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, 360^o/2pi^r=theta^o/theta^r , which could be used to covert radian to degrees or vice-versa.
• This could also be reduced to 180 degrees/(pi)radian=theta^o/theta^r .
• To find how many degrees is 2 radians, we would replace theta^r with 2 using the formula above and cross multiply. So theta=180*2^r / (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 = theta^o/a , or 180/(pi)r=theta^o/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=theta^r*r , but it can only be used in radians.
  Hope you all have a radiant rest of the day.

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 step.....you'll see. Enjoy!