Singapore question: will this come back to haunt us?

[alisoncooks]

No matter what, DD just doesn't understand the different ways Singapore teaches for adding/subtracting (adding in the ones place, adding to make 10, etc). I'm specifically talking about adding in the teens, covered at the end of 1A and in 1B. We're fine with counting on (and back) and some of the facts she simply knows.

 

If we just plow through and solve these problems with manipulatives and such, will we later have problems for not having learned how to do it the Singapore way? Will this come back and make later levels (grade 2 and up) terribly difficult for us?

[boscopup]

Use manipulatives. It will be reviewed each year. That is a hard concept, and it might come easier next year when you hit it again. :)

[Zoo Keeper]

Use manipulatives. It will be reviewed each year. That is a hard concept, and it might come easier next year when you hit it again. :)

 

 

Yup. Just keep on showing, and showing, and saying and saying....it will sink in.

[alisoncooks]

Thanks!

We'll just keep moving on and not fret it for now.

[Five More Minutes]

No matter what, DD just doesn't understand the different ways Singapore teaches for adding/subtracting (adding in the ones place, adding to make 10, etc). I'm specifically talking about adding in the teens, covered at the end of 1A and in 1B. We're fine with counting on (and back) and some of the facts she simply knows.

 

If we just plow through and solve these problems with manipulatives and such, will we later have problems for not having learned how to do it the Singapore way? Will this come back and make later levels (grade 2 and up) terribly difficult for us?

 

I agree with the pps -- it's a good idea to use the manipulatives to keep plugging away with it.

 

I think that there's a difference between genuinely not understanding the concept (how could 7 + 8 possibly give rise to a 10 and a 5?) and not being able to initiate the strategy when presented with a problem. Not understanding the concept is more problematic for future levels, but is also most likely to be solved using manipulatives.

 

I've found that with my younger dd, her default strategy is counting on or back for problems. (Even problems like 9 + 9. :glare: ) After making sure that she did understand the concept of making a ten when I explained it, we have moved on in our lessons, albeit a bit more slowly. Every day we take five or ten minutes and do a few addition / subtraction problems where I ask her to teach me how to solve the problem using c-rods. I sometimes talk about alternative ways to solve a question. After a month of this, I'm seeing her naturally reach for a range of strategies when faced with an addition or subtraction question.

[blondeviolin]

I'd revisit it constantly, even just working through two or three problems together before doing your regularly scheduled lesson.

[serendipitous journey]

Just wanted to toss this out -- for these kinds of hangups (in various curricula) I've often liked to pull in Kitchen Table Math (some topics are in one, more advanced ones in 2, which treats multi-digit stuff, or 3). It's been very useful on these occasions.

[letsplaymath]

One thing that I remember from reading Liping Ma's Knowing and Teaching Elementary Mathematics was that the Chinese teachers considered the arithmetic of the teens extremely important and foundational just exactly because it is the first place that students work with numbers that are too big to count accurately. Ma had asked about student subtraction problems in the upper two-digit numbers, but the teachers continually pointed her back to the importance of teaching addition and subtraction in the teens.

 

This is the time for the student to begin using thinking skills instead of fingers. Counting up and counting back is only reliable with small numbers (up to the fingers on one hand). Students need to consciously practice using other strategies, such as combining numbers to make a 10, or recognizing the doubles and the numbers close to them, or adding/subtracting numbers in pieces.

 

For example, to figure out 7 + 8, the student might:

• Recognize that 8 is almost 10 and then imagine the numbers as stones or pennies: "moving two pieces" from the 7 "pile" over to the 8 "pile" turns the calculation into 5 + 10.
  
• Or recognize that 8 is one more than 7, so the answer will be double-7 + one more: 14 + 1.
  
• Or think that 7 is 5 and 2 more, 8 is 5 and 3 more, so the total is 10 (the two 5's) and 2 + 3 more.
  
• Or use some other method to reason about the problem.
  

It is not important that your student uses exactly the same method as the book. But it is very important that your student begin to think creatively about numbers and not rely on just counting and memory. With counting, it's easy to lose track. With memory, it's easy to forget or get confused. With logic and reason, your student will have a tool she can trust.

[freerange]

I think it's more important that YOU understand the making tens etc, so that as you come across future questions, both in her maths materials and in real life, you can reinforce it for her.

[pitterpatter]

How long have you worked on it? Maybe it's not essential to have it down pat now, but I think it would definitely make things a lot easier. There was a point where we stopped and took it real slow. After about a month (about two weeks on addition and two weeks on subtraction), DD understood and could work wonders in her head. (Wondrous to me anyway, as I never could do such things at her age.) We are nearing the end of 1B now. Everything seems to keep building on the concepts you mention. Can your DD instantaneously recall and implement the number bonds for ten? If not, I'd work on that. If she doesn't have doubles and near doubles down, I'd work on that too. Like I said, maybe it's not essential, but I think it would cut down on future frustration.

[alisoncooks]

Thanks for all the feedback on this!

We'll definitely keep hitting it but it's nice to know that it'll be reviewed some more later on! We'll probably move on into 1B and do the graphs section, then come back to it.

 

Re: number bonds to 10 -- she's got them pretty good but not instantaneous. Good suggestion to go ahead and work more on doubles and doubles +/- 1.

[hsbeth]

My youngest is just now clicking with this (after working on it for a few months). We kept on working ahead with manipulatives, but have done frequent reviews as others have suggested.

 

For some odd reason working on problems with numbers larger than 10 (ie 11+6 or 12+6) was easier for her. She was more comfortable with the idea of reducing down to a group of 10 than completing a group of 10. Once she became comfortable with this concept and could quickly do it in her head we took another shot at completing groups. She can now work those mostly (if she's not fatigued).

 

Although she's always anxious to jump into her books, I insist on doing review first when she's fresh. We seem to get better results in Math and Reading this way.

[Alice]

One thing that I remember from reading Liping Ma's Knowing and Teaching Elementary Mathematics was that the Chinese teachers considered the arithmetic of the teens extremely important and foundational just exactly because it is the first place that students work with numbers that are too big to count accurately. Ma had asked about student subtraction problems in the upper two-digit numbers, but the teachers continually pointed her back to the importance of teaching addition and subtraction in the teens.

 

This is the time for the student to begin using thinking skills instead of fingers. Counting up and counting back is only reliable with small numbers (up to the fingers on one hand). Students need to consciously practice using other strategies, such as combining numbers to make a 10, or recognizing the doubles and the numbers close to them, or adding/subtracting numbers in pieces.

 

For example, to figure out 7 + 8, the student might:

• Recognize that 8 is almost 10 and then imagine the numbers as stones or pennies: "moving two pieces" from the 7 "pile" over to the 8 "pile" turns the calculation into 5 + 10.

• Or recognize that 8 is one more than 7, so the answer will be double-7 + one more: 14 + 1.

• Or think that 7 is 5 and 2 more, 8 is 5 and 3 more, so the total is 10 (the two 5's) and 2 + 3 more.

• Or use some other method to reason about the problem.

 

It is not important that your student uses exactly the same method as the book. But it is very important that your student begin to think creatively about numbers and not rely on just counting and memory. With counting, it's easy to lose track. With memory, it's easy to forget or get confused. With logic and reason, your student will have a tool she can trust.

 

 

I think this is great advice. I’m in 1B now for the second time. My oldest is quite mathy so we kind of just sailed through everything. My second son is good at math but takes a bit more time to get the concepts. One thing I’ve done is skip forwards and do the “fun†sections (which for some reason are always at the end of the Singapore books). So we might cover graphs and time and money while we are still reviewing those previous concepts that he didn’t get.

 

I was someone that was good in Math but never really was able to play with numbers in my head. One thing I like about Singapore is the way that it teaches and encourages that. Some kids will do that easier on their own than others but I think it is worth parking for a bit and cementing those concepts. You can do math games and lots of fun stuff and you can move on a little but I have tried not to make big conceptual leaps until I’m sure they have the previous stuff down pretty well.

 

I do think they don’t have to do it the book’s way though. My middle son had missed a bunch of subtraction problems so I wrote them out and had him explain to me. It turned out the way he does the problems is weird to me. For 36-9 he would say 9-6 is 3 and then you subtract the 3 from 30 to get 27. He described is as “crossing out the sixesâ€. He understood fine (he had missed them all for careless reasons but could explain them all to me fine). While I was looking at him like he was crazy my oldest piped in to say that’s how he does those problems also. I told them they were making my head hurt but as long as they got it I was ok with it.

[letsplaymath]

I do think they don’t have to do it the book’s way though. My middle son had missed a bunch of subtraction problems so I wrote them out and had him explain to me. It turned out the way he does the problems is weird to me. For 36-9 he would say 9-6 is 3 and then you subtract the 3 from 30 to get 27. He described is as “crossing out the sixesâ€. He understood fine (he had missed them all for careless reasons but could explain them all to me fine). While I was looking at him like he was crazy my oldest piped in to say that’s how he does those problems also. I told them they were making my head hurt but as long as they got it I was ok with it.

 

 

My son (raised on Singapore Math) did this, too. He was so good at it that he never really saw the point of learning the standard "borrowing" method.

 

Basically, what they are doing is taking advantage of our base-ten place value system, that numbers are easier to work with when you get them to a multiple of 10. Therefore, you can take away 6, which gets you down to 30, a nice multiple of ten. And then you have three more to take away.

