## Friday, May 6, 2016

### Crowd-Sourcing Brings Personality

Since I teach online, I can have a lot of students writing on the eboard at the same time. I've been using this to my, and their, advantage. Instead of getting everyone to do the exact same thing, I make sure to ask something in which there is potential for a variety of answers. I also get them to own their answers by putting their initials or name next to it on the board. Then we talk about the differences or similarities, or classify them, etc just try to use the variety to get a bigger picture much faster than they could get with one example at a time. Not to mention that attaching students' names to each answer, and then addressing them by those names, lends personality and life to the whole activity. Variety, big picture, personality: Win-win-win!

We did this the day after a GeoGebra lab, in which students used Jennifer Larson Silverman's Drawing an Ellipse GeoGebra to experiment with drawing ellipses using virtual string. I had them keep string length constant while moving the endpoints, then vice versa. It was concluded that:
• When you keep the string length constant, the distance between the ends of the string influences the shape but only in the length of the smaller axis - the longer axis remains the same.
• When you keep the string ends constant, changing the length of the string influences the shape of the ellipse in both directions
• the length of the longer axis is always equal to the length of the string.
Last night, their homework was to watch a voicethread on the parts and vocabulary of the ellipse. At this point, they didn't know any formulas or rules about the ellipse, only the geometry of it. Then today I had them do this all together:

1. (My voice in bold) Draw an ellipse with major axis length 6 and minor axis length 4.

 (After some minor corrections, and with the names changed of course)
Do all of these have the right major and minor axis length? Yes How are they the same, how are they different? All are same shape but oriented differently. If you had had to draw these yesterday, would you all have had the same string length? Yes. And end points? No. Julie and Bridget's ends would be vertical. What would be the same for all endpoints? distance between them. If you had to find their rules, would they all be the same? Horizontal ones will all have same rule and it will be different from the vertical ones.

2. Draw the foci in their approximate locations.

What part of yesterday's lab do the foci represent? ends of string What do you notice about the foci? Lots here: horizontal ones have foci on x axis, vert on y, all hor foci should be in exact same locations and at same distance from each other. Vert ones will be at same dist from each other as the hor but on y axis (based on yesterday that moving the string ends changed the ellipse). Everyone's foci have origin as midpoint. Personality bonus - Julie and Bridget think a bit differently than most - and that's cool.

3. Draw any point on your ellipse in purple.

What from yesterday's lab does your purple point represent? pencil tip What do we call Heather's point? Covertex. Anyone else picked a covertex? Julie. And who picked a vertex? Bridget and Bob. (In both classes, someone picked those key points, fortunately. If they hadn't I would have had to draw my own.)