Long division question

[brokenopen]

Hi, Ladies!

DS11 is working through Singapore 3A and is having difficulty with the long division introduction.

I am working through the examples in the textbook with him, but it is a genuine wall. I am showing him one problem at a time, step by step. He doesn't understand what questions to ask me, and I just don't understand what I am not explaining. I am going to go try to find some Math Mammoth downloads I purchased years ago on another computer to help.

He doesn't understand the why or how of it, unsure where to write the number on top, doesn't understand why to multiply it and write it underneath, or why to subtract. He is really stumped. Then when we talk about bringing the next number down.... bless his heart. He is earnestly trying to be teachable, and I so appreciate that, but there is just no explanation in the textbook i can find to expound on in order to assist him.

[Tansy]

I had my kiddos divide 3 equally then 6 then 9 then 12 then on and on on on. Till it got BORING to divide 90 m&m By hand...

We use the following order

Divide
Record above the number you divided... if you can't divide by the first number we put a tiny x there.
Multiply
Subtract
Bring down
Repeat

Maybe I'll do a quick blog post with pictures for you.

If he's having really hard time slow down and spend some time on this it's so very important for fractions later.
I'd use sites that generate worksheets on the fly for you. And do 2 problems then he does one you do 2 then he does one (with as much support as he needs)
write the steps on the paper so he can refer back to them. He may need to see it 400 times before it clicks for him. Give him that time to memorize the steps and grow into it.

We also do our division on graph paper this reduces confusion as thing now have there own space.

[Tansy]

Here I posted on my blog a step by step method hopefully that will help you and your dc.
http://gardenforsara.blogspot.com/2012/ ... do-it.html

In there is also a link to printable graph paper.

if he doesn't see the reason why we do long division I'd give him a double handful of cheerios, m&m's, or pennies and have him divide up all of them into groups a few times. Hopefully when he sees how long that takes and how open to errors it is. He will see the "joy" long division can bring

[pjdobro]

I'm not for sure how big of numbers you are looking at this level, but I remember when we first started doing long division, I tried to represent it physically for my dc so they could understand the concept. I have base 10 blocks that have a big 1000 cube, 100 squares/flats, 10 sticks, and one individual cubes. They all hook together so that was really helpful. I'm sure there are probably other ways to represent it, probably money would work really well also using dollars, dimes, and pennies. Let me see if I can explain in words, how we would do a problem. As I would represent it physically and do the physical division, we would also do the written part on the board. I'll go through a sample problem using dollars, dimes, and pennies.

If we were dividing a number like 143 by 3, I would start with a dollar, 4 dimes, and 3 pennies. First we start by trying to break the 100 or dollar into 3 parts. Well we can't do it when it was in one piece (without destroying it ) so we convert it to 10 dimes. Now we have 14 dimes (our 10 from our dollar plus the 4 we started with). So we divide those into 3 groups. We have 4 dimes in each of 3 plies and 2 dimes leftover. So what we did in terms of long division is look at that first number 1 and find that we couldn't break it into 3 by itself, so next we converted it to 10s and then looked at dividing the tens into 3 groups. So we took those 14 tens and divided them. So in Tansy's example we have our x above the 1 and now a 4 above the 4. We now need to see how many dimes do we have left that aren't in a pile? So we see we used 4 dimes in each of our 3 piles so we used 4X3 or 12. That is the number we write under 14 and subtracting 12 from 14 shows us that we have 2 dimes left. We should be able to verify that we have 2 dimes in our hand.

Now we need to divide those tens into 3 groups, but we can't as they are in one piece so need to convert them to ones. So we change our 2 dimes into 20 pennies and that plus our 3 pennies we started with equals 23 pennies. So we brought down our 3 and added to our 2 so we have 23. Do you see how what we are doing physically is represented by what we are writing down? So now we divide those 23 pennies into 3 groups. We can put 7 pennies into each of our 3 piles before we can't place them evenly any more. So we write our 7 above our 3. How many pennies did we use? We used 7 in each of 3 groups, so 7x3=21 so that is what we write down under our 23. To find out how many pennies we have left, we subtract 21 from 23 and we have 2 pennies left. We can verify that we have 2 pennies left in our hands. So the answer for 143 divided by 3 is 27R2.

That is so hard to describe in words, but hopefully you were able to follow it. The whole idea of long division is that we are dividing our groups of 100s, 10s, and 1s sequentially and each time taking what we have leftover from the previous group and including it with the next group. So after dividing 100s, the leftovers are added to our 10s, and after dividing up the 10s, the leftovers are added to our 1s. Every step that we write down along the way is just our notations for having done the dividing into groups or piles. When we were first learning long division, we did quite a few examples this way using blocks or money to do the steps along with the written work so that we could visualize what we were doing. After a while the concept stuck and we were able to just do the written steps. I hope that helps and you are able to help your ds visualize the steps along the way. It really does make sense!

[my3sons]

Wow! You already received 2 awesome responses here! I just wanted to ask what page numbers you are on in Singapore 3A Textbook and Workbook? That would help with specific advice - thanks! Also, how does ds do with multiplication? Thanks!

In Christ,
Julie

[brokenopen]

Thank you!!

We are on page 64 of the 3A textbook, and 79 of the 3A workbook. He does well on multiplication, but does not have all his facts memorized. That is not holding him back, however, it is really just not understanding the 'order' or 'rhythm' of long division. Where to place his numbers, when to multiply, subtract and bring down....
He is really trying.

