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Showing posts from November, 2007

Pan balance problems to teach algebraic reasoning

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Today I have a "goodie" for you all: a free download of some pan balance (or scales) problems where children solve for the unknown:

Just right click on the link and "save" it to your own computer: Balance Problems (a PDF). This lesson is also included in my book Math Mammoth Multiplication 2 and in Math Mammoth Grade 4 Complete Worktext (A part).

The problems look kind of like this:

These can help children avoid the common misconception that equality or the equal sign "=' is an an operation. It is not; it is a relationship.

You see: many students view "=" as "find the answer operator", so that "3 + 4 = ?" means "Find what 3 + 4 is," and "3 + 4 = 7" means that when you add 3 and 4, you get 7. To students with this operator-view of equality, a sentence like "11 = 4 + 7" or "9 + 5 = 2 × 7;" makes no sense.

You might also find these resources useful:

Balance word problems from Math Kangaroo

Al…

From the blogosphere

Just some interesting posts from other blogs:

How to read a fraction from Let's Play math. Denise explains how a fraction is not two numbers, a fraction's "first name" and "family name", the line in it meaning division, and more.

Good Math, Bad Math gives an example of the latter: How the lottery company's game "Cool Cash" had to be canceled in Britain. I had hard time believing this one as well!

And some solid tips of How to get past “stupid” Math mistakes from Wild About Math!

Carnival of Homeschooling, 97th edition

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This week, at Principled Discovery, we are attending classes at Homeschool U, our own virtual university for homeschooling families. Each class is worth three course credits.

Go check it out! Lots to read there!

Subtraction question

(from a site visitor)
I have a 3rd grader who is struggling with the concept of subtraction. He has tried number lines which he hates to use, says it makes him feel like a baby and also we have tried the concept of "counting up", but he claims he get confused because it is "take away" not adding. What can I do to help him with this concept? He has an easier time with 8 − 2 but when it is 14 − 3 we run into difficulty. I have even resolved to letting him use the calculator. Any suggestions?

I think he needs to understand the concept of subtraction better, first of all.

My book Subtraction 1 deals with the subtraction concept itself and the three ways it is used:

- take away
- difference
- whole/part

He needs to understand those three ways it is needed. It's not "just" for take-away situations.

Secondly, he needs to realize that addition and subtraction are opposite operations, and THAT IS WHY we use addition facts when doing subtraction problems.

After tha…

Rank #1 in Google search meme

I heard about this from Let's Play Math, and thought it sounded a little fun. It didn't take me too long to find out I come up #1 in Google for these phrases:

singapore's bar diagrams 1.17 M
multiplying in parts 1.8 M
number rainbows 1.7 M
homeschool math blog 1.15M
living loving math 1.5 M

The numbers indicate how many results Google showed (in millions).

The rules are below. If you like the idea, consider yourself tagged!

1. Search for your blog on Google. Try to find 5 different phrases that produce your blog as the #1 hit.

2. You may enclose the search phrase in quotes if necessary, but a search without quotes is preferred.

3. Score your search phrases based on the total number of hits.