Saturday, September 26, 2009

The Dance Steps to Solving an Equation - The Story

This lesson is by far my most well known lesson at my school.  I'll post how the actual lesson goes soon, but I wanted to share the story of its creation because it was integral in forming the teacher that I am today.  Feel free to skip to the bottom for video and lyrics.

A few years ago, I was looking for something to help the kids understand that even if an equation seems really long and difficult, there are solid steps that can be done to get through it.  I'd taught multistep equations, distributing, combining, how to deal with variables on both sides and printed out colored sheets explaining each step.  There were, however, a few students that got totally lost when we tried to put it all together.  I was racking my brain on the ride to work thinking of some way I could get the steps to stick, and hopefully make it a little more interesting for them after we'd been working on solving for so long.

"The steps to solving an equation... The steps to solving an equation... The... DANCE STEPS to solving an equation!!!!"

As with all of my ideas, I knew I had to act on it right away or risk never doing it.  I got through the school day and started to work.  By 10 that night I was finished and ready to do the lesson the next day.

Morning came and I nervously told the head of the upper school before assembly that he should probably check out my algebra 1 class.  After the words left my mouth, I started to panic.   I started seriously thinking that I was about to do something wrong. After all, I was going way off the normal formula that was every math class I had ever known.  Shouldn't I be lecturing? Is this a big waste of class time? Luckily, it was too late to do anything about it. I didn't have a back up plan, and I had already told my boss something interesting was going to happen.

I cleared the desks and chairs to the sides of the room.  Class started, and I ensured my students it would be the most fun math class they ever had.  Full of nerves, I started into my carefully planned dance lesson. The kids were all smiles.  They loved it, and before I knew it there was a crowd forming at the door.  Twenty minutes later the kids had mastered the dance, and knew the words by heart.  We brought the desks back in, and started on a difficult equations solving worksheet.  Students were stuck much less, and when they did ask questions they had a much stronger base to work with.  "Well, what's the first thing you should look for? And then what and then what?"

Later that day, the head of our school came up to me and said he had already heard about my lesson, that he wished he would've known about it and that he most definitely wanted to be in attendance next year. (and he was)  By the end of the week, my 10th and 11th graders were demanding that they get to do the dance ("Hey, we solve equations in algebra 2 too!"), and our 8th grade algebra teacher was asking me to guest teach it to her group.

I really grew as a teacher that day.  I didn't fear taking risks in teaching anymore. When I've had legitimate reasons to do something a little crazy or different to shake things up and get kids learning I stopped questioning it so much. I learned that my school fosters a creative learning environment for not only the students but the teachers, and because of that I am able to thrive.

Okay, enough typing.  Below you'll find the lyrics and video.  The video of me doing it alone doesn't really do the lesson justice. The kids add electricity like you wouldn't believe. More to come soon with audio files and the flow of the lesson.

The Dance Steps to Solving an Equation
First you simplify
put your hands up in the sky

so you distribute
then you do a little scoot

Still need to simplify
Put your hands up in the sky

So you combine like terms
and do the squirm

Add and subtract, x terms alone on one side
So take a step back and do a big slide

Multiply and divide, the answer you will learn
when you jump to the left and do a full turn

Now check check check ch-check check check

Thursday, September 24, 2009

f(a bag of skittles)

Today, I realized mid-class my students desperately needed a review of working with functions to get through the limit definition of derivatives.  The picture below is what spontaneously occurred.  I wrote the left half and then had them tell me should be on the right.  They seemed to really enjoy it, and understood what was going on much better when we tried to apply it to the definition of derivatives.

f(x) = 5x + 1

Monday, September 21, 2009

Systems of Equations Project - Sparking Interest

I started this project last year, and I was amazed at the results. I modified a project I had done in previous years to allow students some room to use math to explore something that they were interested in. (Believe it or not, analyzing the amount of homework they got didn't do much to get them excited!) The vast majority of my students got really into it, especially ones that otherwise were not very motivated.

For this project, students find data online that they are interested in comparing.  (Sales of video games v sales of movies, Wins of their favorite sports team v wins of their friend's favorite sports team, Women's race times v Men's race times, Success of movie with many sequels v another, Sales of Abercrombie v sales of American Eagle, etc)  They graph and find best fit lines for each set of data, then answer some thought provoking questions about the results.

