Wow. This is fascinating and obvious: rather than providing all the links and scaffolding, present the problem completely stripped down.
A photograph of an octagonal, lucite water tank, being filled by a water hose. Ask the class, “How long will it take to fill the tank?” Without all the math notation — coordinate plane, labeled vertices and angles, formulas — everyone in the class gets involved in the conversation, including the kids who instinctively step back and let the “smart kids” do the work.
Students have to (and do, according to Meyer) ask the questions that are normally supplied by the textbook: how fast is the water running? how tall is the tank? how wide is the tank? what’s the shape of the tank? is there a formula that applies?