Goal: Think like a mathematician! Look for a process that repeats then generalize the repetition.
William likes to go sledding, but always struggles to climb back up the hill after sledding down, regardless of the steepness of the hill. When he climbs up the hill, he climbs up 5 feet (and it takes him precisely 30 seconds). He rests for 30 seconds, and at the end of his rest, he slides down 3 feet. At the end of the next 30 seconds, William climbs up 5 more feet, then 30 seconds later, he slides down 3 feet, and so on. The length William has to climb is 21 feet. How long will it take William to get to the top of the hill? How can you figure out the answer for any length hill? (Have students model William climbing and sliding up the hill with manipulatives or by drawing the process to sense regularity.)
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