Reflection: Connection to Prior Knowledge Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites - Section 2: Homework Review


I was pleased with my decision to discuss what can seem to be a very straightforward and simple triangle area problem.  Despite the fact that several students got the right answer, I found that everyone had something to gain in discussing why the formula of a triangle is given by ½bh and how this relates to the area of a parallelogram and rectangle made by the same base and height. 


I set the stage for the whole-class discussion by identifying three triangles that were commonly chosen by students as having the greatest area.  I asked students, “what are some reasons for why these triangles would have been selected?” which surfaced common misconceptions (the triangles with slantier sides appear to be wider, which means they will have more area; the height of a triangle is measured along its slant, not the perpendicular from the vertex to the base) and commentary on how students could avoid those pitfalls. 


I thought this discussion was much more interesting and thought provoking than simply launching into the triangle area formula, which many students have memorized but cannot explain.  What I also appreciated was being able to project particular students’ work to value their sense making (like visualizing the square units within the triangle or copying the triangle to create a parallelogram with the same base and height) and, as a result, assign them status.  Taking time to discuss the square unit approach helped students visualize area; connecting triangles to parallelograms allowed students to reason and connect prior knowledge about the diagonal of a parallelogram dividing it into two congruent triangles.  

  The WHY Behind the Formulas is What Matters Most
  Connection to Prior Knowledge: The WHY Behind the Formulas is What Matters Most
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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.

  Print Lesson
Math, Geometry, Triangles, Measurement, modeling, Polygons, area modeling, kites, paralellograms, trapezoid, space, shapes
  85 minutes
trapezoid area image resized
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