Comments on: Four Points, One Line

By: Melanie

Melanie — Fri, 23 Jan 2015 03:53:34 +0000

My desmos small group activity is to have them graph y = x then play around with changing the slope, then the intercept, then combinations of both (without using those words). They have a sheet they fill out describing the changes, then there are different challenges like trying to get an equation that goes through 2 specific points, or finding an equation perpendicular to a specific line.

By: Michael Fenton

Michael Fenton — Thu, 22 Jan 2015 05:24:21 +0000

Andrew, thanks for playing with the proble, and for all the great feedback/questions. I’ll have to wrestle a bit with what you’ve raised. I’ll be back with more ideas soon. 🙂

By: Michael Fenton

Michael Fenton — Thu, 22 Jan 2015 05:23:05 +0000

Thanks for sharing, shouldbequiltin!

By: Andrew Knauft

Andrew Knauft — Thu, 22 Jan 2015 03:22:19 +0000

Fun question. You may want to include the restriction that the equations be well-formed (or not!) — as soon as you have one equation, you can get another equation that appears different by multiplying both sides by any algebraic combination of those six numbers; if you are allowed to repeat the numbers used, then you’ve got infinite equations possible.

I counted up to 276 before I fully saw the infinite possibilities afforded by the assumption that (0-6)/(8-0) and -3/4 are valid different representations of the slope…

If you do intend for students to be writing fully simplified equations, I’m a touch concerned about what happens with the slope. Since you’re emphasizing where the parameters come from for the standard form / intercept form equations, there’s the potential that a student will see 3/4 and think it has something to do with the (4,3) point. How would you feel about putting fractions in the points so you can include (8/3, 4) and (3, 15/4) instead of (4,3)? I’m not sure if that would really help, though — if a kids going to think (4,3) has something to do with the slope, they will probably think those fraction points have something to do with it, too.

By: shouldbequiltin

shouldbequiltin — Thu, 22 Jan 2015 01:58:56 +0000

I was able to find 4 pretry quickly. Minimum level of proficiency might need to be lower than 4, but the challenge for differentation is present. My students definitely need practice synthesizing what they have learned. Thanks, as always, for sharing.