Stopping distances

Stopping distances

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about interpreting a bar chart.

Question 1Change answer

Two cars have been tested for their stopping distance at 30mph.
Each car was tested 10 times. The results were ordered and shown below.
 
car-stopping-distances.png
 
a)  Which car is safer? Car ACar Bboth the same
b) Explain why?
Task administration: 
This task can be completed with pen and paper or online (with NO auto marking).
Level:
4
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Using language, symbols, and texts
Keywords: 
graph interpretation, range, distribution
Description of task: 
Students interpret a bar chart that shows the stopping distance of cars and are asked which car is safe and why.
Curriculum Links: 
This resource can be used to help to identify students' ability to interpret a graph, including the spread.
Key competencies
This resource involves describing how two . This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y8 (10/2015)
"Car B" and an explanation that states that Car A is less consistent than Car B 
or
"Both the same" and an explanation that states that Car A has a lower average stopping distance, and that Car B is more consistent
 
Examples of correct student responses:
  • Car B - Car A's stopping distances look uneven and unpredictable, so each time you stop it could come up with any outcome. Car B looks consistent and easier to estimate how far its stopping distance will be, so it seems safer.
  • Car B - Because Car A varys greatly in the amount of distance as car B stays around the same.
  • Car B - Because car A's distances vary greatly.
  • Car B- Because car B had similar results each time. But Car A was all over the show and anything could happen.
  • Car B is the safer car because it is more consistent than car A. Car A slides around and even though it has the shortest amount of feet it also has the longest. 
  • Both the same - Because car B has a consistent amount of stopping distances but Car A has a range of stopping distances it can stop very quickly or take a very long time. 
 difficult
Based on a sample of 90 Year 8 students.
Teaching and learning: 
The context of a car braking is important to include. To be safe, a car should have a consistent braking distance. This means that students need to make comparisons about the spread in data, not just comparisons of the location of the data.
  • Spread can be measured by the range, inter-quartile range or the standard deviation; but can also be done visually.
  • The location of the data is measured by the mean, the median or the mode. Again, differences in the location can be detected visually.
Diagnostic and formative information: 
Students refer to the maximum distance travelled, ignoring spread (partial explanation).
Car B - Because Car B has stopped at a maximum of 80 feet and Car A stopped around 90.
Car B - Because its always below 80 unlike Car A.
Car B - Car A's stopping distances are safe except for the last two for it went past 80 feet while Car B didn't. Therefore, Car B is safer since it [always] stopped before 80 feet.
 
(partially explanation).
Car A - Because Car A has shortest stopping times overall.
Car A - Majority of Car A's results are shorter than Car B.
Car A - Because the average distance for Car A is shorter than Car B.
Car A - Car A has an average of about 50- 60, while Car B has an average of 70-80.
 
Students refer only to the minimum distance travelled (incorrect).
Car A - It stops faster because the fastest for Car A was 40, and Car B was 60.
Car A - Car A is safer because it has a lower number.
Next steps: 
Students who refer to the most common or average stopping distances, ignoring spread could be encouraged to look at concepts of spread. At this level, the most common measure used is the range (See ARB resources Jellybeans or Monthly rainfall). Get students to think about how to interpret both the mean and the spread of data.
 
Students who refer to just the maximum , ignoring spread could be asked to list as many difference between Car A and Car B's stopping distances. Encourage them (through discussion, or peer sharing) to include both the maximum and the minimum (See the ARB resource Tennis ball throw). This will give them ideas about the spread, as measured by the range.