Basketball Quadratics

It's been awhile since I've had a math post on here, so I thought it might be time. At my school we are in the process of transitioning from our previous Algebra 1 course to an Algebra 1 course that aligns with the Common Core (Semester 1, Semester 2, although much of Semester 1 will go away next year as we complete the transition). As a result we are going much more in-depth on quadratics than we did previously.

To put this particular activity in context, we will have already discussed factoring, solving by factoring, graphing, completing the square, and quadratic formula. We then touch on graphing using the vertex form of a quadratic equation. As usual, I've borrowed ideas from wherever I can and, once again, this activity is from Dan Meyer.

I've previously done this activity using Geogebra, but with the recent addition of the ability to add images to Desmos, I decided to try to go that route. As is becoming a habit for me, I host the activity in a Google Doc and then link out from there.

One of my struggles is always how much direction to give the students, and I tend to fall on the side of probably giving too much scaffolding for them (compared to some other folks). My experience has been that if I don't, we don't get very far, but I still struggle with where that middle ground should be. So my compromise with myself is to give them a lot of scaffolding as we step through the first example, then turn them loose from there.

As always, I would love your constructive feedback on this.

Air Travel: Google Apps Style

Like pretty much anything good I do in my Algebra class, this is simply a slight modification of something someone else has created - in this case, Dan Meyer. Please go read his post - and the comments - for all the goodness.

But I thought it might be helpful for somebody if I shared the slight modification I've made to it to take advantage of Google Apps. Like many districts, we are a Google Apps for Education district, so I wanted to try to leverage that for this assignment and use Google Spreadsheets instead of Excel. I'm going to have the students gather the data outside of class, following these directions and using a copy of this Google Spreadsheet.

Then they'll come to class, hopefully with the printouts of their two graphs but, if not, I'll hopefully have their shared copy to pull up on screen if necessary. We'll then talk about sketching a line of best fit (they on their printouts, me on the smart board) and coming up with a rough equation for that line. We'll then discuss, hopefully teasing out the same questions that Dan talked about in his post.

Some folks might refer to this as a "flipped" lesson, as I'm having them doing the research outside of class and then we discuss in class. I don't much care what we call it, I'm just trying to maximize my face-to-face time with them and hopefully get them to engage in some interesting mathematical thinking. They'll have two nights to complete the research, which I'm hoping will only take them 20-25 minutes total.

While I'm not a huge fan of homework, given the restraints of our schedule (my Algebra class meets four days a week, 59 minute periods when no special schedules - PLC, assembly, testing, etc.) and the curriculum (still too much for even a 5-day a week, 90 minutes a day Algebra class), I feel reasonably good about 20-25 minutes with two nights to get it done. (Next year I'm hoping to give them 3 or 4 nights to do it, I just didn't figure it out in time this year.)

My interest here wasn't so much in plotting the points, which is why I've created the two graph tabs in Google Spreadsheet for them. My interest is more in the relationship between time and distance and cost and distance, and whether they can think that through. And then translating all of that to an equation to model it. I debated for a while with just giving them the flight/time/distance/cost information up front, as gathering that information isn't the essential part of this activity, but in the end I decided there was some value both in them learning about flights/cost and how to gather the information, and about how to organize it in a way that might help analyze it. I would be interested to hear your thoughts on that decision (as well as any of the other decisions I made with this lesson.)

Three Acts/101qs/#WCYDWT - A First Attempt

So as I'm creating my lesson plans for Algebra 1 for next year (more on that in a future post, hopefully) I'm feeling pretty bad about something. You see, there's all this great material out there developed by other math teachers and I feel bad that I haven't really contributed much to it (other than to publicize it). Not bad enough, however, to not stea . . . borrow all the material. But still, I feel bad.

So as I'm planning I came across a linear equations activity I've done the last few years that involves a story of me going to my recreation center to work out, stretching first and then running on a treadmill, and figuring out calories burned. It's a perfectly fine activity, and it has worked reasonably well, but it's completely text based.

Within the last year, however, we've purchased a treadmill for home. And this morning when I was running on it I thought that perhaps I could dip my toe into creating something useful. So this could fit into a lot of categories, but I'm guessing it might fit into Dan Meyer's three acts, 101qs or perhaps #WCYDWT.

I'm not sure if it really matters where it fits, but I'm posting it here to get some help. My problem with creating material like this is that it's not "natural" for me. I can recognize great stuff that other people create with no problem, but creating it myself is a challenge. My other problem is that I can do basic video editing in iMovie, but that's about it. With those caveats, I think this is a decent start.

In my head, this is how this would sequence.

Update 7-17-13: Split the first video into two videos to make it more obvious where Act 1 ends and the info they're likely to request in Act 2.

Treadmill 1a (Act 1?) - How fast am I running?


Treadmill 1b (Act 2?) - Information they need



Treadmill 2 (Act 3?) - The answer

Treadmill 3 (continuation) - How many calories am I burning? (Internet research based on speed, etc.)

Treadmill 4 (answer to continuation)

Treadmill 5-1 (extension) - How long have I been running?

Treadmill 5-2 (the answer)

Treadmill 6 (Second problem Act 1?) - How long did I walk and how long did I run?

So, constructive criticism/feedback is appreciated - keeping in mind the caveat of limited video editing skills and software :-).

