Manuel is a cross-country runner for his school's team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is three times as long as it is wide. Manuel jogged the perimeter of the track 10 times at the rate of 6 miles per hour for 30 minutes. Manuel's coach wants him to find the area of the field in square feet so that he can include other activities within the rectangle. Manuel does not have access to other information or measurements.
Explain your thinking (including sense-making, reasoning, and estimation) as you approached and solved the problem.
Explain the challenges of going from the verbal representation to the symbolic representation and challenges that your students may face.
Explain how teachers can encourage students to use metacognition (thinking about their thinking) to support estimation, reasoning, and sense-making.
Explain how you would lay the foundation for a problem of this type to prepare learners who may not yet be developmentally ready for multi-step problem solving or for learners in the earlier middle school grades.
Include your symbolic representations, drawings, and solution at the point in the narrative where they are discussed.