Division with remainders

[Country Girl]

My son just started doing division with remainders this week. We have informally touched on division before but this is his first week of doing it "for school". The remainder stuff seems to be tripping him up a little because he is getting confused with when to stop dividing and call it a remainder. The thought crossed my mind to just skip the remainder stuff and start right into finishing out the division problem with decimals. Is this a bad idea? Is there any reason that he needs to know the concept of remainders? (We do test so maybe on standardized tests they will include remainders????).

Thanks!

[Sarah CB]

I think I would just continue working with him on remainders. Explain that you know you have a remainder when you can't divide the number any further and there isn't anything else to bring down.

I've been working with my ds on long division and it's a hard slog. I just keep working through the problems with him, asking him "Ok, what do we do next?" after each step. It's coming, it's just slow and painful :)

[Parrothead]

I looked ahead at dd's MUS Epsilon book. Toward the end of the dividing and having remainders, it goes into turning those remainders into fractions. Like 5 divided by 2 is 2 with a remainder of 1/2. So going from that I think it would be helpful to know the fraction. But if you get into decimals equaling fractions .50 equals 1/2 I think you will be okay.

If you need to let him know that when his subtraction gets him down to where the number is smaller than his divisor he needs to stop. You just can't divide seven into 2

[jcooperetc]

I would go back and demonstrate the division with real objects and show him that when the number of groups (the divisor) is larger than the number of objects you have left, you can't give each a whole cookie or whatever anymore and the 'remainder' is what is left over that you just put aside. At this point I did explain, because my son just looked at it and said we could break the cookies in half, duh, about fractions, but decimals are a little more complex to explain. If he understands fractions though, decimals will be easier to explain later.

[katilac]

You definitely need to teach remainders.

I can't imagine that it wouldn't be on most or all standardized math tests; if they say to put the answer with remainder, an answer using decimals will be incorrect.

Many word problems also require remainders - - if you have 51 eggs, how many dozens can you make, and how many eggs left over; if you have 51 kids and each bus holds 25, how many children won't fit; etc etc. You can see that this has practical applications

You call it a remainder when there is nothing left to 'bring down.'

Could messy work be causing the difficult? Neatness is CRUCIAL for long division (all math with multiple steps, really). Most kids get confused because the problem is not lined up neatly enough, and it is hard to see what numbers you are 'done' with.

Also, most kids need someone to walk them through the steps again and again, until it becomes automatic.

[oakmom]

Something that has helped us is turning the paper sideways so that the lines run vertically instead of horizontally. This way we use the lines as columns to keep the place values lined up.

[kiana]

Try using graph paper for place value.

If he only learns decimals, what happens when he reaches a non-terminating decimal? And as others have stated, there are applications where you might actually need the remainder rather than a decimal -- also, sometimes keeping it in fraction form is much less messy.

[Jen3boys]

I would go back and demonstrate the division with real objects and show him that when the number of groups (the divisor) is larger than the number of objects you have left, you can't give each a whole cookie or whatever anymore and the 'remainder' is what is left over that you just put aside. At this point I did explain, because my son just looked at it and said we could break the cookies in half, duh, about fractions, but decimals are a little more complex to explain. If he understands fractions though, decimals will be easier to explain later.

:iagree:
We used toy cars when we started division w/remainders. How can we divide 23 cars between the two boys? Three boys? How many cars are remaining? Try using something that can't be split, so there are some leftover. Then do the same problem on paper.

[Mandy in TN]

Sometimes it is easier to see with a concrete example. Do this with actual pieces of candy.

If 9 pieces of candy are divided equally among 3 children, how many will each child receive?

Let your ds separate the candy into 3 equal piles.
Write
9 / 3 = 3 Then say- and we know this is true because
9 = 3 x 3

If 10 pieces of candy are divided equally among 3 children, how many will each child receive?

Let your ds separate the candy into 3 equal piles with one left over.
Write
10 / 3 = 3 R 1 Then say- and we know this is true because
10 = 3 x 3 + 1

If 11 pieces of candy are divided equally among 3 children, how many will each child receive?

Let your ds separate the candy into 3 equal piles with two left over.
Write
11 / 3 = 3 R 2 Then say- and we know this is true because
11 = 3 x 3 + 2

Write the two problems one above the other just changing the symbols. HTH-
Mandy

[Country Girl]

Thanks everyone for the suggestions! We have used concrete items to show this and he definitely gets the concept of remainders.... he just gets confused with where he is at in the process. I think it is a neatness problem. Using graph paper/turning the paper sideways sounds like it would help so he will see better which place value he is working with.

Thanks for the suggestions and for the encouragement that this is a necessary concept for him to master!

[oakmom]

Here's a site where you can generate free graph paper:

http://incompetech.com/graphpaper/

Thanks everyone for the suggestions! We have used concrete items to show this and he definitely gets the concept of remainders.... he just gets confused with where he is at in the process. I think it is a neatness problem. Using graph paper/turning the paper sideways sounds like it would help so he will see better which place value he is working with.

Thanks for the suggestions and for the encouragement that this is a necessary concept for him to master!

[Country Girl]

Oakmom,

Thanks for the link!

[Jlynn]

I wouldn't skip to decimals at this point because he will also need to understand remainders expressed as fractions and that will be easier if he sees the remainder as a whole number first rather than a decimal. Like others have said, I used concrete examples for this stage... kids sharing cars or dolls etc.