Monday, 10 September 2012
Really Nice Problem from Greg Ross
Just came across a really neat problem for introducing the Pigeon Hole problem to High School Algebra Students with some deep reasoning about the midpoint of a line segment.
It's all posted, with answers at Greg Ross' Futility closet (which should be a regular read for math teachers because he has wonderful ideas related to mathematical ideas and number relations)
A discovery prelude might be to ask students during mid-point problems to see if they can find two, three, n points placed on the grid where no midpoint will lie on an intersection of grid lines. Lots of practice finding midpoints and hopefully they can discover something of parity relationships that produce intersection. Would seem more ready for approach to a proof.