## Singapore 4A, Specific Lessons

cbollin

### Singapore 4A, Specific Lessons

Math 4a story problem question
nehschooler2three wrote: Thu Oct 23, 2008 4:19 pm I can't figure out how to help my son with this problem without teaching him algebra. We've had a few in the past like this also, but we've sorta skimmed over them. I'm convicted now I need to teach him the singapore way of doing this. The question is

Nicole and Tasha have 2000 stickers altogether. If nicole has 600 stickers more than Tasha, how many stickers does Nicole have?

We drew it out like this (excuse my internet drawing inability)

---- ----
| | + 600 + | |=2000
---- ----

The box represents Tasha and the box +600 equals nicole. He figured out that 2 boxes + 600 is 2000. Now my algebra brain says to subtract 600 from both sides and then divide by 2. But how does singapore teach this in a "non-algebra" way??? I know I should be able to figure this out, but I am held up by my algebraic mind.

Help!!!

P.S. two problems down there was the same type of problem which he figured out ok. It was

2500 people took part in a cross country race. the number of adults was 4 times the number of children. If there were 1200 men how many women were there.

He drew 1 box for the children and 4 boxes for the adults. So 5 boxes were equal to 2500 . He easily figured out 1 box was equal to 500 and replaced his boxes with 500's. Then figured out the adults =2000 and went from there.

It's just the 600 more (the adding part) that is throwing us. TIA
Your algebraic mind isn’t far off or too wrong with this problem. Some of the computations that we think of as algebra can’t be avoided at this point, but it is the abstract parts of algebra are avoided.

So you don’t end up writing the problem with a bunch of T and N and X’s and using a formula process just yet.

Instead, in Singapore you would have been thinking way back in 2A/2B about Whole and Parts and what to do with a problem like this. From back in 2A/2B they learned that when you know the Whole thing and know just one part, you subtract to find the other part. Back then it was problems that were easy such as 5 plus a box = 12. We know the whole thing (12) and we know one part (5). And we learned to subtract in that context. So, it is ok to do that now.

So, you and your kid see the problem correctly so far as
2 boxes (or bars) + 600 = 2000.

2000 is the whole thing,
And 600 is just one part.
2 boxes are the part that we don't know yet.

To solve means we have Whole minus part we know = other part that we want to know something about.
So, they have learned that you do 2000-600. So, you can teach that to your child.
And that leaves 2 groups (2 Tasha = 1400)
That means that we just figured out how many Tasha has, 700. But, that is not the question. We need to know how many Nicole has

She has 600 more than Tasha
700 + 600 = 1300

-crystal
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Math 4a story problem question

nehschooler2three wrote:Nicole and Tasha have 2000 stickers altogether. If nicole has 600 stickers more than Tasha, how many stickers does Nicole have?
Here's we would draw it at our house:

Total = 2000
-----------------/---600---/ Nicole
----------------/ Tasha

Subtract the part we know (600)
& Divide the rest in half (because without the 600, they are equal)

Now you know how much each blank bars is,
so you can add one blank bar (700) + 600 to get Nicole's stickers

Does that make sense?
I think these are fun!
Julie
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
nehschooler2three
Posts: 18
Joined: Sat Mar 25, 2006 8:43 pm
that makes sense now on how to explain it to him; thanks so much for your help.
Wife to Steve for 12 blessed years. Mom to 4 wonderful kids; 10 yo ds, 8 yo dd (ctg), a 4 year old blonde haired blue eyed wild monkey boy tagging along with us and one very special baby boy planned by God;born with congenital hydrocephalus on 5/20/08
cbollin

### Question about a problem in the Singapore 4a textbook

Teresa in TX wrote:Okay. This could possibly just be a really simple problem that I am making complicated (I doubt it, though). This is a word problem, #9 on Practice 2B:

"The difference between two numbers is 2184.
If the bigger number is 3 times the smaller number, find the sum of the two numbers."

