You’ve heard of pile patterns? There are variations but generally you have three snapshots of a growing shape like this:
Questions follow regarding future piles, past piles, and a general form for any pile.
I wanted to know what this old classic would sound like with newer equipment. Would video add anything here, for instance? Here is the result of my tinkering:
Video adds the passage of time. I added a red bounding box to the video, which was an attempt to make the question, “Where will the pattern break through the box, and when?” perplexing to students.
I also added different colors, which allows students to track different things or ask themselves, “What color will be the first color to break through the box?” Different questions require different abstractions. If you care about total tiles, you’ll model the total. If you care about the breakout, you’ll model the width and height. Each one will require linear equations, which is nice.
- The sequel asks about the “aspect ratio” of the growing shape which is a useful way to dig a little at limits.
- Real-world math. Here again I’m thumbing my nose at our conviction that math should be real. This isn’t real in the sense we usually mean. If it interests your students, it will interest them because it asks questions that rarely get asked in a math classroom, questions from the bottom of the ladder of abstraction:
- What questions do you have?
- What’s your guess?
- What would a wrong answer look like?
- What information do you need to know?