# How To Conceptually Teach Quadrilaterals

I don’t know why, but I love teaching quadrilaterals. I’m all about making math relatable to my students through real world application, so the irony that quadrilaterals aren’t regularly used in adult life doesn’t escape me. It’s not the topic per say that makes my teacher heart skip a beat, but instead the critical thinking that comes with classifying quadrilaterals…..if done correctly.

Memorizing the names of quadrilaterals is the most basic understanding of geometry. Examining their attributes and creating a hierarchy of the shapes takes this lesson to the next level. Students need time to explore geometry. They need time to discuss and defend their ideas on shapes.

Provide your students with shapes to play with. YES, PLAY. I start with handing my groups a bag of quadrilaterals and I ask them to fill in a chart outlining their attributes. Again you’re looking to spark discussion amongst students. Some groups will take their attributes to the next level by mentioning types of lines, while others will be minimal. Go over the chart after some time has passed to ensure that each student has all the attributes of each quadrilateral.

On the second day, I hand my students the bag of quadrilaterals again. Only this time I ask them to complete the diagram below. There are no labels for each circle and I tell my students that they need to label and place shapes inside the diagram based on their attributes.

The phrase “hot mess” comes to mind when I think about the beginning of this activity. It’s rocky. There’s a lot of confused faces and my students are dying to beg me to help them out. At this point of the year they know better. After some productive struggle, I ask “what name could we give the large circle that is holding all the sub parts? What could we call all these shapes?”

“And notice how this section is isolated from the others…what shape do we think that is?”

“OH! TRAPEZOIDS BECAUSE THEY ONLY HAVE ONE SET OF PARALLEL LINES, WHILE ALL OTHER QUADRILATERALS HAVE TWO SETS!”

Then I let them go back to work completing the rest of the diagram. Some of your groups will still struggle, but most will complete the task.

This level of exploration cannot be found in a textbook. You have to provide meaningful tasks to your students in order to create meaningful discussion and understanding.

Questioning plays a key role in this standard. How and what you ask about quadrilaterals will determine if your students conceptualize the topic or not. Ask them conceptual questions such as:

True or false:

A rhombus can sometimes be a trapezoid.

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