Reflection: High Quality Task Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures - Section 3: Classwork: Ratios of Similarity for Similar Solids


This was the first time I had used one of Dan Meyer’s Three Act Problems.  I thought the video for this Obscure Geometry problem piqued students’ interest and engaged them in the problem.  Had I simply handed out a worksheet to students with this diagram on it, it likely would have overwhelmed my students.  I think the video hooked students in, sparking their interest and motivating them enough to persist through the challenge. 

The Obscure Problem is particularly rich because there are so many ways to solve it.

  •  Several students wrote up systems of equations to calculate the percentages
  •  Students used proportional reasoning
  •  Students used many geometry ideas to solve:
    •  Triangle midsegment
    •  Diagonals of squares
    •  Similar triangles
    •  Ratios of similarity”: “If these two triangles are similar and their sides compare in a 1:2 ratio, their areas compare in a 1:4 ratio”

 Students also made sense of areas in relation to each other: “If these two triangles have the same height, but one has a base double the length of the other, then that triangle’s area must be double”.      

  High Quality Task: The Power of a Short Video to Spark Interest and Engagement
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Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures

Unit 10: Geometric Measurement and Dimension
Lesson 13 of 14

Objective: Students will be able to solve volume problems and identify 3-D solids generated by revolving 2-D figures.

Big Idea: Through reciprocal teaching, students will gain confidence in solving volume problems.

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4 teachers like this lesson
Math, Geometry, Measurement, modeling, space, shapes, reciprocal teaching
  75 minutes
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