1 / 23

Making Sense of Radians: A New Kind of Protractor

Making Sense of Radians: A New Kind of Protractor. Jennifer Silverman Independent Math Consultant Creator, ProRadian Protractors. How many students would recognize what this table of values is?. It is the cosine function. It’s not your fault. This is why there are 360° in a circle.

preston-nunez
Download Presentation

Making Sense of Radians: A New Kind of Protractor

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Making Sense of Radians: A New KindofProtractor • Jennifer Silverman • Independent Math Consultant • Creator, ProRadian Protractors

  2. How many students would recognize what this table of values is?

  3. It is the cosine function. It’s not your fault.

  4. This is why there are 360° in a circle...

  5. 50 + 9 = largest Babylonian numeral 9 What’s our largest numeral? What’s our number base? 10 What’s their number base? 60

  6. Babylonian Numbers: Why Base 60? You can count to 12 on one hand and keep track of the 12’s on the other. 60 has many divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 6 groups of 60 coincided with the length of the year • 60 has many divisors - (1, 2, 3, 4 ,5, 6, 10, 12, 15, 20, 30, 60)

  7. But what does a degree have to do with circles? Not much. But, it stuck.

  8. So, we teach our kids to measure in degrees, and give them tools to help them learn. Like this:

  9. And life is good; they learn all kinds of things, content and secure in their knowledge of angle measure.

  10. Until...

  11. Imagine precalculus students, encountering their first transcendental functions... with a new unit of measure... with irrational inputs... and irrational outputs... CONFUSION

  12. And this doesn’t help much...

  13. I thought they should have practice measuring in radians, so I went looking for a radian protractor... but they didn’t exist.

  14. So, I made them...

  15. The next day, I brought in my first prototypes. Light bulbs started to go off!

  16. CCSS.Math.Content.HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

  17. CCSS.Math.Content.HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

  18. CCSS.Math.Content.HSF-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

  19. Time to try them. Try to approach them with fresh eyes, as if this was brand new to you!

  20. Now, this made sense! Click to play or pause

  21. Other Ideas...

  22. Don’t wait until Precalculus

  23. Thanks for coming!

More Related