PISA Problem Problem
DECEMBER 7, 2013 AM31 10:30 AM
Ever count ceiling tiles during a boring test? I have. And I run into a problem (besides that people notice me staring goofy at the ceiling). The tiles never fit. How do I count the broken tiles? Does each broken tile count as a full tile, since a full tile had to be consumed to make it? Or should I just be counting the area? My geek game, my geek rules – I count both ways.
One of the released PISA math questions sets up a similar problem – and then does not give even partial credit for a partial geek answer.
Before I share the question, I had every intention of fully ignoring PISA. The results are used to do things like justify attacks on teachers local unions in the US, or to set up charter schools whose kids would never learn to agonize over going with the Geek answer or the normal answer. The test is used to harm us, to create panic over a single data point (is there still a country between Sweden and Russia?)
But I was curious about what the questions looked like. Most of them seemed fine. But here’s the ceiling tile question:
PATIONick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre.Calculate how many bricks Nick needs for the whole patio.
Hmm. The 5 x3.25 patio, there are 5 x 3 = 15 nice squares that could be filled. 15 x 81 = 1215. But now we have a strip a quarter of a meter wide (hate when they have fractional remainders, 1/4, for a metric problem. feels like mixed units), and 3 meters long. We should think about the shape of the bricks.
(by the way, the geek analysis is about to cost me credit).
Since there are 81 bricks to the square meter, the bricks could be little squares. One ninth