Parametric Lines

https://www.desmos.com/calculator/fgd0zrrkrs

This nice problem provides a fundamental introduction to animation in Desmos. The student will learn how to plot points, draw lines between points, and move points along those lines. This will reinforce the students’ capacity to move between the graph and the algebra.

In this animation, P and Q move along the dotted lines bringing the line-segment PQ along with them. Find the times at which the PQ line is horizontal, vertical, or of slope 1.

We still haven’t decided whether this activity belongs to grade 9 or 10. Most teachers we ask have said that their grade nines aren’t ready for this, and around the middle of term they might say that they “haven’t done lines yet.” That’s an interesting comment as it highlights one of the main differences between our approach to curriculum and the standard approach. In a word, when I ask if the students are ready for something, the standard approach focuses on what the students know, whereas we focus on what they are ready to do. Our basic mantra is that knowledge (including technical skill) flows from doing rather than the other way around. This activity works with lines in quite a different way from what is found in the standard resources. Our approach is more relevant to the construction of animations and this animation is a good example of its power.

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