Hare's progress

Hare's progress

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about interpreting a distance-time graph.
 
The Hare's progress in a race
 
In one of Aesop's fables, a hare challenges a tortoise to a race. Suppose the race was 12 stadia in length.
[NOTE: Stadia are old Greek measures of length.] The graph above shows the progress of the hare.
 
a)
Complete this sentence:
"Between A and B the hare travels 6 stadia in 10 minutes. This is equivalent to a rate of __________ stadia per hour."
 
b)
What do you think the hare is doing between B and C?
 
 
 
c)
How much time passes between B and C? __________ minutes
 
d)
Describe what the hare is doing between C and D.
 
 
 
e)
The tortoise starts from A at exactly the same time as the hare, but travels at a steady rate of only 2 stadia in 10 minutes. After 30 minutes he arrives at point E. 
Mark and label the point E on your graph.
 
f)
The tortoise continues on steadily at this rate without stopping.
What is the result of the race? [Complete your graph to show the tortoise's progress].
 
 
 
 
 
 
Task administration: 
This task can be completed with pencil and paper.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
line graphs, distance-time graphs, breakeven points, linear equations, speed
Description of task: 
Students interpret a graph of the Hare's Progress to answer questions about rate, rest, and reading sections of the graph. They also identify the constant motion of the tortoise and explain the result of the race.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 
Y8 (06/1996)
a) 36 stadia/hour. difficult
b) Not running, resting, sleeping. [Other variants are possible.] moderate
c) 40 minutes. difficult
d) Travelling on again, running. [Other variants are possible.] very difficult
e) Point E marked correctly midway between B and C. difficult
f) The hare and the tortoise have a dead heat. [Other variants are possible.] moderate