Welcome to theme week – Music and Math. Using simple ratio and fraction ideas, we develop the C Major Scale today and Tuesday. Wednesday follows with more ratios and a geometric sequence to understand the black notes. Thursday, we introduce you to the roll that Pythagoras had in understanding the musical scale some 2 500 [...]

You hear the phrase: “Think outside the box” a lot, maybe too much. What it really means is to approach a problem, or a puzzle, from a different angle or perspective. I have four new puzzles that help you do that, plus a favourite puzzle, with an answer, that illustrates that there maybe more than [...]

What is really important for learners is to “fool around” with the new concept you are learning. Draw pictures, look for patterns, try different techniques, look at answers and see how you could bet from the question to the answer in a different way. Then you end up learning this for life, and not having [...]

Looking at a geometric diagram, one can get sucked into just thinking of it as lines and circles.  However, this diagram, maybe slightly altered, actually represents some physical object. This post shows how a geometric diagram, may give you a really neat “walking around” formula that you can put in your mental and physical toolbox. [...]

In about 300 BC, some 2 300 years ago, lived a giant of a thinker in Euclid. He was a Greek, but did most of his work in Alexandria, Egypt. Ground breaking ideas in Geometry and some really useful number theory proofs, were just part of his collection called “The Elements”. Click on the name [...]

Since rational expressions are just fractions, I urge you to review adding and subtracting fractions in the previous two days posts. Today we finish off the section on fractions and rational expressions. Saturday has fraction tricks that are applicable to rational expressions as well, so take a boo at Saturday. Also, I have a fraction [...]

Yesterday we looked at adding and subtracting fractions with the same denominator. Today, we extend that into ding and subtracting fractions with different denominators.  We also have our first look at adding and subtracting mixed fractions. Click on the comic below if it needs to be enlarged.
 

Hexa learns that he already knows ow to add and subtract fractions, but he didn’t know he knew. Octa showed him that adding and subtracting fractions are just like adding and subtracting anything. The first “Big Picture” Rule:  ”You can only add and subtract things that are the same”.  (Go to the download section to [...]

Puzzle solving is something that one can learn to get better at with practice. People are not just born, “able to solve puzzles” and “Not able to solve puzzles”. The way to get good at puzzle solving is to try them, and then if you cannot solve it, GET THE SOLUTION, and then go over [...]

The ratio occurs when you get one fraction equal to another fraction. Since we are looking at fractions and rational expressions this week, it is a good time to see how a “ratio trick” can save us a lot of work. Ratios have uses in music, architecture, house building, carpentry, surveying, algebra, even working out [...]