Drowning in SM subtraction and addition methods, please help!

[Trilliumlady]

I am a long time lurker on these boards but recently signed up myself so sorry to jump in with questions before introducing myself! I am really struggling with Singapore, though, and need guidance!

History.... dd8 is in third grade and had done Saxon math since level one in K year. Did well with it until the timed tests (which I quickly just turned into no timed practice) at which point we started having at least weekly breakdowns. I think this was end of first grade or so? Things just did into seem to stick and it was such a battle that we both dreaded that this year I tswitched to Singapore. She tested into 2a. I am using standards edition. Fwiw I switched ds7 to Singapore as well, not because he was struggling but because I figured it would be smoother to have them both in same boat and if I ended up liking Singapore I wanted him in it sooner rather than later.

Today, we tried doing unit 2 chapter five on subtraction and renaming. And oh.my.gosh, my mind just does not does not wrap easily around the ways they have them learning! I was a Saxon brain myself and this new method is really tough for me to guide them through! The whole making 45 into 35 and 10 and subtracting seven from ten and adding the remainder onto 35 and that just being one way of doing it is frying me. I get it, but it is so foreign to me I feel there is no way I can teach the concept clearly! She did subtraction with borrowing last year with Saxon and did o.k. With it if I recall correctly. So I had her try to show me that method again and I think that would get easier for peer than the whole trying to break numbers into their parts bit.

So, question the is, how important is it really for them to get the Singapore concept. From reading reviews, I know that is the whole ide,a but I just don't know how to get her (well them) to that point. Do I just use what she remembers from Saxon? I feel that is missing then whole part of Singapore. I just don't know at all how to teach this and am seeing utter lack of understanding in her eyes which tears me apart. I am feeling helpless with this! Argh.

Thanks for any advice!

[fralala]

Welcome! I am learning so much from these boards.

 

I am teaching SM 2a right now, too, using Standards. We're going through chapter 5 right now and I actually have decided to slow down and spend a lot more time on it because it IS a challenging concept. And we've been doing SM since kindergarten! We play lots of games and only do one or two practice problems per day so that we can talk about them really deeply and play around with solving them different ways.

 

Do you have the number discs and base-10 blocks? Have you worked with number bonds? Have you done lots of playing the recommended games/activities in the first part of unit 2? I find when we're both getting frustrated, it's time to go back to the games.

 

Even if your daughter already knows her math facts, having that number sense and deep understanding of place value will help her going forward, so going back to the first unit might also help (both of) you.

 

 

[TKDmom]

Do you have the HIG? I think it will help you introduce concepts. Singapore was always the way I understood math. And my first 3 kids were the same way. I never needed the extra teaching help, and I sold my HIGs. DD7 doesn't intuitively click with Singapore and I bought the HIG again for her, because I couldn't figure out how to explain things to her in a way she could understand.

 

Manipulatives are the first way to introduce new concepts. So for your example I'd have 35 linking cubes. 3 groups of ten and 5 ones. "Regrouping" (what we grew up calling borrowing) means you take a group of ten and break it into ones. Then take away 7 of them. What's left is 2 tens, 3 ones, and your original 5 ones = 28.

 

I know you already get that...but Singapore usually gives 2 or 3 different ways to understand a problem, and some of those are introduced only in the HIG. Whatever clicks with your dd is fine. I was so frustrated with dd because she is still adding on her fingers. Then DH pointed out that she does understand the concept of adding. She can do it, just not automatically. So I'm spending more time with her letting her draw pictures and stack poker chips until she starts to memorize those addition facts.

 

While you are learning new ways of looking at numbers it may feel like you are rewiring your brain for a while. And it can be frustrating. But SM has a loose spiral. You will see all these concepts again. I've become a believer in using the HIG to slow down and help kids learn math concepts in a concrete way.

