as I said, we're not nearly up to long division this year.
Emonkey -- yes. Thanks anyway. <sigh>

8. kcjo13Phenom

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Jun 4, 2008

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Jun 4, 2008

Have you done lessons with cooking - or just brought in baked goods or something you can cut up?

10. Bored of EdEnthusiast

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Jun 4, 2008

<double sigh>

We did <i>The Doorbell Rang</i>.
I've done candies, dividing a package evenly among the students, but I didn't want to cut up baked goods or anything because they'd start confusing it with fractions (since we did a lot of demonstrations of fractions by cutting up food)

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Jun 4, 2008

With younger kids (or the ones who didn't get it) I used the terms "fair shares" and "left overs."

How can we make sure we all get a fair share of pencils? The package has 12. Are there any left-overs? How many does each person have?

Then, show them on the board how a "mathematician" would have written what you just did. Keep doing it, again and again! (though it sounds like you are doing it again and again!)

12. kcjo13Phenom

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Jun 5, 2008

Bored, don't get down. It sounds like you are doing everything you can, and if I remember right, you have a challenging class. One of these days, when you'd like to divide the hairs you're pulling out of your head, they will get it. Just keep doing what you're doing.

Could your kids teach each other a lesson? Like use what they know to teach someone who knows NOTHING about division. You might be surprised. Maybe they know more than they are letting on!

13. matchstickgirlCompanion

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Jun 5, 2008

I'd be very interested in knowing what you did! Thank you!

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Jun 5, 2008

It's kind of hard to explain without a way to do the equation... but I will try. If you understand partial products, this will make sense to you.

First part of the lesson- I talk to the kids a bit about how they always think addition and subtraction are opposites and how division and multiplication are opposites. Sometimes they will even comment on how the division and subtraction signs are similar and how the addition and mult. signs are similar.

most kids understand how repeated addition can help them solve multiplication problems. 8 x 4, is like 8 + 8 + 8 +8....this they could add fairly easily- and as we know, many kids do this when they don't know a fact by heart. I tell them, it would be a pain though, to do 8 x 452, because it would be 8 + 8 + 8 +8 +8 + 8 + 8 +8 ... they laugh at that. They mostly know how to solve multiplication problems like that by the time I teach the long division method.

So then we talk about division. If I say 32 / 8, we could do the "opposite" of the mult. problem to get the answer, 32- 8 - 8 - 8 - 8 .. until we get to zero. This is actually dividing 32 into groups of 8. They should already know this too, but it is part of the introduction.

But what if I had 452 / 8... would I want to subtract from 452 until I get to zero??? That would take TOO LONG, just like multiplying that huge number would take too long!

So this is what we do next.... I would use a divisor like 7 or 8 because kids don't always know those facts as well as the smaller numbers.

Part 2- I ask the kids what the easiest numbers to multiply are.. they will say 1, 2, 5, 10. I say "GREAT!" To do long division this way, you ONLY need to know how to multiply by those numbers. This method does not require the kids to know all their facts, just those ones. It also requires a lot less estimation.

I'm afraid I'll run out of space... new post!

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Jun 5, 2008

Ok, back to the long division....

So--- they need to know 1, 2, 5, 10 and multiples of those numbers.

If the problem is 452/ 8 they will do the following:

Multiply the divisor by those numbers, and the multiples of ten for those numbers until they get a product which exceeds the dividend. In which case, they cross those numbers out or don't write them down.

So:
8 x 1 = 8
8 x 10 = 80
8 x 100... whoops too big! Don't do it!

8 x 2 = 16
8 x 20 = 60

8 x 5 = 40
8 x 50 = 400

452/ 8

8 goes into 400, 50 times.

452- 400 = 52

8 goes into 40, 5 times,

52 - 40 = 12

8 goes into 8, 1 time

12 - 8 = 4..4 is less than 8, I have gone as far as I can go!

I add up the 50 + 5 + 1 and the answer should be 56 r 4.

When the kids write these, they make the division symbol into a giant 7... they write the multiples down the long side of the seven to help them keep track of the numbers they are adding up.

This shows what it should look like:

http://www.slideshare.net/guestb30cd4/partial-quotients/

I made it easier by instead of estimating, like in these problems, you only need to know the multiples of 1, 2, 5 and 10!

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Jun 7, 2008

we teach division by using multiplication (we call is a messed up multiplication problem). The quotes are actually what I say

so for 104/8

Let's say a student offers 8 x 11

Write the problem like this

104 / 8 =
8 x ___ = 104 (we've already gone over related problem)

8 x ___ = 104
8 x 11 = 88 (now you subtract 104-88 to see how many you need to get to)
8 x ___ = 16 (student's fill in the blank)
then you check with addition (11+2) and (88 + 16)

You get 8 x 13=104 (go back to related problems and you have 104/8=13