Singapore 3a long division

[vaquitita]

Can someone tell me are they supposed to master the long division algorithm at this point in Singapore 3a? Or is it ok if I teach it, but then let him do the work in his head in his workbook? Is this just a first exposure and it will be taught again in 4? Or will they be expected to be solid on the division algorithm already in 4?

 

I must say this is the first point I've been not impressed with Singapore. They basically just throw long division at them. Which makes me wonder if this is just a first exposure, get the idea simmering in their brain kind of thing?

[TheAttachedMama]

I started a thread almost just like this a few months back!   (You can probably find it if you search for it.)

 

Long story short, 3A and 3B is the year where kids are suppose to master the long division algorithm.   Like most math topics, long division will be revisited again in future books.  However, the topic will just build upon itself.  (Example 2 digit divisor, etc.)

 

Like I said, my kids had problems with it too.   In fact, after posting here, I found out that it is common for kids to have difficulty with this no matter what math curriculum you are using!  

 

In my old thread, I was told to do a couple of things....They worked!   And now my kids just finished 3A and they have division down forwards, backwards, and inside out!   I mean they KNOW long division!  A few months ago I thought this would NEVER happen because we spent weeks and weeks camped out on this subject.

 

1)   Keep up the Singapore model of concrete--->abstract.  

 

The concrete is division using the base 10 blocks.   The abstract is division using numbers alone.  

Example:

540/4   (Divide the 100-blocks into four groups first. cash in the remaining 100 block for ten 10-blocks.  Then divide the 10-blocks into 4 equal groups, etc. etc.)  

Right after that, work the problems using numbers on the page. 

 

2)  Do the abstract portion (numbers on the page algorithm) WITH them for as long as it takes.

Right after you work the problem with the base 10 blocks, work the division problem with numbers on the page (abstract) with them for as long as it takes.  Unlike previous units in singapore, I couldn't just send them off to do a workbook page on their own.   We spent their math time working problems together.    Don't be afraid to give them as much help as they need for as long as it takes!  

 

In the beginning, I would actually talk them through the entire process.  I wrote D, M, S, B at the top of their page.   (Divide, Multiply, Subtract, Bring Down).  (We used the acronym Dead Monkeys Smell Bad to remember this.   In rather poor taste, but that is how we remembered it)  We would check off which step we had done so we could keep track of where we were in the algorithm.   As I wrote a number down, I would show them how we had done the same thing with the base 10-blocks.   I did this for what seemed like forever.   And I remember thinking that they would never get this.

 

3)  Start to ween them off of mom-help

After I felt like they were starting to get it, we moved away from working every problem with base 10-blocks.   And I would start to help them less and less.   (I did this only after I felt like they were getting it. That took forever.)

 

I would ask them if they knew what we would do next instead of just telling them.   If they didn't I would be quick to show and tell.   Next, I had them tell me what to do as I worked the problems with them.  (Being quick to correct if they got it wrong.) 

And finally, I had them start working problems on their own with me over their shoulder helping when needing and correcting before they got too far in with the wrong problem..  

 

After all of that, I finally just had them start working the problems in the textbook and workbook and then correcting.   And even then, sometimes they would forget what to do next and I would have to help.   But the algorithm was practiced over and over and over and over again....until now....by the end of book 3A---they finally have it down!  

 

ETA: Excuse all of the typos.  My toddler is "helping" me at the keyboard.

Edited March 1, 2016 by TheAttachedMama

[Rachel]

Following, we will be covering this soon.

[vaquitita]

I remember that thread. That was right when we first hit long division. I chose to work on other stuff for awhile, measurement, etc. We even went quickly through MUS gamma to get down his multiplication facts better. Now we're back to long division and the break from it didn't help at all. We watched the education unboxed video which uses the area model. On one hand it makes since, but in the other hand it's kind of clunky and sometimes makes problems more complicated, like when dividing by two.

 

One thing about the way Singapore teaches if that confuses my son is the bringing down. This time I've stuck with writing down the whole number when figuring out the remainder, and it has helped.

[SeaConquest]

I much prefer Beast Academy 3C's treatment of long division to Singapore 3A's.

