# Birthday Triangles

Birthday triangles. Family Quadrilaterals. Personal Polygons.

Take a date, turn it into a figure.

**How?**

October 31, 1993 –> 10/31/93 –> (1,0) (3,1) (9,3)

March 24, 2008 –> 03/24/2008 –> (0,3) (2,4) (2,0) (0,8)

November 28, 1966 –> (1,1) (2,8) (6,6)

July 4, 1776 –> 07/04/1776 –> (0,7) (0,4) (7,6) or (0,7) (0,4) (7,6) (1,7)

**Why?**

Kids seem to work much harder when they are working on their ‘own’ birthday, or their favorite baseball player’s, etc. In some cases kids who don’t usually work, actually do. Others will go on to do the same work they would normally do, but with more care. They take their own birthdays quite seriously.

**Really?**

Yup. Best evidence, (and mind this, please) almost every class, when they first plot their own birthday triangle, there is one or two sad looking kiddies (it’s not come to tears, but I’ve seen the quivering lip) who thinks their own triangle is ugly. “Nooo” I say “Yours is obtuuuse. Does anyone else have an obtuse triangle that looks as nice as Anna’s?” (it’s usually a girl)

**And do what with these?**

Anything you would do with coordinates.

classify

find slopes

find midpoints

find distances (perimeter)

find area

write the equations of the sides

transform

“show” stuff (particular cases of general laws. Eg, take a quadrilateral and show its midpoints form a parallelogram)

Some more open questions can be nice. I’ve sent kids to look for someone with an equilateral triangle for their birthday (led to a great discussion the next day), find the family member with the greatest (or least) perimeter or area, etc.

**Pitfalls?**

The upset kid.

April 4. (pretend you were born a day later, or choose someone else)

collinear points (degenerate triangles)

**Worth it?**

Definitely.

Nice. Neat idea.

In a few years, you might have to deal with the kid who was born on 04/04/04 or a similar date :-)

I love this idea! Just the thing to get my middle school students playing with coordinates. I will definitely be using this when we get back from spring break.

If you think of a way to twist, alter, jazz up… Or if you think of a new task…. Or come up with a different way to generate coordinates…

This grew from a small idea (to quickly review midpoint) into an extended task that I use for projects. Along the way it has been shaped and reshaped by at least a dozen teachers, and suggestions from students have helped modify it as well.

So, ideas? Please share!

Fun! The kids DO take their birthdays seriously. One wrote a note on her last test mentioning that it was her half-birthday that day… she was 15 and a half. I don’t teach Geometry, but will have to think of how to use birthday-derived numbers for linear graphs or polynomials.

When students ask about my birthday I tell them that math teachers don’t have birthdays: they’re hatched from cubic eggs in a laboratory, and while there is a hatching date attached, it does not carry the significance of a birthday.

i am totally into using this next year, somewhere in my classes. can i use it in calculus? maybe i’ll have them create a polynomial from their birthdate… huzzah.

H,

there are many fine variations on this. One of mine: “Does anyone have a birthday? Wow (looking around), almost 100%”

Sam,

if you find something that works nicely, let us know. I remembered another – I’ll post it next.

How about the Birthday circle? It might get a bit messy, but…

1N,28E