Mountain Goat Hopscotch Math Connections Mrs. Bergeron

Mountain Goat Hopscotch THE SITUATION: On a rocky ledge on a narrow mountain trail, a herd of ten mountain goats travels in a single file, nose to tail. They round a corner and see another herd of ten goats coming toward them. Eventually, the two groups of goats will meet, head to head.

Mountain Goat Hopscotch HOWEVER: The trail is too narrow for the goats to turn around. The cliff on either side of the trail is too steep for the goats to climb. The goats will not back up. Each goat can either move forward or hop over only one other goat. In order for a goat to jump over another goat, there must be a spot on the trail for the goat to land.

Mountain Goat Hopscotch THE PROBLEM: The goats are all determined to get to their destination as a herd. They need your help! How quickly can they make it past the other herd and get on their way?

Mountain Goat Hopscotch ONE METHOD: As is often the case with other problems, creating a similar but simpler problem may help. We can call each of the two herds of 10 goats a 10-herd for convenience. Consider a simpler problem, one where smaller herds of goats are trying to pass.

Mountain Goat Hopscotch You will be given 8 colored blocks that you can use to represent the two 4-herds of goats. But you may begin with even smaller sized herds. Start with a space between the herds, like this: O O O O X X X X

Herd Size (# goats per herd) Least Number of Moves 1 count 2 3 4 n Look for patterns!

Mountain Goat Hopscotch Peg Puzzle site http://matti.usu.edu/nlvm/nav/frames_asid_182_g_3_t_1.html