• What would you add/remove/change?
• Does the sequence work?
• In the end, is it any better than an equivalent text-based problem?
• Anything else I should've thought of to ask.

Thanks.

WCYDWT: Effectiveness vs. Snarkiness

For reference.

Discuss. Amicably.

Google Maps, Google Earth and the Summer Games

Just a quick post to point out this story from the LA Times:

From where do the most Beijing Summer Olympic medal winners hail? Despite Michael Phelps being well on his way to breaking Mark Spitz’s record of seven gold medals at a single Games, it’s not North America that has the most gold medals so far. According to the Google Maps’ Summer Games 2008, as of Aug. 12, 2008, China has won the most Olympic gold. The United States has won the most overall medals.

The Stadium page is my favorite of all the maps. Click on a stadium and watch a video as Google Earth zooms in. They also offer a photo and info about the venue.

Nothing major here, and probably no real educational relevance (other than curiosity, which isn't such a bad thing), just thought it was interesting. I bet there are more creative uses of Google Maps/Earth and the Olympics. If you know of any, please leave a URL in the comments.

I'm way behind in my aggregator (with no hope of catching up now that school is officially upon us), but it sure seems like somebody, perhaps dy/dan, should have a post coming soon with some great problems using current Olympic data. (I'm pretty sure he posted a while back doing some predictions with Olympic data, but I can't find it at the moment - somebody leave that URL in the comments as well and I'll update the post.)

My Personal Learning Network in Action

This article was originally published in the March/April 2008 issue of ISTE’s Learning & Leading with Technology. I’m cross-posting it here because it’s much more meaningful with links, plus it’s more likely I’ll read a comment here than if you write it in the margins of the magazine. As a side note, I found it very difficult to write a column for Bloggers Café with a due date that was two months before publication. And, of course, I found it very hard to write something that was only 500 words or so!



We’ve spent a lot of time at my school thinking about the concept of Personal Learning Networks (PLNs). We live in an age of information abundance. Our students need to learn how to find, evaluate, organize, synthesize, remix and re-purpose information in order to understand and solve complex problems.

A PLN isn’t a particularly new idea; learning networks have existed for a long time. What’s new is the reach and extent that’s now possible for a PLN, with technology and global interconnectedness providing the opportunity for a much wider, richer and more diverse PLN than ever before. This is a complex topic that can’t be fully addressed in a short article, but let me provide an example of my own learning that resulted from my PLN.

I’ve been a big proponent of publishing student work on the web, of using Web 2.0 tools to provide our students with a wider, often more authentic audience. But I’ve struggled with the quality of that work and question whether publishing student work that at times is pretty mediocre is such a good thing after all. My PLN helped me think more deeply about this.

Christian Long posted, “are we really prepared to drown in a sea of "just good enough" presentations.” That led me to several posts by Dan Meyer, “But if they and their teachers aren't immersing themselves constantly in better, clearer work than their own . . . work which for the first time in history is available freely and quickly, how in that vacuum can they rise to any greater occasion?” Dan led me to read Cult of the Amateur by Andrew Keen (books are still part of my PLN). Both Dan and Carolyn Foote led me to a post by Garr Reynolds, “Perhaps if all of us smart experts, with our massive intellects, tried to approach problems with ‘the beginner's mind’ we could get much better at solving problems.” A couple of posts by Vicki Davis got me thinking again about how it takes a “special kind of individual to make connections to be able to see things that specialists on their own cannot see. How do we teach that?”

I had multiple conversations with teachers in my school to further refine my thinking (direct conversation is still part of my PLN). Finally, I came upon a post and a Technology, Entertainment, Design talk by Larry Lessig, who suggested that the “read/write culture” is “a literacy for this generation.”

My thinking has evolved; I have a more refined, nuanced viewpoint on students publishing their work on the web. I believe even more strongly this is something we need to do with students, but I’m also thinking more critically about how to nurture the quality of that work.

As I envision the future, I think it’s critical for our students to create, nurture and expand their PLNs. It’s also critical to include varied viewpoints in our PLNs, to make sure we don’t continually reinforce our already held beliefs. I thank the members of my PLN for all they’ve taught me and encourage all of you to help your students – and yourselves – develop powerful, meaningful and effective PLNs.


Due to space limitations, I couldn’t include this portion with a very long quote from Howard Rheingold that I think is relevant.

A post by Will Richardson led me to an article by Howard Rheingold writing about the importance of developing critical and analytic skills:

Loss of certainty about authority and credibility is one of the prices we pay for the freedom of democratized publishing. We can no longer trust the author to guarantee the veracity of work; today’s media navigators must develop critical skills in order to find their way through the oceans of information, misinformation, and disinformation now available. The ability to analyze, investigate, and argue about what we read, see, and hear is an essential survival skill. Some bloggers can and do spread the most outrageously inaccurate and fallaciously argued information; it is up to the readers and, most significantly, other bloggers to actively question the questionable. Democratizing publishing creates a quality problem, the answer to which is—democratizing criticism. Critical thinking is not something that philosophers do, but a necessary skill in a mediasphere where anybody can publish and the veracity of what you read can never be assumed.

I would also highly recommend that anyone interested in learning more about Personal Learning Networks regularly read both Will Richardson’s and Clarence Fisher’s blogs, as well as the work of George Siemens on Connectivism.