## Task

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can hold at most eight people. Additionally, each boat can only carry 900 pounds of weight for safety reasons.

- Let $p$ represent the total number of people. Write an inequality to describe the number of people that a boat can hold. Draw a number line diagram that shows all possible solutions.
- Let $w$ represent the total weight of a group of people wishing to rent a boat. Write an inequality that describes all total weights allowed in a boat. Draw a number line diagram that shows all possible solutions.

## IM Commentary

This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.EE.8 to 7.EE.4 to A-REI.12.

This particular task could be used for instruction or assessment. The context lends itself to the use of inequalities, so it could also be used to introduce inequalities.

Note that the solutions to part (a) are discrete points and the solutions to part (b) are any points on a line segment (continuous).

Note that this problem introduces notations not explicitly required by the standard, such as $\le$ and $\ge$, and the notation for combining two inequalities, as in $0 \le p \le 8$. This task would be suitable for a classroom where the teacher has introduced these notations.

## Comments

Log in to comment## Steven says:

over 3 yearsI too think that this is above the standard, but I also think that it is great to show students where they are going to be headed with combining inequalities! Great discussions were had in my class when I posed questions about whether we could have decimals or negative numbers!

## jmirabel says:

over 6 yearsI like these items a lot. I like the algebraic and number line representations. And I like the idea of whole numbers only for the first part and rational numbers for the second part. I also like the idea that negative numbers do not make sense in this context. However, is requiring students to write a combined inequality "above" the standard? If so, I would leave these questions because I think they're good, but you may want to include a note regarding this.

## Bill says:

over 6 yearsThanks, I've added a comment as you suggested.