Texting Algebraic Expressions

I try to read as many other blogs as I can. Sometimes I'll find a really cool idea and it somehow gets lodged into my brain somewhere, waiting to be used at just the right moment.

One of the posts/podcasts that I read/heard was from Dan Meyer and his lesson on scientific notation (I think I got it here). In it he explains how writing numbers in scientific notation can be related to texting. When texting, we often abbreviate or use acronyms to speed up the process (ttyl = talk to you later). Or maybe we do this because we're lazy. Or maybe we do this because it's the cool thing to do. Or maybe there is an annoying limit on how many characters you can use.

Yesterday I was teaching how to write algebraic expressions and this idea popped back into my head. We were looking at the expression "seven more than a number". This has twenty-four characters, and being the ancient 34-year-old man that I am, would take a while for me to text. (And it doesn't help that I only just got a cell phone a couple of months ago.) I then demonstrated how long it would take for me to text this expression to another teacher. I sent her the text which was a little odd for her since I didn't explain why I was sending it. She was nice enough to send back a response:

Not bad for an English teacher who curls up into a fetal position every time I talk about math. And look! She used a variable! That saved a lot of time. And only five characters were needed! Awesome! What a convenient way to write that expression! Now kids, here's 200 to do on your own. Good luck.

Good Day or Bad Day? (Adding Integers)

I love this clip from Seinfeld where Kramer describes what happens at the dinner table when you're married. It would seem that one of the worst parts of marriage is the time when you talk about your day. Was it a good day or a bad day? Eventually this became the inspiration for how I chose to teach integer operations.



I used to teach adding integers with gang violence. There were two gangs (positives and negatives) who would fight and kill each other. The only problem with this metaphor was that it was only really good for adding integers. It didn't help me teach some of the other operations (subtracting a negative, negative times a negative).

I also had the problem of offering students too many ways to think about adding integers. I used gang violence, money, number lines, drawn positive/negative signs, and the boring rules. But it was way too much information. I was trying to offer my students choice, but many were becoming confused.

So I'd like to say that I have one way to explain integers, and it all has to do with having a good day or a bad day. I start the lesson off by showing this slide:

I ask my students how they know if they've had a good day or a bad day. What kind of things could help you move to either side of the spectrum? I then use specific examples, always in pairs (see below). I use little arrows to indicate which way we are moving on the happy face (soon to be number) line.

The first two examples are pretty obvious. If two good things happen, then it's a good day. If two bad things happen, then it's a bad day. 

This third scenario (the lost cell phone) had some debate. Maybe the loss of a cell phone was a good thing...perhaps this would convince your parents to buy a new/better phone. But the point was to show that when a bad thing happens, and then an equally good thing happens, you end up back where you started. It was neither good nor bad.

The kids laughed at this one. Not sure why hamster death is so funny. Perhaps it was the juxtaposition of the two scenarios that made the second seem so ridiculous. But this is exactly what I wanted. Sure, it was nice to find the dollar. But your hamster is dead. Finding the dollar does not make up for the fact that your hamster died, so overall, it was a bad day.

And finally, the lost/found money. This last scenario transitioned into the use of a number line (at which point my students thought, "Oh, so this is a math lesson").

Where do I go next? Basically negatives are bad things that happen and positives are good things that happen. If more bad things happen, it's a bad day. Or if there are more negatives, then the answer is negative.

I can easily see how I can relate this now to subtracting and multiplying. Taking away bad things helps make your day better (subtracting a negative). When bad things happen over and over again, it is a bad day (positive times negative). Taking away bad things over and over again makes it a good day (negative times negative).

Nathan Kraft

Exploiting My Son for Math

At some point I'm going to have to apologize to my four-year-old son, Emmett. Over the last year I've been using him for all sorts of math lessons - many times under the guise that I'm spending quality time with him. It all started with this video:


I posted this on facebook and lot of people thought it was cute. But many also wanted to know the answer to the question. I used the same video in class and one of my students went home and worked on the problem with her dad. She was so proud when she came in the next day with the right answer.

I quickly learned that I could use his "cuteness" to teach math. He was helping me teach probability:


He was helping me teach problem-solving:


And sometimes he'll even inspire lessons. The other night I was sitting in the kitchen doing some work. Emmett should have been in bed sleeping, but instead he was in the living room stacking cups.


He was so proud of his design and he wanted to make an even bigger pyramid. So we went out the next day and bought a bunch of cups, and hence, a new math lesson was created.


So again, I apologize to Emmett for using him this way. But I think he's having some fun in the process. Besides, how many kids have had the chance to do this?


I only hope his cuteness doesn't run out any time soon.

Nathan Kraft

Gang Violence and Adding Integers

This is my borderline inappropriate way to teach integer addition to students. It was inspired by a presentation I saw by Dr Kadhir Rajagopal on solving equations (NCTM 2009, DC). Check out his website here.

Algebra tiles are a great way to teach integer addition. But I like to represent positives and negatives as members of two rival gangs.

The yellow gang member is basically the same as a yellow algebra tile (+1) and the red gang member is the same as a red algebra tile (-1). Yellow gang members get along with other yellow gang members. Same goes for the reds. But when a yellow and red meet up, bad things happen.

To a 13 year old child, this explanation is much more satisfying than some nonsense about "zero-pairs". And when one of my students is confused about an addition problem, all I have to say is "gang violence", and they know exactly what to do.

Say a student is presented with a problem like this: -4 + 7. I have to ask two questions: Which gang will win? (the positives) How many will be left? (three)

To me, this is much better than some silly rule that students have to memorize. They are visualizing the numbers. And they are seeing positives and negatives as opposites that cancel one another out. And best of all, they remember it.

Credits: Graphics are from the Smart Notebook software. I'm sure the people at Smart Technologies appreciate that I've found this use for them.

Nathan Kraft