Reflection: Connection to Prior Knowledge Using Coordinates to Prove a Quadrilateral is a Parallelogram - Section 1: Activating Prior Knowledge

I had to make a decision in designing this lesson. Would I ask students straight away to use coordinate geometry to verify that a particular quadrilateral satisfies the definition and possesses the properties of a parallelogram. Or would I first show students how to use coordinate geometry to verify things like parallelism, bisecting of segments, and congruency of segments.

I chose the latter route, fearing that the lesson would fizzle out if I didn't prepare students to be successful before asking them to jump to the more complex tasks. I think this turned out to be the correct decision. Students did end up needing instruction on how to use coordinate geometry for the purposes we'd be using them for later in the lesson.

Because I did a thorough job of making sure students had the prior knowledge to tackle the tasks in the heart of this lesson, I felt more comfortable allowing students to struggle through it. When students struggled I knew that it wasn't because they lacked the knowledge but because they had yet to make the connections they needed to make in order to transfer that knowledge to this new situation.

Some students, for example, were stuck on how to verify that a quadrilateral satisfies the definition of a parallelogram. My first question to them was "What is the definition of a parallelogram?" That was a stuck point for some. Once we established that the definition was a quadrilateral with two pairs of parallel sides, I would ask "How can we use coordinate geometry to verify that sides are parallel?" The students would typically know that using the slope formula to verify equal slopes wold be the way to do that. So in having these conversation with students, I would always emphasize to them that they knew everything they needed to know to complete the task. They just needed to expend more mental energy understanding the problem and rephrasing things to make the task more clear.

Reflecting back on the lesson, I realize now the importance of separating the prior knowledge aspect of a problem solving task from the actual problem solving aspect.

Activating Prior Knowledge
Connection to Prior Knowledge: Activating Prior Knowledge

Using Coordinates to Prove a Quadrilateral is a Parallelogram

Lesson 6 of 8

Big Idea: Impostors beware! In this lesson students learn to distinguish the real parallelograms from the pretenders.

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Standards:
Subject(s):
Math, Geometry, Polygons, properties of quadrilaterals
65 minutes

Anthony Carruthers

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