This document describes an activity where students are split into groups and tasked with figuring out how to transport a group of adults and children across a river using a canoe. The first group solved the problem of transporting 8 adults and 2 children, determining it would take 33 crossings. When one adult was sick, reducing the group to 7 adults and 2 children, they calculated it would take 29 crossings. The students then realized the function for determining the number of crossings was to multiply the number of adults by 4 and add 1. They tested this with examples of 5 adults equaling 21 crossings and 3 adults equaling 13 crossings. The activity helped students understand patterns in algebra.

1. Crossing the River
By: Alpha-Adventurer 20

2. About Crossing the River
Crossing the river is an activity based on algebra and
patterns.
This activity can really help you understand how to
figure out patterns in algebra and to use logic to figure
it out.

3. Introduction
First, we got split up into small groups of 3 (one group
of 4). I was in a group with Alpha-Adventurer 6 and 18.
In those groups, we had to figure out problems that
our teacher gave us.
Next, our teacher read the instructions to us, here are
the instructions:
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.

4. The Process
Then, my group and I did some planning and thinking
on how can the 8 adults and 2 children go to their
home island, and finally, we came up with a solution.
Our solution was the 2 children go across the river
back to the home island, then a child goes back to the
camping island, the child gets off the boat and an adult
goes back to the home island. After the adult goes
back to the home island, the child who was left there
goes on and gets the child from the camping island.
For this process (8 adults and 2 children), they go back
and forth 33 times.

5. The next step
After that, we had another set of instructions:
What if one of the adults was sick and didn’t end up
going camping? How would that change the number of
crossing? (that will be 7 adults and 2 children).
Next, my group figured it out again and we got the
number 29.

6. The last step
After all of that, we had to make your own number of
adults and had to find the function of the problem.
My group did a few and found out the function is x4
+1, that is multiply by four, and add one.
Here are examples:
5 adults = 21 times
3 adults = 13 times
100 adults = 401 times

7. Conclusion
Overall, this was a great activity for algebra and to
figure out patterns using your brain (logic).
I would really want to try this type of activity again!
Hope you enjoyed this presentation!