Would you stop and solidify model-drawing for two-step word problems?

[Sneezyone]

DS is using SM3 (standards) this year. This is my second time through this but with a very different learner.

 

DS is solid on one-step addition and subtraction word problems.  He uses part-part-whole diagrams to finding a missing part or whole and uses the correct operations. DS, however, is balking at using bar models for two-step word problems despite me demonstrating how the circles he prefers can morph easily into rectangular bars. This is very different from my older who had no trouble making this leap and never needed or used models.

 

Would you or have you stopped to focus on model-drawing for a few days?  Does it make sense to keep going since model-drawing and two-step word problems will be repeated in SM4?

 

Any experience with this?

[mom2bee]

Can you do 1-2 modeling problems a day, but continue with the curriculum otherwise?

Since he has a method of modeling them (and assuming that it works everytime) I would keep going in the main book.

 

Maybe do the same problem with both processes side by side, and keep working on the bar models gradually.

[Monica_in_Switzerland]

We are right in between SM 2 and 3 and I've chosen to spend the next 4-6 weeks going through SM2 CWP and teaching the bar model method to my second child (as well as mental math solidification and multiplication fact work).  I didn't do this with my oldest.  

 

I don't think there is a right answer.  For oldest, I drew or at least started a lot of his bar models for him at the beginning of SM3, but by the end of SM3 had handed that over to him.  I also didn't "require" a bar model, but if he said, "I don't know how to do this problem" I would always ask, "Where is your bar model?"  He'd draw it, and generally, the question would disappear because the bar model would make it clear what needed to be done.  

 

Often times, just asking the clarifying question, "How many steps will this problem take?" is enough to set them down the right track for solving the problem.  

 

We are now in SM5b with ds and we have barely used bar models this year.  I find them clumsy for multiplication and division problems, and they just haven't really been necessary.  So, while I really love them as a tool, at least with my first kid, he's been able to move very easily into a more abstract way of thinking and the bar models are only used when he is really, really stuck.  

 

So how is that fora  non-answer for you?  My final word:  They are useful, but they don't need to be the end-all-be-all of word problems.  A kid should be comfortable enough with them to use them on any problem where the work needed isn't obvious at the start.  

 

 

[SparklyUnicorn]

No

 

I'd either do one problem a day or every other day.  OR I'd just let it go/find another method.  There is more than one way to approach these things. 

 

 

[regentrude]

If he has an alternate method he prefers (you mention circles), I see no reason to harp on the bar diagrams. One can learn math just fine completely without bar diagrams - they are one particular teaching tool that not all children need, not a vital concept in itself.

Edited October 11, 2016 by regentrude

[SparklyUnicorn]

Yeah I went a little crazy on method with my first because I was afraid if I didn't follow it he wouldn't get it.  So you spend years on these specific methods just to move on and discover that really that is all they are.  Methods.  After a certain point you won't ever talk about them again in those terms.  Looking back I understand better where they were going with it, but I can now imagine other ways to accomplish the same thing.  Now with my second kid I sometimes let go of a method if it doesn't speak to him.  Either way I don't feel like I've done damage.  My first kid does well in math.  My second kid does too.  I have approached it in a very different way with both.  My first probably didn't love being my guinea pig, but it is what it is.

 

 

[Sneezyone]

Thanks. This is comforting. He's really good with mental math and rarely misses those. He just can't tease out the relationships between the two unknowns without prompting. So he'll set the first problem up and solve it correctly and then set the second one up incorrectly, e.g. using the wrong givens. I think we'll just keep talking it through so he can see exactly what information he's solving for and how the answers fit together. I can draw the models for him too and have him fill in the givens and question marks. When he has that visual aid, he has no trouble at all. Labeling the circles and not just writing the numbers inside might help as well.

 

Moving into multiplication will also be a nice change of pace. He loves that.

Edited October 11, 2016 by Sneezyone

[SparklyUnicorn]

One tactic I sometimes use is to take the same wording of the problem and use small numbers to make the answer very obvious.  Then I say ok so how did you get that?  Work backwards and what did you do to get that answer?  And then when they get that, use the bigger numbers. 

 

Another tactic is to put everything in terms of money.  There is something about money!  LOL  Probably because it's familiar. 

There are other ways too.  Some word problem books have various techniques for "seeing" the problem if it's not immediately apparent.  And I think if you get too hung up on a particular method then when for whatever reason it doesn't "speak" to you you give up.  Some people need permission to try something else and not be forced into the one method. 

 

 

[Sneezyone]

One tactic I sometimes use is to take the same wording of the problem and use small numbers to make the answer very obvious.  Then I say ok so how did you get that?  Work backwards and what did you do to get that answer?  And then when they get that, use the bigger numbers. 

 

Another tactic is to put everything in terms of money.  There is something about money!  LOL  Probably because it's familiar. 

There are other ways too.  Some word problem books have various techniques for "seeing" the problem if it's not immediately apparent.  And I think if you get too hung up on a particular method then when for whatever reason it doesn't "speak" to you you give up.  Some people need permission to try something else and not be forced into the one method. 

 

I will definitely do this. I'm not terribly freaked about it because part of it is a maturity thing. DS is as bull-headed as they come and very rigid in hs approaches! But doing two-step problems with smaller numbers would take the focus off the calculation and put it back on to the thinking. 

Edited October 11, 2016 by Sneezyone

[Monica_in_Switzerland]

One tactic I sometimes use is to take the same wording of the problem and use small numbers to make the answer very obvious.  Then I say ok so how did you get that?  Work backwards and what did you do to get that answer?  And then when they get that, use the bigger numbers. 

 

Another tactic is to put everything in terms of money.  There is something about money!  LOL  Probably because it's familiar. 

There are other ways too.  Some word problem books have various techniques for "seeing" the problem if it's not immediately apparent.  And I think if you get too hung up on a particular method then when for whatever reason it doesn't "speak" to you you give up.  Some people need permission to try something else and not be forced into the one method. 

 

 

 

Glad it's not just my kids who can IMMEDIATELY understand the same problem if I switch from counting chickens to counting dollars.  LOL.    

[forty-two]

Bar diagrams don't come easily to my oldest - showing her thinking in general doesn't come easily for her (it took several months before writing the equations and then her answer in a sentence became natural, and even now she still tends to get the answer first and works backward to figure out the equations at least half the time (an improvement from the 100% of the time it was when we started)).  Just seeing the examples in the text and CWP and the Singapore Model Method book wasn't enough for her to really understand what was going on and how to use bar diagrams as a problem-solving *tool*.  If she had *another* way to visually show her thinking, I'd have let it go, but she struggles at getting what's in her head out in general (whether orally or on paper), and when she can't intuitively see what she's supposed to do, she locks up and has no tools for getting out what she *does* know to aid her in figuring out where she can try to go from there.  She needs *some* method of laying it out, and as bar diagrams make sense to *me*, that's what I'm going with for the moment. 

 

I bought the Process Skills for Problem Solving books - they build up drawing bar diagrams from the ground up, plus several other methods of problem solving (including other kinds of visual diagrams) - and we're going through that alongside her usual work.  As she gets better at diagramming her thinking, I'm going to start requiring bar diagrams along with her equations and answer - I think it's important to be able to show another person *how* and *why* she got the equations she did, as well as have tools for getting your thinking out on paper where you can look at it and mess around with it.  Bar diagrams aren't the only way, but as dd currently has *no* way, that's the one I'm going with for the moment - I think it will do her good.

