## Singapore 5B, Specific Lessons

cbollin

### Singapore 5B, Specific Lessons

problem #20 in review 3, pg 104
Jenn in NC wrote:DS is finishing up 5b today and can't figure out how to solve problem #20 in review 3, pg 104 (last page of the book.) I'll just type it out:
• David and Peter had \$90 and \$200 respectively. They were each given an equal amount of money. Then Peter had 2x as much as David. How much did each boy receive?
For some reason I am stumped in trying to explain this to ds. I can see intuitively that the answer is \$20... b/c that would bring David to \$110 and Peter to \$220. But I am sure there must be a more proper way to come to this answer. Help, anyone?
Grabbing my daughter's book....

This is what my oldest did. I'm sure there are other ways.

first she call 90 one bar
David = ___
Peter = ___ + ____ + 20

now, they each get same amount of money (how to draw that on here. I know. I'll use a ?. She actually drew a box.)
(edit drawing)

David now has + 90
Peter now has + 90 + 90 + 20

ok. What Peter has is 2 groups of David, right?
Well, she has a good enough understanding to go to this:

? + 90 + ? +90 = ? +90 +90+20
2 groups of David = 1 group of Peter

Then she crossed out equal things on each side leaving
? = 20

edit to clarify: in reality she didn't write 90, she wrote it with bars, I just got lazy typing. So when I say she crossed out equal things, she crossed out bars and ? (boxes).

but.... as you'll see below in my edit... it is easier than what she did.

if we double Peter's new amount it is the same as DAvid's new amount
make a mirror image of Peter's amount

double Peter + _________ + _________ +
David + ________ + ________ + 20

they have in common one and 2 _________
that leaves is the same as 20

I don't know if that makes sense on the screen. But for her, the trick was to start off thinking of Peter's money in terms of how it related to groups of David's money plus extra.

-crystal
Last edited by cbollin on Mon Feb 02, 2009 6:34 am, edited 3 times in total.
Jenn in NC
Posts: 144
Joined: Fri Jun 23, 2006 2:00 pm

### Re: stumped on singapore 5b problem

aha! Thank you very much. That does make sense on my side of the screen, and it is ever so much more mathematical than my not-so-logical method

(these smilies are so fun)
mommy to four boys & two girls... and another boy on the way
completed K, 1st, ADV, ECC, CTG and RTR
2009--2010 Enjoying Exploration to 1850
cbollin

### Re: stumped on singapore 5b problem

FreshKid wrote:By George, I think I got it! 2(90 +x) = 200 + x solve for x. I don't know if that is the Singapore way, but I got your answer. I feel better now. And, yes, smilies are fun!
That's algebra to solve it. You will not need abstract algebra to do Singapore. My child didn't need to be able to set up the equation like that in 5B. Yet, she could see and set up the problem with understanding with the bar diagramming and walking through the meaning of the problem.

You'll be fine when you get there

When my oldest was in 4th grade, I would have freaked out if someone told me she'd do problems like this one almost in her head within 1 year and not use algebra to do it

-crystal
cbollin

### Re: stumped on singapore 5b problem

cbollin wrote:
? + 90 + ? +90 = ? +90 +90+20
2 groups of David = 1 group of Peter
I want to try to re draw this. It is very easy to do at home. Not as easy on computer for me.

peter = _______ (90)
David = _______ + ________ + 20

they get each so it becomes

Peter = + _________
David = + _________ + ________ + 20

we know that if Peter doubled his money, it would be the same as David
Let's just make a mirror image double. we double Peter's new amount , but don't double David's new amount

Double Peter = + ________ + _______ +
David = + __________ + ___________ + 20

now it is very easy to see that each of them has in common one and two bars, and what is left is one and 20. so, is 20.

That might be helpful for kids who are less abstract thinking than my oldest. I'm sure it is how I will teach it my middle girl and thought it was worth trying to re draw it. They never need the abstract equations.

-crystal
Jenn in NC
Posts: 144
Joined: Fri Jun 23, 2006 2:00 pm

### Re: stumped on singapore 5b problem

cbollin wrote:That might be helpful for kids who are less abstract thinking than my oldest. I'm sure it is how I will teach it my middle girl and thought it was worth trying to re draw it. They never need the abstract equations.
Ditto on this for my ds 9, when he gets there. Went through it with ds11 the way you had it the other day and he was able to see it right away. (thanks!) But for ds9 I am sure something like the above would be necessary.

Must be a birth order thing, perhaps? Don't know, but he would definitely need the more simple visibility on this one.

