Need help with question in Singapore CWP 3

[lisabees]

I'm really embarrassed. We don't use Singapore, but we pull out CWP every so often. I cannot figure out the answer to this problem nor would I know how to teach it to dd9. This is from CWP 3 (US Edition 2006), Topical Problems 2, number 20.

 

Laura had 24 clips more than Holly. After she gave 5 clips to Holly, Laura had twice as many clips as Holly. How many clips did Laura have left?

 

Should I be using bar diagrams? I know the answer; it's in the back of the book. Should I share? :)

[Dana]

Bar models work.

Show 24 as the difference between Laura and holly.

Then draw the 5 clips Laura gives to holly... So now their difference is 14.

Laura has twice as many as holly, so one unit is 14.

Holly has 14 and Laura has 28.

[lisabees]

Oh my word. I finally get it using the bar diagrams! Thank you so, so much, Dana!!!

 

Now I am smarter than a...oh forget it. They're all smarter than I am. :)

[boscopup]

This is the type that is really easy once you draw the bar models. If you look at the example problems in the beginning of the section, they usually tell you how to do each type of problem.

 

L [-----H------][--------------24------------------]

H [-----H------]

 

Now give 5 of the clips to Holly:

 

L [-----H------][--------------19---------------]

H [-----H------][--5---]

 

If you draw it somewhat to scale-ish (hard to do on the computer) with new L being twice new H, you'll see that the original H + 5 is equal to 14, so H must be 9, and thus Laura now has 9+19=28.

 

There are different ways to draw that, and I usually draw them on the same bar diagram, just putting dotted lines to show where one is losing something and the other is gaining.

[lisabees]

This is the type that is really easy once you draw the bar models. If you look at the example problems in the beginning of the section, they usually tell you how to do each type of problem.

 

L [-----H------][--------------24------------------]

H [-----H------]

 

Now give 5 of the clips to Holly:

 

L [-----H------][--------------19---------------]

H [-----H------][--5---]

 

If you draw it somewhat to scale-ish (hard to do on the computer) with new L being twice new H, you'll see that the original H + 5 is equal to 14, so H must be 9, and thus Laura now has 9+19=28.

 

There are different ways to draw that, and I usually draw them on the same bar diagram, just putting dotted lines to show where one is losing something and the other is gaining.

 

Thank you so much for writing this out. There was no example at the beginning of the chapter that involved losing/gaining. Now I totally understand it. Interesting that Dana had me see it in one way (14+14) and you have allowed me to see it it another way (9+5/9+19). That is just fabulous. Thank you for taking the time to draw the diagrams. :)

[Dana]

I really see the benefit to the bar models as an easy stepping stone to algebra, especially starting in 4 and 5. It's really cool to see how the idea of a "unit" applies in their work in 5 with fractions, percents, and decimals.

I've also found the process skills books very helpful for practice with setting up the bar diagrams.

 

I don't make my son do bar models for every CWP, but I do make him do some for each section.

[fourisenough]

Lovely explanations, ladies! My 8 year-old is officially a better bar-diagrammer than I am. It usually take me twice as long to set up the problem. I agree that it is a great foundation for early algebra work.