Let’s represent the positions of the hare and the tortoise. One way is to have time on the horizontal axis, from morning on the left to evening on the right, and distance traveled on the vertical axis, from the start at the bottom to the finish at the top. For each moment of the day, plot the positions of both characters using a continuous curve.

The tortoise is easy to represent: she moves at a constant speed, starting at the bottom left and finishing (first!) at the top right. Represent her path with a straight line. The hare starts quickly (a steep line), travels half the distance, then rests (horizontal segment), and repeats. The curve never moves left (back in time). The slope indicates speed: the tortoise’s slope is small but sufficient, the hare’s slope is steep but interrupted by rests. How do we see he lost? At the moment the tortoise reaches the top, the hare’s position is lower.

We have plotted the hare (steep then flat) and the tortoise (gradually rising). Similarly, graph Paul’s distance from home in this story: he leaves home in the morning, waits at the bus stop, realizes he forgot his pencil case, runs back, finds it with his little brother, then runs to catch the bus. At school, he spends the morning, then returns home for lunch.

Second phase: here is a graph. Invent the story that corresponds to it.

The first part can be done individually, then shared collectively, highlighting that the curve never moves left, time only moves forward, and slope represents speed. The bus moves faster than Paul running, who runs faster than walking. When returning home, slope goes down. When waiting or working, speed is zero (horizontal segment).

Depending on students’ receptiveness, you can graph positions in other stories or compare multiple stories using graphs.