Friday, February 4, 2011

Update on McGoldblog

The third post was from Abby. I think hers has set the bar a bit higher. She wrote: (my italics)

Today in class, we continued our lesson on radians and degrees, and how to convert from one to another.
  • We know that the number of degrees in a circle is 360, and the number of radians in a circle is 2(pi).
  • So then, we have a proportion, 360o/2pir=thetao/thetar , which could be used to covert radian to degrees or vice-versa.
  • This could also be reduced to 180 degrees/(pi)radian=thetao/thetar .
  • To find how many degrees is 2 radians, we would replace thetar with 2 using the formula above and cross multiply. So theta=180*2r / (pi) , would come to approximately 114.6 degrees.
  • To be exact, just multiply 180*2, leave pi as is, and we get 360/(pi).
  • To find how many radians is in 30 degrees, replace 30 by theta degrees instead, which I’ll leave you to figure out – exact or approximate amount.
Arclengths -another new thing we learned. :)
  • If we have an angle, we get an arc or a section of the circumference. This is called the arclength.
  • And the bigger the angle, the bigger the arclength. :O
  • If we take 360 degrees of the circle, the arclength would then be the whole circle, or its circumference. And its formula is C=2(pi)r.
  • a (arclength) = 2(pi)r when theta=360. From this, we get a proportional formula similar to the one with radians.
  • 360 degrees/2(pi)r = thetao/a , or 180/(pi)r=thetao/a
Another sample question:
  • If we had r=5cm, and an angle=45 degrees, find the arclength subtending this angle. Mrs. McGoldrick also gave us a formula for arclength: a=thetar*r , but it can only be used in radians.
    Hope you all have a radiant rest of the day. :P
Things I love about this:
  • She didn't leave any content or formulas out
  • She put in subtitles
  • She asked not one, but two questions
  • Her personality came through, especially at the end with the "radiant day"!
  • The clarity of it suggested to me that it was a pretty well-done lesson (pat on the back for Audrey)
Things I would like to see in the future:
  • diagrams - slides from the lesson or their own
  • colour coding
  • worked out examples
  • math notation - how the heck do you get that into a blog post - to find out
When we discussed Abby's post, many things came up - math things, that is. For example, one question was not properly answered so we corrected it, or rather, Fred worked it out because I knew he did have the right answer. It all just seemed so much more relaxed and natural than when I am once again trying to get them as enthusiastic as I perpetually (and probably annoyingly) am.

Today's lesson was on the unit circle. Introduction to. Here's the powerpoint for the lesson that Shelley will be blogging about this weekend (lucky girl!):

feb 4 unit circle intro  

I know....97 slides! But don't worry, that's only because I show each little'll see. Enjoy!


  1. I love your reflections! Your perpetual enthusiasm is contagious not annoying! I will continue following both of your blogs with interest.

    Am I allowed to tweet out the link to your amazing blog to my twitter followers? I am sure that we can get Darren Kuropatwa to comment!! (Just thought I would throw in his name one more time!)

  2. Sure, Dianne, tweet away! Hey, you never know! And thanks again for all your support!

  3. woo hoo - the power of twitter at work!!!! Let me know how many new followers you get this week :)