Edited October 11, 2016 by TKDmom

[Clemsondana]

I would take the time to work on this with your daughter because this skill is helpful in being able to do math in your head.  Singapore writes a lot of their problems horizontally instead of vertically because it makes the assumption that students are doing this regrouping in their heads.  It will continue to use this idea as it adds new digits (hundreds, thousands) over the next few years.  I was worried about teaching this to my math-averse younger child (my older child immediately understood it) but she picked it up pretty quickly.  We started with numbers in the teens because it was easier to see that it really was just 10 + ones, and then moved to twenties and bigger numbers.  Good luck! 

[forty-two]

Agree with pp that the HIG and manipulatives and games can help.  I think the way SM does, so I haven't gotten the HIGs - my go-to method of teaching is to work out the textbook's pictorial examples with manipulatives (cuisenaire rods, the RightStart abacus, and a "treasure chest" full of "jewels" are my go-to manipulatives).  But if that's not enough, sometimes I end up flailing around a bit in my attempts to come up with alternate ways to explain what SM's trying to do - go through several failed tries until I hit something that sticks.  If that happened a lot, or I myself didn't quite understand the point of what SM was trying to teach (and why I should care about it instead of skip it), I'd probably get the HIG in order to have some tried and tested teaching helps.

 

Also, since she knows one way of working the problems, it can help to do the problem the way she knows and then do it the new way, explicitly connecting the two together - so she can see how this new way relates to what she already knows.  I have the old 3rd edition of 2a, and they teach differently than it sounds like the standards edition does - their approach to the standard algorithm sounds like it might be a good bridge between what Saxon taught and SM's mental math techniques (which is how I think of the "subtract from nearest ten" technique).  SM math teaches the mental math techniques *first* (1a and 1b are all about adding and subtracting completely mentally) and uses them as a bridge to the standard algorithm - but there's no reason you can't work the other way.  Since you *know* the standard algorithm, you could use it as a bridge to learning the mental math techniques.  SM teaches several ways to regroup before applying regrouping to the particular type of regrouping that is carrying and borrowing in the standard addition/subtraction algorithms.  You know how to carry and borrow - that's a form of regrouping - and you can apply that understanding of regrouping ones into tens when you carry and tens into ones when you borrow to regroup numbers in other ways, too.

 

IDK how Saxon used manipulatives to illustrate the standard algorithm, but to me (and my Singapore brain) it seems like it would be fairly similar to how 2a illustrates the standard algorithm (let me know if that's not the case).  Looking at my part 5 of unit 2, they have the problem illustrated with a hundreds/tens/ones chart and counters.  I'm pretty sure I just used base-10 blocks instead (actually I used cuisenaire rods as base-10 blocks).  So let's do 62-43.  So you have 6 tens and 2 ones (actually set them out with counters or blocks or rods).  There's not enough ones, so you exchange 1 ten for 10 ones (and do it for real with your manipulatives), so you have 5 tens and 12 ones.  Then you subtract 4 tens and subtract 3 ones (again, actually taking them away physically).  That seems like it ought to connect pretty well with what she knows from Saxon.  Changing 1 ten into 10 ones when you borrow and changing 10 ones into 1 ten when you carry - having *different* groups that represent the *same* amount - that's just *one* way to regroup numbers.  And SM is going to teach you some *other* ways to group and regroup numbers, too.

 

Ok, so now how to connect that to SM's mental math techniques.  Probably the easiest "breaking numbers apart" SM technique is "add tens and ones" and "subtract tens and ones" => it's the exact same thing you do when you add/subtract without regrouping (no kidding, as an adult it seems positively trivial as a mental math technique).  Only, they teach you to think about it in terms of breaking up the numbers into tens and ones, and first adding/subtracting the *tens* part and then adding/subtracting the *ones* part.  For example, for 54+3, you break apart 54 into 50 and 4, and then add the 3 and 4, and then put the 7 back with the 50 to get 57.  (When you do this with base-10 manipulatives, it's very natural to see the two parts.)  For 54+30, you break apart 54 into 50 and 4, then add the 50 and 30, and then put the 4 back on to the 70 to get 74.