Honestly, even my algebra level dd was puzzling over this one. Everything else around it was standard 4a stuff. Am I/are we missing something here?? She got the right answer, but it wasn't by working the problem according to their wording. Anyone want to shine a light on this for me?
Practice 2B, problem #9
Let me see if I can type through this.
Think in bar diagrams.

Smaller number is 1 bar ________
Bigger number is 3 bars ________ ________ ________

The difference between them is 2 bars. (3 bars - 1 bar)
Those 2 bars equal 2184.
That means that one bar is 2184 / 2 = (2184 divided by 2) = 1092

There are 2 ways from here:
The sum of Smaller number plus Bigger number is 4 bars.
4 bars of 1092 = 1092*4 (1092 times 4) = 4368

The other way is longer by a little bit as the student would figure out what the bigger number actually is and then add them.
Smaller number is 1092
Bigger number is 1092*3 =3276
1092+3276 =4368

********

It seems right on pace with learning multiplication and division in the unit.

did that help? and how did your child approach the problem? I'm very curious.

-crystal
Mommyto3boys
Posts: 32
Joined: Tue Mar 21, 2006 12:24 pm

### Problem # 10 on page 41

It helps if you can draw the problem out. There are 3 piles.

3rd Pile is 1 unit/bar long= ___ (1 unit or bar long)

2nd Pile is twice the 3rd Pile = ___ ___ (2 units or bars long)

1st Pile is 10 plus the 2nd pile = ___ ___ + 10 (2 bars + 10)

The sum of the 3 piles is 3000:
1 bar + 2 bars +2 bars +10 = 3000
5 bars + 10 = 3000
5 bars =2990

1 bar =598 which is 3rd pile
2 bars = 1196 which is the 2nd pile
2bars +10 = 1206 which is the first pile

HTH,
Debbie in NC
Mom to 3 ds (9.75, 7, and 4.5) and 1 dd (1.99)
Teresa in TX
Posts: 74
Joined: Fri Mar 16, 2007 4:20 pm

### Re: Question about a problem in the Singapore 4a textbook

Ugggg!! That is so obvious when you draw it out. that method is right there in the textbook. It was hard for me/us to bring it into a word problem and apply it! I think THAT is what I'm having a problem with is that I'm not used to drawing the problem out like that.

My dd got the final answer by doubling the 2184, which is not according to ideal way of handling it, but I can see where she was coming from.

I am wondering if I need to go back to the very beginning of Singapore and get a good handle on their method of teaching, so I can be retaught. I can tell that it is obviously a better math program than I ever had, and it is head and shoulders over MUS, which my 8th grader did 4 years of. Tips? I shake my head that I am unable to think through a problem in a 5th grade math book...and I have always considered myself pretty good at mental math!!

Crystal, you always said it was better than the other program, but I just didn't want to believe it because we had 4 years invested in that program (plus a ridiculous amount of \$\$). Now I see how much better it is and I hate that dd didn't have the advantage of this rather than our other choice. I'm sure this is part of the learning curve for me.

Thank you both for your help. I really appreciate it!!
Teresa (hanging her head in shame)
Teresa, Mom of 5: 15yo dd, 12yo ds, 7yo ds, 5yo ds, and 1yo ds

4th year with MFW
Using:
MFW 1st w/ 7yo ds
MFW RtR w/ 7th grade ds
MFW World History with 10th grade dd
So far we have used: ECC, 1850-Present, CTG, RtR, High School Ancients and MFW K
cbollin

### Re: Question about a problem in the Singapore 4a textbook

It's alright Teresa ((hugs)) That's part of the strength of Singapore. It turns hard problems into ways to see math, and think about it.
Teresa in TX wrote:My dd got the final answer by doubling the 2184, which is not according to ideal way of handling it, but I can see where she was coming from.
Practice 2B, problem #9 essentially, that works because it is the same thing. The difference (2184) is 2 bars. if you double that, you get the same thing as 4 times 1 bar. But does she really have a good explanation in her mind of why it made sense to double it, or did she just double it after trial and error? By using the using the bar diagrams it helps to think through the process of why it works that way. It's all about showing your work or at least explaining what you are doing.

