Crossing The River Reflection

Today our class split up in little groups to do a math game that was about crossing a river! The game was:

1. On the weekend, friends of mine went camping. They were camping on a small island in the middle of the lake. There were eight adults and two children in all. When they went to cross the lake and return home their boat was missing. They searched and searched but all they could find was an old canoe. It wasn’t as big as the boat and they were worried it wouldn’t carry them all. So, they tested it and found the boat could carry either: One adult, or one or two children. At first they thought some of them would be stranded forever, but finally, they figured out how to get them all safely across the lake. Can you figure it out?

Repeat the problem using counters. I want to know the number of crossings it takes to shift the 8 adults and 2 children. What if one of the adults was sick and didn’t end up going camping? How would that change the number of crossing? Let’s adjust the number of adults. How does the number of crossings change when the number of adults changes? Record all your data. Can you find an algebraic pattern?

The formula to solve this is:

1. 2 children go across the lake

2.  1 child stays at the land, while the other one goes back to the island

3. The child gets of the boat and the adult rows across

4. The adult gets off the boat, and the child left on the land rows to the island

5. Both children are now on the island with one less adult. Repeat process until no adults remain

I was the first person in my class to solve this and I think this could take a long time, or if you think out of the box it could take a few minutes(I solved this in about 2 minutes). Then my teacher asked us how many crossings it would take for 25 adults and 2 children to get across. The actual “formulae” is: number of adults(25) x 4 + 1. So the real “formulae” is 4n + 1. So the answer is 101!