Tales from the Nerdery

I think math is neat.   I like to play with math.  And sometimes I come up with something that supports my theory that math is neat.

First, I took the numbers 1 – 100 and spiralled them around some regular graph paper.  I wondered what would happen if I colored in the multiples of 4.  I examined my work and thought, “Huh.  Well that’s neat.”


Of course then I needed to spiral even more numbers and test out everything I could think of.  Multiples of 5, 6, 7 and so on.  Linear patterns, quadratic patterns, prime num…nope, nevermind.  I don’t do prime numbers.

Anyway, it’s that time of the school year where stress relief is necessary so I have been playing with these spirals for over a week. Today I came up with something worth sharing on my blog.  I took the positive y-values of y = x^2, y = x^2 + x, y = x^2 + 2x and so on, and colored those squares.  Then I put the images together and made a gif. Obviously, holding the camera at a steady angle is not a skill I have mastered.  But I still think it’s pretty darn neat.


Number Talks – Bumps in the Road

Today, I presented, with my colleague, Denise Anderson, a session on Number Talks at the Minnesota Department of Education.  The topic was ‘Where do we go from here:  Managing bumps in the road.’

Here are the slides if you are interested:  https://docs.google.com/presentation/d/1jMvhEoxexddOA7e3ncYIhbNM62iy3CGUeyfeNpqYH34/edit?usp=sharing

I’ll be presenting this session as a webinar on Tuesday, May 24th.  Details here:  http://education.state.mn.us/MDE/Welcome/MDE034256

My favorite slide:  0513161500



Heavy Armor


Here’s a picture. This happened in my classroom last week. This simple, beautiful moment is one I will cherish more than a million free burritos.

Look closely. It might not be apparent, but this student is behind my desk, fiddling with some of my chachkies. He’s telling me about a concert he got to go to this weekend.

It might not be obvious from the picture but this kid isn’t a huge fan of mathematics. In fact, he might be convinced that the whole discipline has it out for him.

There’s more to the story. This child walked into my room two months ago with his headphones in his ears and a chip on his shoulder. He made it completely clear he was there for one reason: to earn his credit.  Often he would refuse to complete any work and when he knew that wasn’t an option, he was quick to proclaim that he “didn’t get any of this.” He maintained his angry demeanor like a coat of armor.  Mathematics had let him down so many times before. Why would this trimester be any different? But what manifests as anger on the surface is perhaps pain, sadness, or fear underneath.
Every day I have this student for a “homeroom” of sorts. This means that after lunch, the class comes back to my room for 25 minutes. During this time, I saw this kid slowly open up.  Without the anxiety of the mathematics in play, I began to see underneath scars from an educational system that doesn’t help him thrive. He started taking off the headphones when he walks in the room at the beginning of class. Even though he usually responds with “sick” or “tired” when I ask how he is, at least there’s an acknowledgement of my greeting.

Then he begins to do math. Not just to “get his credit,” but he really wants to figure it out. His work becomes more than numbers on the page for his daily points. “Don’t look at my answer. You need to figure it out yourself,” he begins saying to his classmates. “My brain hurts. This class makes me feel like I’m growing a brain tumor.” And he keeps working. I know brain tumors aren’t joking matters, but I’ve never loved them more.

Consecutive Sum-mer

So May is a fun month.  In Minnesota, we can be reasonably certain the sub-40 day temperatures are behind us, the goslings have hatched, and the student countdown to the end of the year has begun.  In my classroom, they not only know that there are 18 days left, but that there are also only 3 Mondays remaining as well.

In John Stevens and Matt Vaudrey’s new book The Classroom Chef, they state that the opposite of bored is not entertained.  It’s curious.  While I agree, I needed some solid evidence to combat the never-ending question of “Can we go outside today?”   (For the record, I’m not totally opposed to taking them outside for math class.  It’s just not warm enough yet.)

Me:  Number your paper from 1 – 30.  (I’m off to an outstanding start, clearly.)  So and So, pick a number (hoping he/she doesn’t pick a power of 2).

Student:  Seven

Me:  Seven is interesting because it can be written as the sum of 2 consecutive numbers, 3 and 4.   What about 6?  Can you think of a way you could make 6 using the sum of consecutive numbers?

We talk about what consecutive numbers are, how many we should be able to sum, which kinds of numbers count as consecutive, whether addition is the only operation allowed, and so on.  Pretty soon, the entire class, (Yes, 100% of my juniors and seniors who have been beaten down by mathematics for 11+ years) is engaged, on task, and curious about the nature of these sums of numbers.

Student:  So you’re telling me that any number, except the powers of 2 which are few in number anyway, can be written as the sum of consecutive numbers?  

Me:  Nope.  I’m not saying that at all.  You discovered it.

Here is the Consecutive Sums problem poster from nrich: