MP2: Reason Abstractly and quanitatively.
I can solve problems in more than one way.
Task
My Work
I started this task by pulling out the pieces of information that were necessary for solving the problem. Then I wrote an inequality that took all of the information into consideration.
I used the inequality to create a table/number line to represent the information. I also graphed the inequality on paper and on Desmos (see below).
To solve portion b of the task, I substituted values of p into the inequality to represent a group of that size. Groups 1 and 2, with 4 and 5 people respectively, can safely rent a boat. A group of 8 people would exceed the maximum weight allowed.
As the graph created in Desmos shows, the maximum number of people that could safely rent a fishing boat from Fishing Adventures is 6.
Reflections
This task requires the student to "make sense of quantities and their relationships in problem situations", as mathematical practice standard 2 states. The student must gather the relevant information and rearrange it in a meaningful way to write an inequality that represents the information completely and concisely. In the description of the task, the student is given information about a boat rental company, people, weight, and gear. The student is first tasked with decontextualizing all of that information and use numbers and symbols to represent it in an abstract way.
This task contains several pieces of information to make sense of. A struggle that some students may have is reassigning the 10 pounds of gear per person to the weight of each person instead of trying to make it part of the gear variable as the task would indicate.
To make this task more engaging to students, a teacher could change the context of the problem to be more relevant to specific groups of students with particular interests. It might also be a fun task to use a Geogebra balancing activity for to explore the relationships between the variables in the task and how many people would cause the balance to reach its tipping point.
I think that task could be made more accessible by using a balance demonstration to represent the restrictions of the number of people allowed to rent a boat, either hands-on or with Geogebra. This would also lend itself to a conversation about the constant variable of 200 pounds of gear for all trips regardless of the number of people.
The ceiling of this task could be made higher by adding additional variables like children with lower weights - how big could a group be with only 2 adults and some children? What combination(s) of adults and children would result in a weight of exactly 1200 pounds? What would the maximum weight need to be in order for your family to safely rent a fishing boat? Your family and 2 friends?