# Trig Curve Sketching

Previously, my Pre Cal students were messing around with the graphs of sine and cosine. Some common errors rose to the surface. The assessment that came a couple days later revealed that students were having trouble calculating periods and getting the subtle details of cosine correct. To top it off, now I'm throwing tangent graphs at them and they just found it weird.

Luckily, Frank says it best.

Some days before we had started any of this trig graph stuff, Kate Nowak shared an excellent curve sketching game for Algebra II. Instantly I knew I needed to try it. It was too good not to. In fact, it spawned activities for Pre-Cal AND Calculus. More on the Calculus one later.

### Setup

To summarize Kate's game: distribute decks of cards with different features on them, require students to draw something that has those features, and judge one another for accuracy.

I made a few modifications for my purposes.

• Deck of 22 half index cards
• One six sided die
• Whiteboards
• Markers

On the cards were sets of features that could apply to a sine, cosine, or tangent graph. Students pick a judge, the judge flips a card and rolls the die. A 1/2 means you draw a sine with those features, 3/4 cosine, and 5/6 a tangent. Student groaning when it comes up tangent is optional.

I printed this off on Avery 5160 labels (just like Log War and Inverse Trig War):

I threw a couple goofy ones in there because that's how I roll.

### Let's Play

I told someone to keep score and to make sure they rotated the judges. For two classes we awarded a point for the "best" interpretation of the graph. I noticed the same kids were getting the point every time so I changed the rules for class three. Anyone who does the graph correctly gets a point.

I thought they'd get through about 15 cards in the 40-45 minutes. In reality it might have been closer to ten. A few cards caused some confusion. In a few cases the judge wasn't sure if anyone had done the graph correctly. I suspect if we played this towards the end of our time with trig graphs I would've had fewer debates to settle. There were still lots of good things going on here. If anything it hammered out the differences in sine and cosine for lots of them. And we solved the period calculation problem. The goofy cards produced some excellent results.

It was a lot of good graphing practice and discussion without feeling like graphing practice and discussion. It kept their attention for quite a while. I think we could easily do this again for some other stuff. The Calculus version went equally well.

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