### 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.

## Comments

Have you tried doing this with Cuisenaire Rods?

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.

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.

In solution 2, why not just compute the difference between H and L? 19 - 5 = 14. this is half of L, then L = 28

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.

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.

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