A car journey

A car journey

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about interpreting a distance-time graph.
Car journey from home
graph of car journey from home
Susan and Mei went to town by car. The graph shows their journey.
 
a) Describe each section of their journey in words. Compare their speeds in each section to other parts of the journey. The words in the box might help you.

 

stopped     constant speed     acceleration     slowing down

faster than     slower than
 
i)
 
 
ii)
 
 
iii)
 
 
iv)
 
 
v)
 
 
b)
Use the following paragraph to draw lines to complete Susan and Mei's journey on the graph above. 
 
... After shopping they got back in their car and drove back home along the motorway. They drove faster than at any time on the way to town.
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships, Science, Communicating in science, Physical World
Keywords: 
time, distances, graphs, speed, distance-time graphs, graph interpretation
Description of task: 
Task: interpret a graph of a car's journey and add to the graph to represent a further description of the journey. Assessment focus: graph interpretation.
Curriculum Links: 
Science capabilities
The capabilities focus is brought about by the conversations you have and the questions you ask.
Capability: Interpret representations
This resource provides opportunities to discuss the challenges of turning written texts into visual texts.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Science capabilities: 
Interpret representations
Answers/responses: 
  Y10 (11/2003)
a)
i)
ii)
iii)
iv)
v)
 Travelling at constant speed. This was the fastest part of the journey.
Stopped.
Travelling at constant speed, slower than 1.
Travelling at constant speed faster than 3. (Or slower than 1.)
Stopped.		 very difficult
moderate
very difficult
very difficult
moderate
b)
  
Line goes from end of section 5 down to time line. Line is at a steeper gradient than any other line.
difficult
 
 
 
 
 
difficult
Diagnostic and formative information: 

Although the vertical axis is clearly labelled "distance from home" most students appeared to have interpreted this as a speed/time graph. This is a common trap because the graphs look so similar but have different meanings. Just 8 percent of the sample consistently completed answers for a distance/time graph.

The following examples show two common types of responses to question b). Some students drew the return line above the plotted line, but more drew a straight line back to zero below the existing plotted line.

Students who completed the graph in these ways appeared to think of "home" as a physical place/point rather than recognising that the entire horizontal axis represents zero distance from home and so is, symbolically, "home". You could check this explanation (and indeed the range of other types of responses we saw) by asking students to explain why they drew the line that they did. Students may need repeated opportunities to explore the symbolic nature of axes, especially when concepts such as "home" are part of the question.