 

And then when 1b does that with subtraction, they integrate the idea of moving a ten over to the ones when needed.  So for 57-30, you break the 57 into 50 and 7, subtract 30 from 50, and then put the 20 back together with the 7 to get 27.  And for 57-3, you break the 57 into 50 and 7, subtract 3 from 7, and then put the 4 back together with the 50 to get 54.  And for 60-3, you break the 60 into 50 and 10, subtract 3 from 10, and then put the 7 back together with the 50 to get 57.  For 82-6, you break the 82 into 70 and 12, subtract the 6 from the 12, and put the resulting 6 back together with the 70 to get 76.  For 56-14, you break the second number, 14, down to 10 and 4, and first subtract the 10 from 56 to get 46 and then subtract the 4 to get 42.  Doing those sorts of problems makes up a *lot* of 1a and 1b - cements place value and practices the idea of breaking up numbers.  (You could quickly run your dd through your ds's SM1 textbook, practice working with numbers in those ways.)

 

Another big SM "breaking down numbers" technique is "using number bonds".  This is going to extend the idea of regrouping numbers in ways *others* than changing 10 ones to 1 ten and 1 ten to 10 ones.  The "add/sub ones and tens" method builds builds off place value to practice breaking numbers into tens and ones, doing something to the tens and ones, and then putting the new amounts back together into one number - it gets you used to seeing numbers as a collection of tens and ones (and carrying/borrowing extends that by *changing* tens to ones and ones to tens - not only are numbers a collection of tens and ones, there are *several* ways to group them as tens and ones).  "Using number bonds" builds off math facts to practice breaking numbers down along math fact lines.  With 24+6, you'd break the 24 into 20 and 4, group the 4 and 6 together to make 10 (that's your math facts at work), and then put the 20 and 10 back together to make 30.  With subtraction, 30-6, you'd break 30 into 20 and 10, group the 10-6 together to get 4 (again, math facts at work), and then put the 20 and 4 back together to get 24.  With 39-6, you'd break the 39 into 30 and 9, group the 9-6 together to get 3 (again, math facts at work), and put the 30 and 3 together to get 33.  For a more interesting example, with 34-8, you can divide 8 into 4 and 4 (math facts at work), subtract the first 4 to get 30 and the second 4 to get 26.  (You can see a large crossover with the previous method.)

 

Another big SM "breaking down numbers" technique combines the previous two: "making tens".  This is the one that SM is known for - but the above two build up necessary skills that underlie making tens.  In making tens you are using the number bonds that make 10 (1&9, 2&8, 3&7, 4&6, 5&5) to guide you in breaking down the numbers to form one of those adds-to-ten number bonds.  So with 15+8, you ask yourself, "how much does 8 need to make 10?  => 2" so you then break 15 into 13 and 2, combine the 2 with 8 to make 10, and then put the 10 and 13 together to get 23.  You could also ask the opposite question: "how much does 15 need to make 20? => 5" and then break the 8 into 5 and 3, combine the 5 with 15 to get 20 and add back on the 3 to make 23.  With subtraction, 34-8, you break the 34 into 24 and 10, subtract the 8 from the 10 to get 2, and then recombine the 24 and 2 to get 26. 

 

That last one is the technique that you mentioned in your post.  It's probably the most complicated of all the mental math techniques, because it involves *adding* within your *subtraction* problem.  It's taken a lot of manipulative work to illustrate this for my oldest, and also it helps to be firm in all the previous add/sub mental math methods.  Because all the previous methods work by breaking numbers into groups, doing *something* to one or both groups, and then putting the two groups back together.  Once you've got the idea of ending the problem by putting the two groups back together - ending your making tens subtraction problem by putting the remaining two back with the other group is just like what you always do.  You can do a lot of manipulative work here - have a number in manipulatives, physically separate it into two groups, do something to one or both groups, and then shove the groups back together.  You can illustrate carrying and borrowing this way, too - separate your number into hundreds/tens/ones groups, and then for carrying you'd add to each group, then regroup your ones into a ten, and shove them all together again.  For borrowing, you'd separate them by place value, look to see if you can subtract, find there's not enough, so you regroup your ten into 10 ones, and then subtract each group, and shove the groups together at the end.  And to show the different ways of regrouping that all get you to the same answer, you could start with the same number, break it into *different* groups and do whatever needs doing to those groups, and put them back together and show how the ending amount is the same.  (Also you can show connections between the different groupings and what is done to those groupings - how it's not magic that there's different ways to get the same answer.)

