Friday, May 10, 2013

Visual Exponential Patterns

The kids. They have no intuitions about the exponents. Especially when we get going backwards down the number line. And they just cannot walk out of my classroom only knowing how to graph and write equations for linear stuff.

Solution: ripping off Fawn Nguyen and Dan Meyer (Week 10).

You know the drill: find the missing things. 

I actually liked my second version of this activity a bit more. I gave them a bunch of patterns and equations and had them match them up on the whiteboards. 

This significantly lowered the barrier to entry, and I had some good conversations with some struggling Algebraists.

(A close eye will notice that in this second activity not all the patterns match up with equations, and not all the equations match up with the graphs. This was a good idea, because it was a nice twist, required some creativity in the pattern making, asked kids to review linear modeling, and took away some of the pigeonholing that often annoys me about matching activities.)

Here lie the files, in case you want 'em:
  1. Graph/Equation/Pattern
  2. Matching Patterns with Equations
Extensions and spin-offs in the comments, if you please.


  1. Thank you for posting your work. I had already made a note to steal your duck thing for next year. Always on the lookout for more visual representations.

    We did a bunch of visual things with systems this year like this, and this and this. Worked very well.

    I am a little leery of the matching the equations with the patterns activity. Did you find students doing things like plugging 4 into a function and then checking which pattern has that number of items in the fourth step? Or just focusing on the number of items in each step rather than how the objects themselves change? Basically ignoring the physical development of the pattern and the hints at an equation that come with that physical development?

    1. I am a little leery of the matching the equations with the patterns activity.

      I actually encouraged my weakest students to do this, and I don't feel bad about that. The connection between test points and equations is real and important, and it's also a low access point for some of these kids.

      But, basically: you're right. I think the second draft of this activity could have more "blank" patterns and equations to draw more attention to the good stuff that you're talking about.

  2. Oops, messed up the links… this, and this and this.

  3. I liked them all, Michael. I think it's so important to take a problem and poke it in different places or approach it from different angles. Your "given the equation, draw the pattern" is a nice one to follow up with the first one. While the matching, as you stated, allowed easier entry. You're still asking them to manipulate the variable x as an exponent in those equations, so it's a win-nguyen!

    Thank you, Michael.