The most time consuming part of this project was having students find good data.  Anything sports related is easy, finding movie sales is easy, but other things got pretty difficult to find.  When things got difficult, students often wanted to take the easy way out and pick something they didn't really care much about, but could find easy data for. I discouraged that heavily because the key to this project is bringing in their specific interests and showing them how math is involved.  When students worked hard, but couldn't come up with data, I did my best to point them in the right direction. (Try this search or website)

I used 3 40 minute classes for this, but that's because I only expected students to do work at home if they were getting behind. You could significantly cut the in class time down by giving most of it as homework.  If you decide to do this or a similar project  with your class, I would highly suggest making your students check their data with you before they continue onto the rest of the project.

See the project description here.

One of the coolest things about this project was that I stuck excellent projects on my back wall and a number of times saw students from other classes thumbing through and actually reading the results on their own!

Any suggestions for more conclusion questions?  What kinds of things do you do to get your students working with what they are interested in?  Let me know.

Thursday, September 17, 2009

Graphing Stories Remix

As you might have heard on Dan Meyer's blog I've started making some of my own Graphing Stories videos.  Dan Greene (other Dan) on twitter suggested I make one that shows a system of equations. I filmed one of me in a no holds barred footrace versus myself. (Don't worry, I won)  Here's how it came out:

Once I'm finished I'm going to make a bigger post about all of the videos for this, and by then I will hopefully have found a way to provide them in better quality than Youtube. In the meantime, I'm looking for some input...

I'm not sure how well it translates at this angle.  What do you think?  Do you think what's going on in this one will be discernible to students?

Also, I'm looking to make some more of these (it's really easy now that I have a template).  Anyone have any more good ideas?    Let me know in the comments.

Monday, September 14, 2009

Life skillz: Shopping

(the z makes it cool)

For about 3 years between high school and college I worked as a cashier at a grocery store. If I had a dollar for every time someone came through my line and spent way more than they thought they were going to...(Wait, scratch that, I technically did make a dollar every time this happened)  Anyway, from that experience I realized that many adults have trouble estimating the amount of money they spend when going shopping.

I decided my students could use some help with the matter.  So, I went to the grocery store to buy some things for a cookout and video taped parts of the experience.  It was really busy there, so the video didn't come out that great as I was trying to avoid getting anyone on camera. (Converting for youtube didn't do the video any favors either)  This is the finished product:
Granted adding and estimating isn't complex math, but students have no trouble in seeing the activity's use in everyday life.

I had some extra time at the end of class on Friday in two of my classes, so I told them we would have a competition.  Of course, the winner would receive candy.  I didn't tell them what the contest was (though it became pretty obvious), I just told them to pay close attention and to follow these rules:
  1. No talking
  2. No writing anything down during the video
I stopped the video before it gave the answer, and told them to write their guess for the total on a small scrap of paper.  Many of the answers were pretty off (up to about a $20 difference), and surprisingly my 9th graders guessed considerably closer than my 12th graders. (Which made me feel better about taking their class time for it)  Then we did some discussion where we talked about estimating and general paying attention.  Despite the lack of complexity, it was definitely a worthwhile activity. It certainly was an eyeopener for those whose guesses were way off, and all of the kids really got into it.

Anyone have any ideas on how to extend this to add some higher level math and make a full lesson out of it?

Friday, September 11, 2009

I was sure I would never sign up for twitter...

But then I clicked on this:    Curse you Sam J Shah!

Follow me:

Thursday, September 10, 2009

Pick up - Algebra Game

The first couple lessons I shared were from my Algebra 2 class, so I figured it was time to share something from Algebra 1.  This lesson revolves around a game that I think a student taught me years ago, but was similar to a game that we played in my college game theory class.  The kids have a lot of fun, because they get to compete and figure out strategy.  I call the game Pick up.
 I split students up into groups of twos, and give each group a few pieces of scrap paper.  I tell each group to rip up the paper to get 21 scraps of similar size.  On one of those scraps they write the words "Math Fun." Then I give them directions for the game, which goes like this:
  • The 21 pieces are placed down on a desk or the floor with the "Math Fun" piece showing and visible the whole game, like above.
  • Players take turns picking up at least 1, and up to 3 pieces at a time.
  • Whoever must pick up the Math Fun piece loses.
Then I let the students play.  They get to practice for awhile to get a feel for some basic strategy, but soon we start a tournament. Students that don't win the first round play off for a wildcard spot or two later in the bracket.  Excitement builds, someone wins candy and then we begin discussion.

I prompt them with questions like "Well, what worked?"  The winner will definitely have figured out what to do at the end, but they won't need to step it all the way back to the start to win games, so they don't.  Then we start discussion around the question "Well, in what situation are you sure to win?"  We decide to not count the Math Fun piece because it's pretty much irrelevant and we go through each situation that occurs at the end of a player's turn assuming their opponent is playing perfectly.  It's fun for them think their way through it, and my students have been able to figure out the situations below with minimal prompting.