 

An even more advanced way to think about this is reflected in your son's "crossing out the six's" explanation. Subtraction finds the difference between two numbers, how far apart they are. Imagine the numbers on a number line, and subtraction will tell you the number of spaces in between them. Now, if you move both numbers UP the number line by the same amount (add the same number to both) or DOWN the number line by the same amount (subtract the same number from both), can you see that the distance between them would stay exactly the same?

 

Therefore, your son can "cross out 6" from each number without changing the difference, the answer he is looking for: 36 - 9 is exactly the same as 30 - 3.

[ECMD]

I taught my kids to regroup them not borrowing because when you borrow you need to return. If you have Calvert books I think that's how they taught. I am not very sure though.

[poiema]

I am loving this thread! I am going through 1B with 2nd ds and I am overwhelmed/excited at the same time. I was good at math so when I went through it the first time I just reverted to how I knew it, but with 2nd ds I really want to do it more the SM way. We have been using the Education Unboxed videos and I am getting more excited about math than my kids. They are not so excited yet, but hopefully my enthusiasm will catch on. I love math! That "crossing out sixes" is brilliant! I can't believe I never knew that before.

[Alice]

My son (raised on Singapore Math) did this, too. He was so good at it that he never really saw the point of learning the standard "borrowing" method.

 

Basically, what they are doing is taking advantage of our base-ten place value system, that numbers are easier to work with when you get them to a multiple of 10. Therefore, you can take away 6, which gets you down to 30, a nice multiple of ten. And then you have three more to take away.

 

An even more advanced way to think about this is reflected in your son's "crossing out the six's" explanation. Subtraction finds the difference between two numbers, how far apart they are. Imagine the numbers on a number line, and subtraction will tell you the number of spaces in between them. Now, if you move both numbers UP the number line by the same amount (add the same number to both) or DOWN the number line by the same amount (subtract the same number from both), can you see that the distance between them would stay exactly the same?

 

Therefore, your son can "cross out 6" from each number without changing the difference, the answer he is looking for: 36 - 9 is exactly the same as 30 - 3.

 

Thanks for the response! I was being a bit facetious when I said they made my head hurt. I do get why it works, although as someone raised on the more traditional algorithm it’s not natural to me. But it’s absolutely one of my favorite things about Singapore. I went fairly far in Math in high school and then college (as a science major) but I always knew that the real math kids somehow got math in a way I didn’t. I was smart and could memorize the formulas and plug in the numbers but never saw things the way they did. I feel like Singapore (and Beast Academy) is helping me to teach my kids in a way I wasn’t taught and they are much more comfortable with numbers and with playing with them.

[Nart]

I agree with everyone else. An example of when this comes in handy:

 

205-147

 

When you go to borrow from the tens column and then write your 1 next to the 5 you now have 15 - 7. It's a lot easier to think in terms making tens than to add onto 7 or count back 7 (or to have this memorized). If you think in terms of tens you think...15 is the same as 10 and 5. How many do I add to 7 to get to 10. Three. Three plus 5 is "6, 7, 8"...the answer is 8.

 

Just keep doing it over and over. It's reviewed over and over again really. For example, you will spend time adding/subtracting using measurements (mass, volume, length) aside from just plain ole addition and subtraction.

 

Does Singapore Math eventually teach that you can add three to both numbers to get 208-150, then count up 50 to 200 plus 8 more is 58? My son is finishing 1B and I haven't seen this strategy introduced yet.

[happypamama]

 

I do think they don’t have to do it the book’s way though. My middle son had missed a bunch of subtraction problems so I wrote them out and had him explain to me. It turned out the way he does the problems is weird to me. For 36-9 he would say 9-6 is 3 and then you subtract the 3 from 30 to get 27. He described is as “crossing out the sixesâ€. He understood fine (he had missed them all for careless reasons but could explain them all to me fine). While I was looking at him like he was crazy my oldest piped in to say that’s how he does those problems also. I told them they were making my head hurt but as long as they got it I was ok with it.

 

 

That's how my son does it as well, and Singapore is a good fit for him. I did teach him the traditional way of regrouping (and we won't talk about the complicated way that I taught it to DD, but it's what made it click in her head), turning that 6 into 16, because I said that he might need it when he gets to larger numbers that might be hard to keep straight in his head, but for now, this way makes sense to him, and he gets the problems correct. He's just started 2B, and for the problem that someone mentioned above, 205-147, he goes "200-147 is 53, plus the 5 from 205 makes 58." I'm not overly concerned about what strategy he uses, and for the OP, I would suggest using c-rods or coins (pennies, dimes, and dollars), or even toothpicks in bundles and have her DD move the items around on a place value chart to add and subtract.