Cat and Mouse (Modeling with Linear Systems)

This Saturday, cat lovers everywhere will spend time with their feline friends as they celebrate Answer Your Cat’s Questions Day. A cat’s behavior can be very unpredictable at times, so this is a “purr”fect day to try to get to know your cat better.

One well-known behavior of cats is chasing mice. In the Cat and Mouse (Modeling with Linear Systems) Gizmo, students can analyze the chase using systems of linear equations. Will the cat catch the mouse? Will the mouse escape into its hole? It all depends on the head start of the mouse (y-intercept) and the speeds of the cat and mouse, represented by the slope of each line. In the Gizmo, students can analyze the chase using a graph and a table. First, students observe that the cat catches the mouse if the line representing the cat crosses the mouse’s line before it reaches the hole. Next, students use tables to estimate the time of capture (or escape). Finally, students explore the algebraic solution. Good luck little mouse!