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.

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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.

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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.

Math Teachers at Play #8

Go visit Math Teachers at Play carnival at Let's Play Math. Lots of neat stuff this time!

I definitely want to try this with my daughter for multiplying by 7s. I also really liked
Four things I used to think about calculus, and what I’ve replaced them with
- a teacher whose teaching has evolved towards conceptual understanding.

Research on conceptual understanding

Just an interesting piece... a recent study has found that teaching conceptual understanding in math makes children learn better, as opposed to teaching procedures.

You Do The Math: Explaining Basic Concepts Behind Math Problems Improves Children's Learning

The children were taught about solving equations such as

4 + 5 + 3 = ___ + 3

either procedurally, or conceptually. Procedural instruction went kind of like this:

"Add the three numbers on this side, 4 + 5 + 3. That's 12. Then subtract the number here from that, 12 - 3 = 9. That's the number that goes to the blank."

In the conceptual group they were taught about equivalence, the equation having two sides that have to be equal.

Of course... the conceptual teaching is the way to go!

Here's a link to the research paper (in press):
Matthews, P. & Rittle-Johnson, B. (in press). In pursuit of knowledge: Comparing self-explanation, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology.