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.