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Maria's Math news - a FREE math newsletter for parents and teachers
Latest from my blog
Various worksheets on TONS of math topics you can generate for free!
Basic operations worksheet generator is updated! Make worksheets for whole numbers or integers - all four operations, including add & subtract or multiply & divide - horizontal or vertical - add a border and/or extra workspace, use a variable, and more.
Advice, reviews, and resources to help you choose a math curriculum!
Online math games, tutorials, and activities
Games you can play online, interactive tutorials, fun math websites and more. Arranged by topic/level for ease of use.
Learn how to TEACH concepts or about general concerns in math education.
In-depth reviews of math products
Math help & tutoring
A list of free message boards, math help websites, and online tutoring services.
Fun and games
I have two games on my site, plus links to many.
Game: Choose Math Operation
Word guess game (easy hangman)
Word guess game (difficult)
A proof that the square root of 2 is irrational
How do we know that square root of 2 is an irrational number? In other words, how do we know that √2 wouldn't have a pattern in the decimal sequence? Maybe the pattern is very well hidden and is really long, billions of digits? Even if you check it till million first digits, maybe the pattern is just longer than you were able to print the digits out with your computer?
Here is where mathematical proof comes in. The proof that
is indeed irrational is usually found in college level texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead it is a "proof by contradiction"—if √2
WERE a rational number, then we'd get a contradiction. I encourage you to let your high school students study this proof since it is very illustrative of a typical proof in mathematics and is not very hard to follow.
Calculators and Irrational Numbers
Irrational Numbers; Rational Square Roots
Adding Rational and Irrational Numbers
First 100 Irrational Numbers