# Angry Birds Project - Results and Post-Mortem

In my post last week, I detailed what I was having students do to get some experience modeling quadratic functions using Angry Birds. I was at the 21CL conference in Hong Kong, so the students did this with a substitute teacher. The student teams each submitted their five predictions for the ratio of hit distance to the distance from the slingshot to the edge of the picture. I brought them into Geogebra and created a set of pictures like this one:

After learning some features of Camtasia I hadn't yet used, I put together this summary video of the activity:

I played the video, and the students were engaged watching the videos, but there was a general sense of dread (not suspense) on their faces as the team with the best predictions was revealed. This, of course, made me really nervous. They did clap for the winners when they were revealed, and we had some good discussion about modeling, which videos were more difficult and why, but there was a general sense of discomfort all through this activity. Given that I wasn't quite able to figure out exactly why they were being so awkward, I asked them what they thought of the activity on a scale of 1 - 10.

They hated it.

I should have guessed there might be something wrong when I received three separate emails from the three members one team with results that were completely different. Seeing three members of one team work independently (and inefficiently) is something I'm pretty tuned in to when I am in the room, but this was bigger. It didn't sound like there was much utilization of the fact that they were in teams. I need to ask about this, but I think they were all working in parallel rather than dividing up the labor, talking about their results, and comparing to each other.

Some things I want to remember about this:

• I need to be a lot more aware of the level of my own excitement around activity in comparison to that of the students. I showed one of the shortened videos at the end of the previous class and asked what questions they really wanted to know. They all said they wanted to know where the bird would land, but in all honesty, I think they were being charitable. They didn't really care that much. In the game, you learn shortly after whether the bird you fling will hit where you want it to or not. Here, they had to go through a process of importing a picture, fitting a parabola, and finding a zero of a function using Geogebra, and then went a weekend without knowing.

While it is true that using a computer made this task possible, and was more enjoyable than being forced to do this by hand, the relativity of this scale should be suspect. "Oh good, you're giving me pain meds after pulling my tooth. Let's do this again!"

• A note about pseudocontext - throwing Angry Birds in to a project does not by itself does not necessarily engage students. It is a way in. I think the way I did this was less contrived than other similar projects I've seen, but that didn't make it a good one. Trying to make things 'relevant' by connecting math to something the students like can look desperate if done in the wrong way. I think this was the wrong way.
• I would have gotten a lot more mileage out of the video if I had stopped it here:

That would have been relevant to them, and probably would have resulted in turning this activity back around. I am kicking myself for not doing that. Seriously. That moment WAS when the students were all watching and interested, and I missed it.

Next time. You try and fail and reflect - I'm still glad I did it.

We went on to have a lovely conversation about complex numbers and the equation $x^{2}+4 = 0$. One student immediately said that \$ sqrt{-2} \$ was just fine to substitute. Another stayed after class to explain why she thought it was a disturbing idea.

No harm done.

P.S. - Anyone who uses this post as a reason not to try these ideas out with their class and to instead slog on with standard lectures has missed the point. I didn't do this completely right. That doesn't mean it couldn't be a home run in the right hands.

# How Good is Your Model (Angry Birds) Part 2 - Refining my process

A year ago, I wrote about my attempt to integrate Angry Birds as part of my quadratic modeling unit. I was certainly not the first, and there have been many others that have taken this idea and run with it. This is definitely a great way of using the concept of fitting parabolas to a realistic task that the students can have fun completing.

As I said a year ago, however, the bigger picture skill that is really powerful with modeling is making do with less information. I incentivized my students last year to come up with a model that predicts the final location of the collision of a bird earlier than everyone else. In other words, if Thomas is able to predict the correct final location with ten seconds of data, while Nick is able to do so with only seven, Nick has done the better job of modeling. I did this by asking the students to try to do this with the earliest possible frame in the video.

This time, I have found a better way to do this. Five videos, all of them cut short.
I'm asking the students to complete this table:

The impact ratio is defined as the ratio of the orange line to the yellow line, as shown in this image:

Each group of students will calculate the ratio for each video using Geogebra. Some videos reveal more about the path than others. I'll sum the errors, rank the student groups based on cumulative error, and then we'll have a great discussion about what made this difficult.

The sensitivity of a quadratic (or any fit) fit to data points that are close together is what I'm targeting here. I've tried other techniques to flesh this out in students before - I still get students 'fitting' a table of data by choosing the first two or three points. I'm hoping this will be a bit more interesting and successful than my previous attempts.

Trimmed Angry Bird Videos:

# How good is your model? Angry Birds edition

With Algebra 2 this week, I decided it was time to get on the Angry Birds wagon. I didn't even mention exactly what we were going to do with it - the day before, the students found the above image in the class directory on the school server, and were immediately intrigued. This was short lived when they learned they weren't going to find out what it would be used for until the day after.

To maximize the time spent actually mathematical modeling, I used the video Frank Noschese posted on his blog for all students. They could pick any of the three birds and do the following:

Part A:
Birds are launched at 6, 13, and 22 seconds in the video. Let's call each one Bird A, Bird B, and Bird C.
• Take a screenshot of any of the complete paths of birds A, B, or C.
• Import the picture into Geogebra. Create the most accurate model you can for the bird you selected. What is the equation that models the path? Does it match that of your neighbors?

Part B:
• Go back to the video and the part in the video for the bird that you picked. Move forward to a frame shortly after the bird is launched, take a screenshot, and put it again into Geogebra. Can you create a model that hits the landing point you found before using only the white dots that show only the beginning of the path?

If not, find the earliest possible time at which you can do this. Post a screenshot of your model and the equations for the models you came up with for both Part A and Part B.

My hope is not to just use the excitement of using Angry Birds in class to motivate knowing how to model using quadratic functions. That seems a bit too much like a gimmick. The most interesting and realistic use (and ultimately the most powerful capability of any model) of this source of data is to come up with as accurate of a prediction of the behavior of the trajectory as is possible using minimal information. It's easy to come up with a quadratic model that matches the entire path after the fact. Could they do this only twenty frames after launch? Ten?

The students quickly started seeing how wildly the parabola changes shape when the points being used to model the parabola are all close together. This made obvious the importance of collecting data over a range of values in creating a model - the students caught on pretty quickly to this fact.

I think Angry Birds served as a cool "something different" for the class and has a lot of potential in a math class, as it does in physics. I am hoping to use this as a springboard to have students understand the power of models and ultimately choose something to model that allows them to predict a phenomenon that is of some importance to their own adolescent worlds. I don't exactly know what this might be, and I have some suggestions for students to make if they are unable to come up with anything, but this tends to be one of those ideas that eventually results in a few students doing some very original work. Given my interest in ultimately getting students to participate in the Google Science Fair, I think this is just the thing to push them in the right direction of making their own investigation.