 

IDK, does any of this help it make more sense?  There's a lot of practice with number bonds in the SM 1a - practicing seeing 6 as both 2&4 and 3&3 and 1&5 and 6&0.  And there's a lot of practice using all those techniques to add/sub within 20 in 1a.  Maybe you and your older kid could work through some of them with manipulatives - move things around to help really *see* the different ways to group and regroup - to before going back to 2a and applying those techniques with and without manipulatives to figure out those bigger numbers. 

Edited October 11, 2016 by forty-two

[kiwik]

If you were doing the problem mentally how would you do it?

[SparklyUnicorn]

First step is to practice making tens.  There are various games out there that practice this concept. 

 

 

That video demonstrates the concept.  You take the cards out that don't make ten.  You can also use more than one deck to have more cards.  Or make your own cards with numbers on them.  The rods are not a necessity to play the game. 

 

You can also write out the numbers 1- 9 and draw a line from the 1 and the 9, from the 2 to the 8, from the 3 to the 7; and so on.  Then let them use a number line if they want while doing calculations. 

Then the next step is to practice counting by 10s forward and backward so the step of taking 10 from 45 is easy.  Your kid may already have that part down, but if not that won't take long to work on that.

Then each day do 2 of these sorts of problems talking them out.  You can write out the steps that are the mental parts even though they are the mental parts so they can see them.  Keep doing this little by little, but keep going in the SM book.  They will show the usual ways of adding and subtracting that you are used to.  And even though it moves onto other topics, the concepts are mostly no different.  For example, there is adding and subtracting.  Then the numbers get bigger.  Then they add and subtract using units.  Etc.  It's all the same really with some added vocabulary or it builds on with larger numbers. 

They may pick up on this quickly and they may not.  I had one kid who picked up on this almost immediately.  My second kid I think i went over this daily for half a year.  Overall milestones have been reached at a similar time even though it seemed like it wouldn't. 

This may seem like a stupid concept, but I think it's worthwhile in the long run.  It really does not need to take tons of time per day.  And there are instances where it makes sense to use it and other times where it's just too annoying to use it.  What is difficult is knowing when that is or not.  In other words, you can rearrange the numbers in more than one way depending on what makes the most sense to you, but that might be individual and that might just vary on the numbers.  It's hard to teach that EXACTLY.  But with practice it comes more easily.  I think people are under the impression that this is something that is learned very quickly or that if you don't learn it quickly it must be a stupid method.  Not at all.  I don't think either of those things is true. 

[mamaraby]

I'll second the suggestions to slow down, use manipulatives (legos, coins, unifix cubes, toy cars, etc), and use the HIG. I was a good math student in school, but teaching my oldest via Singapore seriously upped my mental math game. I absolutely would not skip this part. It's definitely part of what makes SM....SM.

 

How is she at making ten? If she struggles with the number bonds for making ten, then I'd maybe back up and work on that until she has a good sense for what you add to 3 to make 10 and so on. Make it fun and play some card games -

http://www.whatdowedoallday.com/2012/01/fun-math-card-game-make-ten.html

http://mathgeekmama.com/pyramid-fun-and-easy-math-card-game/

http://excusememrsc.blogspot.com/2011/09/make-10-card-game.html

http://kapolei.k12.hi.us/investigations_pdfs/mathactivities.pdf

http://www.granby.k12.ct.us/uploaded/faculty/wyzika/Dice_and_Card_Games_to_Practice_Math_Facts.pdf (Pg 3 of the PDF, it'/ a game called 10-20-30)

 

Once kids can make 10 using all of the different number bond pairs, it makes it quicker and easier to do so with bigger numbers).