Now to go and bookmark this thread (love that!) and make a note in the textbook...
mommy to four boys & two girls... and another boy on the way
completed K, 1st, ADV, ECC, CTG and RTR
2009--2010 Enjoying Exploration to 1850
cbollin

### Singapore Primary Math US 5B wkbk review 1, #23

tkrapfl wrote:I have the answer key for this book but not the solution manual and I cannot figure this problem out! I have struggled with this type of problem this year and would really love to be able to show my daughter how to really work it out even though I can honestly say that I don't think I ever solve this type of problem in the 'real world'. If anyone could help show how to solve it I would really appreciate it.
• Here is the problem: String A is 30 cm longer than String B. String B is 60 cm longer than String C. The total length of the three strings is 3 m. Find the length of String C.
As Julie says, there are several ways to think about problems. I'd use the bar diagrams again.

I'd draw String C as my bar. It is the string we know the least about.
C: /----/

string B = /----/ + 60 (that is how to draw that string B is 60 cm longer than C)

string A = /----/ +60 +30 (that tells us that string A is 30 cm more than string B)

it says the total length of the strings is 3 m. Make sure the student can convert to to cm. 300. you have to have the same units. centimeter will be easier.

so you have
/---/ + /----/ +60 + /---/ +60 +30 = 300 cm (which is the total of all 3 strings)

3 bars + 150 = 300

going back to 2A where we learned about whole and parts.

do we know the whole?
yes. 300
do we know a part?
yes. 150

so the other part, which is 3 bars is the same as 300-150 or 150
3 equal size groups = 150
one of those groups is 50.
and it turns out that the length of each bar is group C

so.... it is 50 cm for string C.

-crystal
cbollin

### Singapore 5b help!!!!!!!! Ratios, p96 in the workbook, #18

AnnieMarie wrote:I switched my dd from MUS to singapore and there are somethings that neither of us have seen before. She had completed alpha to zeta in MUS and tested at 5b level in singapore. Everything has been great until we got to the reviews.

How do I teach her about switching ratios? I don't even know where it was taught in the curriculum. ex... if at the beginning of the problem the ratio is 1:2 and one side of the ratio adds 24 but nothing changes on the other but the ratio changes to 2:1 what was the actual quantities of the first ratio? Does that even make sense?

I looked at singapore forums to see what was going on and they were showing blocks without any equations. I was so confused I had her solve it by trial and error. If anyone can help with this I would greatly appreciate it.
I could probably help... i know my oldest daughter did mus through Zeta, tested into 5A, but I decided to drop back to 4B and do it all. By the time we were at ratios in 5B, it was easy. so it must have been in one of those books, probably 5A.

but what page or problem in 5B (text?) is an example of what you're struggling on?

you draw one bar for the 1 part
------
and then 2 bar for 2nd part
----- -----

now you add (---------- 24) to the top.
and nothing to the bottom.
right?
well that changed the ratio so that on top it is now
2
to
1 ratio! think equivalent fractions here...

well.. if the bottom stays at two drawn bars, then the top must have how many bars to be in a 2 to 1 ratio? that's right. 4 bars are up top.

so, that means
1 bar that was there
plus 3 new bars . those 3 bars = 24, right.
so that means each bar is 8 items.
four bars on top means 32
two bars on bottom mean 16.

that means that you started with 8 and 16 items, which is 24 items total.

write it down
talk it through.

with ratio, think equivalent fractions.
AnnieMarie wrote:It's p 96 in the workbook # 18
The way you explained it made so much more sense to me than what they were showing. I don't remember MUS getting that complicated with ratios. I , being an engineer type, was looking for an equation to plug numbers into and was NOT seeing it.
Thank you!
ok.... that was what I wasn't sure on. Yes, Lina had 8. Suling had 16.

One of the nicest things that I found when I switched to Singapore was that we got to unlearn the idea of plug and chug in an equation. Equations are too abstract at age 11. I mean, we had done the stuff in Zeta with "inverse coeffiency of a whatzamawhoit"... but she never understood what to set up or anything. So, yes, the problems had to be less complicated than Singapore. I'm not slamming mus with that. I'm just trying to describe the difference in depth and the reason I think it is different.

with Singapore, we got to do "more complicated" or more involved problems with ratios, because it was all in concrete/pictorial method. I know the type of thinking problem for me having the eye opener was in 5A workbook. There was no way we had a clue how to set it up as an equation. Here's a link
http://board.mfwbooks.com/viewtopic.php?f=6&t=11448

but yeah, with ratios and all of that... once we were drawing it out and building it...it just jumps out there.

oh well.. big thing in 5A-6B with ratio and changes..... draw it out with bar diagrams, and use equivalent fractions. don't try to make it X plus blah blah, equals the whatever of the whatnot.

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

### Singapore 5b help

SarahP wrote:Can someone please help me out with ALL of the problems on Singapore 5b Practice 9a on page 85. I am stumped on how to figure these out (can we say math is not my strong point!). I don't feel like the textbook is explaining well enough how to do these types of problems. Thank you very much for any assistance one can provide.

Also, are there any good online resources for videos or more in depth descriptions that could be a help both for myself and my son?
Hi again, Sarah,
I don't have the book here so I'd need to have the problem typed out in order to chime in. Maybe someone else will, but meanwhile I thought I'd keep you company.

You may have seen this thread on Singapore 5B. http://board.mfwbooks.com/viewtopic.php?f=23&t=7071
I don't see your problems in there at all, but I just thought that reading through the answers might give you a sense of the thinking process at this level.

I remember that somewhere in level 4 or 5, my son *had* to start using the Singapore methods of bar diagrams and such, even though he'd passed them off in previous levels because he could do so much in his head. Fortunately, I had always went through every textbook lesson with him, so he'd had some exposure to the various methods, but he hadn't needed to use them very often in the earlier years. But when he had to start using the method in order to solve difficult problems, I know we did a lot of problems on the marker board. I wanted to illustrate to him the method of just trying different things, and somehow when he used paper & pencil, he only wanted to do it once so he wanted to know the "right way" and didn't want to keep trying different things, compared to marker boards which we could easily mark up all over the place.

HTH,
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
Amy C.
Posts: 200
Joined: Thu Apr 30, 2009 9:12 am

### Singapore 5B problem

ChandraK wrote:I am having a complete brain lapse here. We need some step by step help with practice 9A problem 1A. Thanks!
I looked the problem up. The answer is found by dividing the volume by the area. So 360cm3/90cm2.

I went back to page 81 to refresh myself. In problem 3 on page 81 both answers are found by dividing the volume by the area (side known x side known). In the practice 9a problem the area is already given instead of having to multiply 2 sides together.

Does that help?
ChandraK wrote:That gives you the height but it is asking for the side marked AB. Right?
It is my understanding you use the same formula to find the unknown side whether it is the height or another unknown side. Going back to problem # 3 on page 81: To find the unknown side you would divide 216m3 by the area which is the product of 3x6. The unknown side in that problem is not the height. Problems 5a and 5b on page 82 are solved with the same formula: volume/area. The unknown side in problem 5b, page 82, is the height, but the unknown side in problem 5a is not the height.

I don't know but each time I use that formula, it gives me the correct answer.

Amy C.
ChandraK
Posts: 2
Joined: Wed Apr 16, 2014 12:16 pm

### Re: Singapore 5B problem

THank you Amy! That is what I was doing but I guess I am too locked into my whole Area has to be l x w so therefore 4cm is the height, even though that is what the answer book clearly says. I guess I was trying to make it more difficult that it needed to be. Thanks for helping me.
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore 5B problem

Hi Chandra,
If you could type up the problem, it would allow some of us to give it a try even if we don't happen to have 5B on hand.
ChandraK wrote:Julie - The problem is asking for the measurement of a marked side of a cuboid. There are no measurements given for length, width or height. The area is 90cm2 and the volume is 360cm3 it is asking what AB is which would be the width of the cuboid. Does that make any sense? Hence why I didn't try to explain it originally
Ah, a geometry problem, I see why you didn't try to write it out! Another friend explained it to me, as well, because she wanted to help you, too.

In a cuboid, you can tip the figure any way, so if you need the measure of a "base," then whatever area you already know can be the "base." Just "tip over" the figure so the front is now on the floor.

Having the base can help you use one of the formulas you've been working with, "area of base x height = volume."

In this case, you can tip the figure so you use the known area as the "base" and the other known is the "volume," and then all you need to figure out is the "height":
90 x AB = 360

I find it confusing that the post office (or fedex) always want to know the length and width and height. Why don't they just say the 3 sides, since it all depends on which way the box is tipped? Oh, well, I suppose any method could get confusing

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
Amy C.
Posts: 200
Joined: Thu Apr 30, 2009 9:12 am

### Re: Singapore 5B problem

Thanks for your explanation about flipping the cuboid, Julie. I actually thought about that after I posted but was on my way to church and didn't have time to repost. However, your explanation was much better than mine would have been.

Amy C.
ChandraK
Posts: 2
Joined: Wed Apr 16, 2014 12:16 pm

### Re: Singapore 5B problem

MelissaB
Posts: 364
Joined: Sun May 09, 2010 10:01 pm

### Singapore math...almost done...boy is it tough

klewfor3 wrote:
Fri Jan 29, 2016 5:37 pm
We are finally on book 5B and since ds is in 6th grade we are on schedule. Math typically has been my ds "thing". I am running into a weird situation for us though.

When he did the daily work in 5A...he generally did well...but often made simple mistakes (he's always in a hurry). However, when we got to the review sections, he REALLY struggled. The fractions were hard for him. In the end, we'd have to go over most of the problems together after he has tried them first. There have even been a few I couldn't figure out!!! &) Thankfully, my confidence is still in tack...although I want to make sure his is!!

