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Turn It In The Hare and the Tortoise Name: When we make graphs in math, we are trying to visually tell the story of an equation. For instance, if we have the equation y = 20x + 30 where y is how much it costs to attend a gym with a membership after x months where $30 is the membership fee, then the graph will show a visual story of how much the gym membership will cost over time. We’re going to use stories to help us understand graphs and we’re going to take graphs and try to tell their stories. Now consider a race between two unlikely contestants. You will draw a graph to represent each contestant's movement and explain how you know each graph is correct. You will also analyze and interpret additional graphs of the Hare's performance in subsequent races. Finally, you will create your own graph and story to accompany it. The Hare and the Tortoise Aesop (translated by George Fyler Townsend) A hare one day ridiculed the short feet and slow pace of the tortoise. The latter, laughing, said, “Though you be swift as the wind, I will beat you in a race.” The hare, deeming her assertion to be simply impossible, assented to the proposal; and they agreed that the fox should choose the course, and fix the goal. On the day appointed for the race they started together. The tortoise never for a moment stopped, but went on with a slow but steady pace straight to the end of the course. The hare, trusting to his native swiftness, cared little about the race, and lying down by the wayside, fell fast asleep. At last waking up, and moving as fast as he could, he saw the tortoise had reached the goal, and was comfortably dozing after her fatigue. (Source: http://www.pitt.edu/~dash/type0275.html#townsend. Retrieved July 27, 2016.) Answer the following: 1. a. On a coordinate grid, draw a graph to illustrate the tortoise's distance from the starting line over the time it took her to complete the race. (An example of a coordinate grid is below. You can use Desmos to graph as long as you label the axes and graphs). On the same grid, draw a graph to illustrate the hare's distance from the starting line over the time it took him to complete the race. Include a picture of the graph.

b. Explain how you know each graph fits the story of the tortoise and the hare. The graph of tortoise is two pieces: move with constant speed and then not moving after reaching the goal. The graph of hare is having a rest and then moving with speed much faster than tortoise’s. When hare reaches the goal, the tortoise is already having a rest.

2. Study Graphs A, B, C, and D (below). Each graph shows the hare's movement in subsequent races.

Write a story to go with each race. Graph A  Where does the hare start the race in relation to the starting line? Finish the race in relation to the starting line? The hare starts the race at the beginning of the starting line and finishes at the end of it.  Write a story about the race the Hare ran. How fast is the hare moving on each time interval compared to his speed on the other time intervals? What direction is the Hare moving (toward the starting line? Away from the starting line? Staying still?) The hare moves in the direction to the end with constant speed, then stays still, and then moves with the same speed as at the first time interval to the end of line.

Graph B  Where does the hare start the race in relation to the starting line? Finish the race in relation to the starting line? The hare starts the race at the beginning of the starting line and finishes at the end of it.  Write a story about the race the Hare ran. How fast is the hare moving on each time interval compared to his speed on the other time intervals? What direction is the Hare moving (toward the starting line? Away from the starting line? Staying still?) The hare moves in the direction to the end with constant speed, then returns half-distance back with the same speed, and then moves 1.5 times faster to the end of line. Graph C  Where does the hare start the race in relation to the starting line? Finish the race in relation to the starting line? The hare starts the race at the quarter distance between the beginning and the end of the starting line and finishes at the end of it.  Write a story about the race the Hare ran. How fast is the hare moving on each time interval compared to his speed on the other time intervals? What direction is the Hare moving (toward the starting line? Away from the starting line? Staying still?) The hare moves in the direction to the end with constant speed, then stays still, and then moves with twice the speed of the first time interval to the end of line.

Graph D  Where does the hare start the race in relation to the starting line? Finish the race in relation to the starting line? The hare starts the race at the end of the line and finishes at the beginning.  Write a story about the race the Hare ran. How fast is the hare moving on each time interval compared to his speed on the other time intervals? What direction is the Hare moving (toward the starting line? Away from the starting line? Staying still?) The hare moves in the direction to the beginning with constant speed, then moves three times slower for the same distance, and then moves with twice the speed of the first time interval to the beginning of line. During the race between the tortoise and the hare, the fox recorded the speed at which both the tortoise and the hare were traveling. The fox observed that the tortoise plodded along at a rate of 20 meters per minute throughout the 1000-meter race. 3. a. Complete the table below indicating the distance traveled by the tortoise in the time elapsed. Time elapsed in minutes, t Distance traveled in meters, D 0 0 1 20 2 40 3 60 4 80 5 100 6 120 7 140

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