singapore math peeps: help me solve this CWP3 problem?

[Halcyon]

Hey there! My son and I are working on a question from CWP 3 (#21 on p 10) and while I can solve it quite easily algebraically, I am trying to od it using bar method so he understands more clearly.

 

Here is the question: Marie and Sharon have the same number of paper clips. When Marie gives sharon 16 paper clips, Sharon has 3 times as many paper clips as Marie. How many paper clips does Sharon now have?

 

Okay, so bar model-wise, I made part equal M-16 and the whole equal M+16. So then logically 3(m-16)=M+16. But this already is getting too algebraic, no? How would I proceed using just a bar model approach?

[Diviya]

This might be incoherent because it's hard for me to explain without drawing, but try this.

Draw two bars. One is for Marie and one is for Sharon, and they are equal. Then you slice off the part representing 16 on maries bar ( do it in the middle) and add it onto sharons. You can then divide sharons bar into 3 sections ( the part you just added is one section) and maries bar will be the same as one section, which represents sharons amount being 3 times maries amount. Now you should be able to see that Marie has 16 and Sharon has 48. The trick is to see it as going from 2:2 to 1:3, so that you know the part being moved is one part.

And I am sure you can do it with one bar only, but I am not seeing how to do that at the moment.

Someone with the Hig would be able to give you a clearer, more elegant solution!

 

Hope that helps

[Halcyon]

Thabk youfor responding! It still seems to me that your approach involves more a 'feeling' of how to approach the problem thana truly mathematical approach, no? And if the 16 that I removed from marie and added to sharon is one part, how would I 'know' that without trial and error, which I'd like to avoid? I am going to sit down with your approach and see If I can make it work for me. And does the hig help out with CWP?? I have the hig but don't see any explanations for CWP problems... Thanks!

[Halcyon]

Meant to say, if the 16 that I am removing from Marie does acually represent one 'part' of the three (which I know it does, from solving it agebraically beforehand) how would I 'know' this using a bar method without trial and error? Am I making sense? If I had a scanner handy I'd draw it out and scan it lol

[Diviya]

Sorry I got confused. The HiG probably doesn't have cwp solutions. I understand what you are saying about my solution. Maybe if you do it as one bar, it will be more clear. You draw one bar, with a line down the middle. Left is Marie and right is Sharon. Then you draw a line in Marie's portion to represent the 16 paper clips. That section now belongs to Sharon. So, now you know that Marie has one piece and Sharon has 3 pieces. I don't know, has ratio been covered yet? It looks to me obvious that 16 must be one section, but I think you need to have covered ratio maybe to get there.

Sorry I can't be more helpful. I've heard you can get proper solutions at the SM forums. Or maybe someone more articulate than I will chime in. :001_smile:

[Dana]

The HiG doesn't have anything about CWP.

I also use the iExcel books. The first part of the book has general problem-solving approaches, but the last half of the book is about using bar models. They start with numbers so you'd do a bar model for 31-15 for instance, then do word problems. Those have been a significant help with moving to the bar models.

 

The problem you're looking at was a challenge for us :)

What worked with bar models was using the two bar model for Marie and Sharon and then using "before" and "after" models.

 

So the "before" picture has Marie and Sharon with the same length. Cut off (shade) a 16 for Marie and add it to Sharon's length. We can't know what ratio it is, so in our drawing, we don't see any specified length.

 

Then we draw an "after" model with Marie and Sharon, but now we know that Sharon has 3 times as many clips as Marie, so we draw the diagram to represent this.

 

I think we needed some adaptations when my son was drawing the model and there definitely was a lot of discussion about this one. The key was seeing the comparison... that since Marie lost 16 and Sharon gained 16 and they started with the same amount... now Marie has to have 16 and thus Sharon has 3*16.

 

The drawing did work... but I do think this was the toughest one in this section.

 

I don't know if anyone else has other suggestions for books on bar models. It's been quite a change for me, but I'm liking them. iExcel books have been useful as well.

[Halcyon]

Thank you so much_we haven't covered ratios yet, so I didn't want to go there, but I did end up eventually working it the way dana did. And thx for the headsup re the sm forums-are those over at singaporemath.com? Now I'm struggling with how to explain #24 in that same chapter-again, my mind just wants to do it algebraically, and to be honest, I'm tempted to explain it that way to my son. I read somewhere that bar models begin to present more difficulty in some questions, and that in some cases it's easier to do algebra. Anyway, for anyone who wants to take a crack at the final question in the section, here it is:

 

Julie had 43 pencils more than pens. When she gave away 17 pens, she had twice as many pencils as pens. How many pens and pencils did she have left altogether?

 

Again, with bar models got as far as my 'part' equalling p-17 and my 'whole' equalling P+43. So 2(p-17)=p+43. But again, algebra. I really need to train my mind to use bar method. I will look at those iexcel books you recommended...

[Dana]

Yup, the forums are at singaporemath. They're good.

 

FOr 24, I was pleased after the hassle of 21 (and a few days later), my son was able to do 24 on his own (if I'm not misremembering!) :)

 

Our model is two bars again (a comparison)

Pencils

Pens

 

Start with the bar for pencils and pens with 43 as the difference between.