So...my theory...is to keep going. I think much of the same type of problems from book 5A will be covered again in 5B...right? Just at a deeper level? I am praying that I am handling my ds right... I guess I just wanted to talk it through on here.
Hi, Kathy! ~

We aren't using Singapore Math, but just to help restore your "confidence" : I can't remember everything i've learned either. And that's O.K.

I'm learning that the most important thing our children know is how to investigate and explore to find/learn what they need when they need it.

Since we're doing Algebra I this year, "I don't remember this," is a common phrase around my home. When we're stumped, we generally ask Dad first, and if he doesn't know, we look online, call family members ...whatever it takes. We've called our math curriculum for help before, too - and they're very helpful!

I hope another Mom will share with you what you can expect with Sing.5B. In the meantime, yes, keep going!
Melissa B. (Arkansas)
Girls ages 16 & 13
Completed K, 1st, and Investigate {ECC; CTG; RTR; Expl.-1850; and 1850-Mod. Times}
"That they may teach the young women to be sober, to love their husbands, to love their children,.." Titus 2:4
twinsmomxtwo
Posts: 1
Joined: Thu Aug 15, 2013 6:21 pm

### Re: Singapore math...almost done...boy is it tough

Maybe something like Khan Academy (free) which gives tutorials and lessons for a variety of subjects and topics. Or computer "games" that target the skills he seems to have trouble with - maybe making it fun may make the task less daunting for him and you. Or create your own games with some of the topics. You can Google each topic, such as "games to learn fractions, games to learn multiplication tables, etc." There's lots of ideas out there that are more fun than workbooks, and they're free. Hope that helped.

Oh, and a great way to motivate and keep his interest high is to offer a prize. Start small for accomplishing smaller tasks, then maybe a big one at the end.
klewfor3
Posts: 80
Joined: Wed Nov 09, 2011 4:14 pm
Location: Illinois

### Re: Singapore math...almost done...boy is it tough

Thanks Melissa and Twinsmom for the replies! We have a great homeschooling community where I live but no one I know is using Singapore math.

I will have to check out the Kahn website...I hadn't heard of that before. Although, I am trying to avoid extra work if I can.

My ds is the "race through school to get done" kid and balks at the real benefit of doing some extra work. Sigh, I might have to pull the I Am The Mom card and have him work through fractions more. He's is such a great kid...but school is not his thing right now. He reminds me of me at his age. School came easy for me but I didn't want to put any more time into it than I had to.

As I read through some of the archives last night it seemed that 5A and B were tough for a few families. I got some tips from there too.

For right now I will KEEP CALM AND CARRY ON. That is practically scripture in my world.
Kathy
Mom of Tyler 13, Paige 10, Brooklyn 9 and Chase 3
God bless us!
We've used:
MFW-K
MFW 1st (both versions)
ECC
CTG
RTR
Expl-1850
Currently using 1850-Modern Times (2016/2017)
Julie in MN
Posts: 2909
Joined: Mon Jun 28, 2004 3:44 pm
Location: Minnesota

### Re: Singapore math...almost done...boy is it tough

MelissaB wrote:I'm learning that the most important thing our children know is how to investigate and explore to find/learn what they need when they need it.
Love this. It's so true. And Singapore is really immersing your son in this skill -- attacking problems with different tools and finding out what works, what's more likely, why, etc. I'd give credit for trying things out even when they don't work.
twinsmomxtwo wrote:You can Google each topic, such as "games to learn fractions, games to learn multiplication tables, etc." There's lots of ideas out there that are more fun than workbooks, and they're free. Hope that helped.
This could bolster the other side of math -- the endurance and sharpening of accuracy. You might set aside a separate "math facts" time each day, maybe 10 minutes a day. He could use that time to work with fractions in different ways until he really "gets" how they work without thinking about it. Fractions aren't intuitive, since a smaller number (say 1/2) can be bigger than a bigger number (say 2/5), and +/- works differently than x/: , etc. Just working with those fractions over and over, in games, videos, reciting aloud outdoors, creating his own cheat-sheet etc., can sink them into the mind.

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
klewfor3
Posts: 80
Joined: Wed Nov 09, 2011 4:14 pm
Location: Illinois

### Re: Singapore math...almost done...boy is it tough

Hi Julie,

Thanks for the tips. Starting tomorrow I am going to make flash cards for concepts to review. I think that'll help a lot since the pace seems to be going very fast.

Monday is a new week! Here we go.....
Kathy
Mom of Tyler 13, Paige 10, Brooklyn 9 and Chase 3
God bless us!
We've used:
MFW-K
MFW 1st (both versions)