This document summarizes an activity called "Crossing the River" that was meant to teach algebraic patterns. The activity involved figuring out how to transport a given number of adults and children across a river using a small canoe that could hold 1 adult, 1-2 children, or 1 adult and 1 child. The summary explains that it takes 33 crossings to transport 8 adults and 2 children, and 29 crossings for 7 adults and 2 children. An algebraic pattern of 4n+1 was determined, where n is the number of adults.

1. The Game of
Crossing the River
Stargirl aka Alpha-Adventurer 13

2. Introduction
Today we did an activity in groups called Crossing the River
I’m going to tell you the instructions of the game and write an
explanation about the process
This game’s purpose was to improve our knowledge on algebra
(and algebraic patterns)

3. The Instructions
Here are the instructions for the activity:
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
•
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?
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Repeat the problem using counters. I want to know the number of crossings it takes to shift the 8 adults and 2 children.
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What if one of the adults was sick and didn’t end up going camping? How would that change the number of crossing?
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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?

4. The Process/Explanation
Crossing the River is a game that helps with your knowledge of algebra. You have to try and get a specific
number of people across to the next island. But remember, someone has to row the boat over!
I was in a group with Alpha-Adventurer 23 and 24. We took quite a long time to figure out the first part, but
finally, Alpha-Adventurer 24 got it. We tried it out (to make sure it worked, and it did! So we got that part
finished. Here is the final solution: First, bring the 2 children over. Then, leave one child at the safe island and go
back. Bring one adult back to the safe island. After that, bring the child over and take the other child back to the
safe island. Take the child over again, then take only one of the adults back. Repeat this process until the very
end, when you have to bring both the children back.
Next, we tried solving the next part. We repeated the process, bringing the people there and back. We figured
out that the number of times to bring everyone (8 adults and 2 children) over is 33.
After that, we had to figure out how many times 7 adults and 2 children would take to cross the lake. We went
back and forth again and figured out that the number of times is 29. We then made a table with a specific
number of adults and 2 children. The table was quite successful.
We finally figured out that the solution is 4n + 1 (n is the number of adults). I thought that this activity was
pretty cool because it helped improve my algebra, thinking and strategising skills,

5. Hope you enjoyed
my presentation!