Now that you've seen a few examples to think and see the math, give them a try. I don't know if you will have to go all the way back in Singapore with this child, or just keep going as you learn together. The next kids can have the benefit of you knowing that bar diagrams rock.

My oldest started Singapore in book 4B. I remember hitting a problem in 5A that made me scream. how on earth do you do this problem? But I quickly learned how to see the problems and draw them of course thanks to a great lady on this forum. I was sold on Singapore at that point.

-crystal
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Question about a problem in the Singapore 4a textbook

Teresa in TX wrote:I am wondering if I need to go back to the very beginning of Singapore and get a good handle on their method of teaching, so I can be retaught. I can tell that it is obviously a better math program than I ever had, and it is head and shoulders over MUS, which my 8th grader did 4 years of. Tips? I shake my head that I am unable to think through a problem in a 5th grade math book...and I have always considered myself pretty good at mental math!!
Teresa,
It's not a matter of going back in Singapore. It's a matter of spending this time playing with the bar method for figuring out word problems. And I wanted to emphasize that you won't always instantly visualize the correct way to lay out a bar diagram. For instance, with the first problem you gave, my thinking process would wander around like this:

Practice 2B, problem #9
(1) First, I read: The difference between two numbers is 2184. So I try drawing that out:
---------------/ = number 1
---------------/--2184--/ = number 2

(2) Then I read: The bigger number is 3 times the smaller number. I try to fit this info into the bar diagram that I have already made. Hmmm. I feel something's there, but I can't quite wrap my brain around it.

(3) So, I put the new info into a separate bar diagram.
---------------/ = number 1
---------------/---------------/ ---------------/ = number 2

(4) Okay, I can't seem to produce any more information about the problem using that diagram alone, either. So, I go back and try to fit the pieces of information together. That's when I have the "aha" moment: 2 bars must equal 2184. I might scribble that across the last 2 bars in the second diagram.

(5) I go back and re-read what I need to answer the question: Find the sum of the two numbers
I see that the 2 numbers would mean 4 bars. Then I decide I can easily come up with that by adding 2184 + 2184.

Each of our brains works differently, and Singapore allows for that. But I hoped that "seeing" my thinking process starting from scratch would make sense on your end?
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
MJ in IL
Posts: 119
Joined: Sun Jul 17, 2005 5:23 pm

### Re: Question about a problem in the Singapore 4a textbook

Oh, I remember the day we agonized over this one! We finally got it...only after mom and son had a couple wrong answers! I really like the word problems that make me think too! (and I am glad I have the solution manualfor 4-6!)
Molly
dd14 enjoying AHL; ds12 & ds10 in RtR & dd5 working through K!
have done K (2X), 1 (2X), ECC, CtG, & 1850MT
cbollin

### Singapore math 4A workbook - Page 28

TheLordisAwesome wrote:Please explain page 28. me and my son can't help David find his way home.
The path that is NOT colored in
is the path home

the colored parts (aka the answers from the problems) are the boundaries of the path, but not the path.

...... most of those pages the path tends to be followed the colored in blocks.... this one was different. it plays with the brain and optical input.... my gal and I were tripped up too for a moment.

-crystal
TheLordisAwesome
Posts: 2
Joined: Fri Feb 06, 2009 9:48 am

### Re: Singapore math 4A workbook - Page 28

Of course, I see that now. Thank you. I hope you laughed. I know I did.
cbollin

### Singapore 4A HELP!

courthart246 wrote:I am stuck with a couple of story problems in Singapore 4A. It is page 40, Practice 2B. Numbers 8 and 9. Can someone tell me how to do them? I feel so silly not to understand how to do 4th grade math, but this stuff seems like algebra to me. I am definitely NOT ready for algebra.
It can be done with algebra... but in Singapore 4A, they haven't learned abstract algebra methods yet. So, they use bar diagrams. These bar diagrams help the concrete learner do these advanced problems.

