1. Khan opens with this shot (a continuation of a previous video) in which he had shown how to calculate the area of an equilateral triangle in terms of its side length.
1. We open with an introduction to the figure. Students explore how it is changing at each iteration, attempt to solve for the area, and identify what they think we will need/what will be important.
2. Khan begins to organize information by showing the viewer that you can set up a table that will compare the number of sides to the overall area.
2. We pursue the "meaning" of area and investigate these irregular shapes as a way of developing the concept of total area as a sum of parts (or taking things apart and putting them back together).
3. Here Khan starts to show the viewer a pattern that is emerging. He points out that the number of sides is multiplied by four at each successive iteration and that the side length of the new triangle is 1/3 the length of the previous.
3. We look at how the area of the "new" triangle is changing at each iteration.
4. Khan has now shown the calculations for the first four iterations. Each iteration is color coded. He has also written the terms of the sequence in a way that helps the viewer recognize patters.
4. Next we were concerned with looking at the total area at each iteration. As a class, students brainstormed what to include in a chart and then worked in teams to create it, complete it, look for patterns, and create any generalizations.
5. Khan has identified the portion of the series that is geometric and is demonstrating the calculation of an infinite geometric series.
5. Our next move was an introduction to sequences. Students attempted to look for patterns to help make predictions and used structure in the visuals to make connections to any generalizations.
1. The two approaches tackle the same question. Are students learning the same things in each?
2. What does each method imply about the definition of mathematics?
3. How would you choose to measure/evaluate student progress in each approach? What is valued?