Edited October 11, 2016 by forty-two

[Sneezyone]

Bar diagrams don't come easily to my oldest - showing her thinking in general doesn't come easily for her (it took several months before writing the equations and then her answer in a sentence became natural, and even now she still tends to get the answer first and works backward to figure out the equations at least half the time (an improvement from the 100% of the time it was when we started)).  Just seeing the examples in the text and CWP and the Singapore Model Method book wasn't enough for her to really understand what was going on and how to use bar diagrams as a problem-solving *tool*.  If she had *another* way to visually show her thinking, I'd have let it go, but she struggles at getting what's in her head out in general (whether orally or on paper), and when she can't intuitively see what she's supposed to do, she locks up and has no tools for getting out what she *does* know to aid her in figuring out where she can try to go from there.  She needs *some* method of laying it out, and as bar diagrams make sense to *me*, that's what I'm going with for the moment. 

 

I bought the Process Skills for Problem Solving books - they build up drawing bar diagrams from the ground up, plus several other methods of problem solving (including other kinds of visual diagrams) - and we're going through that alongside her usual work.  As she gets better at diagramming her thinking, I'm going to start requiring bar diagrams along with her equations and answer - I think it's important to be able to show another person *how* and *why* she got the equations she did, as well as have tools for getting your thinking out on paper where you can look at it and mess around with it.  Bar diagrams aren't the only way, but as dd currently has *no* way, that's the one I'm going with for the moment - I think it will do her good.

 

Yes. This is one of my older child's weaknesses. She intuits answers based on conceptual knowledge but has a hard time explaining her process. We're working on that this year and I was hoping to avoid that with DS. He actually likes/needs the visual cues (flashcards, drawings, etc.) to start and then discards them when they're no longer needed. Anyway, I'll get the process skills book too and see if there's another method, besides the bar model, that would help him visualize the two-step process. 

[Tanikit]

My 9 year old daughter has rules for word problems - she can do what she likes, but she cannot ask me for help unless she has done the following:

 

1. Attempted using smaller numbers

2. drawn a picture and/or a bar model

3. Reread the question at least 3 times

4. shown some written work of some kind 

 

and if she thinks she has the answer (no matter how she has worked it out even if she ignores all of the above) and wants me to check it she must either have written a sentence as an answer to the question asked or she must be able to verbally give me the full sentence required as an answer and not just a number.

 

Only that way can I find out what the problem and usually having done these steps there is no problem except that she may be writing too messily (and I have found a way to fix that too - just cross it all out and tell her to come back when it is neat and legible)

 

Bar models required a lot of me drawing it for her while explaining before she could draw them herself and even now with new concepts she needs help understanding how the bar model fits together or how to go from the picture in her head to the bar model (this may be age related). My youngest doing Singapore 1 is nowhere close to understanding bar models, so I am just introducing them so she will have seen them and understand they can work.

[Sneezyone]

My 9 year old daughter has rules for word problems - she can do what she likes, but she cannot ask me for help unless she has done the following:

 

1. Attempted using smaller numbers

2. drawn a picture and/or a bar model

3. Reread the question at least 3 times

4. shown some written work of some kind 

 

and if she thinks she has the answer (no matter how she has worked it out even if she ignores all of the above) and wants me to check it she must either have written a sentence as an answer to the question asked or she must be able to verbally give me the full sentence required as an answer and not just a number.

 

Only that way can I find out what the problem and usually having done these steps there is no problem except that she may be writing too messily (and I have found a way to fix that too - just cross it all out and tell her to come back when it is neat and legible)

 

Bar models required a lot of me drawing it for her while explaining before she could draw them herself and even now with new concepts she needs help understanding how the bar model fits together or how to go from the picture in her head to the bar model (this may be age related). My youngest doing Singapore 1 is nowhere close to understanding bar models, so I am just introducing them so she will have seen them and understand they can work.

 

DS is a liiiiittle different. I have to force him to seek help because he will either sit there, frustrated and mute, or plow ahead in the wrong direction. In his mind smart=do it yourself without help. He has a system and model that works well for simple problems. It's just failing him when he needs to represent two unknowns. Meh, we'll just keep working at it.

[forty-two]

He has a system and model that works well for simple problems. It's just failing him when he needs to represent two unknowns. Meh, we'll just keep working at it.

