One of my goals for this week was to get fluent at embedding Geogebra in the blog. Kate Nowak already laid out the directions, so it should be easy peasy.
Fraction Multiplication - Area Model
In this picture, the grey rectangle represents one unit of area. Two fractions can be shown relative to that rectangle, as well as their product.
Can you see how the sketch shows the red fraction? The blue fraction?
If you uncheck show product, can you predict what it will be?
Can you see why the unsimplified product is what it is?
Does the simplified product make sense compared to the grey rectangle being equal to 1?
Created with GeoGebra
Also available as a standalone webpage or the original file. My only difficulty embedding was getting the first line of the applet correct. It needs to be as below, where the height and width are what's appropriate for sketch. (The archive value was without the web address in my html export from Geogebra.)
applet archive="http://www.geogebra.org/webstart/geogebra.jar" code="geogebra.GeoGebraApplet" codebase="./" height="560" name="ggbApplet" width="639"
As for the Geogebra, here's what I did. Construct a rectangle, and measure the dimensions. Set up sliders for numerators and denominators, by limiting the range and setting step size to 1. Debated about allowing improper or not. When I decided to allow it, made the numerator sliders proportional, so the visual would support the comparison. I made the fraction rectangles by using the slider fraction to establish a proportion of the unit dimensions. So if the unit width was 9 units and the fraction was 2/3, made a circle with radius (2/3)*9. (literally (e/f)*distanceAC) The partition lines were made similarly, by making a unit distance and then translating the lines. The trickiest bit was the conditional visibility of the partitions. I set them to be visible if the the numerator was large enough. (I.e. the 12th line is only visible if the numerator is >= 12.) Then when I made the show/hide buttons, I lost all that. Sigh. I went back in and used the boolean variable and AND (^ from the menu, not the up carat which is for exponents), like w ^ j>=12.
I haven't ever had critical feedback on my sketches, so if you feel inclined, please let me know. (Well, students let you know, but I mean collegial feedback.)
OK, here's my Camtasia student film. I'm definitely interested in screencasts, but am not sure as to what features make them effective (or annoying), and how to use them effectively. This must be the most boring one, ever.