Singapore 6A-6B, Specific Lessons

[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

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 - Staff]

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 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]

Oh I'd like to hug you! That problem kept me up til 2am thinking it through! lol Thanks so so much!

[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

[Julie - Staff]

We have discovered an error in some Singapore 6A Workbooks. Please check the 6A workbook and correct it if needed.

Errata:
Singapore Math U.S. Edition
6A Workbook
p. 7

The text should read:
5. Find the value of each of the following expressions when n = 15.