 

I'd also maybe go back and make sure she has a good grasp of place value. Unifix cubes can help here, but you can cut two of the cups off a egg cartons and use counters or pennies. So, you give her a number of counters, say fifteen and she makes ten by filling up the first ten frame egg carton and puts the remainder in the other ten frame egg carton. How many tens? How many ones. Let's subtract 8 from 15. Right now there are ten counters in this ten frame and five in the other. Where can we subtract 8? From the ten or the five? We'll subtract 8 from the ten. Now we have two left from the ten and we still have the five. How many are left? Repeat that with different numbers. Stick with numbers within 20 first and then work to numbers within 40 and so forth.

 

I might also consider backing up to 1B. A lot of the foundation for the approach is laid down in 1A/1B. You wouldn't have to cover the whole book (just the addition/subtraction sections), but it might help both of you to just go through those sections together. Be gentle with yourself too! :0) You'll both get it!

[Trilliumlady]

Oh my goodness I am going to have to mull over those above posts daily for quite awhile. Thank you all so much. I think I have seen mentioned a book people recommend for teaching this method but I can't seem to remember the title. Would that be helpful in getting me to understand *why* this is necessary and useful?

 

I do have the HIG and that helps me at least have an idea where I am going but I still feel we are hanging by threads off a cliff. I think we do need to slow down and get solid solid solid on place value and making tens. I think my ds will benefit from it as well as we are just starting to get caught in that in 1b as well.

 

I have been having her vertical problems horizontally, should I not be doing this if it doesn't tell me to? And on the mental math pages in the back of the HIG am I just to allow them to figure out the answer using any technique they can? Number line, fingers, dots on page, or by mental math do they mean no tools like that should be used? I am feeling many posts along these lines coming up over the next months. I guess I just need confidence that 1. I made the right choice in this switch 2. I am not setting them behind in my fumbling attempts at teaching it and 3. Somehow they will (and I will) indeed understand these methods, not to mention understand the why behind them. Sigh.

 

Disclaimer.... I am usually not so morose about things like this! Thanks for understanding!

[mamaraby]

Do you have both Singapore 1A and 1B or just 1B? If you've got it, I would review the addition/subtraction lessons from the HIG/textbook plus the games suggested in the HIG to help shore up her foundation before moving back to the 2A lesson in question. That's what I would do if it were me, but I own all of them so it's just a matter of pulling it off the shelf. I wasn't going to suggest it to you if you only owned 2A, though.

 

I own the US edition, and making ten is covered in 1A first within the context of adding and subtracting w/in 20. I don't know where it's first addressed in Standards, but you can check the scope and sequence on the SM website of you don't own both 1A and 1B.

Edited October 12, 2016 by mamaraby

[vonbon]

Just signing in to say that I can 100% relate to your questions and concerns.  We've used Singapore since K and are now in 3A.  

 

I specifically recall the addition/subtraction units last year in 2A as being really long and more difficult than other units.  It helped to know that a friend whose child is about 1 1/2 years older than my DD struggled with the same concepts.  They're both bright kids in multiple ways, so hearing her "warning" about the +/- units kind of geared me up and let me anticipate that they might be hard.  Otherwise, I probably would have freaked out.  I was sick of the subtraction part by the time we got through all of it (very long, if I recall correctly?), but it went well and we've moved on.

 

I approached it by doing what's been mentioned above: slowing down!  I got off the recommended pace (pacing guide set out by the book) and just ignored it.  We ended up with a few extra units at the end of the year but they were the "softer" units (geometry, measurement, time, money, etc.), so it was no big deal to do them over the summer and/or finish up at the beginning of this year.  It was worth it--not glossing over the subtraction.  