For #9, take a look on this thread for the replies given by me (cbollin) and Teresa in TX and Julie and MJ_in_IL. [above]

Textbook 4A, p. 40, #8
basically after you read the problem, make sure you and your student understand what it tells you and what you are looking to find out:
300 kids in 2 groups.
Group one has 50 more than group 2.
How many in group 2?

Ok. let's draw a bar to show that info
/-----/ (one bar) = group #2
/-----/ + 50 = group #1

Using what we have learned all the way back in Singapore 2A with “whole and parts”
We know
That having /-----/ (group 2) + /------/ + 50 (group 1) gives us the whole of 300 kids.
Do we know the whole?
Yes. 300
Do we know a part?
Yes. We know the 50.
So when we know the whole and know one part
300-50=250
250 is the other part, which is shown with the 2 equal sized bars.

So, now we know that the thing left: 2 equal sized bars is the same as the 250.

Well, if we have a new whole of 250 and it is divided into 2 equal sizes….
How many are in each group?
125.
So, we know the size of the bar is 125.
One bar is the size of group 2.

Note: it is the mental thinking process for algebra. But it is not abstract with symbols. You aren't asking them to come up with an equation for it or do all of that flipping of coefficients. It is very concrete.

-crystal
Julie in MN
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Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore 4A HELP!

courthart246 wrote:Thank you for your directions. I followed them exactly to get the answer. I cannot say that I will be able to do another problem on my own, as this really confuses me for some reason. But thanks so much for the help on these.
Courtney,
You know, it's just a matter of digging in and trying different things. Don't be afraid of making the wrong bar diagram, even in front of your child (especially in front of your child!). Just say to yourself, "Hmmm, here is the info I see, two separate bars. Okay, that isn't helping me, let's try drawing it in one bar..." and so on. (Even, "Wow, should we ask on the boards about this one?!")

I think the biggest thing is to learn how to think through math. I, myself, never took college entrance tests until I'd been out of high school for over a year. I hadn't had math for several years at that point. But I'd had a teacher who helped me feel confident I could think through math & figure it out in the end. I wasn't afraid to just try something and then try something else. That was the best gift he gave me -- much more valuable than the formulas

Julie
Last edited by Julie in MN on Thu Feb 11, 2010 9:52 am, edited 1 time in total.
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
cbollin

### Re: Singapore 4A HELP!

Courtney,

I was nervous too that I wouldn't be able to do all of the problems or get it without emailing Julie all the time. My advice? Practice it a few times like Julie has said. Don't be afraid if you mess it up and have to start again. It will get easier -- just like cooking, or cleaning a bathroom, or even driving a car.

There will be certain problems in each review that are the "challenge" problem. It's ok. do like many homeschoolers do and ask for help on those.

-crystal
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore 4A HELP!

courthart246 wrote:Julie - I appreciate your thoughts. I am just so frustrated right now. I have worked and worked and worked at this problem and just don't get it. I don't know how I can teach it without specific directions if I can't even do the problem myself. I am very much leaning toward changing math curriculum for next year to something he can do through a video or on the computer. This is the one subject I feel so unqualified to teach, and it is such an important subject. In high school I would get straight A's in everything and a C in geometry. I may order the HIG for 4A to get me through the year and see if it helps. If it does not, I will have to switch. The frustration is not worth it to me. We love homeschooling so much, but this issue with the math is starting to make me have doubts, and I don't want that. My ds likes math, and I don't want my aversion to it to affect him.

