Adapted from the May 2012 issue of Mathematics Teacher:
A dog is running to fetch a ball thrown in the water. Point A is the dog’s starting point, point B is the location of the ball in the water, and point D can vary. Given that the dog’s rate of swimming is 1 meter per second and its rate of running is 4 meters per second, determine where point D should be located to minimize the time spent fetching the ball.
Some questions to consider here:
- In what ways has this context already been abstracted?
- Can you de-abstract (recontextualize? concretize?) the context? Describe a task that would allow students to learn about the process of abstraction rather than just encounter its result.