Reflection: High Quality Task Tri-Mind: Perpendiculars and Squares - Section 5: Tri-Mind Differentiated Individual Product


I made a lot of changes to the Tri-Mind this year given the transformations thread I have been trying to weave in throughout the curriculum.   The ultimate learning objectives of the Tri Mind are to copy segments angles and to construct perpendiculars, so I was happy with my decision to let students choose from a special quadrilaterals lens, transformations lens, or creative lens while working on the Tri-Mind.  Students chose what interested them the most, and it showed in the work they submitted, which had required detailed explanations and illustrations. 


The Tri-Mind was not without its challenges, however.  Option 1 (special quadrilaterals) and Option 2 (transformations) posed non-routine constructions problems to students, especially because I used this task on only the third day of the unit. 


For students who chose Option 1, I found that encouraging them to sketch each special quadrilateral beforehand helped them to visualize the constructions they would need to perform for each problem.  For students who chose Option 2, I found that activating their prior knowledge from the transformations unit and using the same language from that unit really helped.  For example, I reminded students of how they rotated figures in the past by connecting a vertex to the point of rotation and measuring the angle from that segment—this helped e perpendicular bisector, which t perpendicularly bsiected over the line, which must be along the perpendicular bisector, which them see exactly where they would need to copy the given angle to locate the vertex’s image for the rotation.  Similarly, I helped students see how they could reflect a figure over a given line by having them imagine the reflection of one of the figure’s vertices over the line and asking students what they think is “special” about the segment connecting those points—this helped them see that the segment connecting corresponding points must be perpendicularly bisected by the line of reflection, which then helped them to figure out how to perform the construction.

  High Quality Task: Raising Expectations and Infusing Constructions with Transformations
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Tri-Mind: Perpendiculars and Squares

Unit 5: Constructions
Lesson 3 of 11

Objective: Students will be able to construct perpendicular bisectors and squares.

Big Idea: In the Tri-Mind, a differentiated task, students will choose the format through which they will explain how to construct perpendicular bisectors and squares.

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Math, Geometry, modeling, Constructions, compass and straightedge
  80 minutes
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