 

Do you understand how his model works?  *Could* it be extended to work for two unknowns?  Or is it limited and only works for simple problems but inherently can't be extended to more complicated ones?

 

If his model *could* be extended to work for two unknowns - he just doesn't know how to do it - then I'd probably stick with his model method and teach him how to apply it to the more complicated problems. 

 

If his method *can't* be extended to work for the more complicated problems, or if his method would be much more cumbersome and/or prone to error, or you really like bar diagrams, then I'd try to use his method as a base for teaching bar diagrams.  Work through several simple problems doing both his method and the bar method and showing how they connect together.  (With my dd, it helps a lot to teach bar diagrams with problems she intuitively gets, so the only "new" thing is the diagram itself.)  It may or may not help to explicit show him how his method falls apart with two unknowns (if it does indeed fall apart), but if his works but is cumbersome, I've found that working through several problems both ways, till he really *gets* the new method, is sufficient for illustrating how the new method is less work/more elegant.  (It's how I got my second dd to acknowledge that multiplication instead of repeated addition might actually be better - doing both together helped her see how they connected and were doing the same thing, and once she understood what was going on, she did kind of tire of writing 4+4+4+4+4+4 instead of 6x4 and saw the point to multiplication ;).)

 

[mamaraby]

We gave up on CWP and moved to "Process Skills for Problem Solving" instead. If bar diagrams are a struggle, I find "Process Skills for Problem Solving" works into it more incrementally (and the answers at the back have better explanations, too).

[Sneezyone]

Do the levels of FAN math correspond to grade levels?

[forty-two]

Do the levels of FAN math correspond to grade levels?

 

Yes, level 3 of FAN math lines up with Primary Math 3, and so on.  The ToC matches up pretty well - you could teach FAN math alongside Primary Math - take a few days to work through FAN math until you catch up to where you are in your main text, and then work FAN math alongside - my plan is to teach the text and then teach the section of FAN math, then do the wb.  (Right now we're working through a lower-level FAN book to get dd's confidence up - I expect we'll be skipping up to our tb level soonish as she feels more confident.)

[forty-two]

Pulled out our books and compared.  The FAN math books are divided into two parts: the model approach and the heuristic approach, each about half the book.  The model approach chapters line up pretty well with the first half of the year (the A books), and you could work through the heuristic part during the B books.  FAN math level 2 is pretty good for teaching the models from the ground up.  Level 3 has a quick review of the basic models and then jumps into two step problems.

[Sneezyone]

Pulled out our books and compared.  The FAN math books are divided into two parts: the model approach and the heuristic approach, each about half the book.  The model approach chapters line up pretty well with the first half of the year (the A books), and you could work through the heuristic part during the B books.  FAN math level 2 is pretty good for teaching the models from the ground up.  Level 3 has a quick review of the basic models and then jumps into two step problems.

 

Thanks. It sounds like book 3 might be the right place for us. I just need a quick review of the methods to get some alternative ideas. Your suggestion for extending his existing model gave me a lot to think about last night and, after thinking about it, that could work too. I think I'd just need to have him physically link the two part-part-whole diagrams to show how the first unknown feeds into the second problem. I'm going to give that a shot.

[Sneezyone]

Just a quick update since I end up buying the FAN math book for grade 3.

 

DS is down the the last unit in SM 3A but we stopped to work through the FAN Math addition and subtraction sections. We'll work on the multiplication and division sections with SM 3B and do the heuristics part over the summer.

 

DS doesn't draw the models exactly as the text does but his problem solving approaches are sound and his number sentences are correct. It's only been a week since we started so some slack is in order. I can already see some improvement.

 

He is now 'seeing' that there are multiple parts to the questions, multiple number sentences that need to be written, and multiple answers that can be achieved. Now I just need him to understand that there are multiple questions that he could answer and make sure he's answering the right one by referring back to the problem.

 

So, thanks for the suggestion! :hurray: