## Graphing Sine and Cosine – Graffiti Wall

April 16, 2012 by Molly Kate

~~Graffiti~~ Graph-iti Wall. That was an amendment made by kids.

Students had filled in their own unit circles (measuring the angles with protractors etc.), created charts to help them easily identify the sine, cosine, and tangent of all the angles, and worked out several unit circle problems.

Next came graphing.

We began our journey with this “guided notes”/discovery activity.

I won’t lie – the intent was students would move seamlessly from their unit circle into this x/y table and plug in and graph away. They would work individually or with a partner discovering and having a grand ol’ time.

Uh no. With my two lower level classes I did need to provide more scaffolding. I started off with a simple x/y table of a line and reminded them how we chose the values for x and so on. Then I placed this table on my smart board and explained I had chosen my x values as certain angles around the unit circle and we used the unit circle to find the y values. I also drew a “regular” x/y plane with 1,2,3 but then explained those are not my x values so it doesn’t make sense… and so on.

The students did a fantastic job after the appropriate scaffolding and continued the project for the rest of class and then for homework. The next day we practiced graphing with the Graph-iti Wall. All around the room I had placed different charts like the one below.

Students began at one station and were timed for 5 minutes. Everyone had a marker and everyone had to write. *Everyone had to write, even though they were writing the same thing. *They did as much as they could until the timer rang (or the music stopped, I couldn’t get my music working though!) and then faced the center of the room. The next task was to head to the next station and *check *the work completed before them. They had to actually **check off ** each answer and again *everyone was checking off* then they could move on from where the last group left off. They rotated around to about 4 stations and then were sent back to their original to see what happened.

There was a lot of writing – in fact you could barely make out the first group. Hence the graffiti idea. It’s an awesome activity for anything multi-step and I look forward to doing it again!

Students got the amplitude and vertical stretch/shrink DOWN after this activity – which made teaching period (horizontal stretch/shrink) easier without the confusion of the “inner” number and “outer” number.

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on April 28, 2012 at 11:10 pm |lmhenry9Am I understanding correctly that you had one station per student set up or were students in small groups? Also clarifying – students worked through what was in front of them, then moved. When they got to the next station, they had to check what was already done (essentially working out the new problem) and then continue from where the last person left off? I’m just trying to clarify so that if I implement this in my class with a different topic, I understand the mechanics. Thanks – looks like a great activity!

–Lisa

on April 29, 2012 at 7:30 am |Molly KateHey Lisa – thanks for the comments/questions. Happy to clarify. I had students in groups of 3 and they got to pick a station to start at. Each station covered the same concept – graphing a vertical stretch of a basic sine or cosine wave and describing the transformation. Although some stations had a reflection as well and some had a shrink etc. I wanted each (set of) student(s) to practice the same concept at least four times.

They were given 5 minutes to start the station (mostly could fill out just the table and maybe start plotting points). I had them face the center of the room before they rotated to clarify that their task next was to CHECK and then correct, if necessary, and then continue on where the last group left off until time ran out again. The next stations received 7-10 minutes depending on work progress I saw. This way they had about 3-4 minutes to check previous work and 4-6 minutes to continue forward.

The great part of this is that you can monitor ALL progress by walking around the center of the room. Great way to formatively assess what is happening in your classroom.

I think it is important that each station has a variation of the same concept and at a similar level of difficulty so that students are actually reinforcing the concept instead of trying to learn something new. Although I did put a predict and construct a list of things you notice to make it less plug and chug at the end.

100% of the students got this correct on the test – both in finding and describing the amplitude of the function and graphing the wave. At the end of the exercise they were pretty sick of it (a tell tale sign they’ve practiced the skill enough).

I like this kind of exercise for repetition though because the students are moving, checking for mistakes, building off each others answers, asking each others questions, and everyone is contributing. Let me know how you use it and how it goes!!

on August 16, 2012 at 11:26 am |findingemuOh my! I just found this through a Twitter link to your current post blah, blah blah…

Soooo many ideas crashing into my brain right now. I teach Eighth Grade (Algebra and “Regular” Math 8) so, obviously the whole Unit Circle concept is out the window, but the structure of the activity is awesome! I WILL be using it (moe than once) this year. Thanks :)