 

Also wanted to mention Reflex Math, which I learned about on these boards.  It's $35/year, which I debated about for quite awhile. Totally worth it for my DD.  It's an Internet-based, game-based program that really helps a student improve their math facts knowledge.  This has been so helpful as we've started the year because she's not wasting brain space and energy on figuring out basic facts.  Very important as we begin working with numbers to 10,000 and beyond.  I'm not a veteran homsechooler yet, but I just don't think you could ever go wrong with continually improving math facts knowledge.  The ability to "make 10's" = very valuable!

 

One other thing related to your post--  When I was a kid, I learned all addition and subtraction--actually all math--via algorithms.  "You write it out this way on paper and do these steps..."  I never learned to do math in my head.  Through high school, college math, my first career jobs--  I never understood how people arrived at various answers in my field of work so quickly and easily without paper and pen!  Since teaching Singapore, it's become almost comically (or tragically, LOL) obvious what I should have learned way back when.  Estimation and making 10's are now my friends!   :001_smile:

 

It wasn't until my late 20's...30's?... that I started to understand the importance of estimating and using round numbers, or of using mental math.  Singapore is SO strong in this--cementing the mental math aspect.  Problems I could never do without a pencil and paper in the past have become so easy for me using mental math.  Real-life math problems too--not just DD's math problems.  It's very cheesy and cliche that I'm learning right alongside my DC, but it's true.  

 

I can already see that my children are going to have a much easier time with math throughout their schooling years and lives because they're learning mental math at such young ages.  

 

You received a lot of good, specific advice up-post...The only tidbit I'll add (and I think I learned this from someone else who uses Singapore): I try really hard not to assign workbook pages until I think DD is truly ready to complete them independently.  I try to teach the given concept so thoroughly that, by the time we arrive at the workbook pages, she can do them herself.  We immediately check answers and she corrects any missed ones.  This way, I have a high level of confidence that the material was "absorbed".  That's not to say it won't be forgotten or we won't have to review--I expect to have to do that over the years.  Some days it's hard to not "check that box" if I don't feel we're at a level of understanding of a lesson to complete the workbook pages, but I do try to make sure it's "cemented" before turning her out to do it independently.  With some concepts in Singapore, that has equated to slowing way down.  Too many questions while doing the workbook pages tells me I did not teach it in a clear, understandable way or that she is just not ready to fully grasp it yet.  This approach requires slowing down sometimes or going deeper, but I think, for us, it's worth it.  YMMV.

 

Just wanted to encourage you to stick with it!  I'm not a mathy person or an expert in anything even remotely related to math, but I think Singapore is awesome and I can see how it would set a person up to truly understand numbers down the road.  

 

ETA: I'll be coming back to this to re-read some of the longer posts above...great, detailed info on how to get these concepts across!  Glad you brought this up, OP--

Edited October 12, 2016 by vonbon

[SoCal_Bear]

Don't give up...the strength in the mental math pays off tremendously down the line especially with multi-digit multiplication and long division as well as with working with expressions in order of operations. It goes so much smoother and quicker when these skills are reflexive and essentially done by memory. I really like how these concepts help lay the foundation for decomposing numbers which a skill that makes algebraic thinking so much easier to grasp. Plus being able to recognize the reasonableness of an answer is so valuable.

[Monica_in_Switzerland]

A few helpful things:

 

- the HIG

- manipulatives, especially cuisinaire rods, but base ten blocks would work

- the videos at educationunboxed.com  She presents all the various concepts in sinapore with manipulatives and it's very helpful to see how she is presenting lessons.

 

It's important that you know WHY you are subtracting from a ten rather than from the 5 in the ones spot, so you need to get comfortable with it before you can teach it.  It isn't hard and makes good sense once you've stared at it for a few days!  Remember that SM is a very mental-math heavy program, and so you will be learning a LOT of mental math techniques for addition and subtraction.  At first, they may not feel intuitive, but once they are understood and mastered, they make mental math 10 times easier.  

