# How I Teach the Quadrilateral Family Tree

When I first started teaching Geometry, the quadrilaterals unit was a little overwhelming.  There were several shapes all with a bunch of properties, and I found myself forgetting some of them.  #teacherfail  It was not my favorite unit.  My second year, I pieced together this little story and have shared it with my students ever since.

Disclaimer:  I have seen a few cute stories floating around the internet.  This is not one of them.  My story could be considered slightly risquÃ©.  However, my kids think it is funny and remember it.  Use common sense before deciding to share this with your class.  :)

If you read my post about my student’s awesome quadrilaterals projects, some of my students mentioned family relationships.  They were referring to this story as they made their projects.

At the risk of writing this in an annoying way, I’m going to try to share this exactly as I share this in class.  It’s better if you ham it up a lot.  I usually try to make it sound like a soap opera (I make my own sound effects).  By this point in the year, my students are used to my craziness.  I do not use a powerpoint or anything, I just draw it on the board.  As I go, I also list the properties off to the side.  I write them in shorthand as I’m telling the story.

#### The Story

“Put your pencils down for a few minutes.  I’m going to tell you a story.  You’ll have time to write any notes that you want in a few minutes.

So, in the quadrilateral family, there were three kids: parallelogram, trapezoid, and kite.  What are the properties of parallelograms?  What are the properties of trapezoids?  What are the properties of kites?

Now, in your family, you have a lot of the same traits as your parents.  My dad has green eyes and I do too.  I know you’ve talked about genetics in Biology.  Well, in the quadrilateral family all of the kids have the same traits as the parents.  Notice, that parallelograms, trapezoids, and kites all have four sides.  Their interior angles all sum to 360.

Parallelogram got married and had two kids: rhombus and rectangle.  Since rhombus and rectangle are parallelogram’s kids, they have all the same traits.  Their opposite sides are parallel, their opposite sides are congruent, etc.  They also have the same properties of their grandfather, quadrilateral.

All right y’all, this is where things kind of get sketchy.  So, rhombus and rectangle…  Well, they had a kid, named square.”

**At this point, some kid is going to make a comment.  I let them, as long as it’s relatively PG.  Usually, they say something about incest.**

“Square’s mom and dad are from the same family.  So, square doesn’t have any extra properties.  He’s just a little bit special.

Trapezoid only had one child.  He named his son, isosceles trapezoid, after him.  Isosceles trapezoid has a few extra properties.

Kite didn’t have any children.

So, this is the quadrilateral family tree.  Just like all families, they have some issues, however, they all get along and are happy together.”

If you don’t end up sharing this story with your class, I hope it at least inspires you to do something interesting to help your students remember the properties of quadrilaterals.

1. If you haven't already seen it, you might enjoy the hexagon version that Chris Danielson wrote about:
Heirarchy of Hexagons.

It was inspired by his antipathy toward the quadrilateral family tree so, if you love the classification of quadrilaterals, just get past his complaining and you will see something rather cool we can do with our students.

2. That's interesting! Thanks for sharing!

3. rhombus and rectangle are siblings...how can they have a child! incest?

4. Yep, it is! That's what actually keeps my students interested in the story and helps them remember :)

5. Thanks a lot!

6. Cuter than cute! Love it, thanks for sharing; will definitely be sharing with my students! :)

7. Thanks! Cute story and helped a lot!

8. This is awesome. I think this will really help my class!

9. I teach in VA and I have my kids imagine that we are in the mountains and that we are hillbillies. I was wondering the order you teach this in? I have my kids add to their family tree as we got through each quadrilateral. In the past, I spread it over 3 days (we have 90 min blocks), doing the properties first and then going into using algebra in the same day. If you go through this whole story do you teach all the properties in one day?

1. I actually do the family tree at the end of the unit. I do parallelogram; rhombus, rectangle and square; trapezoid and kite. Of course, I have review days in there.

10. Great story, I am writing a lesson on the quad family and this story made me smile!

11. My kids act like this is so so terrible but they actually love hearing it and it is the only thing I have discovered so far that makes them remember that a square is part of both the rectangle and the rhombus

12. I use the inclusive definition of a Trapezoid: a quadrilateral with at least one pair of parallel sides with my students. It makes more sense that a parallelogram is really just a special trapezoid. Then it will follow that a Rectangle is really a special isosceles trapezoid.

13. I teach 3rd grade in Tennessee and my students are required to know and be able to draw quadrilaterals that match specific categories (i.e. draw a quadrilateral that has one right angle and one set of parallel sides). I've not thought of teaching shapes using the "family tree" method before; great idea! I will note that I also use the inclusive definition of trapezoid (as outlined in the Euler's Diagram on Wikipedia: https://en.wikipedia.org/wiki/Quadrilateral#/media/File:Euler_diagram_of_quadrilateral_types.svg ) so I think my tree might have some more cousins :)

14. Kite and Parallelogram had a baby called Rombus :D

15. that's so interesting, thanks for sharing :)

16. thank you for sharing this <3

17. How about the right trapezoid?

1. You can throw a right trapezoid in. I normally don't teach it as anything different. We don't have a special name for a kite with a right angle either.

18. I wonder why so many teachers accept to mix inclusive and exclusive definitions. Current knowledge on didactics already show that this is one of the biggest explanation to confusion and misconception in geometry for students.

19. I've used this same story for decadess--even in a private church school for a couple of years--and I have to say that it does indeed help get and keep the kids' attention!

20. Also, I do an in-depth symmetry unit in the beginning of the course. That makes it MUCH easier for the students to work with the properties of quadrilaterals--most students can 'see' the properties and don't need to memorize them.

21. You could probably avoid the incest idea all together if you related it to crossing plants rather than people having babies. The same generation of plants cross-pollinate all the time, and that's something they've probably learned about in any basic heredity class.