Monday, April 12, 2010

Snail up a wall

I didn't learn nor read any text regarding Model Drawing as taught in Mathematics classes in Singapore. I am trying this out. Let see if I am on the right track.

Question: A snail is climbing up a wall 20m high. Everyday it climbs up 5m & slips down 2m at night. How many days will it take the snail to reach the top of the wall?

A typical old-days approach would be: each day up 5m and down 2m giving net up of 5-2=3m. To cover 20m, it would take 20/3 = 6 2/3 days. However, this is not exactly correct. This knowledge led me to draw a diagram that gives the above wrong answer. This is a common mistake by many students.

The model is a process to help us get the answer, and after that, it also acts as a tool to help us explain or present the solution. However, many a times, we somehow "calculated" an answer and figure out how to draw the model to show that answer.

Here is the diagram I drew. By drawing slowly, "day" by "day", you will realized that after 5 days and nights, the snail is at a height of 15m at the begining of day 6. Thus, by the end of day 6, before night fall, the snail would have reached the top of the wall and it wouldn't slip down 2m on the 6th night.

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