## Friday, June 17, 2016

### Math Links for Week Ending June 17th, 2016

In Ontario, when we introduce Pythagorean Theorem, we are supposed to do so by considering the Pythagorean Relationship instead. That is, the fact the the area of the square on the hypotenuse equals the sum of the two squares on the sides of the legs. This is the geometric version of PT. And as it turns out it doesn't have to be a square on each side. As it turns out it can be any shape as long as the size of shape is scaleable based on the sides of the right triangle. You can test that out in this simple multipage WebSketch that shows the relationship works for many different regular shapes and finishes showing that it works for any irregular shape too.
Curriculum Tags: Gr8, MFM1P, MPM1D
http://engaging-math.blogspot.ca/p/web-sketches.html

I was skeptical at first when I saw the blog title "Worst Problem Ever" from @MarkChubb3 but like any good title, it gets you in the door. He talks about giving a simple surface area of a rectangular prism problem where it happened to work out the that both the surface area and volume worked out to the same number (with dimensions 5x5x10) - obviously not the same units. But the cool thing was the opportunity for learning that he took at that time. He challenged his students to find other rectangular prisms that had the same property. Those kids probably will never ever get the volume or surface area wrong because of this because they had a purpose for doing both and they were engaged to do it.
Curriculum Tags: Gr7
https://buildingmathematicians.wordpress.com/2016/06/07/worst-problem-ever/

I love this site from @c0mplexnumber on the cross between Art and Math. Artfulmaths.com gives us man different ideas of how art and math mix. There are a lot of ideas here that fit many different grade levels. Thanks to @MathGarden for pointing this one out.
Curriculum Tags: All
http://www.artfulmaths.com/

I totally love this use of Desmos Activity builder by @ddmeyer. It's a great example of having kids discover something rather than just giving it to them. In this case it's the fact that if you take the diameter of any circle and create a triangle using it and any point on the triangle, it creates a right triangle. This way it is hidden until you use the overlay feature in the activity. The result is magical. The result would be a cool way to do analytic geometry.
Curriculum Tags: MPM2D
http://blog.mrmeyer.com/2016/math-improve-the-product-not-the-poster/

A great little @ddmeyer video that make students think about linear relations where there is an initial value (partial variation). Very simple yet the video makes it just that tiny bit more engaging
Curriculum Tags: MPM1D, MFM1P
http://blog.mrmeyer.com/2016/the-cup-is-the-y-intercept/

I though this was a totally interesting way to consider how a function works. A bit of warning though, it might not be for sensitive students (and probably not vegans). Thanks to @GrayKimBKim for pointing this one out.
Curriculum Tags: MCR3U, MCF3M

This is a really great problem that, when I heard it, wasn't sure it was true. Consider two people, one who invests \$2000 for 8 years starting when he was 19 and then stops but lets that collect interest for another 27 years. Another starts investing \$2000 each year at 27 and does so for 39 years. Who will have the most money in the end. The answer will suprise you. Even if you can't get the artificially high interest rate used (12%) it does show the power of compound interest. Thanks to Giovanni Spadafora for this one
Curriculum Tags: MCR3U, MCF3M, MBF3C