Apple pickers

Apple pickers

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.

Sue and her brother Peter picked apples during their summer holidays. One day they kept a record of how many kilograms each of them picked per hour. Sue drew an unusual bar graph, turned on its side, with the bars placed 'back-to-back', at hourly intervals. This graph is shown below.

a)
In what hour did Sue pick her largest weight of apples? __________
 
How many kg did she pick? __________
 
b)
 
In what hour did Peter pick his smallest weight of apples? __________
 
How many kg did he pick? __________
 
c)		  
How many kgs more did Peter pick than Sue in the whole afternoon? __________
 
d)
 
Look at the two graphs as a whole. Now write down one thing about the 'picking patterns' of Sue and Peter that is the same, and one thing about their 'picking patterns' that differ.
 
  i)
Same:      
 

 
 
 
   
ii)
 
Different: 
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
bar graphs, graph interpretation, mode, distribution
Description of task: 
Students interpret a back-to-back bar graph about apples picked by comparing and identifying patterns.
Curriculum Links: 
This resource can be used to help to identify students' ability to  compare two bar graphs.
Key competencies
This resource involves comparing distributions visually to identify patterns variations and relationships and explaining their rationale. These relate to the Key Competencies: Thinking and Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
Statistical investigations, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  
Y7 (10/1996)
Y8 (10/1996)
a)   10-11 a.m. Sue picked 60 kg. easy very easy
b)   4-5 p.m. Peter only picked 30 kg. easy very easy
c)   30 kg more [170 kg, compared with 140 kg]. difficult difficult
d) i)

 

 

 

 

ii)

 Same
Any 1 of:

  • They both picked more apples in the morning than in the afternoon;
  • They both slowed down just before lunch;
  • They both slowed down just before knocking off for the day (tired!).


Different
Sue tended to start off slowly and work up to a peak, in both morning and afternoon, before slowing down again, whereas Peter tended to work more steadily.
[Accept other logical statements, but they must be generalised to gain the last two marks, e.g., 'Peter picked more than Sue between 4-5 p.m.' is not sufficient to gain a mark.]

 very difficult

 

 

 

 

very difficult

 difficult

 

 

 

 

difficult
Diagnostic and formative information: 
  

Common errors

Likely misconception

a)
b)

340 kg
360 kg

Daily totals for Sue and Peter.

c)

2 or 3

Reading x-axis in units not tens.

c)

20 kg

Used daily figures not afternoon ones.