Shade 17 for removal from the pens.

At this point, there are twice the number of pencils as pens, so this should be at the halfway point for the pens.

(It may take some rough attempts at the bar models on scratch paper to get to this so the model looks accurate!)

 

So now you can see that the amounts of pens is 43+17 (since that's equivalent to 1/2 the pencils).

This means there are 60 pens and 120 pencils, so 180 writing implements.

 

We are starting to use some algebraic approaches (variables for the bars in some cases... on this one, ds wrote pg in the pencils bar twice... then labeled to the side "pg = pen give amont left" I'm encouraging defining variables :) )

 

We're in the mult/div problems now. They're going much smoother - and so far have been easy enough that I haven't forced the bar models (although I will soon again).

[Ray]

Attachment has a ms paint 'drawing' where I tried to show the gist of what DD did for the first cwp problem in thread. Looks like a fraction pizza gone crooked:D

 

Anyway the bar modeling has not really taken off here, but I do encourage drawing things out and it looks like this time she nailed it. I confess to not checking everything she does and was surprised at her answer .

Edited October 2, 2010 by Ray
trying to reword thought

[Dana]

There are also some problems (thinking it was in this section) that were MUCH easier to solve with bar models than with algebra. Gave my husband the problem and he tried with algebra but it was significantly easier with the bar model. My son was so pleased to be "faster" than Daddy. :D

[Halcyon]

Thank you ray-i appreciate the attachment!

 

Ah, I see what you did. Wow, that is so different than the way I instinctively taught it. I wonder what's the harm in introducing algebra at this point? I'm quite sure it would make sense to him, but there must be a reason SM doesn't "allow" it yet.....

 

Yup, the forums are at singaporemath. They're good.

 

FOr 24, I was pleased after the hassle of 21 (and a few days later), my son was able to do 24 on his own (if I'm not misremembering!) :)

 

Our model is two bars again (a comparison)

Pencils

Pens

 

Start with the bar for pencils and pens with 43 as the difference between.

Shade 17 for removal from the pens.

At this point, there are twice the number of pencils as pens, so this should be at the halfway point for the pens.

(It may take some rough attempts at the bar models on scratch paper to get to this so the model looks accurate!)

 

So now you can see that the amounts of pens is 43+17 (since that's equivalent to 1/2 the pencils).

This means there are 60 pens and 120 pencils, so 180 writing implements.

 

We are starting to use some algebraic approaches (variables for the bars in some cases... on this one, ds wrote pg in the pencils bar twice... then labeled to the side "pg = pen give amont left" I'm encouraging defining variables :) )

 

We're in the mult/div problems now. They're going much smoother - and so far have been easy enough that I haven't forced the bar models (although I will soon again).

[Dana]

 

Ah, I see what you did. Wow, that is so different than the way I instinctively taught it. I wonder what's the harm in introducing algebra at this point? I'm quite sure it would make sense to him, but there must be a reason SM doesn't "allow" it yet.....

 

It is a very different way of thinking.

I'm using some variables so my son gets used to a variable representing a quantity. I think a reason for not using algebra at this stage is that the bar models are more concrete. I think it'll give a good foundation for the abstraction of algebra.

 

It'd be a good question to ask at the singapore forums though... see if there's a clearer explanation of the reasoning.

 

I don't see any harm in introducing the algebra, but I do think that keeping at the concrete stage a bit longer may be helpful in our family. And it has been neat to see a few problems that the bar models are faster than algebra.

[nansk]

Is this right?

 

One Unit = 43+17

= 60.

 

So pens + pencils = U + 2U

= 180.

[Halcyon]

Yep, that's it. My dh, who is a math whiz, could only do it algebraicially and is still trying to wrap his head around the bar model solution LOL.

 

So if I wanted mored worked problems like this, iexcel is the go-to book? I'm enjoying these type of problems, as is my son, but I can see how in some cases, worked solutions would be helpful.

[nansk]

Yep, that's it. My dh, who is a math whiz, could only do it algebraicially and is still trying to wrap his head around the bar model solution LOL.

 

So if I wanted mored worked problems like this, iexcel is the go-to book? I'm enjoying these type of problems, as is my son, but I can see how in some cases, worked solutions would be helpful.

 

 

I'm not sure about iExcel, but here, in the book stores, Fan-math appears to be popular.

 

I had the same issue, btw; I would be able to solve these problems algebraically but didn't understand the model method at first. I used the Singapore Model Method book to understand all the types of models that are used. The problems used in this book are very simple and repetitive, but atleast one can start solving them the correct way, which is a confidence-booster for the parent :tongue_smilie:

[Capt_Uhura]

"Singapore Math Peeps" :lol::lol::lol: You made my day!

 

That's what I have here....my math peeps!

[stripe]

I have Brain Maths, which is from Pan Pacific in Singapore, but I have to tell you, most of the problems are nothing new; their references list math books published by Dover, many by Martin Gardner. I'd check his stuff out; your library likely has things like this.

 

Zaccaro's Primary Grade Challenge Math (and his other titles) are also useful. They're American books and still in print.

