Reflection: Student Ownership Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites - Section 5: Individual Processing Notes / Exit Ticket

 

This year, I asked students if they could make connections between the area formulas for triangles and trapezoids.  Almost every student readily noted that we could use our approach of doubling a triangle (or trapezoid) to create a parallelogram with the same base and height, stating “b1+b2” represented the base of the parallelogram (when making sense of trapezoid area), which is similar to “b” of the parallelogram (when making sense of triangle area).  This was clearly a point in the lesson at which students were able to make sense of structure and use geometric reasoning to ground their ideas. 

 

I had a student think out loud, “Triangles are sort of like trapezoids, right?  I mean, a triangle has two bases, just one of them is like zero.”  This “Aha!” moment was a pivotal one, getting this student’s peers to make even more connections in the structure (substituting 0 for either b1 or b2 in the trapezoid area formula and even making sense of the lengths of the midsegment of a triangle  (half the base) and of a trapezoid (half the sum of the bases).

  Triangles Are Sort of Like Trapezoids, Right?
  Student Ownership: Triangles Are Sort of Like Trapezoids, Right?
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Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites

Unit 10: Geometric Measurement and Dimension
Lesson 2 of 14

Objective: Students will be able to make sense of and explain basic area formulas.

Big Idea: By critiquing others' written explanations of triangle and trapezoid area formulas, students will develop strategies for determining areas of other 2-D shapes.

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2 teachers like this lesson
Subject(s):
Math, Geometry, Triangles, Measurement, modeling, Polygons, area modeling, kites, paralellograms, trapezoid, space, shapes
  85 minutes
trapezoid area image resized
 
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