## Posts

Showing posts from December, 2006

### 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

### 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 .

### Multiplication, division, laser TVs, logs.

Well today I hopefully have something for everybody. The site DoubleDivision.org shows you an alternative long division algorithm, which takes the guessing away from estimating how many times the divisor goes into what needs divided. Also called 1-2-4-8 division. This is a pretty cool way of dividing! The interactive tool shows you the steps right there for any problem you might come up with. At MathLogarithms.com you can download an ebook by Dan Umbarger explaining logarithm how's, why's, and wherefore's in all detail for students. Great resource for precalculus students. You might also enjoy an alternative way to multiply called lattice multiplication . I did! It seems pretty simple. And lastly, if the math topics didn't interest you, how about my hubby's newest website called Laser-TVs.net ... It's about a totally new way of making TVs using lasers.

### Nullity and dividing by zero by professor James Anderson

Recently this was highlighted at Slashdot and Digg.com both. A math professor James Anderson has made a new 'number' or entity that he calls NULLITY, in order to solve problems such as 0/0, which traditionally is left undefined. Basically he first defined 1/0 as infinity, -1/0 as negative infinity, and 0/0 as nullity, using Î¦ (Phi) as a symbol for it. He said this nullity lies outside our normal number line, not on it. I watched the video shown on BBC news , and there he went on to show what happens with the "age-old" problem of 0 0 , (zero to zeroth power) using just normal rules of arithmetic plus these definitions: 0 0 = 0 (1 − 1) = 0 1 × 0 -1 =(0/1) 1 × (0/1) -1 Now, for every number, the 1st power is the number itself, while the -1 power is its reciprocal: = (0/1) × (1/0) = (0 × 1) / (1 × 0 ) = 0/0 = Nullity. Anderson said in the comments following the main article on BBC that two other professors have helped him develop axioms for this new theory, and one