Tennis ball throw

Tennis ball throw

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about reading information from a stem-and-leaf graph.

At Defoe College, the Year 9 students challenged the Year 10 students to a ball throwing contest.

Each student threw a tennis ball and this distance was measured and recorded to the nearest metre.

Their results are plotted on the back-to-back stem-and-leaf graph below.

 

DISTANCE TENNIS BALL THROWN

Year 9

Distance
(metres)

Year 10

a) What was the distance of the:
 
  i)
longest throw? ______ metres
 
  ii)
shortest throw? ______ metres
 
b) What was the median distance thrown by:
 
  i) Year 9 students? ______ metres
 
  ii)
Year 10 students? ______ metres
 
c)
i)
 

ii)
Tamiti said that Year 10 students threw the ball the furthest.
Is he correct?   YES  / NO  (circle one)
 
Explain your answer.
 
 
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Statistics, Statistical literacy
Key Competencies: 
Using language, symbols, and texts
Keywords: 
composite graphs, stem-and-leaf graphs, graph interpretation, median, distribution
Description of task: 
Students interpret a back stem-and-leaf graph to answer questions about a measurement investigation.
Curriculum Links: 
This resource can be used to help to identify students' understanding of comparing distributions visually to identify patterns, variations and relationships.
 
Key competencies
This resource involves interpreting a graph, and explaining why a person has a correct interpretation of the graph.These relates to the Key Competencies: Thinking and Using language, symbols and text.

For more information see http://nzcurriculum.tki.org.nz/Key-competencies
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, sets 4-5
Interpreting statistical and chance situations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (10/1998)
a) i)
ii)		 62
8		 easy
easy
b) i)
ii)		 28
38		 difficult
difficult
c)   YES, and
Any argument based on the following:

  • The median, mode, average (mean) is larger for the Year 10 students.
  • The distribution of the graph is higher overall for Year 10 students.
  • Most people who threw over 40 metres were Year 10 students.
  • Added up, the Year 10 total is higher.

NOTE: It is not sufficient to comment on the maximum or minimum throws only, nor the range.

 moderate

 

Diagnostic and formative information: 
  Common error Likely reason
a) i)
    ii)		 6
0		 Assumes the numbers in the stem stand for 0-6 rather than 0-60.
b) i)
    ii)		 20
31		 Counts along the leaves in the wrong direction to find the median.