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Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic development, learners connect observed properties with their mathematical justifications.
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CCSS:
Designed
Concepts
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Instructional Ideas
- Students could investigate whether shapes with other numbers of sides demonstrate similar properties
Classroom Considerations
- Concrete examples of coordinates might be necessary before abstract example using generic points is attempted
- Assumes students are familiar with slope formulas and the rules of slopes for parallel lines, along with the midpoint formula
Pros
- Elegant development of algebraic thought provides an approachable entry to higher-level thinking
- Effective mix of computer or paper-and-pencil modeling with more abstract concepts
Cons
- None