Learning fractions visually

First of all I want to mention that Henry at Why Homeschool is looking for homeschooling carnival submissions for an anniversary edition next week. Check here for instructions.

And then, about fractions. I have now updated and improved my two fractions workbooks.

In these books, I've strived to teach all fraction operations visually, and explain why the various rules for fraction operations work.

I know, most math books have pie charts for fractions as well, but here's the difference: in my books, the kids do a lot of exercises using those pies, and not just see them once in the beginning of the lesson.

And these are not manipulative exercises but simply picture exercises in the book.

I've always felt you need to first get the kid to understand what fractions are and only then start dealing with rules.

Those rules so often just get confused with each other. (Have you ever had a child try add fractions by adding the numerators and the denominators...?)

I've strived to create lessons that gently guide the student in discovering the "rule" for multiplying or dividing fractions, while doing all those picture exercises.

We need to strive that our students first remember some simple pictures in their minds before they start applying some half-forgotten rule and just hoping it's right.

So that's the goal of these two fraction workbooks. They are sold as PDF files that you download and then print; the first book is $4, and the other is $3.50.

Check also the free sample pages!

Square root of 11

Is square root of 11 an irrational number? How do you know from using a calculator? Thank you.

Well, I happen to know that if the square root of a natural number is NOT a whole number, then it is an irrational number. There are no other possibilities.

Of course you can't tell by the calculator. The calculator will show you 8 or 10 decimals, but you won't know from that if it's going to continue or not, or if it is periodical or not.

But pure mathematics and established, proven theorems will tell you that! : )

A proof that the square root of 2 is irrational

Lots of proofs of the same... plus one proving that any root is irrational if it's not a whole number

Proof that the square root of any prime is irrational

Cute circle terminology song

This was sent to me... I thought it was a very cute, melodic song about learning circle-related terminology such as radius, diameter, and circumference, and the two formulas with Pi (area formula and circumference formula):




Here's a direct link in case you want to spread it around:
http://www.youtube.com/watch?v=-z4SUypJZxo

This is done by Dave Mitchell who also has a website Arithmecode.com.