Reflection: Grappling with Complexity Lines in Space - Section 2: Share


The most difficult part of this lesson is grappling with the fact that so many equations (in infinite number) can be written for the same line. When students are working together, they may have different equations and think their answer is wrong when in fact it is correct.

While teaching I kept going back to two dimensions to drive the point home that there could be many different equations of the lines. The line y = 2x + 1, for example, can also be written in standard form and point-slope form. Additionally, there are an infinite number of points that can be plugged into point-slope form.

It was important for my students to see this in 2D (something they know so well) in order for it to also make sense in this new context of three dimensions.

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  Grappling with Complexity: So Many Options
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Lines in Space

Unit 12: Math in 3D
Lesson 6 of 9

Objective: SWBAT to write the parametric equations and symmetric equation for a line in three dimensions.

Big Idea: Parametric equations are back! This time they will help us write the equation of a 3D line.

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Math, three-dimensional, Geometry, parametric equations, PreCalculus, lines, 3D coordinates, shapes
  50 minutes
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