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 river 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
• 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.
1.Can you figure it out?
2.Repeat the problem using counters. I want to know the number of crossings it takes to shift the 8 adults and 2 children.
3.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?
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When me and my group got the problem, we figured that the children must be important because 2 of them can fit in the canoe. When I thought about it, I came up with a solution: First, the 2 both children crosses the river, 1 stays on the 2nd island and the other goes back to the island. After he reaches the island, he gets of and lets 1 adult get on to cross the river. After the adult has crossed, the child on the 2nd island quickly gets on crosses the river, and brings back the child on the 1st island then starts the whole cycle agian.
Then we got our next challenge, to calculate how many crossings it takes for 2 children and 8 adults to cross the river. To solved that, me and my group did the whole process by counting it with chips and tally marks, and figured out it took 33 crossings.
For our 3rd challenge we needed to figure out how many crossings it would take 2 children and 7 adults. To answer that question, we retraced our steps and counted that it would take 29 crossings.
Lastly, we tried thee problem differently this time, 5 adults and 2 children. Made a chart with all the number of crossings along with different numbers of adults and found out the algabraic pattern was x4+1.
I thought these problems were a fun way to practise my thinking, problem solving and algabraic skills!