Anyway, if someone could walk me through this latest problem, I would so appreciate it. 4A p. 41 Review A Number 10? This one is even more confusing than the others to me.
Courtney,
I surely think that your concerns are valid. I have certainly changed things up for my kids over the years. I've even used a second math program just for variation while we are "pausing" and letting things sink in. And my son didn't finish 4A until 5th grade. I'm big on flexibility

But I do have one suggestion, though, and that's to wait until you're past the frustration stage before you decide to totally pitch something. Frustration stages are just part of teaching math, IMHO. I work at a tutoring center and sometimes I giggle because I've just heard a math tutor patiently repeat the same words at least 5 times, and the student keeps asking but is totally not hearing the step he needs to take. Similarly, at home sometimes even when I "do" understand something, I can't seem to communicate it to my children's brains. Most of the time, the only thing that helps is to wait. I visualize the information just sitting on top like water sitting on flour, and eventually it slowly sinks in and is absorbed, til one day you look over and they have become one with the concept.

And when I "don't" understand it? I always feel it's good modeling to show my son that sometimes I need to look it up or ask for help, but I don't give up and I "do" learn math! Now of course, there would be limits and only you can know when you've totally reached your limits, but I like your idea of the end of the year, when you can look back over the year and reflect outside of an immediate frustration.

As far as this problem, it would help if you post the actual problem rather than the page number, for those of us who would have to go down to the basement to find their old Singapore book But I found one of my old posts that shows a little bit of how we would "think through" a problem at our house -- I really wanted to show that we often draw bars that don't work and then discover ones that do.
http://board.mfwbooks.com/viewtopic.php ... 167#p47412

I must add that I almost always did this "with" my son, on a marker board, but I was only teaching one student most of the time, so he had no one else to bounce things off of except me.
Julie
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
courthart246
Posts: 55
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### Re: Singapore 4A HELP!

Julie - Thank you for your encouragement. I do think I will get the HIG and then see what happens for the rest of the year. Overall we have really liked Singapore. It is just when we get to points where I don't understand or I know how to do it, but don't know how to explain. I'm also teaching a first grader and preschooler, so it is difficult for me to take a lot of time to figure out concepts.

Here is the current problem that I need help with (though Crystal did send me something [ http://board.mfwbooks.com/viewtopic.php ... 176#p47400 ], I am still a little puzzled. I need to take some more time to figure it out):

Problem # 10 on page 41 3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile?

Thanks, ladies for your encouragement and help. I am so very thankful that I have people on this board to help and give support when needed. It makes the homeschooling journey that much more joyful (and some days bearable! ).
Courtney
Married 20 Years to Jamie
Loving MFW along with my three kids:
ds - 16 (World History and Literature)
ds - 13 (Exploration to 1850)
dd - 10 (Exploration to 1850)
cbollin

### Re: Singapore 4A HELP!

courthart246 wrote:Problem # 10 on page 41 3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile?
looks like we were posting at the same time on this..

The Hint to give to you and your student:
If you are having trouble with this problem, it may be helpful to know that sometimes when we solve a problem, the bar is not always the first thing mentioned. It is ok to try again now. Let's try with the 3rd pile.

so, start with the 3rd pile as your bar. -------

Now draw what you know about the 2nd pile: -------- ------- (2 bars)
now, draw the first pile., oh that's 2 bars ----- ----- and the number 10.

when we look at all of those piles together we have a total of 5 bars and the number 10. that is equal to 3000.
ok.. now we have 5 bars + 10 = 3000.
when we find how much is in one bar, we will know the number of books in the "3rd pile".

do we know the whole?
yes. 3000
do we know a part?
yes. 10

subtract
3000-10 = 2990.

we now know 5 equally sized bars is the same as 2990. (emphasize to your student EQUALLY SIZED BARS --that should be a hint that it is going to require division. 2990/5 (and let them write that problem down -- don't ask them to mentally do that if their head is spinning.write it down). so, when we have 2990 divided by 5 equally sized bar, we can learn that each bar is 598 books.

it was our 3rd pile that we drew for one bar, so there are 598 books there.

The big thing to help your child on this challenge/advanced problem is to help them realize that sometimes you have to start over with the problem, and that it is ok. No one expects them to never slow down and think a moment. The other thing -- you don't always draw your bar for the first thing on the list.

as a side note to all: all three of the problems that were mentioned in this thread -- p. 40 #8, 9 and p. 41 #10 -- are the tough challenge questions on those reviews. They are among the most commonly asked about problems in 4A on this forum and another one I read. So -- they are the challenge problems, designed to stretch their abilities a tiny bit.

