How to work a Primary Math 4 Challenging word problem?

[sewpeaceful]

Okay, this is the first time I've been stumped since I've started homeschooling (it is humbling and it is only the beginning). I have a math background and I can't figure out how to explain to my dd how to solve this word problem without using algebra. :confused1:

 

Using the Singapore bar method explained in chapter 1, can someone please help me understand how to explain the following problem to my kid? Again, the solution must use the bar method Singapore is using... no cheating with algebra or trial and error.

 

Ch.1, #22

Gina had 3 times as many strawberries as Fanny. After she had given 24 of her strawberries to Fanny, Gina had twice as many strawberries as Fanny. How many strawberries did they have altogether?

 

Altogether? I'll be lucky to figure out how many strawberries Fanny has! :lol: Seriously, help, please?

[Cosmos]

Ch.1, #22

Gina had 3 times as many strawberries as Fanny. After she had given 24 of her strawberries to Fanny, Gina had twice as many strawberries as Fanny. How many strawberries did they have altogether?

 

Fanny Before [------]

Fanny After [------][24]

 

Gina After [------][24][------][24]

(because it's twice Fanny After)

 

Gina Before [------][24][------][24][24]

(because it's Gina After + 24)

 

But now remember that Gina Before is three times Fanny before:

 

Gina Before [------][24][------][24][24]

3x Fanny Before [------][------][------]

 

You can see that 1 bar unit must be 24 + 24 + 24 = 72

 

So originally, Fanny had 72 and Gina had 216 for a total of 288.

[zoo_keeper]

Fart, I can only think it through with algebra...

 

(g-24)=2*(f+24)

g=3f

3f-24=2*(f+24) >> 3f-24 = 2f+48 >> f=72 >> g=3*72=216

[Dovie]

In the beginning, Gina has 3 times as many, so:

 

G: [---------][---------][---------]

F: [---------]

 

After giving F some, G has twice as many, so the third part above needs to be divided in a two to one manner, or into three pieces and shared where Gina keeps 2 and Fanny gets 1.

 

G: [---------][---------] [---|---|---]

F: [---------]

 

G: [---------][---------] [---|---]

F: [---------][---]

 

The portion given to F was 24, so the original units bars we were dealing with were 3*24=72 strawberries each. Altogether there were 4 of them, so altogether there were 4*72=288 strawberries.

 

That's another way to look at it.

[sewpeaceful]

Wow. It took me a minute to wrap my head around what you both did (granted it is a Friday night :D).

 

This bar method is new to me so I appreciate your help.

 

Thank you very much. Now... onto number 23. :lol:

[Beth in SW WA]

My dd's Singapore tutor (in New Delhi) explained it this way via email to me last night....

 

Please make 9 units for Gina and 3 units for Fanny.

After that, give 1 unit from Gina to Fanny. That will make 8 units for Gina

and 4 units for Fanny which we need.

That one unit is 24 and then in all there are 9+3 = 12 units. Each is 24

so all 24 X 12 = 288 strawberries.

 

You need to make two bar diagrams for this, one before and one after case.

Thanks

Rachna Yadav

[JadeOrchidSong]

Fanny: (......)

Gina: (......) (......) (......)

 

After Gina gave Fanny 24:

Gina: (......) (......) (......)-24

Fanny: (.......)+24

 

To find (......), do this:

"(......)+24" x2=(......)+(......)+(......)-24

(......)x2+24x2=(......)+(......)+(......)-24

48=(......)-24

(......)=72

So Fanny has 72.

So the total # of the Fanny and Gina is (......)x4=72x4=288

 

This is definitely the way my 8 yr old son would do it since this is the way I teach him and it is very intuitive.

Edited September 10, 2011 by aomom

[zoo_keeper]

My dd's Singapore tutor (in New Delhi) explained it this way via email to me last night....

 

Please make 9 units for Gina and 3 units for Fanny.

After that, give 1 unit from Gina to Fanny. That will make 8 units for Gina

and 4 units for Fanny which we need.

That one unit is 24 and then in all there are 9+3 = 12 units. Each is 24

so all 24 X 12 = 288 strawberries.

 

You need to make two bar diagrams for this, one before and one after case.

Thanks

Rachna Yadav

 

Wow, this is the clearest to me, so far. I could see even my younger children working it through this way. Thanks!

[nmoira]

Ch.1, #22

Gina had 3 times as many strawberries as Fanny. After she had given 24 of her strawberries to Fanny, Gina had twice as many strawberries as Fanny. How many strawberries did they have altogether?

 

This is the bar diagram similar to the solution in Beth's post.

 

Gina is in black, Fanny in Red

 

We need the number of unit blocks to be a multiple of both 3+1=4 and 2+1=3, so we need 12 unit blocks.

 

Before:

|---|---|---|---|---|---|---|---|---|---|---|---|

 

After:

|---|---|---|---|---|---|---|---|---|---|---|---|

 

As you can see from the diagram, one unit block was transferred and we're told this is equal to 24 strawberries.

 

They have 12X24 strawberries altogether.

[Homemama2]

Don't feel bad! I was getting on here tonight to post a problem from CWP 3 that I can't figure out---it is essentially the same problem but using add/sub not multiplying. I'm embarrassed that after all of the math I've been through that I was stumped too! (Off to read all the explanations and see if I can make sense of it!) :tongue_smilie: