In the class, we are currently studying problem solving strategies. This particular problem came from the 'Look For A Pattern' lesson. The problem asks the student to find the next four rows in Pascal's Triangle. Now, the majority of my students have not seen or worked with Pascal's Triangle before, so to them this is a seemingly random set of rows of numbers. I did not give them the background knowledge of the Triangle beforehand either because I wanted to see what they came up with as their answer. Usually students get it correct right away. This, however, was new to me. Because I only gave the first five rows, if you look at them as whole numbers rather than individual digits, they are all powers of 11. Pretty neat. This student went with that and continued. Unfortunately, Pascal's Triangle differs from this point on. She did find a pattern, thinking outside the box. Now, I did mention specifically in the problem that it is Pascal's Triangle, but she found a pattern.
Does she have an understanding of finding patterns? I believe so. Do I mark her wrong because her answer is different than what I've got on my answer key? If I'm grading on finding patterns (which I am), then no. If I'm grading on their understanding of Pascal's Triangle (which they may have never seen before), then yes. But then again, why would I grade on something they've never been exposed to?
I thought this solution was interesting; thought I would share.
Fascinating! I would be interested to know the reason why the Pascal rule gives rise to powers of 11 in the first few rows of the triangle.
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