Help with Singapore Std 6A question

[homecool]

Can anyone help me with this problem from the Singapore 6A STD textbook? There are errors  in the answer guide and I am not sure I am understanding what I see in the textbook.  I understand the answer but I can't figure out how to decide where to divide the units.

 

PagIe 111 Exercise 4 # 7

Edited November 28, 2016 by homecool

[cbollin]

I hope my answer helps.  The textbook should be showing equivalent ratio of 15:18. I can't get the pic big enough on my side to make sure the pic is right. But that's the equivalent ratio that makes this easy to see what's going on. 

Basically you take the 5:6 ratio and make it equivalent so that it's easy to subtract 28 dollars from both and end up with what you want.

I'd suspect some/many students would need a little bit of trial and error to get the right ratio if they didn't have that second picture. But the picture is given so they now have it as a 15:18 ratio problem. both people subtract 28 dollars, which is 14 x 2. (the units will be a factor of 28 so it divides evenly. or at least that always was the case in the levels of singapore I used)  so each unit is 2. and Wayne has 1 unit left. Stef has 4 units left.

Does that help answer your question? or did I confuse it more for you?

 

[homecool]

Yes I think that does help - thank you.  With the picture both my daughter and I understand the answer but I wasn't sure how they knew to make the equivalent ratio 15:18 as opposed to something else. I am not sure we would have been able to do it without the picture.  We are going to work on some more tomorrow.  I really wish this level of Singapore had the Home Instructor Guider.  Thanks again.

[cbollin]

Yes I think that does help - thank you.  With the picture both my daughter and I understand the answer but I wasn't sure how they knew to make the equivalent ratio 15:18 as opposed to something else. I am not sure we would have been able to do it without the picture. 

 

Without the picture being clear enough on my screen, I had to do it trial and error a bit. and for some reason my brain went to 20:24 . That didn't work. so I tried something else. First thing I did was write down several ratio. I even did quick bar (blank lines for me) to help my brain click.

 

And that trial and error can be part of the process to learn how and why it is working in my experience with US edition of Singapore. I don't think it was supposed to be obvious to be 15:18 on first try (for average student) so the picture was there as the hint.  If I were writing a home guide for it, I would encourage parent and student to try a trial and error process and give the hint about "which of those equivalents would be the same as 1 plus a factor of 28" and discuss that angle a bit.   There may even be some other obvious thing that didn't occur to me as a hint.

 

But one has to write down some equivalent ratios and try for it. and it's ok to not get it right the first time.  I seldom did in the US edition when helping my dd.

I don't know if the way I think and talk it out is helpful or not.  But see if some of those insights talked out loud together

[letsplaymath]

In my opinion, this problem is pushing the limit beyond which bar model diagrams are not useful, and just-plain algebra works better. I suspect that is why the book gives the diagram, rather than expecting the student to produce it.

 

It is useful for kids to understand that ratios can be split to make equivalent ratios -- that 5/6 or 10/12 or 15/18 all name the same relationship. Then the student can use her knowledge of equivalent fractions to identify other similar ratios, and maybe make up a couple similar-ratio problems of her own.

 

Making up problems is a great way to wrap one's brain around a challenging topic.

[homecool]

Without the picture being clear enough on my screen, I had to do it trial and error a bit. and for some reason my brain went to 20:24 . That didn't work. so I tried something else. First thing I did was write down several ratio. I even did quick bar (blank lines for me) to help my brain click.

 

And that trial and error can be part of the process to learn how and why it is working in my experience with US edition of Singapore. I don't think it was supposed to be obvious to be 15:18 on first try (for average student) so the picture was there as the hint.  If I were writing a home guide for it, I would encourage parent and student to try a trial and error process and give the hint about "which of those equivalents would be the same as 1 plus a factor of 28" and discuss that angle a bit.   There may even be some other obvious thing that didn't occur to me as a hint.

 

But one has to write down some equivalent ratios and try for it. and it's ok to not get it right the first time.  I seldom did in the US edition when helping my dd.

I don't know if the way I think and talk it out is helpful or not.  But see if some of those insights talked out loud together

Thank you - very helpful and very reassuring.   I felt like I was missing something.  

[homecool]

In my opinion, this problem is pushing the limit beyond which bar model diagrams are not useful, and just-plain algebra works better. I suspect that is why the book gives the diagram, rather than expecting the student to produce it.

 

It is useful for kids to understand that ratios can be split to make equivalent ratios -- that 5/6 or 10/12 or 15/18 all name the same relationship. Then the student can use her knowledge of equivalent fractions to identify other similar ratios, and maybe make up a couple similar-ratio problems of her own.

 

Making up problems is a great way to wrap one's brain around a challenging topic.

 

I struggle with this a little with Singapore b/c often I think using  algebra would be much easier but having  too many options has proven challenging for my daughter.  The bar diagrams work with her brain.  

 

We will review this one along with equivalent ratios tomorrow.

[letsplaymath]

I struggle with this a little with Singapore b/c often I think using  algebra would be much easier but having  too many options has proven challenging for my daughter.  The bar diagrams work with her brain.  

 

We will review this one along with equivalent ratios tomorrow.

 

Bar diagrams work very well for showing simple equivalent ratios. To go from 5/6 to 10/12 is to cut each unit in half. 15/18 cuts each original unit into thirds. Beyond that, the diagram isn't helpful -- but once the idea has been mastered with smaller numbers, students should be able to come up with impressive equivalent ratios like 55/66 or 300/360, just playing around.

 

Not that they will probably ever use monster ratios like that in solving a math problem. But proportional thinking like this is very important. Playing with ratios helps solidify the foundation for linear equations in algebra.

 

Bar diagrams in general are a pictorial form of algebra, and the type of thinking involved in solving them will carry through to manipulations with letters later on. Especially in the ability to translate a word problem or real-life situation into math equations. Very helpful!