[vaquitita]

In the 4a HIG, they mention the inferiority of the'area model' of division. Which I think the method shown in the education unboxed video on long division is an area model...

 

On the plus side using the EU video and writing out the whole number, rather than the 'bringing down' numbers my son at least understands the algorithm now.

[vaquitita]

I have beast 3c somewhere... Does it teach the algorithm?

[vaquitita]

My son loved the dead monkeys! Lol only we did Dead Monkeys Stink, for divide multiply subtract, we aren't doing bringing down.

 

It's going better today. I have a little hope now

Edited March 1, 2016 by vaquitita

[sweetpea3829]

My son has had some difficulty with this concept as well.  Partly, I am to blame, as I had never learned long division conceptually and the HIG was a little confusing to me.  That showed in my teaching of the concept to him.  

 

At the time, I pulled up some various videos online, etc.  He learned the "short division" method where the multiplying was done in his head with the remainder placed next to the next digit in the dividend and did just fine with that.  I thought all was peachy until recently, when he came across a division problem where the short division approach was not amenable (the dividend was large and the divisor was large but "easy"...something like 25).  I tried showing him how short division and long division were related, how the steps of short division were really the same thing as long, just written differently and that was a bust.

 

This is a smart kid that absorbs math concepts easily.  So I knew I was missing the mark somewhere.  

 

I ended up purchasing the entire MM set when it was on sale at Homeschool Buyer's Co-op.  I went baaaaack to the beginning of division, conceptually, using MM and he's picked right up on it and transitioned easily to the long division algorithm.  Initially there was a lot of push-back from him.  A lot of, "Mom, this is stupid!  I hate this!"

 

But now it's, "Oh...well now I see!  I like this method better!"  

 

Incidentally, he HAS completed all of Beast 3 and I don't recall him having any difficulty with the long division algorithm in that chapter.  But...in hindsight, I think he was actually solving those problems using short division. 

 

When does Singapore have them solving long division with multiple digit divisors?  I don't think it's in level 4, is it?  

[Porridge]

I didn't think Singapore 3A taught long division clearly. My mathy DD struggled.  She'd master it, only to struggle with it a few months later.  Beast teaches a different technique in level 3 and then reviews it again in level 4. It's not the standard long division technique, but it was easier for my daughter to understand and the place value aspect is less confusing. It does take a lot more paper (aka more space in the page) :)

[Monica_in_Switzerland]

I started a thread almost just like this a few months back!   (You can probably find it if you search for it.)

 

Long story short, 3A and 3B is the year where kids are suppose to master the long division algorithm.   Like most math topics, long division will be revisited again in future books.  However, the topic will just build upon itself.  (Example 2 digit divisor, etc.)

 

Like I said, my kids had problems with it too.   In fact, after posting here, I found out that it is common for kids to have difficulty with this no matter what math curriculum you are using!  

 

In my old thread, I was told to do a couple of things....They worked!   And now my kids just finished 3A and they have division down forwards, backwards, and inside out!   I mean they KNOW long division!  A few months ago I thought this would NEVER happen because we spent weeks and weeks camped out on this subject.

 

1)   Keep up the Singapore model of concrete--->abstract.  

 

The concrete is division using the base 10 blocks.   The abstract is division using numbers alone.  

Example:

540/4   (Divide the 100-blocks into four groups first. cash in the remaining 100 block for ten 10-blocks.  Then divide the 10-blocks into 4 equal groups, etc. etc.)  

Right after that, work the problems using numbers on the page. 

 

2)  Do the abstract portion (numbers on the page algorithm) WITH them for as long as it takes.

Right after you work the problem with the base 10 blocks, work the division problem with numbers on the page (abstract) with them for as long as it takes.  Unlike previous units in singapore, I couldn't just send them off to do a workbook page on their own.   We spent their math time working problems together.    Don't be afraid to give them as much help as they need for as long as it takes!  

 

In the beginning, I would actually talk them through the entire process.  I wrote D, M, S, B at the top of their page.   (Divide, Multiply, Subtract, Bring Down).  (We used the acronym Dead Monkeys Smell Bad to remember this.   In rather poor taste, but that is how we remembered it)  We would check off which step we had done so we could keep track of where we were in the algorithm.   As I wrote a number down, I would show them how we had done the same thing with the base 10-blocks.   I did this for what seemed like forever.   And I remember thinking that they would never get this.

