Drawing and Interpreting

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Sketching Graphs. Sketch graphs to represent (a) a parachute jump, (b) a car passing a slow moving vehicle on a two lane road, (c) a baseball that bounces off the outfield wall, from the beginning to the end of the play; (d) an oven used to make a roast from the time it is turned on until it is shut off and cooled down.

Height vs. Age. Given data on the relation of height to age of humans, of trees, and of corn, compare features of the graphs and seek a mathematical model that explains the data.

Telling Stories. Given a graph with time on the horizontal axis, write stories that explain the graph if it represents (i) dollars as a function of time, (ii) temperature; (iii) position; (iv) height; and (v) velocity.

Taking a Bath. Sketch graphs representing the height, temperature, and volume of water in a tub when a person takes a bath. Explain the events represented by these graphs.