The Common Core standard includes the phrase “a hierarchy based on properties” regarding classification of polygons. Students need to understand that some classifications or groups are inclusive of all examples of other groups, and some classifications are inclusive of some other examples.
These activities use observation and recording of the key properties of quadrilaterals, questioning designed to clarify definitions, and Venn diagrams to help students classify quadrilaterals logically and precisely. This is intended to be used with physical quadrilaterals, but in their absence students can be asked to draw everything or use Geoboards instead.
There are several properties essential to classifying quadrilaterals; students list all those for each quadrilateral, and then discuss the implications. The key questions are, “Is a square a rectangle?,” and “Are squares, rhombi, and rectangles all parallelograms?” Students are helped to deduce the resolution to these questions. We also clarify just what the words parallel, perpendicular, and opposite mean, and what parallelograms, rhombi, and trapezoids are. Students usually encounter more accurate ways of naming these shapes than they knew before.
The inclusion of rectangles, squares, and rhombi in the set of parallelograms is modeled clearly and experientially with The Parallelogram Machine. The file includes templates with which you can make several different sizes of rectangles and squares that morph into parallelograms in students’ very hands.
Common Core Standards:
5.G.4: “Classify two-dimensional figures in a hierarchy based on properties...”
Subject: Math, Geometry, Logic
Level: Grades 4 – 6
Length/Duration: 9 pages of student work, 2-3 days