 

3)  Start to ween them off of mom-help

After I felt like they were starting to get it, we moved away from working every problem with base 10-blocks.   And I would start to help them less and less.   (I did this only after I felt like they were getting it. That took forever.)

 

I would ask them if they knew what we would do next instead of just telling them.   If they didn't I would be quick to show and tell.   Next, I had them tell me what to do as I worked the problems with them.  (Being quick to correct if they got it wrong.) 

And finally, I had them start working problems on their own with me over their shoulder helping when needing and correcting before they got too far in with the wrong problem..  

 

After all of that, I finally just had them start working the problems in the textbook and workbook and then correcting.   And even then, sometimes they would forget what to do next and I would have to help.   But the algorithm was practiced over and over and over and over again....until now....by the end of book 3A---they finally have it down!  

 

ETA: Excuse all of the typos.  My toddler is "helping" me at the keyboard.

 

 

This is the method we used, moving side-by-side through the base ten block or cards and the written algorithm, so that it was clear why we "bring things down", why we subtract, etc, etc.  Long division is the first area in elementary math where division, multiplication, and subtraction are used simultaneously, and it is a notoriously hard algorithm to master, so just keep working away at it!  I'd suggest that once you finish the section, continue to do 1-2 problems a day as warm up so that the algorithm becomes more firmly placed in the brain and you don't need to start from scratch when it comes up again.  

[SeaConquest]

I have beast 3c somewhere... Does it teach the algorithm?

 

3C does not teach the standard algorithm. They teach repeated subtraction.

 

7/808 would be 100

7*100 = 700 

808-700 = 108

7/108 = 10

7*10 = 70

108-70 = 38

38/7 = 5

7*5 = 35

38-35 = 3

 

Quotient would be 100 + 10 + 5 = 115 with a remainder of 3

 

We haven't gotten to Beast 4 yet, so I don't know if they teach it later. 

[chicagoshannon]

I would make sure he knows his multiplication tables really well.  That is usually one of the big problems with long division.  It is revisited in 4 and 5 but more to add in how to divide decimals ect.  We are almost done with 5B and decimal division was introduced in 5A and the decimal portion was the only part taught.  They were expected to have the whole number part mastered.

 

But really once dd was a lot more solid in her multiplication facts long division was so much easier.  We used Times Attack for fun practice.

[Alessandra]

We have done Attached's method.

 

I only wanted to add that we work on whiteboard. It's easy for kid to see my work and vice versa. Plus you can change colors every so often. And hands don't get tired.

 

You can also print a page with giant squares, put it in a write on page protector, and use dry erase markers. Helps with lining up the numbers.

 

I find that if I help with the visual and find motor, it frees up the mind for the actual math, lol.

 

Btw, I teach to look at the answer to see if it makes sense. You shouldn't have a remainder of 20 when dividing by 3, for example.

 

ETA

 

Oh, and I talk through steps and ask dd to do the same. Does that make the experience multi sensory, lol?

Edited March 23, 2016 by Alessandra

[Alessandra]

I would make sure he knows his multiplication tables really well. That is usually one of the big problems with long division. It is revisited in 4 and 5 but more to add in how to divide decimals ect. We are almost done with 5B and decimal division was introduced in 5A and the decimal portion was the only part taught. They were expected to have the whole number part mastered.

 

But really once dd was a lot more solid in her multiplication facts long division was so much easier. We used Times Attack for fun practice.

Excellent advice. And TimezAttack is addictive. By the time we got to SM 3a, facts were rock solid.

 

But it was still challenging to figure out how many times one number went into another. Our beloved Cuisenaire rods helped at the beginning. Dd went from not wanting to use the 'babyish' rods to 'I see now.'

[Heathermomster]

3C does not teach the standard algorithm. They teach repeated subtraction.

 

7/808 would be 100

7*100 = 700 

808-700 = 108

7/108 = 10

7*10 = 70

108-70 = 38

38/7 = 5

7*5 = 35

38-35 = 3

 

Quotient would be 100 + 10 + 5 = 115 with a remainder of 3

 

We haven't gotten to Beast 4 yet, so I don't know if they teach it later. 

