Is it possible to create a shape with one right angle and no parallel lines? Give it a try! At the end of this post you'll see what some of the 3rd graders came up with.
For over a week now we have been delving into Geometry. The big idea of this unit is "relationships," specifically the relationships between shapes. We began by exploring different quadrilaterals (4-sided shapes) using 3 criteria: parallel lines, side length, and right angles (which we call "square corners.")
Side note: I taught them my famous "parallel" song which is to the tune of Earth, Wind, and Fire's "September." Ask your child to sing it to you!
Looking at our quadrilaterals and the properties we found, we were able to see a sort of hierarchy of terms. For example, a square is a special type of rhombus, which is a type of quadrilateral, which is a type of polygon. After becoming familiar with these properties and relationships, the students were put into groups of 3. Each group was given a Venn Diagram and a set of quadrilaterals. They were to choose 2 properties for the diagram, and place the shapes in one category, the other, or the "both" category. Interestingly, every group chose to label one side "square corners" and the other "parallel lines."
What they found was that 0 quadrilaterals fit in the "square corners" category alone. Each shape was either parallel, or parallel with a square corner. This led to a natural question: Is it possible to create a shape with a square corner, but no parallel lines?
After lots of trial and improvement, they were able to come up with a right triangle!
A few days later, our reasoning about relationships led to a similar natural quandary. The students were constructing polygons using rubber bands and a pegboard, per my directions. For example, "Use 1 rubber band to create a polygon with only 1 set of parallel lines." This direction had them creating trapezoids, and we noticed some trapezoids had square corners and some didn't. In fact, the ones with square corners all had 2 square corners. So I asked, "Is it possible to create a trapezoid with only 1 square corner?" They were so enthusiastic about trying to solve this mystery! What they discovered is that once you give a trapezoid 1 square corner, you have to give it another, or else you will create 0 sets of parallel sides, rendering that polygon no longer a trapezoid.
Through these types of challenges, the students are discovering the relationship between shapes, and the relationship between the properties that define the shapes. All of which is developing their higher-order thinking skills and ability to reason abstractly and defend their thinking. What little mathematicians they are!
Little people, big minds.