My ninth graders are working on building functions and modeling in the final unit of the year. There is plenty of good material out there for doing these tasks as a way to master the Common Core standards that describe these skills.
I had a sudden realization that a great source for these types of tasks might be my Calculus materials. Related rates, optimization, and applications of integrals in a Calculus course generally require students to write models of functions and then apply their differentiation or integration knowledge to arrive at a result. The first step in these questions usually involves writing a function, with subsequent question parts requiring Calculus methods to be applied to that function.
I dug into my resources for these topics and found that these questions might be excellent modeling tasks for the ninth grade students if I simply pull out the steps that require Calculus. Today’s lesson using these adapted questions was really smooth, and felt good from a vertical planning standpoint.
I could be late to this party. My apologies if you realized this well before I did.