Unit Rates and Scratch
I’m back to teaching pre-algebra after a long time off – and the more things change, the more they stay the same! A key staple of middle school math is learning about rates – how they work, how to calculate unit rates, how to predict with rates, and different representations of rates – including tables, graphs, equations, and story problems. I love to make the connection between the story problem and the equation by doing a coding activity. For our final project on unit rates, I assigned the students a pair programming project in Scratch. The structure of the activity is really similar to what I’ve done in my 6th grade computer science classes.
- The background knowledge. We have a discussion about a specific situation involving rates – I chose “toilet paper math”, because what is a more confounding consumer decision than buying toilet paper? I picked a couple of examples of toilet paper packages from the weekly grocery ad and put them into a Google Doc for the kids here. https://docs.google.com/document/d/1zM4wwf2GDSEEaB31IWDeJPTqibtPsG1zLN_XA_k35uM/edit We had a class discussion about what clues on the package might help me figure out what toilet paper to buy. One class mentioned that I could figure out the number of squares / sheets of toilet paper in each package, and another class wanted to go by the number of square feet in the package. Together, we wrote a Scratch program that would help me figure out what toilet paper to buy. For the class example, I showed them how to use the “ask” block to get input, the “set” block to set variables to values, and operators to do math. We created variables for the price of the toilet paper, the number of square feet in the package, and the number of square feet you can get for a dollar. The main character would then report out the square feet per dollar unit rate to help us figure out our purchasing decision. Our class program is here: https://scratch.mit.edu/projects/291422012/editor
- The norms before the worktime launch. I explained to the students that when I was an engineer, we often used a protocol called “Pair Programming” to solve problems. As an adult, this meant I prairie-dogged my head up above the cubicle walls and shouted to my friend Jerry: “Jerry! Can you help me solve a coding problem? I can’t figure it out.” Then I would type at the computer while Jerry stood behind me and read over my shoulder, and we talked together about what the code did – line by line. It was really helpful to have a partner talk it over with me. I explained that in middle school, we can also use Pair Programming and some of the norms are pretty much the same. Then I showed the Code.org pair programming video on YouTube.
https://www.youtube.com/watch?v=vgkahOzFH2Q After the video, we went over the do’s and don’t’s.
- I gave the students a choice of word problems having to do with Unit Rates, and their task was to solve one of them with a partner using the Pair Programming protocol. The choices are in this document: https://docs.google.com/document/d/1h8r2z0o2FtOr8N4IjqGaiNrhn_DGAJLIyNREeg9iR0g/edit I change up the celebrities in the document every so often. Students love Marshmello and also Ariana Grande this year and I got some cute programs with these characters.I swear the Pair Programming video is magic. Students for the most part peacefully navigate partner work after watching and processing the video. I only had a couple of groups that had any trouble at all. This activity took a whole class period for most classes, and a little longer for one group. All of the students were engaged and trying hard, and most groups enjoyed the creative storytelling part of the project. I wish I had introduced Scratch sooner in this year’s math cohort, but we had a lot of manual math to do and so we’re just now starting to automate things. Now that the kids are on board with it, I can’t wait for the next project.Here are a few example programs the students made for the word problems.
Marshmello’s road trip: https://scratch.mit.edu/projects/293136380/editor/
Hagrid’s Animals (these students modified the prompt a little bit, but I really enjoyed how theirs turned out and they had fun with the creative storytelling): https://scratch.mit.edu/projects/292456078/editor/
Ariana’s Carpet (this group of kids decided to include their favorite K-Pop star and I’m embarrassed to say I don’t know who this guy is): https://scratch.mit.edu/projects/293139904/editor/
I really believe in computer programming as a modeling tool for math expressions. Students love the instant feedback and the creative storytelling, and I love that they can test many inputs and it is a check on their number sense. Often I see students modify their model when they try plugging in a few numbers and then they say “Wait a minute! That gas mileage doesn’t make sense!”
Other programming languages work just as well. I’ve had older middle schoolers do a similar task in Processing and it really stretches their brains!