1- You lose, opponent takes 1.
2- You lose, opponent takes 2.
3- You lose, opponent takes 3
4- You WIN, opponent has to leave you with 1, 2 or 3.
5- You lose, opponent takes 1, leaving you with 4.
6- lose
7- lose
8- win
9- lose
10- lose
11- lose
12- win

At #8, they might see the pattern, at 12 they are sure of it.
"So, could we.... write a linear equation that would tell us the winning numbers?"
"If we counted the Math Fun piece, how would our winning situations change?  How would the equation change?"
blahblahblah Slope, blahblahblah y-intercept.  Hooray for math!

     Which player has the advantage if both play perfectly?
     What if you could take up to 4 pieces?  Only 2? 10?

Super Extension:
     What if you split it into 2 piles, with two special pieces, and could only take from one at a time?

Friday, September 4, 2009

First day of school

School starts for me on Tuesday.  There's always a lot going on during our first day of school, so the schedule for classes is shortened to about a half hour.  Now, there's nothing particularly different or spectacular about the way I run my first day, but there are a few things I think are pretty important about what I do.

I start by handing out a kind of "Getting to know you" sheet that doubles as a record for book numbers.  There's space for student name, what they did over the summer, and three things they like. (Vague, I know)  After books and everything are handed out I go through and have all the kids share what they wrote, but first share about myself. I always try to pick things about me they'd never guess. (Like that I enjoy dancing, and I'm pretty awesome at it)  If you have any trouble learning kids' names, as you're going through on the first day make sure you say the name a couple times out loud back to them ("And, Jamie, what three things do you like?") and listen carefully as they answer.  This first day activity is probably pretty standard, but here's what I think is really important...  As they give their answers, I do everything I can to make some connection with one of the things they've said.  If they say they like video games, I tell them about the time I won a Halo tournament without owning an xbox.  If they went to the shore, I tell them about when I went to the shore over the summer too and what happened while I was there.  If I can't think of ANYTHING, I'll ask them some more questions until I can.  It's pretty helpful to get you to remember each kid, but more importantly it helps make connections with them, making it easier for them to buy into what you're teaching and to respect you as their teacher.  You can figure out some interesting things too.  A few years ago, we figured out that when I was in high school I worked with the older sister of one of my students!

Anyway, I'm really excited about starting school this year.  I hope your first day goes/has gone well!

Tuesday, September 1, 2009

M&M Catapult project pt. 2- The project

In all honesty, I have probably always liked this project a little more than the kids, but over the past few years I've improved the delivery so that they definitely get into it. My biggest mistake the first year with this was not giving the students an overview of what they were going to do and trying to let the packet speak for itself. That failed... miserably. Now I give an general overview complete with pictures and a discussion of why the lesson is important beforehand and they seem to enjoy and understand it a lot better.

I think one of the reasons I like this project so much is that it actually works. When the kids are consistent and do their calculations correctly, they will hit the center of the target with ease. It's one of the all too rare opportunities that students get to see that the math they did directly affected something in real life.

Some tips for the teacher:

  • I generally work the stopwatch for them. I've found myself wincing at how much the kids think the timing is "fine" when they do it on their own. I'll start a countdown out loud, and if I feel like my button presses weren't as good as humanly possible, I'll tell them not to count the trial. Letting them do it on their own (poorly) could I supposed be a "lesson learned" but I feel like after all the calculations they do, they won't realize what exactly went wrong or take such a lesson to heart. It would probably be worthwhile to let your kids try it on their own first, but keep a close eye on the timing aspect.
  • Strongly encourage the students to make sure they are shooting consistently before they do official trials, and to start over if their official trials aren't close together. You'd think the bold, caps, and underlining in the description would be enough, but my kids tended to be a bit overconfident and tried to rush through without frequent reminders.
  •  This project takes me ~2 40 minute classes based on class size and skill level. I'm sure it could be done  faster with more space and more student independence.
  •  Having some backup Skittles might be a good idea in case of allergies or dislikes. (I mean, what fun would it be if they couldn't eat some leftovers?)

I realize that there is a bit of hand holding, some of which could be removed to get kids thinking more on their own (especially if you were to give this to an honors class), but it's mostly to get it to fit within time constraints. As with any lesson or project on here, I encourage you to use and edit this to meet your own needs. Let me know what you come up with or if anything is unclear.