In an effort to weed extraneous & irrelevant material from algebra our curriculum to both make it more relevant, it might be tempting to remove Unit Circles because they are not included in the list of widely applicable prerequisites of the Common Core. The unit circle is traditionally taught by having students memorize “special angle” positions like they do multiplication facts in grade school. Instead of eliminating unit circles, however, it makes sense to change the focus and develop it within data and statistics modeling*. Students need to understand all data is not linear, and sinusoidal curves are common.
Intended Unit circle objectives, from CCSS functions progression, pg 18 link :
- Sine and Cosine can be used to model periodic functions students find interesting such as average daylight per month in a favorite city, or sales of seasonal clothing. Example link . Digital signals that produce sinusoidal data are prolific in our high-tech culture. They are cross-disciplinary: physics and music.
- Physical differences between degree measure and radians naturally connect & stretch G-C.5 and reinforce understanding of proportional relationships, a deficiency that has often been noted by science teachers before CCSS.
In CCSS-alligned curriculum, unit circle objectives would not include memorizing special angles. Most of the intended objectives can be met in 3-4 lessons, 5 if students don’t know where pi comes from (7th grade geometry standard). NCTM hosts a powerful activity “Sine Curves and Spaghetti” link to connect unit circles to sinusoidal waves. My Algebra 3 students did not ask why we were doing the activity. They found it fun, interesting, and memorable. This kind of activity tends to pique their interest in higher level math.
Today’s activity started with a link to a Google Drawing in the Google classroom feed:
Students were directed to work in their groups to search for “hours of daylight” and find out the average for each month in a city of interest. Next, each group plotted their data, using a different color so we could visualize differences. Here’s what ended up on the screen:
When they were finished, I showed how I could snip and extend the data for the next years:
Since many of these students also take marketing, we talked about how sales for seasonal items might follow similar patterns.
No one asked, “When are we ever going to use this stuff?” probably because they had fun in math class, but also because they saw the connections. Students who see the connections are much easier to motivate. Here’s what one student did with time left at the end of the hour:
Anytime a student takes a mathematical concept and willingly extends it beyond what I expect, I consider that a win-win.