Hens & Rabbits [for teachers]

The Hens & Rabbits applet describes a well-known word problem in two different representations. A farmer has 50 animals. Some are hens & some are rabbits. Among them they have a total of 140 legs. How many hens and how many rabbits does the farmer have? One representation of the problem shows the {animals, feet} plane and the other representation shows the {hens, rabbits} plane. [the 'answer' to the question posed in the problem is 30 hens and 20 rabbits - the point {30 hens, 20 rabbits} is plotted in the right panel - the point {50 animals, 140 feet} is plotted in the left panel.] You can choose to set the number of rabbits and hens in the right panel by dragging the GREEN and BLUE DOTS, or - you can choose to set the number of feet and animals in the left plane by dragging the GREEN and BLUE DOTS. Study the two representations carefully - How are the numbers of rabbits and the number of hens represented in the {animals, feet} plane? How are the number of animals and the number of feet represented in the {hens, rabbits} plane? How are the quantities feet/rabbit and feet/hen represented in each of the two planes? Which representation do you think provides you with more insight? Why? How can you use this applet to generate more problems of this sort? What questions could/would you ask your students? What have you learned about word problems from this applet?