Saturday, September 22, 2007


We started trigonometry at the end of last week, and I know from past experience that my fraction-phobic students have trouble with placing pi/3, pi/4, pi/6, etc. angles in standard positon, so I tried something new this year.

I drew a semicircle (flat-side down) and made up some story that involved having and "em(pi)nada" for lunch and said it was so delicious that other teachers wanted to share it with me. I had them draw 4 em(pi)nadas and draw how they'd slice them in pie cutting fashion into 2, 3, 4, 6 equal parts to share and eventually they shaded the 1st piece (thinking of angles in standard position). They had no trouble slicing them equally, and I think it helped later on when I linked pi radians to 180 degrees, and they then drew pi/3, etc angles around the circle.

Then I introduced radians by first saying that for so-and-so's birthday I gave her a circle, and her mom gave her a string, and so-and-so was SO bored that she decided to do math by cutting the string the length of the radius, and she wanted to see how many times it would go around the circle. They were then to discuss how many times they thought it would fit. I got various responses, 3, 4, 6, 10... We finally got to the fact that you're just measuring the circumference. They then proceeded to equally tell me the formula for circumference was pi*r*r and also 2*pi*r. So then I had to sing them a song a student taught me, and then we all sang it together a few times:

Twinkle, twinkle little star
Circumference equals 2, pi, r.

Lovely (it brings a tear to the eye). We then defined radians.

Anyway, after I used my math tools (thin spaghetti to sweep out angles on the overhead), and we practiced placing various radian angles in standard position, we called it a day.

An interesting side note: another teacher friend mentioned a while ago how he linked the clock with the unit circle and that seemed to help his kids place 30, 60, 45 degrees more successfully around the circle. Well, I also brought that up, and in a side note, one student mentioned, "you know, I have a hard time reading analog clocks. I never learned, and now it takes me a while to process it."


  1. Neat idea. I'm making myself a note when we get to trig in the spring.

    Did the student actually use the term "analog" clock?

  2. Anonymous8:10 PM

    I KNOW! And it was a girl, so that nicely broke some stereotypes about the people that toss around the word, "analog". I then told the next period the story and asked if any of them had trouble, and a few bravely raised their hands. Hmmm.

    Ms. Cookie

  3. I think the skill of reading analog clocks is left out of many elementary math curricula these days. It is seen as not so important anymore in this age of digital clocks. It would be interesting if this were having unforeseen consequences years down the line!

  4. Anonymous8:33 AM

    You'd think it would still be necessary, but most likely other "newer" skills have pushed it out of favor. I did see some websites that walk you through learning to tell time, so I don't know if I'll guide those students to the sites, or print out some practice sheets or something.

    Ms. Cookie

  5. Anonymous10:26 PM

    i teach high school and I will never forget the time when a girl asked me what time it was. I of course referred her to the big clock on the wall. When she said she couldn't read it, I asked her where her glasses were. To which she replied, can't read "that" kind of clock.

  6. Anonymous11:41 AM

    ima student so i wouldn't think of anything educational to be fun but...anyway, i'll bring that to my teacher's attention