In my geometry class, I'm trying to keep their algebra skills fresh (AND exciting!), so lately I've brought back lines: find the equation of a line parallel to ____ going through point ____; find 4 points on the line ______; etc. I reviewed point-slope form, slope-intercept form, standard form.
Well, many students came in for tutoring and were stuck on this problem:
Find 4 points on the line 3x + 2y = 12.
Them: "I don't know what to do."
Me: "How many points on a line?"
Me: "Yes, infinITE. What do you think is true about this equation and any point on this line."
Them: chirp chirp of crickets.
Me: explanation, showing, bla bla bla.
Them: "oh yea" .... work furiously.
Them: "I'm stuck. I can't find any more."
Me: looking and seeing that they have guessed and checked their capacity of integer valued (x,y) values.
Me: "Just pick an x and solve for y."
Them: "I tried, and NOTHING ELSE WORKS!"
Me: "Decimals and Fractions! They're not just for special occasions."
Them: "Oh, I didn't know you could have non-integer points."