My favorite show of all time with no question about it is Friends. I have watched those episodes probably an unhealthy amount of times, and they're somehow still funny to me! This is a math blog though, so how does Friends have anything to do with math? Well, Friends itself doesn't at all, but as I was exploring teacher.desmos.com for various classroom learning activities, I stumbled across one called "Central Park" (https://teacher.desmos.com/centralpark), which led me to think about New York City, which led me to start thinking about Friends. So, as much of a stretch as that probably is, I likely have your attention now if you're still reading, don't I?
Desmos, for those of you readers who don't know, is a combination of many things: a website, an online classroom activity source, a place to turn in work, or in other words, a math teacher's heaven. What I'm setting out to achieve as you read this today is not only to help you explore what a specific teacher.desmos.com activity would look like to use with students, but hopefully in the process, convince you to integrate Desmos or another technological source in your teaching as well.
"Central Park" is a Desmos activity that has students "use their knowledge of computation to inform their algebra understanding, and...see that representing their ideas with algebra can save a lot of computation time," or in other words, convince students of their need for algebra to do arithmetic more efficiently. Through the activity, they will be designing parking lots for various cars, first only visually, then slowly integrating numbers and mathematic concepts to help them understand the transition. Almost every Desmos activity will have a "how the activity works" section, or something similar (as pictured below).
So let's go through the activity, and try to experience it as students would. First, we simply guess what the spaces should look like, no numbers included. This allows students to develop a practical understanding of a situation before adding numbers, which may be overwhelming before they understand why the numbers are there.
Students can then "try it" to see if they were successful in their setup or not!
Next up: adding numbers. This is where you take the basis of understanding these students have for a hypothetical situation, and apply mathematics practically, thus demolishing the ever present student question "when am I ever going to use this?" The order of these is integral: helping them understand the need, then giving them the solution. The students now get a chance to calculate how wide the spaces need to be to fit the cars instead of just guessing. They will see through this that we are giving them a much more efficient method, even though it is not what they are used to! Below are some examples of this in the activity.
We have them in our grip, now! They love the numbers! Now, we transition into variables, help them understand how those will help, then tell them they have begun doing algebra. Before they know it, algebra has become something they are excited to use instead of such a daunting word! Below are a couple more pictures of how "Central Park" transitions this in the activity.
Then dive in and experiment with even more variables...
Almost as if by magic, just 45 minutes later, you have a full classroom of students excited about algebra. Unheard of! Although this obviously isn't foolproof in every single classroom, hopefully I have convinced you that it will at least help, and definitely not hurt students' learning. If you have any thoughts on this activity, or Desmos in general, please feel free to comment below and let me know! I'm open to thoughts, and I'd love to hear what has worked (or not worked) for you. And as always, be on the lookout for what comes next from my thoughts outside the glass tank.