[TrueGRIT]

Thanks for asking this, brokenopen.
It came just when my friend asked for some help, since she doesn't have online access.
My friend's child is having problems at the same place. It was good to read some of the suggestions and pass them along to her.
Looking forward to seeing more.

M

[Mom2Monkeys]

Have you tried dividing in parts with easier numbers to show what each step accomolishes?

636÷6= best way i can show is 6|637
Parts are...
600 ÷6 is 100
30 ÷6 is 5
7 ÷6 is 1 with 1 left.
Add the parts and you get 106 R1.

To show same thought process in tne problem..
6 will go into first number, 6, which is really 600. It goes one time, place 1 over the 6. It is in the hundreds place and shows 6 goes into 6 1 time, but really says 6 goes into 600 100 times. So we multipky the top number by the divisor to know how much to take out that weve already worked with. 6x1=6 which goes under the hundreds place 6, meaning we take away 600. Drop down the next number, 3. (It is tens place so represents 30) 6 wont go into 3 so put zero in tens place and you can just bring 7 down bc you didnt work out any numbers. 7 is in the ones place so it is 7. 6 goes into 37 6 times (that is 5 times into 30 and 1 into 7 like shown in parts above). Multiply to know how much to subtract out. 6x6 is 36 written under tens/ones. Leaves 1. Too small to divide so it is the remainder.

Think of multiplying as a way to expand the place values...or how we know how much to subtract. Wording it as multiply to find out how much to subtract helps keep the order. You bring down just to shiw only how much is left to work with, and work with smaller number.

My daighter has troubke too, but she is getting it down well underxtanding the place values and purpose of each step now.

[my3sons]

Thanks for sharing what page you are on, as that helps so much! Textbook 3A p. 64 along with Workbook p. 79 is the very first introduction to long division. At this point, long division is meant to be an introductory skill. Generally, math skills fall into one of three categories... introduction, practice, mastery. Long division in 3A at this point is in the introduction phase. It comes around again several times in the coming pages of 3A, and then again around near the middle of 3B. Those pages provide good practice of long division. I feel the skill really isn't meant to be truly mastered until 4A/4B.

I am on my second time through these levels (my oldest is completing 6B, and my middle ds is in nearing the end of 3B. Singapore's method of introducing a skill, practicing it a little, going away from it for awhile, coming back to it and practicing it a little, and then reviewing the concept the next year for more practice is purposeful and very effective. I remember being concerned with my first ds when doing long division. He needed help with every step of it with every problem, and generally, he is good at math and quite quick to catch on. I decided just to help him with each problem, talking through them out loud as we worked through them together on a marker board, and then move on. It worked great! Each time he came back to long division after a break, he needed less reminding of the process. Now, he is great at long division. I see the same thing happening with my middle ds. At the introduction in 3A, he was pretty lost. We worked through the process together on a markerboard for each problem. At the practice phase in 3A and mid-3B, he needed ample reminders and practice with the practice. Now that he is nearing the end of 3B, he is starting to be able to do long division without so many reminders of the process. Usually, if I work through a few with him, he can do the rest successfully.

So, I'd view your ds as being in the introduction phase right now, heading for the practice phase. I'd pull out the markerboard and talk through the process out loud, working it on your markerboard as you go, partnering with him on this right now. They need to see the process over and over again for it to stick. I taught 3rd and 4th grade over the course of 7 years in ps before homeschooling, and this is super normal for dc to need lots of help with long division. To avoid frustration, I'd set the timer for 30 to 40 minutes, and fully work through problems together, stopping when the timer rings, and picking it up there the next day. You will begin to see progress, but remember, this is a skill to practice off and on as it comes up in the plans other times throughout the year. It is important to give a rest to working on this skill when it does in the plans. It helps dc to move to a different skill they do better with, and then come back to the harder skill later.

Here is an example of how to talk through problem #2f on Workbook p. 79, saying the bolded parts out loud, and doing the unbolded things on your markerboard...
Let's see how many 9's are in 452 by dividing. Write the problem on your markerboard in black marker.

Can 9 go into 4? (Underline the 4 on your markerboard). Well, no there are no 9's in 4. 4 is too small.

Hmmm. Well, can 9 go into 45? (Underline the 5 so 45 is underlined now on markerboard). Yes, it can, but how many 9's are in 45? Pause to see if he can begin to figure this out. If not, say, Hmmm. Well, we could try counting by 9's until we get as close to 45 as we can without going over? Then, encourage him to count by 9's out loud, keeping track of how many 9's he counts by holding up a finger for each or jotting a tally on the markerboard for each as he goes, and helping him if he gets stuck. When he gets to 45, say, Well, that's as close as we can get, right?!? How many 9's did it take then? So, we need to write 5 above 45 to show there were five 9's in 45. Then, we put 45 under 45 and subtract to see how many are left. Well, that's easy, 0 are left! Write on markerboard as you talk through it.

Now, are we done? No, we still have this 2 left. We need to bring it down. I usually make an arrow and bring down the 2. Now, we have to ask ourselves, how many 9's are there in 2? Oh, none? Well, you are right. So we need to put 0 above the 2 to show that. Now, how many do we have left over that cannot be in a group of 9? That's right, 2. We write that by writing R 2. I write that on the markerboard.

Pretty simple, but it works! Just keep working through the problems together like this, and trust me, it will stick. But keep moving on in the plans, going away from the skill, coming back to it later, going away from it again, and then coming back again to it later, is an incredible effective way to teach this difficult skill. HTH!

In Christ,
Julie