## Monday, November 17, 2014

### Sine Graphs and desmos.com

We have finished all of the transformations for sine and cosine graphs, and soon I want to have an application day where they can write models for various data: blood pressure, tides, weather, oscilloscope readings.... but first I assigned them the following homework:

Think of a city in the world, maybe you want to visit, or it's exotic, or it's far away, or it's a place you have never heard of but searched for online. Then find weather data for a 12 month period for your city. We quickly logged onto desmos.com and they got accounts and we practiced making/plotting table data and changing window settings and such. They were to come back with their city weather data entered and saved.

The next class, we practiced on paper with "weird data":

I made them just draw a generic sine graph with no axes or numbers around it. I then prompted them for numbers, and then got (say) the "28" for the top x value and the max (71) and min (-31) y values. I made sure to wait until I heard things I wanted before I committed them to the paper.

Then they had to find the amplitude/vertical shift/horizontal shift/period. We talked it through and then got an equation. We did it again for a cosine graph.

Then we went on the laptops and they brought up their weather data. I asked them to do what we just did to find an equation that would model their weather data. Most importantly, YES they could guess and check, but it would be WAY better to think things through and come up with an equation first and some justification for the 4 key values as we practiced and then play around.

It made for some interesting conversations about "not normal" data points (I picked Timbuktu, Mali, and the year's data had a cold snap for 4 months that should have been hot) .... and about north of the equator and south of the equator cities (one student's data was warm in January and cold in August) ... and cities that were near the equator (all the temperatures stayed basically the same all year).

My Prague data worked out better than my Timbuktu data: