The whole reason I created this 3-act task was to have students realize that not everything is linear. The students watched the first act and I encouraged them to make guesses, just a number from their gut. Many students used linear reasoning for their guess. I heard this over and over again today: "Since he's a little lower than half the height of the pole, he must have a little less than half of the points."

Then I gave them a sheet with the photos on it and asked them to try to come up with an another answer (maybe it was the same) but to put some reasoning behind it. I recorded their answers on the board.

You can see that many of their answer came down quite a bit in this class and here's the reasoning. When I handed out the paper with the three photos on it, one student noticed that in the third picture the score had to be a three-digit number because of the location of the part of the zero that I neglected to crop out of the photo.

For my other classes that didn't notice it being a three digit number, many of the numbers seemed to stay the same, or close to the same, as their initial guess. Some got out their rulers and did some measurements to find about 1500. Again, a linear assumption.

Next I showed them my work. We found the equation of the line that passes through the two points (1.2, 100) and (8.8, 4000). Where x is the height from the top of the castle like thingy to Mario's nose in cm., and y is the points scored. Our linear equation: y = 513.16x-515.792

Now what? One student suggests measuring the height of the third photo and plugging that number in for x to find the score. We get a height of 4cm, and plug in to find y = 1536.85. We know that we would never get a score like that in the same, so we round it to 1500. The students still stand their ground with a three-digit number.

We watch the third act (the answer). Once we are getting close to the third jump, the students are hooked, their eyes are glued to the screen, and one students rubs his palms together and says, "Here we go!". When they see that the answer is 400, one student stands up, throws his pencil down, and complains that he was so close.

In the other two classes the reaction was similar. They all assumed that I was right, because I'm the teacher. We watch the video and when they saw that the answer was truly 400 and not 1500 there was a short hesitation followed by a few "WHAT?!?!?!" going around the room. What happened? We must have measured wrong. The slope is undefined. We should have measured from his nose. The time affects the score too. We addressed all of these concerns and realized that nothing was wrong with our math or our measuring and the score on the flagpole is not effected by the time in the game. So what happened?

Eventually we get around to finding out that assuming it was linear was a mistake. Not everything is linear. This helped to lead us to my next question: What are some things that are linear and some things that are non-linear. I gave a few examples of each type, then asked the students to create their own and post them on the board.

At the end of the day one of my students from first period enters my classroom. He looks like he's on a mission. I see him go to his folder and get of the paper we did our work on for this problem. It's the same student who took pictures of the board. So here's the thing. It a well known fact that this kid thinks he sucks at math. But he thought about math during 1st period because he had to, then it interested him enough to remember to come back to my room to get this paper, THEN he's going to go home tonight and post on a forum about what we did in MATH class. How awesome is that?!?!?!?

Here are all the goods:

Act 1:

Act 2:

Act 3:

Download here:

How did you do the screen-capture? I have this game, and I have noticed some other interesting mathematical patterns, but I've not figured out how to capture a reasonable copy of them for playback.

ReplyDeleteBelieve it or not, I just put my camera on a tripod. I have a cannon rebel. I've been trying to think of an interesting linear relationship in video games, but I'm coming up short. Any ideas?

DeleteThanks for the interesting lesson idea. If you need to do screen captures in the future, try out Jing. You can download it here...

Deletehttp://www.techsmith.com/download/jing/

It's great for stuff like this. You can capture video or take pictures easily of whatever you want on your computer.

This is so cool! My inner geek loves this...and I could totally see students enjoying this as well. Awesome.

ReplyDeleteOh man, now I am going to be playing video games looking for linear relationships - this is great stuff.

ReplyDeleteLove this! I will definitely be using this with my lovelies!!! Thank you.

ReplyDeleteThis. Is. Great.

ReplyDeleteIs there a way to download those videos? Is there a YouTube address for them? My school is not streaming video friendly.

I updated the post with the links to download each act. The links are at the bottom of the post. Enjoy!

DeleteThank you so much! This is such a perfect lesson for so many things. I might even try it with my algebra I kids just to introduce the idea of non-linear models, like you mention.

DeleteAwesome idea. I'm going to use it next week.

ReplyDeleteYour link to Act 3 is identical to Act 1. Could you fix it please?

Oops! That should be fixed now. :)

ReplyDeleteTried this today with the kids... it was awesome! Great idea!

ReplyDeleteNice work this is a great resource for us all! I will most definitely use this with my preservice teachers, who are now student teaching. If you are interested in getting your students to design games, I've created a set of video tutorials using a free tool called GameSalad. Don't worry...no coding required. There is a lot of mathematics that you can reinforce while designing games.

ReplyDeleteHere is the link: http://cultureplayllc.com/category/blog/

Best,

Roberto

I love the idea of incorporating video games into the classroom -- it's an integral part of kids' lives, lol.

ReplyDeleteI came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we're putting together. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter -- bringing math to children in an innovative, adventurous way. I’d really appreciate your help in getting the word out about the project.

http://www.kickstarter.com/projects/564889170/the-number-hunter-promo

I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We're teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.

Our concept is to create an exciting, web-based TV show that’s both fun and educational.

If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you'd be interested in link exchanging (either on The Number Hunter site, which is in development, or on StatisticsHowTo.com which is a well-established site with 300,000 page views a month) please shoot me an email. We're also always looking for input and ideas from other math educators!

Thanks in advance for your help,

Stephanie

andalepublishing@gmail.com

http://www.thenumberhunter.com

http://www.statisticshowto.com

http://www.kickstarter.com/projects/564889170/the-number-hunter-promo

Hi from Spring-Ford, thanks for sharing! What a great way to get the students involved in something they are interested in. What, if anything, would you do differently next time? #inspired

ReplyDeleteHi Spring-Ford!!! How's PARLO treating you? Hmm, one thing differently? For starters, I would make sure the students couldn't tell it was a three-digit number in act 2. Also, before handing out act 2 I would like to ask the students for a number that is too high and one that is too low along with their guess.

DeleteIt was really difficult for the students to come up with their own examples of things that are linear and non-linear, so next time I would like to do a card sort instead.

Is there a way to find this answer out without watching the video?

ReplyDeleteWhen I used the 2nd Act, I was able to find an exponential model that fit pretty close. You can see it circled in the 2nd photo in the blog post. x is the height of his nose from the top of that little castle thingy in cm (measured on the act 2 paper) and y is the score.

DeleteI believe it is actually an exponential step-function.

great work, how did you derive your exponential function?

ReplyDeletealso I just wrote nintendo to see if we could get more info on how they program their point functions. Hopefully we will get a response.

NICE BLOG!!! Education is the process of bringing desirable change into the behavior of human beings. It can also be defined as the “Process of imparting or acquiring knowledge or habits through instruction or study”. Thanks for sharing a nice information.

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I was *just* thinking of a (different kind of) Mario-based problem today and happened to find this while I was doing some Googling. Awesome problem!

ReplyDeleteVery good and fun,

ReplyDeleteWhere can i play this game? is available to download on my PC?

ReplyDeleteLove this idea! I think all of my students will love it! What age were you working with - I do K-5 and I can see this working with my 4th & 5th graders!

ReplyDelete