Analyzing Distance Algebraically

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Students will be able to apply the Pythagorean theorem to find the length of a diagonal line segment on a graph.

Big Idea

Some students would rather use coordinates and formulas, than measure distance on a diagram. I like to offer both as an option.

Bellringer - Warm-up

10 minutes

I begin class by saying that our unit is quickly coming to an end and we need to review the major concepts while also practicing the length of line segments on the coordinate plane, continuation from previous day.  A fun way to review the major concepts in Pythagorean Theorem is to show a video clip from the Wizard of Oz just after the Scarecrow gets a brain.  The Scarecrow tries to quote the Pythagorean Theorem but says this instead, “The sum of the square root of any two sides of an isosceles triangle is equal to the square root of the remaining side.” 

I play the video and rewind the part where he misquotes the Pythagorean Theorem a few extra times.  Then I script his speech on the board and give students a few minutes with their partner to discuss all the editing that should be done to correct his speech - I never tell them it is supposed to be the Pythagorean Theorem.  Then I allow volunteers to take markers and edit the speech on the board and we review how and when the Pythagorean Theorem is a useful tool.

Wrapping Up

5 minutes

To close the lesson, I put the coordinates of two points on the board and I ask students to find the length of the line segment connecting the points using either using algebra or a diagram.  One possible example could be distance between A (-4, 7) and B (8, -5).  This task is today's Exit Slip. When I review their work I will get a pretty good sense of which students have mastered this concept.

I will likely provide sections of graph paper for the students to use.  A great website for graph paper is


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(Accessed May 13, 2014)