-crystal
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore 4A HELP!

courthart246 wrote:Julie - Thank you for your encouragement. I do think I will get the HIG and then see what happens for the rest of the year. Overall we have really liked Singapore. It is just when we get to points where I don't understand or I know how to do it, but don't know how to explain. I'm also teaching a first grader and preschooler, so it is difficult for me to take a lot of time to figure out concepts.
I admire you for teaching all these young ones. It is a very hard time in your life, and will definitely be easier in the future. I mean, I'm just as busy probably, but it's not the same kind of all-encompassing need that was there when I had little ones.

We do all have our weaknesses and are learning along with our children. I for one had no knowledge of grammar or history until I started homeschooling, and here I am today, pretty confident in my knowledge of grammar and history -- all thanks to MFW and the other homeschooling materials I have had the opportunity to use!
courthart246 wrote:3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile?
Problem # 10 on page 41
I just start out trying something...

3 piles? Okay...
1 ---------
2 --------
3 --------

10 more in the 1st pile? Okay...
1 --------/10/
2 --------
3 --------

Woah, the third pile needs to be half as big as #2? My drawing isn't big enough to do that! So, I think I'll expaaaaaand everything, so I can make #3 half as big as #2...
1 --------------------------------------------------------/10/
2 --------------------------------------------------------
3 -------------------------

Okay, now I look at what I've drawn and see if absolutely everything in the problem fits this diagram.
I think it does, except I can now say for sure that #3 is exactly half of #2. I think I'll use slashes to show the things that I can be very exact with:
1 --------------------------------------------------------/10/
2 /--------------------------/-----------------------------/
3 /-------------------------/

And then I can go back and see that #1 is exactly the same as #2, plus 10, so...
1 /---------------------------/-----------------------------/10/
2 /--------------------------/-----------------------------/
3 /-------------------------/

Okay, now I see that I've got 5 bars that are exactly the same length, plus one bar that's 10. There are no unknowns. All of these together equal 3000. So by now, my son is doing the math in his head -- all 5 bars equal 2,990, and then the "10" makes 3000. So each individual bar is 2,990 divided by 5.

I thought that maybe if you read different thinking processes from several of us different posters, you could see how there is no one right way to dig into these. And who knows, maybe something will click with "your" thinking process?!
courthart246 wrote:I am so very thankful that I have people on this board to help and give support when needed. It makes the homeschooling journey that much more joyful (and some days bearable! ).
Amen! The boards have been a lifesaver for me.
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
hsmom
Posts: 29
Joined: Tue Jan 15, 2008 9:58 am

### Re: Singapore 4A HELP!

Just a word of encouragement about Singapore math. I don't want you or anyone else to have the impression that everyone who uses Singapore needs to be very math inclined. I went through school getting A's and B's in math (alg 1 and 2 and Geom) but never really "got it". I just knew the right steps to complete the problems.

We are only up to level 4 in Singapore, so I can't know how much I will understand when I'm done, but already I feel like I'm learning to better understand math. I think the bar diagrams are a great way of tackling word problems. A few years ago, I would see some of the challenging word problems that would be posted to the Yahoogroups Singaporemath group, and would wonder if I would ever be able to do them, much less teach them. Now I am able to figure out most of them on my own with the bar diagrams. There are still some that leave me stumped, and there are others that we set aside a while so I can have some time to figure them out. And, I am sure there will be more of those as we go through the upper grade levels.

For me one of the main things is that I feel I am giving myself the chance to improve my math education. In so doing I am moving from the type of mom who was certain that a video curriculum would be my only option for high school, to a mom who is thinking I may not only teach algebra to my kids, but might even study a bit of upper level math for my own benefit.
cbollin

### Singapore 4A, Rev 2, page 64, #21 - help!

asheslawson wrote:Ok...so maybe I'm off, but I just don't follow this problem (I have struggled with some similar to this before but always understood once I saw the explanation - this one though, I just can't follow the logic).

2500 people took part in a cross-country race. The number of adults were 4 times the number of children. If there were 1200 men, how many women were there?

My solution: 2500 / 4 = 625 (and conversely, 625*4=2500)
Then: 2500 - 625 children - 1200 men = 675 women

But - answer guide shows it differently: It says that the children & adults should be divided into 5 units, meaning essentially divide 2500 / 5 = 500 children
Then 2500 - 500 children - 1200 men = 800 women
I'm trying to understand this - but it just doesn't make sense to me because 4 times the adults for 500 kids would be 2,000!! Why is this not clear to me? I see how the answer was obtained by dividing into units, but I just don't get how it's correct if the problem states, "The number of adults were 4 times the number of children." Help - please! I really think my answer seems right and I don't know what I'm missing!
4 times the adults for 500 kids = 2000

plus
500 kids
equals 2500 total.

does that help?

think of this way
Adults plus Children = total
A + C =2500
Adults = 4 groups of Children.

so we can rewrite it as:
c + c +c +c + c = 2500
children = 500

now...that means 2000 adults... 1200 of whom are men.. that means
2000-1200=800

The problem is divided into 5 groupings not 4.

bars are
children ________
adults _________ __________ __________ ___________ ________

5 bars
gabby3312
Posts: 2
Joined: Wed Apr 11, 2012 6:53 am

### Re: Singapore 4A, Rev 2, page 64, #21 - help!

You have the answer in your question You are right 4 times 500 is 2000. You are just forgetting to add the original 500. I think the last post answered your dilemma.
HTH.
Gabby
asheslawson
Posts: 213
Joined: Tue Oct 05, 2010 1:37 am
Contact:

### Re: Singapore 4A, Rev 2, page 64, #21 - help!

Thank you...why did that not make sense to me - but the way you explained that in the first line made it make sense - I was skipping ADD the kids to the adults!! Can you come teach math to us????

Thank you so much - and you are so quick too - I posted on Singapore's forum and I'm still waiting! Very much appreciated....gotta go show my ds now!
"So then, just as you received Christ Jesus as Lord, continue to live in Him" Colossians 2:6
dd-28, ds-25, ds-24, ds-22, ds-14, dd-10, student 13, granddaughter 3
MFW K, 1st, ECC, CTG, RTR, EX1850, 1850-MOD
http://texashomeschooler.blogspot.com/
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Singapore 4A Text pg.37 onwards

albanyaloe wrote:Hi there,
We've hit a bit of a bump in the road, and I'm not too sure how to handle it. I have not ordered the Singapore Home Instructor guides as I never found that I needed them. Suddenly my son has bombed out. I must admit (to my shame) that he has been ahead of me for some time in Singapore and I have totally relied on the MFW teacher guide for answers but managed to work out from the text also, what was going on, and he grasped it all fine.

Now, from this lesson, he has not managed to do this mentally. My husband says he cannot believe it is supposed to be done mentally and I said I am sure it is. But hubby is not familiar with Singapore and I tried to explain the SM method and showed him the little pictures.

What confuses us all is that the little problems are drawn out for us on the right in Ex 15, for example, so does he work them mentally or may he do his working out the usual way? He was doing everything mentally, and managed fine with the division unit before mentally, but when they started to add examples with numbers without the 0's he started to bomb out. ie: he can do the 60 x 500 fine but the 648 x 78 he still needs paper.

I am not at all mathematical so I hope I have explained myself clearly. I just need to know what to do. I certainly cannot do these in my head. I was so impressed with what he was doing so far and do not want to discourage him.

Lastly,it is not just a simple matter to get the Home guide here in South Africa, I just checked and it'll cost me more than \$50 for just one little book!

Thank you in advance,
Lindy,
<hugs> as you try to teach your kids.

I wish I had my son's 4A books on hand, but I don't, so I'm just going to chat theoretically. Hopefully someone else will join in who's right where you are.

Okay, a couple of things come to mind as I read of your dilemma.

1. There were definitely a couple of problems in level 4 which were "challenge" problems going above-and-beyond. I can't remember where they were, and I don't know if they're mentioned in the MFW lesson plans (those weren't around when we were doing that level), but I DO know the extra-hard problems were there. So allow yourself some slack for an occasional problem here or there that's not really necessary, but more of an extra challenge for kids who are ready for it. Not many, just once in a while, maybe one problem every couple weeks?

2. I never taught my son that he had to do Singapore problems in any particular way. He had to listen and show understanding of the lesson, but he was free to do the problems in whatever way he chose. I have always felt that "formula" math is more of a problem in American math than anything else. Yes, there are definitely better ways and shorter ways and more useful ways, but in the end, understanding is more important than the ways. And I do think that eventually most students gravitate towards those shortcuts, when they are ready.

3. In the problem, "648 x 78," I'm wondering how he does it on paper.

Does he set it up this way:
648
x78

Or this way:
600 x 70 = 42000
40 x 70 = 2800
8 x 70 = 560
42000 + 2800 = 44800 + 560 =

Or another way?

Does he know there are different ways to do it? I think it's a pretty big problem to carry completely in your head and not all kids are going to get there, but they should start to feel comfortable working with those numbers in some way, and realize there are more ways, too -- some of which require less writing than others.

Level 4 introduces a lot of topics. Level 5 cements and expands them. I wouldn't worry at this level. My son is very mathy but sometimes he would get frustrated and we'd just do something else for a time, such as math games or another program or jump to one of the "measuring water" type lessons, and let the "hard topic" simmer or maybe do one hard problem a day. Each kid is different, but I've never seen a kid without occasional bumps in math.

Blessings,
Julie
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs
albanyaloe
Posts: 40
Joined: Sun Apr 29, 2012 11:17 am

### Re: Singapore 4A Text pg.37 onwards

Thank you Julie for responding to my plea again

Okay, he can actually do it in both those ways. The thing is in the second way you showed, he cannot remember all the numbers and has to jot them down before he adds them up. That is what I am unsure of. Is he allowed to do that?

He's actually super quick with working things in his head, it's just when he is carrying (sorry I can't remember the American word for carrying) too much, like with big calculation, he needs to write something, though he still does the working out in his head. Otherwise he just bombs. Should I just let him for now or is that wrong?

The text actually showed us three ways to do it, and all three made sense to him. He was getting the answers correct in the text and student book, till today. When I asked yesterday which method he liked best, as it was in his head and I couldn't see which method he was using, he said he'd have to think about that as he didn't "think about methods" when he was doing it. I was very happy with that- to me he can do it, and has then 'internalised' what he has learned and is putting it into practice naturally. Just today the numbers got super big and we needed paper to scribble on.

I see from searching the board that tomorrow we hit some of those challenging ones that you mentioned. Thanks for the heads up.

Sleepy time here in the southern hemisphere

Lindy
Lindy,
Our first year with MFW, doing ECC 2012, Our 7th year of HS'ing
Joel 11 yo, Emma-lee 8 yo and Shelley 6 yo
We're from Sunny South Africa!
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore 4A Text pg.37 onwards

Hope you're getting some sleep and you read this tomorrow! I just googled "what time is it in South Africa" and easy-as-pie it came up as 10:32 -- it's 3:32 here in MN That is so cool.

I think it sounds like your son is doing just fine. He is doing a lot in his head, but jotting some of the halfway points down is a help for him. Actually in high school, jotting some things down along the way gets to not only be helpful but even required by some teachers, so I wouldn't worry at all about letting him do that. I'd keep an eye on whether he's getting the ideas presented as far as understanding numbers and place values, like you have been, and it sounds like he's got it, by George!

I didn't know if this was one of the more challenging problems, but it sounds like it's just a warm-up LOL. Have fun,
Julie
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002+)
Travis (32) engineer; never hs