Singapore 6A-6B, Specific Lessons

Julie in MN
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Location: Minnesota

Re: Singapore math help please 6b

Unread post by Julie in MN »

Singapore math 6b - Day 51
Textbook page 87 # 10


My previous plug-and-chug method may not have been perfect. Someone has shown me the HIG answer key, with a diagram. There are a few of us Singapore nerds around ;)

I still had trouble reasoning through how to mesh a ratio with real numbers in this case, but I think I finally see what they did, so I thought I'd share. (I think visualizing the "after" diagram was the part that tripped me up, but once I could see the "after" Roses bar, the rest fell into place.) So here’s how I’d expand on their answer.

There's a reason this problem is an optional challenge problem %|
Julie
SarahP wrote:There were twice as many carnations as roses in a flower shop. After selling 50 carnations and 10 roses, there were 3 times as many roses as carnations left in the shop. How many roses were there in the shop at first?
BEFORE:
/----------R----------/
/----------C----------/----------C----------/

AFTER:
/-R-/-R-/-R-/
/-C-/

We don't know the value of R or C, but we know that one /R/ is equal to one /C/ in each pair of diagrams.

TO GO BACK TO THE "BEFORE" AND INCORPORATE INFORMATION FROM THE "AFTER":
If we add back the amount sold, we go back to the original ratio (2:1):
/-R-/-R-/-R-/ + 10 SOLD = before
/-C-/ + 50 SOLD = before

so this "before"
/----------R----------/
/----------C----------/----------C----------/
becomes this "before"
/-R-/-R-/-R-/-10-/
/-C-/---------------50 SOLD--------------/ (twice as long)
or we could look at 2:1 like this...
/-R-/-R-/-R-/-10-/ (roses)
/-R-/-R-/-R-/-10-/-R-/-R-/-R-/-10-/ (carnations)

MAKE USE OF CONCRETE NUMBERS:
We could compare the two "after" carnation diagrams, making use of all the concrete numbers we have (50 and the 10),
and I start to ignore one bar in each, because I know that one C is equal to one R,
so I can focus on narrowing down the red info:
/-C-/--------------50 SOLD--------------/ (carnations)
/-R-/-R-/-R-/--10--/-R-/-R-/-R-/-10-/ (carnations)

Then, rearranging a bit:
/-C-/--------------50 SOLD--------------/ (carnations)
/-R-/-R-/-R-/-R-/-R-/-R-/-10-/-10-/ (carnations)

COMPARING NUMBERS TO BARS:
Okay at this point, we can see that 5 of the unknown bars are equal to 30, right?
/-C-/-------30 SOLD-------/-20 SOLD-/ (carnations)
/-R-/-R-/-R-/-R-/-R-/-R-/-10-/-10-/ (carnations)


So one unknown bar is 6 (because 5x6=30 in the purple area),
which can be plugged back into every /R/ and /C/ in the "after" diagrams.
/-R-/-R-/-R-/-10-/ (roses) = 28
/-R-/-R-/-R-/-10--/-R-/-R-/-R-/-10-/ (carnations) = 56
OR
/-R-/-R-/-R-/-10-/ = 28
/-C-/---------------50 SOLD---------------/ = 56
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
Julie - Staff
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Singapore 6B help

Unread post by Julie - Staff »

MuzzaBunny wrote: Wed Mar 14, 2018 11:26 am DD and I are determined to finish this book, but we've got two problems that are killing us. I can solve them through trial and error but I'm at a total loss to show her how using the correct methodology. My hubby and his crew of electrical engineers 8] cannot do it, nor can my brother with a bachelor's in math. I know I'm overlooking something simple, but I've poured over this for hours and even called mfw to no avail. Please, help! :~

First problem:
The ratio of Emily's money to Alyssa's money was 2:3 at first. After Alyssa spent $30, the ratio became 3:4. How much money did Alyssa have at first?

and

Second Problem:
There were twice as many carnations as roses in a flower shop. After selling 50 carnations and 10 roses, there were 3 times as many roses as carnations left in the shop. How many roses were in the shop at first?

Thank you Thank you!!!
Vicki
Hi Vicki,
I cheated and checked the archives ( viewtopic.php?f=23&t=13775 ). I found a conversation about the second problem, so I'll copy that here first. If no one chimes in on the other problem, I'll take that challenge on later :)

Also, I like to say that Singapore throws in a challenge problem here or there over the years. No worries if a couple of problems aren't solved.

So about the 2nd problem,
Singapore math 6b - Day 51
Textbook page 87 # 10


In my first post at that link, I showed what we did at our house - perhaps not ideal, but we can have a variety of tools in our tool belt.

In the next post (from page 2 of the link above), I used a more Singapore-like method with bar diagrams.
MuzzaBunny
Posts: 63
Joined: Wed Aug 04, 2010 2:52 pm

Re: Singapore 6B help

Unread post by MuzzaBunny »

Oh I'd like to hug you! That problem kept me up til 2am thinking it through! lol Thanks so so much! :-)
Bunny
Julie - Staff
Moderator
Posts: 1068
Joined: Fri Nov 03, 2006 11:52 am

Re: Singapore 6B help

Unread post by Julie - Staff »

You're welcome :)

So, here's one way to approach the other problem. I'll be interested to hear whether there are other approaches that worked!
The ratio of Emily's money to Alyssa's money was 2:3 at first. After Alyssa spent $30, the ratio became 3:4. How much money did Alyssa have at first?
BEFORE
/----------------/----------------/ Emily
/----------------/----------------/----------------/ Alyssa
AFTER
/----------------/----------------/----------------/ Emily
/----------------/----------------/----------------/----------------/ Alyssa

NEXT, CREATE SOMETHING IN COMMON BETWEEN THE TWO SO WE CAN COMPARE APPLES TO APPLES – I.E. find a common factor.
SINCE EMILY’S AMOUNT NEVER CHANGES, I’LL FIND A COMMON FACTOR TO MAKE EMILY HAVE THE SAME # OF BARS BEFORE & AFTER -
I.E. I'll give her 6 bars in both cases

BEFORE, ratio of 2:3
/----/----/----/----/----/----/ Emily {2 bars x 3 = 6}
/----/----/----/----/----/----/----/----/----/ Alyssa (3 bars x 3 = 9)
AFTER, ratio of 3:4
/----/----/----/----/----/----/ Emily (3 bars x 2 = 6)
/----/----/----/----/----/----/----/----/ Alyssa (4 bars x 2 = 8 )

SINCE EMILY IS THE SAME BEFORE & AFTER,
AND ALYSSA IS THE SAME BEFORE & AFTER EXCEPT SHE SPENT $30,
PLUG IN ALL THE INFO WE HAVE ON ALYSSA
/----/----/----/----/----/----/----/----/----/ Alyssa BEFORE
/----/----/----/----/----/----/----/----/$30/ Alyssa AFTER SHE SPENT $30

HOW MUCH DID ALYSSA HAVE BEFORE? 30 X 9 = 270
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