Accuracy vs. Understanding

Let’s say you’re teaching a Grade 8 or Freshman level class. Algebra 1-ish. You’ve got some data here.

x y
1 3
2 5
4 10
6 10
8 12
10 17

You want to show how data may be modeled as an equation. We could go about this two ways.

We could follow some TI-84 instructions via a handy dandy set of instructions.

We could also do something like this in Desmos, using the sliders feature.Students would be asked to manipulate the sliders until they think they have the line of best fit.

Discussion questions:

  • Which of these activities leads to the more accurate answer?
  • Which of these develops a better understanding of how a data set may be represented by an equation?

I wouldn’t say that conceptual understanding and accuracy are always juxtaposed, but it seems that they sure can be. I think I’ll leave it at that for now, but I’m a bit terrified to pursue this line of thinking much further. There might be drastic implications that I’m not sure I’m emotionally ready to handle right now.

If the sun is an 8 foot diameter balloon, what is Pluto?


The following clips are cribbed from Nova: The Pluto Files in which Neil deGrasse Tyson sets up a model of the heavenly bodies of our solar system, comparing their sizes relative to the sun and each other. Not all of the clips were able to be chopped to give the appropriate bleep sound. So we just have a few. More on that in a moment.

Side note: for the record, if you want to see a kid from the age of 4 to 14 get animated about something, tell them that Pluto isn’t a planet and/or let them watch this episode of Nova. They’ll go berserk. Neil’s right: people are crazy when it comes to Pluto’s planetary status.

Anyway, on to the entry events.

Intro & Mercury



Bonus!: Diameters of Uranus vs. Pluto

I’m not sure you need all three or four of these for kiddos to get the point. And I’d get some predictions on the board before having students explore this on their own or make and calculations.

The Process

  1. Show the Intro & Mercury clip
  2. Get some predictions.
  3. Reveal just the Mercury solution. Show some of the calculations involved. You can find all the heavenly body sizes from our solar system here or here.
  4. Show the Saturn clip.
  5. Let students make some predictions and do some research on the actual sizes of the heavenly bodies. More predictions on the board.
  6. The big reveal. For the solutions, you can just watch the clip straight from the home site linked above.

Here’s a potential accompanying worksheet.

Possible Extension

Neil says that we can’t properly represent the distance of the planets from the sun on this scale of a field. So my question is, how could we represent a scale model of the planetary orbits and distances from the sun?

Here we have Mercury five yards away from the sun. If Mercury is 5 yards away, how far away would Pluto be then?

field ss