 

Marilyn Burns' Math for Smarty Pants is also fun.

[Capt_Uhura]

Dana - which i-Excel books would you recommend for the bar models?

[Mom-ninja.]

The bar method is confusing!

[Dana]

Dana - which i-Excel books would you recommend for the bar models?

 

We're in book3. Bar models were introduced in book 1.

I haven't seen the model method book mentioned above, but I imagine that might be a better place to start.

 

I teach math at a cc and have taught solving word problems for years. It's been rough going to bar models since I'm so used to the algebraic approach.

As I've struggled with them, I'm more impressed with the bar models though. I'm going to keep pushing my son with them since I see some benefit to them.

 

The iExcel books helped me with seeing set up with the models and with starting my son with doing a model for a math sentence, then using a model for a word problem. They are like CWP in that they have one example, then they have a few (only 3-5 problems for each topic) problems for the student to do.

 

I found the iExcel books good for that transition - and I often make my son do the bar models even if he can get the answer without them. I think that setting up the bar models on "easy" problems helps him on later trickier problems (like the ones above!).

 

The iExcel books don't give more in the way of solutions though. The answers have the math sentences but don't show the models. The book a PP mentioned may be better than the iExcel for getting set ups. I'd also start with book 1 and just work from there.

[stripe]

The bar method is confusing!

I think the bar method is the heart of the "Singapore method" and is covered in The Essential Parents' Guide to Primary Maths by Fong Ho Kheong (author of My Pals are Here! maths). ISBN 981-01-7458-6 but OOP. There are a few copies used on Amazon.com for $10+S&H.

[Arch at Home]

I really like to build bar charts using Cuisenaire rods. We used to have a lot of trouble with getting the proportions right and my dd did not like to redraw. With the rods we can easily trial and error proportions. In addition it is easy to show how a bar is made up of a number of components. As the problem type in question gets harder I like to rearrange the rods to show how the various bars match up. It is also easier to see what happens when quantities get transferred.

 

Rods are my manipulative of choice behind M&M's. Unfortunately I have not seen any books on how to do this.

 

Sarah

[8filltheheart]

The bar method is confusing!

 

Don't feel like a failure if you can't envision bar diagrams. There is nothing wrong if your brain solves them algebraically.

 

The first time I heard about Singapore my oldest was in 6th grade. I bought all 6 grade levels. We went through them rapidly (like hrs for all of them). My ds, who had never studied alg and was only finishing Horizons 6, answered all of the questions w/o any difficulty using alg. The only problems he couldn't solve initially were the water flow and rate problems b/c he had never learned the formula r*t=d.

 

My 14 yos is very gifted in math and has incredibly strong mental math skills. He also solves things mentally via algebraic manipulations.

 

From our personal experience, bar diagrams do not make or break mental math abilities or math skills. What bar diagrams do exceedingly well is allow concrete thinkers to understand what is occurring conceptually.

[Mom-ninja.]

Thanks for the encouragement. I'm always afraid I'm doing something wrong. I automatically solve the problems with algebra. My ds is able to answer the problems, but also not with the bar method. I'll ask him how he came to his answer and he just says, "I don't know. I just figure it in my head."

[nansk]

...I think that setting up the bar models on "easy" problems helps him on later trickier problems...

 

:iagree:

 

Bar diagrams enable younger students (not yet mentally ready for algebra) to interpret and solve challenging problems using arithmetic.

 

...What bar diagrams do exceedingly well is allow concrete thinkers to understand what is occurring conceptually.

 

:iagree:

 

Bar diagrams help students to form the correct algebraic equation, by showing the relationships and change described in the word problem in a clear visual.

[Joyofsixreboot]

I'll ask him how he came to his answer and he just says, "I don't know. I just figure it in my head."

 

A kid after my own heart. If only my teachers would have let me use that answer.

[Dana]

A kid after my own heart. If only my teachers would have let me use that answer.

 

The problem is that this approach breaks down as material gets more complicated. I could just "see" answers through high school. I didn't understand what was going on behind the problem nearly as well as I thought. It kicked my butt a couple of times in college. I'm going to be sure my son is better prepared than I was, so I'm not accepting that from him.

 

YMMV.

[Mom-ninja.]

Yes, I was (am) the same way. I know what the answer is but not really the why.

 

I also use RS math and I have had many light bulb moments of, "So that's why it's like such and such."

 

So I do work with ds to have him try and explain what he has done. I tell him that part of being good at math is being able to explain the problem. So far though that has not been with the bar model.

 

I need to get on the ball and really learn how to do the bar model so he learns it.

[texasmama]

I haven't read the other replies but wanted to chime in that we have encountered problems in SM 4A which were clearly algebraic. I was at a loss, but finally figured out that the text wanted us to use the model method. I could solve it algebraically, but my fourth grader cannot. My poor brain is having difficulty wrapping itself around math that is very different from the way I was taught at times, though it has gotten better. (And yes, I have read Liping Ma's book, which helped a lot but didn't cure my lack of conceptual math.:tongue_smilie:) Just wanted to chime in and say that you are not alone!