Unit Circles: Relevance in CCSS

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:

daylight

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:

daylight2

When they were finished, I showed how I could snip and extend the data for the next years:

Daylight5Since 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:

Daylight4

Anytime a student takes a mathematical concept and willingly extends it beyond what I expect, I consider that a win-win.

*Page 10 from the AP course description, “…the computer allows the student to fit complex mathematical models to the data… “


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s