 

ETA:  I started writing this comment hours ago, then came back and finished it, but see that in the mean time, everyone else has already said what I just said!  

Edited October 12, 2016 by Monica_in_Switzerland

[Alice]

We've used Singapore all the way through (oldest went from 1-6, others are still in it). I think it's a great Math program and really love it. 

 

You've gotten great advice about how to work through the addition/subtraction mental math. Just to add a few things....

 

The book you probably were thinking of earlier in the thread is Knowing and Teaching Elementary Mathematics by Lipang Ma. I found it really interesting and somewhat helpful. It's fairly dry and not an easy read (if you aren't someone who has a strong math background). It's not really a how-to book but it does give you an idea of the why behind the method. 

 

I agree with slowing down through the fundamental chapters. One thing we did was to skip ahead and do some of the chapters at the end (shapes, symmetry, etc) while we were still working on the mental math techniques. That kept my kids from getting bored and feeling like we were just doing the same thing over and over again. 

 

Another thing I found was that it's ok to let your kids come up with their own ways for doing mental math. My kids all did that. It's really important that they understand the "make 10" concept but all of mine have other ways for doing addition and subtraction mentally that are equally correct and equally quick. You don't need to teach them other ways....but if one of them does a problem a different way and then can explain to you how and why, that's ok. I think allowing them to do the problems different ways helped them to become more comfortable with numbers and manipulating them in their heads. All my kids are much much better at mental math than me and I think it's because of Singapore.

[fralala]

Another thing I found was that it's ok to let your kids come up with their own ways for doing mental math. My kids all did that. It's really important that they understand the "make 10" concept but all of mine have other ways for doing addition and subtraction mentally that are equally correct and equally quick. You don't need to teach them other ways....but if one of them does a problem a different way and then can explain to you how and why, that's ok. I think allowing them to do the problems different ways helped them to become more comfortable with numbers and manipulating them in their heads. All my kids are much much better at mental math than me and I think it's because of Singapore.

 

Absolutely, this! In this country, we often approach math as a subject teachers need to impart to children, but I love this particular approach of letting our kids use their natural problem-solving skills...I will present a single problem from the textbook and ask "How would you solve this?" giving pencil, paper, and our small box of manipulatives. Then I am genuinely interested to hear about and understand how my child solved it-- I think the learning comes in explaining WHY, and that's why a lot of us parents using Singapore end up getting a lot stronger in math (and doing much of the work for our kids).

 

After all that, I can say, "Well, that is cool. I'm going to do it another way and let's check to see if we got the same answer." And then I will go through another mode of doing it. And then we'll see if we can think of another way, or if we haven't already proven it with manipulatives, we'll do that.

[TKDmom]

Oh my goodness I am going to have to mull over those above posts daily for quite awhile. Thank you all so much. I think I have seen mentioned a book people recommend for teaching this method but I can't seem to remember the title. Would that be helpful in getting me to understand *why* this is necessary and useful?

 

I do have the HIG and that helps me at least have an idea where I am going but I still feel we are hanging by threads off a cliff. I think we do need to slow down and get solid solid solid on place value and making tens. I think my ds will benefit from it as well as we are just starting to get caught in that in 1b as well.

 

I have been having her vertical problems horizontally, should I not be doing this if it doesn't tell me to? And on the mental math pages in the back of the HIG am I just to allow them to figure out the answer using any technique they can? Number line, fingers, dots on page, or by mental math do they mean no tools like that should be used? I am feeling many posts along these lines coming up over the next months. I guess I just need confidence that 1. I made the right choice in this switch 2. I am not setting them behind in my fumbling attempts at teaching it and 3. Somehow they will (and I will) indeed understand these methods, not to mention understand the why behind them. Sigh.

 

Disclaimer.... I am usually not so morose about things like this! Thanks for understanding!

