Where We've Been: Students have just learned the distance and midpoint formula. Or, should I say (given this is an 8th grade standard) students have just had their memories refreshed on these formulas.
Where We're Going: Soon we'll be getting into analytic geometry and proof in the coordinate plane. Students will need to have full command of these formulas.
In this section I give students Activating Prior Knowledge_Coordinate Plane Formulas, which has three problems involving the relevant formulas for the day.
In this section students will be following directions (on their own) to complete the Independent Practice: Midpoint Quadrilaterals activity. As students are working, I walk around. I do my best not to answer questions. Instead I pose open ended questions that force students to read and interpret directions and/or confront their misconceptions. I also check to see that students are meeting the specifications that were laid out for quadrilateral ABCD. If they've failed to meet one or more of the specs, I'll ask them to explain to me how they met ALL of the specifications. As they do, I'll pop an open-ended question that forces them to confront their misconception...if they don't see it for themselves first.
As we know, the quadrilateral formed by joining successive midpoints of the sides of any quadrilateral is a parallelogram. In this section of the lesson, I get students together in groups of three or four to compare the work they have done with midpoint quadrilaterals and try to arrive at some general conclusions.
Each will be given the Cooperative Activity: Midpoint Quadrilaterals handout to complete.
Note: If any students in a group have congruent quadrilaterals ABCD, it's a good idea to put them into different groups.
When the time has elapsed for the activity, I randomly call students to share their paragraphs with the class. As students read them, I provide feedback.
By the end, I want everyone to walk away having a basic understanding that it seems whenever we join midpoints of the sides of a quadrilateral, two pairs of opposite sides will be both parallel and congruent.