One of the simplest, and yet deepest, ways to explore geometric properties is through an activity called Guess My Rule. Students describe, analyze, compare and classify two-dimensional objects and explain their reasoning.
Begin by putting three or four polygons that follow a certain rule inside a circle and a few that do not follow the rule outside of the circle. Introduce a new shape and ask, "Where does this shape belong, inside or outside of the circle?" With this example, some students might guess that the new shape belongs on the outside with the other triangles. But when the teacher moves it to the inside, the students have to find a different rule that would apply. Consider repeating the process with additional shapes and then have the students induce the rule. In this case, each shape must have at lease one right angle. In preparing for this activity, consider how geometric properties may be used to classify figures. Students can use side length to classify triangles (equilateral, isosceles, scalene) and angle size (acute, right, or obtuse). Students can examine the number of sides, side length, and if the sides are parallel or perpendicular. Emphasize using mathematical vocabulary during this activity.
This activity can be easily differentiated for varying levels of student readiness. The rule can be simple or complicated by employing multiple geometric properties and cross classification. For example, can you guess this rule? The shapes must have at least 2 acute angles and no parallel lines. Also consider using a placemat and actual shapes (instead of just pictures) so students can employ a tactile approach as well.
With Guess My Rule, students develop explicit awareness of the concepts they've been developing and they use mathematical vocabulary to explain their reasoning. It's an engaging way to build problem solving perseverance and deepen understanding of geometric properties.
How would you determine whether or not a shape belongs? (using geometric properties: angle size, perpendicularity, parallelism)