## Reflection: Quizzes Distances in the Coordinate Plane - Section 3: Concept Development

I noticed this year that my students love formulas with a passion. To them, formulas are great because they can memorize them, plug numbers into them, and get correct answers if they calculate correctly.

I this the first lesson of the year requiring students to derive a formula, I noticed that many students seemed to be tuning me out as I was teaching the deriving of the formula. These same students perked up when I revealed the actual formula. They copied the formula into their notes and eagerly began to attempt the practice problems that would require them to use the formula.

My main goal, though, was to have them be able to derive the formula and understand its connection to the Pythagorean Theorem. So I had to stop and explain in very clear terms that the main learning objective was for students to be able to derive the distance formula on their own and that this learning objective would be assessed on a quiz. This announcement definitely upped the level of engagement and concern about how to derive the formula. All of the sudden, students had questions about the PowerPoint. For example, students weren't clear on where x2-x1 and y2-y1 came from.  These and other questions gave me an opportunity to go more into depth with my explanations and made the lesson more rich.

I encountered this type of situation several times during the year. These were times when I had a goal for students to derive a formula or prove a theorem and also be able to apply the formula/theorem. I would spend lots of time and energy teaching students how to do the derivations but sometimes I would not require them to do the derivations on the unit tests. It got to the point where students would just ask me, as I was teaching a derivation or proof, "Do we have to know this for the test?"

Ideally, students would be intrinsically motivated and I would not include these types of items on a unit test. These items require lots of time for students to complete and for me to grade. In the real world, where many of my students are motivated by grades, I have to find ways to quiz them on these derivations and proofs and assess them on unit tests. For example, I might ask on a multiple choice test, "In the distance formula, which of the following is the length of a leg of a right triangle?"...

This experience taught me that I need to strategically convey to students that this is a high school geometry course that is different in nature than their middle school geometry course. Whereas the focus in middle school was learning the formulas and applying them, the focus in the high school course is formally deriving the formulas and explaining why they work.

Putting the focus on deriving
Quizzes: Putting the focus on deriving

# Distances in the Coordinate Plane

Unit 2: Geometry Foundations
Lesson 3 of 14

## Big Idea: May the formula be with you. In this lesson students wield the power of the distance formula.

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Standards:
Subject(s):
Math, distance formula, Pythagorean Theorem, coordinate plane
85 minutes

### Anthony Carruthers

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