Word problem Singapore way

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?

This is from Singapore Challenging Word Problems book 3 (which they are now discontinuing, I heard).

I found two ways to solve this using the bar diagrams.

Solution 1. Notice that this is showing how I solved it initially, and at one point I had to adjust the length of the bar. Solution 2. In either case, once you get that x = 9 (the amount of clips Holly had in the beginning), it's easy to solve that Laura had 28 clips left after giving 5 to Holly.

Algebraically:

Initially Laura has L, Holly has L - 24. (Obviously you could also choose to use H and let Laura have H + 24.)

Then Laura gives 5 to Holly, so now Laura has L - 5 and Holly has L - 24 + 5 which is L - 19.

At this point Laura has double as many clips as Holly: L - 5 = 2(L - 19) and we can solve.

L - 5 = 2L - 38
L = 33.

Laura had 33 - 5 = 28 after she gave 5 to Holly.

There are probably other ways to solve this as well. Evelyn Saenz said…
This is a great way to help beginning algebra students visualize word problems.

Have you tried doing this with Cuisenaire Rods? Maria Miller said…
No, I'm not that familiar with how to use Cuisenaire rods to teach something like this. jjlc2 said…
Yes, but L = 33 is not the right answer. The question asks "How many clips did Laura have left?" That is 33 - 5 = 28.

Just for comparison, I wish that I could show you how to think of this in the CSMP curriculum I use with my kids, but I can't draw pictures in a text comment.

But, the point that they are solving for needs to have a name or a star or something by it, so kids don't lose track of what the original question was asking. Anonymous said…
I'm excited that I got the same answer as yours, Maria.

I used the following equation:

x + 19 = 2(x+5)

x + 19 = 2x + 10

2x - x = 19 - 10

x = 9

Therefore, Laura has left x + 19 = 9 + 19 = 28

(x representing Holly's initial possession)

This is how I did the above:

Since Laura gives away 5 chips to Holly, then Laura now has x + 24 - 5 = x + 19 and Holly now has x + 5

And, since we know Laura has twice as many chips as Holly after giving away 5 to Holly, then x + 19
should be 2(x + 5)

I do not know how I can help children learn this with understanding, but to me it is definitely an application of the concepts of addition, substraction, multiplication and equations, combining to solve a problem. The use of bars was definitely helpful to me. Burt said…
Maria,
In solution 2, why not just compute the difference between H and L? 19 - 5 = 14. this is half of L, then L = 28 Sidney said…
How about just using algebra alone?
Laura has L.
Holly has L-24

then: L-5=2(L-24+5)
L-5=2(L-19)
L-5=2L-38
L-5+38=2L
33=L
The question was how many left to Laura after she gave 5 to Holly which is L-5 so 33-5=28. Anonymous said…
I used algebra also. Initially,
you have Holly+(Holly +24)

2h+ 24

After the trade you have
(Holly+ 5) + 2(Holly +5)or
3h + 15.
There are the same number before and after, so

3h+15 = 2h+24
-2h -2h
h+ 15= 24
-15 -15
h = 9

Laura has 2h=10 left after the trade or 2(9)+10= 28. Jeff said…
Hi Maria,

Your diagram was very informative in solving this problem, and some of the text comments has illustrated more information and simplified this diagram even more.

Jeff