I had no idea that Singapore was using the partial quotient method.  Do they ever teach the traditional algorithm?  

[FairProspects]

I had no idea that Singapore was using the partial quotient method.  Do they ever teach the traditional algorithm?  

 

She is actually describing the partial quotient method in BA 3C. Yes, Singapore does teach the traditional algorithm. Somewhere in 4, and again in 5A.

[Janeway]

Long division can be difficult to teach. So I laid a big dry erase board on the ground. I used blocks to build the numbers. And we worked it out there. I actually wrote the problem in big numbers. Then I put the blocks right below the numbers. And worked the problem, right there, with the blocks. We did it over and over again. It worked. But, yes, they do need to master it. It is not revisited. Later, they teach more complex division problems, but they do not reteach anything in Singapore Math.

[quelques_fleur]

For us, it was his multiplication facts that made it the most challenging while in SM level 3.  He would get stuck on a multiplication fact, which occupied all of his mental activity.  There was no real space mentally to comprehend the steps of the standard algorithm of long division. I didn't get too hung up on division then as I felt we needed to spend more time mastering his times tables. So I helped him with most problems during that level.  In 4th grade, he had a better handle on his math facts and was better able to mentally focus on the concept behind long division but still struggled a bit.  Again, I simply gave him a bit of extra assistance.  This year in level 5, he has truly mastered all his times tables through the 15 times tables and long division is no longer a challenge. Since SM does spiral the concepts taught year in and year out and you have level 3 as a reference, I would do your best and resolve to delve into it at a deeper level in level 4.  At that time, you can simply refer back to level 3's HIG if you need a refresher in how to teach the standard algorithm prior to work on long division at level 4. 

 

Side note, I always used the mnemonic Does Mcdonalds Serve Burgers Raw....lol 

[SereneHome]

Can someone explain to me what is considered traditional algorithm in long division?

[SoCal_Bear]

Scroll down on the wiki page to method. The example shows you the standard algorithm.

 

https://en.wikipedia.org/wiki/Long_division

 

[Smiles]

I don't want to derail this post but I read that they need to know their math facts. We just finished Singapore 2B, my boy knows the math facts that they want him to know but he is not even close to having them down to 15! Is this something that I missed somewhere? Sorry for my ignorance he is my first born and math is scary to me anyways. I am ashamed to say I don't even have my facts memorized. I plan on my children knowing theirs, hopefully! Thanks in advance. 

[SereneHome]

Scroll down on the wiki page to method. The example shows you the standard algorithm.

 

https://en.wikipedia.org/wiki/Long_division

 

so, is "algorithm" just a fancy word for the steps that are taken?

 

[kateingr]

I don't want to derail this post but I read that they need to know their math facts. We just finished Singapore 2B, my boy knows the math facts that they want him to know but he is not even close to having them down to 15! Is this something that I missed somewhere? Sorry for my ignorance he is my first born and math is scary to me anyways. I am ashamed to say I don't even have my facts memorized. I plan on my children knowing theirs, hopefully! Thanks in advance. 

 

No, no need to panic! The first long division section in 3A only has children dividing by 2, 3, 4, and 5, and the second section has them dividing by 6, 7, 8, and 9 (along with review of those facts). 

[kateingr]

so, is "algorithm" just a fancy word for the steps that are taken?

 

 

Yes, exactly. Any set of steps that you can repeat over and over to get a certain outcome is an algorithm. There's a "standard" set that we use in the US for addition, subtraction, multiplication, and division, but there are other algorithms for those operations that get the correct answer, too. (

[kateingr]

There's lots of good advice up-thread, but one more thought: Part of what makes Singapore's presentation of the long-division algorithm so challenging is that the program moves very quickly from reviewing the concept of division in real-life situations to using place-value disks (disks with 1, 10, and 100 on them) to learn the long division algorithm. As a result, there's a loss of context and meaning as kids start to learn the algorithm. The place-value disks help to make the algorithm more concrete and hands-on, but they don't help much with making the algorithm more comprehensible and connected to anything in the real world. 

 

My son struggled with this recently as he was working through long division, and I found that using Monopoly money helped him to make sense of the algorithm. When 528 divided by 5 is framed as $528 divided up among 5 kids, the algorithm makes a lot of sense ("Let's start by doling out 1 hundred dollar bill to each kid.")

 

If anyone would like more specifics on how to do this, I made a quick video a couple weeks ago that demonstrates it step-by-step. 

[quelques_fleur]

I don't want to derail this post but I read that they need to know their math facts. We just finished Singapore 2B, my boy knows the math facts that they want him to know but he is not even close to having them down to 15! Is this something that I missed somewhere? Sorry for my ignorance he is my first born and math is scary to me anyways. I am ashamed to say I don't even have my facts memorized. I plan on my children knowing theirs, hopefully! Thanks in advance. 

 

Singapore math only requires memory of the facts through the 10 times tables actually.  We are part of a Classical Conversations campus and it was part of his memory work this year to learn them through 15x15.  So, it is definitely not something that you will need to worry about!  If they know their math facts well through 10x10, they can easily handle 14x8 via the Singapore way because they would do that mentally as this: (10x8)+(4x8).  Does that make sense? 

 

Sorry to mislead you!!  The 11s through 15s was something we did beyond what SM was expecting of my child. :)

[SereneHome]

Yes, exactly. Any set of steps that you can repeat over and over to get a certain outcome is an algorithm. There's a "standard" set that we use in the US for addition, subtraction, multiplication, and division, but there are other algorithms for those operations that get the correct answer, too. (

 

Thank you. 

[Heathermomster]

Here is an excellent link that explains Singapore style long division with manipulatives. I wish I had used this with DS when he was 4th grade.

 

 

[quelques_fleur]

Heathermomster, this is explained in the HIG and in the textbook, no?

[abcmommy]

We ended up getting the Stamp Game to help but drilling multiplication has always been key.

 

 

 

Edited for a better video

Edited March 26, 2016 by abcmommy

[Targhee]

Partial quotients method really helped my kids understand what was going on. Later when we introduced the standard algorhythm keeping track of place value was easy.

[Heathermomster]

Heathermomster, this is explained in the HIG and in the textbook, no?

I assume so.  We are currently working through 2B.  Videos can be good, yes?

[Kathleen.]

I would suggest using objects like rods if he learns best that way and then move on to something pictorial and abstract like the idea of using money mentioned above sounds helpful.

A really great resource is educationunboxed.com

Also, most schools do not formally introduce the traditional algorithm until fourth grade. So take it slowly and go at your son's pace. Keep us posted.

[quelques_fleur]

I assume so.  We are currently working through 2B.  Videos can be good, yes?

 

Yes, videos are definitely useful.  I was just confused by the comment about wishing you had used it with your son when he was in 4th grade.  I was trying to figure out what was different in the video than what was presented in the book and hoping I didn't overlook anything last year when we went through level 4. Or was it that you used a totally different math curriculum with your son?  I never thought about looking for videos on YouTube to watch tutorials on the methods, so thanks for sharing the video!!

[Heathermomster]

Yes, videos are definitely useful.  I was just confused by the comment about wishing you had used it with your son when he was in 4th grade.  I was trying to figure out what was different in the video than what was presented in the book and hoping I didn't overlook anything last year when we went through level 4. Or was it that you used a totally different math curriculum with your son?  I never thought about looking for videos on YouTube to watch tutorials on the methods, so thanks for sharing the video!!

You are welcome!  I looked up the videos to better understand the discussion.

 

DS used an entirely different curriculum and learned long division at school. DD uses SIngapore and is in 2B.  I don't even own the level 3 materials yet,  Like you, I have been reviewing our HIGs to ensure we haven't missed anything.

Edited September 13, 2016 by Heathermomster

[kristin0713]

We had trouble with this and so I bought the math mammoth $5ish long division unit. That helped so much! I have also found that for my DD, as she moves into different topics in Singapore, she needs a LOT more review of multiplication, long division and now multi-digit multiplication. (She's now in 4a.). So everyday, in addition to her work in the Singapore book, she has to do a full page of regular multiplication facts, one long division problem, and one mult-digit multiplication problem. She still needs me to walk her through the steps of both and I do let her use a multiplication table.