Content+(Math)


 * Content (Math)**

[] for examples)
 * * sample problems/topics in the Ontario secondary school math curriculum (OSSMC) that you can solve but forgot how to do
 * list of video clips you have viewed to supplement your knowledge of OSSMC
 * OSSMC
 * creating educational mini-clips demonstrating understanding of problems (see
 * creating a web-page with links to educational mini-clips that could be used to cover units in the OSSMC
 * creating a mind-map of how concepts are related within a grade level ||

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 * Curriculum Links:**

Note that there are also exemplars for some of the curriculum


 * The Commutative Law of Multiplication:**

The Commutative Law of Multiplication is something that we take for granted, but when we really know what it means, then it is quite astonishing. Here is an article that I wrote about it. I had to embed the pdf because I can't seem to insert pictures into Wikispaces.



Here is a proof of the law, again as pdf, because I like pictures:

Here's an interesting post that I stole from Jess:
 * Calculating the Square of Numbers Near 100**

Watch this video to quickly square numbers around 100. Now explain why this method works?

I'll add to this by explaining why it works: First note that any number like 104 can be represented by a two term sum: (100 + 4). Then it's just a simple matter of applying the distributive law of multiplication: Likewise, this can be peformed in general:
 * Minds-ON Activity for Dividing Fractions**

Here's the link to a video that I made of a Minds-ON exercise for the esoteric subject of dividing by fractions: []


 * A Fermi Problem**

I like Fermi problems that have some relevance rather than just being silly. Here's a Fermi problem that I came up with that has a lot of societal relevance:

You get your Mom to drive you to the Mall. How much carbon dioxide (in grams) does this add to the atmosphere?

Hint: Gasoline is a “Hydro-carbon” which means that it is made up of Hydrogen atoms and Carbon atoms only. Hydrogen atoms are negligible in weight compared to Carbon atoms. When gasoline burns, each carbon atom pairs with two oxygen atoms (ie “Carbon DI-Oxide” = one Carbon plus TWO Oxygens). Carbon atoms and oxygen atoms are approximately the same weight.

For a 20km round trip, your car will emit something like 6kg (that's 13 pounds!) of CO2. I think that most students should be surprised by the size of their "carbon footprint". This is because we **see** only a wisp of vapour being emitted out of the tailpipe of our family car and tend to think of it as "lightweight gas". If to reinforce the notion, it might be worthwhile to estimate the carbon footprint of an entire tank of gas from the family car.

We live in a society where we are all willing to lend vocal support to being "green", and especially to point fingers at industry - but we are quite blissfully ignorant (and hence hypocritical) about our own carefree behaviours that cause significant pollution.


 * An Idea for Manipulatives**

I think that Linking Cubes can be useful for validating edge length and surface area of prismatic shapes. Even I have difficulty sometimes with accounting when I try to do this in my head. So this gave me an idea for a high-tech linking cube: Using LEDs create linking cubes that can light up on all individual edges and sides to assist in the accounting. But there's probably no money it.


 * The Difference Between "Division" and "Quotient"**

Back in school, you were probably told that "find the quotient" means the same as "divide". Well, it turns out that that is not quite true. Here is a video I made explaining the difference.

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