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Showing posts from May, 2009

Word problem Singapore way

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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 othe…

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.…

Recommendations for pre-algebra

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Folks often ask me how far I'm planning to write my Math Mammoth complete curriculum (the Light Blue books). Right now I'm finishing up 5th grade. After that, I will be writing 6th grade. But, I'm not really planning to go on after that.

I feel a child who will have finished Math Mammoth 6th grade (once it is available) is probably ready for pre-algebra for 7th grade. Perhaps not all children won't be, but a good portion of those who use Math Mammoth should be.

Pre-algebra is sort of "in-between" course. It is bridging the world of numerical computations of elementary math, and the world of algebra where we manipulate variables. Pre-algebra courses typically cover these topics:



Photo by ecumaniac
* integers
* fractions, decimals
* factors, exponents
* solving linear equations
* solving linear inequalities
* ratio and proportion
* percent
* graphing linear functions
* Pythagorean theorem and other geometry topics
* some statistics and probability.

Most students tak…

Newest Blog Carnival is online

Check out the latest edition of Math Teachers at Play blog carnival. It's up at Homeschool Bytes. As a carnival pick, I enjoyed Plat Diviseur (Fractions on a plate) post. It's about a dining plate... Go see!

Long division and dyslexia

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Photo by laura.bell
I have a dyslexic 9 year old and I wish to find out if your program can benefit him. I have tried Math-U-See and it became too boring or frustrating for him. I have tried various other programs in hope of not overwhelming him. He has completed the delta Math U See level but I feel needs more work on long division. He simply gets very frustrated with it, as the length of time and knowing where to place number due to dyslexia. Is your curriculum a spiral curriculum? Any suggestions would help. One of my books from the Blue Series goes through long division in several small steps: Math Mammoth Division 2

I would suggest that for a dyslexic child, have him do ALL the problems on a squared paper (grid paper). That will help him place the numbers right. Not all the problems in my division book are done with the grid... but for your son, it may be necessary to always use such paper.



Secondly, when you teach on board or on paper, at each step COLOR the whole column…

Chocolate and mental performance

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Photo by Cacaobug

You might have seen this piece of news about a new study:

Scientists reveal how eating chocolate can help improve your maths
Eating chocolate could improve the brain's ability to do maths, a new study suggests.

I think I have experienced this effect. Whenever I eat several pieces of dark chocolate, it definitely seems (while I do various computer work) that my brain works faster and I'm more alert. I also think that this effect is not because of sugar, because the dark chocolate does not have high amounts and because I definitely don't feel the same if I just ate, say, a sweet apple or a cookie.

I like both chocolate and the "alert" feeling after eating it. I don't like it when I start feeling the "brain drain" (your brain can definitely get tired after several hours of researching/writing emails & blogposts/devising math problems etc.). I don't know if this effect is from flavanols in chocolate like it mentions in the study,…

Math Teacher's Carnival

This week's edition is posted at I Want to Teach Forever blog.

CurrClick has a Spring sale

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Discounts vary up to 75% off in CurrClick's Spring sale for all kinds of downloadable products (this includes all school subjects).

Math Mammoth titles at Currclick are discounted too.