Reflection: Connection to Prior Knowledge Distance in Geometry - Section 2: Notes: The Pythagorean Theorem in Coordinate Geometry (Distance Formula)


One of my main goals in this task is to help students see the connections between the distance, slope, and midpoint formulas.  I never want my students to memorize formulas without understanding.  For this reason, I thought putting all three formulas in one place would help students to see that they are all grounded in same concept: the Pythagorean Theorem.

Because the word “formula” can easily frighten students, I decided to do something that is not typical for my practice: I decided to directly lead students through the notes right from the start.  I decided to use direct instruction at this point in the lesson because I wanted to clarify notation, which has been troublesome for students in the past; I also wanted to ensure students had time to discuss with partners and in groups—this allowed me to circulate the room to listen in on questions and key points and share them with the entire class.  As a result, direct instruction helped me reinforce the language of “change in x” and “change in y” as a way for students to make sense of the notation and to visually connect components of the formula to how they see them graphically.

  Connection to Prior Knowledge: Making Connections Between "Scary" But Related Formulas
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Distance in Geometry

Unit 11: The Pythagorean Theorem
Lesson 4 of 6

Objective: Students will be able to derive the distance formula by making connections to the Pythagorean Theorem.

Big Idea: Understanding why the distance formula works with respect to the "change in x or y," enables students to solve novel problems requiring the measurement of distance.

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distance formula
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