 

I think the book you're thinking of is Knowing and Teaching Elementary Mathematics by Liping Ma

 

You have my permission to solve things vertically, horizontally, with fingers, toes, or whatever works. ;)

I think the key is that you practice different ways of looking at those numbers over and over as you work on problems together. Over time, she will naturally adopt what works for her in her mental math. The assumption for mental math, though, is that you won't be using any tools at all. Like when you're in the grocery store trying to figure out if the cans that are 3 for $5 are cheaper than the ones that are $1.75. But...if she struggles with mental math, don't make her do a whole page of those drills. Choose maybe 5 at a time to start with. My dd is using XtraMath.com as a supplement to practice memorizing math facts.

[letsplaymath]

A few points, in no particular order:

 

(1) Liping Ma's book is great, for what it does. It will not show you why the Singapore Math subtraction model is necessary. Its purpose is much more general, namely to open the readers' eyes to the fact that elementary arithmetic is deeper and richer than most of us realize.

 

(2) On 45 - 7: If you had 4 dimes and a nickel, and you wanted to buy a piece of candy for 7 cents, what would you do? Wouldn't you hand the clerk one dime, and then put the change back with the other money still in your pocket? That's all the Singapore method is asking you to do!

 

The most important key to mental math is to make the problem simpler. Children make mistakes in subtraction much more often than in addition, so this "making change" method turns the subtraction problem into a simpler addition. Very few children will make a mistake when adding 35 + 3, but many will get confused trying to borrow and subtract 45 - 7.

 

(3) Subtraction is one of those stumbling-block topics that causes trouble for lots of kids. With three out of my five children, we had to walk away from subtraction for weeks or even months, doing other math in the meantime. It's not worth the tears (from mom or kids), when there are plenty of other interesting things to do and subtraction will still be waiting when we come back. That's one of the joys of homeschooling -- the freedom to do things out of order, to follow rabbit trails, without worrying about an artificial schedule imposed by textbook writers.

 

Flip ahead to the fractions chapter, or geometry, or bar graphs, or whatever topics are waiting later in the book. We usually found the Singapore math B semester books more interesting than the A semester (which tended to focus on basic arithmetic). Or take time out for living math with library books. Enjoy your break, and come back to subtraction one of these days....

 

(4) When I was teaching mental math to my kids, and we ran into a new method they found confusing, we divided the lesson. In the textbook part, which we did orally, they were supposed to try at least a few problems by the new method. In the workbook, though, they could use any method they wanted. I mention several useful thinking strategies for mental math in my PUFM post on subtraction:

• PUFM 1.4: Subtraction

(5) Making tens (ten bonds, the pairs of numbers that add up to ten) are super important. Another good game for practicing those is Concentration/Memory. Fun for all ages:

• Game: Tens Concentration

Edited October 13, 2016 by letsplaymath

[Bocky]

 I think I have seen mentioned a book people recommend for teaching this method but I can't seem to remember the title. Would that be helpful in getting me to understand *why* this is necessary and useful?

 

 

 

The book that really helped me learn to teach the SIngapore way was Jana Hazekamp, Why before how: Singapore Math computation strategies, grades 1-6.

 

It goes through teaching all of the basic operations using Singapore methodology, actually scripting what you should say and do.

[TKDmom]

 

A few points, in no particular order:

...

 

I want to like your post a couple times. 

[The Governess]

I have used Singapore from levels K-5, and  that method for subtraction never really felt right to me either.  I taught my kids to do it a different way. 

 

for 45-7, instead of breaking up the 45 into 35 and 10, I would break up the 7 into 5 and 2.  Subtract 5 to get to 40, then 2 to get to 38.  This worked for me and both of my kids better than the way you described, although we did give it a fair try.  The main point is getting them to think in terms of number bonds rather than simply counting backward, to see the smaller parts within the whole that can be manipulated in various ways to make mental math easier. 

 

I wouldn't sweat it, and I wouldn't give up on Singapore, either.  It's a great program, but if one strategy isn't clicking for you, don't feel like you can't try another!