Each one of my geometry classes had a different homework assignment today.
Over the next day or two, we will be transitioning from the basics of points, line and planes, into more formal methods of logic and proof. One of the problems from their homework last night was a perfect segue to this.
"Given the following coordinates for points A, B and C, determine if these points are collinear"
I like this question a whole bunch as it allows me to illustrate that the phrase "it looks like it" doesn't really belong in mathematical debate.
We went through the idea of logical statement in a very informal way, with my tweaking their language as we went.
Me: What does it mean for 3 points to be collinear?
S: They are on the same line.
Me: That's true. More technically, it means there is some line that contains all three points. So what would we need to do to show that they are collinear?
S: If we found that line, we could show they are all on it.
Me: That's interesting. How do you think we could find that line?
Me: How many lines are there that contain any two points?
S: Just 1.
Me: So, if we find a line that contains two points...
S: We see if the third one is on that line.
The first class seemed to a bit more practice with the actual calculations so their assignment for this evening was to do so. I set the other two groups to looking at the ideas of conjectures and what conclusions can be drawn from certain statements.
In looking forwards, I'm debating whether or not to do The Lady and The Tiger (modified to remove the misogynistic overtones of women as prizes).
The last time I did it, it went VERY well and the kids were pretty excited.