Discussion: This student attempts to answer the problem by reducing it to a simpler problem and finding the answer recursively by finding the number of paths to each point on the way to getting to (4,6) and obtains the correct numbers. A recursion pattern is discovered, namely that the number of paths to any point is the sum of the number of paths of the two points which lead into it. This is the same as the recursion used to create Pascal's triangle and, indeed, this is Pascal's triangle but at this point the student doesn't recognize it.

Written response: Good investigation. Next, stare at Pascal's triangle awhile and finish this problem after you come up with two explanations: one based on the recursion ou derived and a second, combinatorial, explanation.

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