Pocket money

Pocket money

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about comparing two dot plots.
Two school classes graphed how much pocket money each student got.
They compared their graphs.

Question

graph of room 4 and room 5
 
a)  In which class do students usually get more pocket money?

    • Room 4

    • Room 5

    • You cannot tell which class has students who usually get more pocket money.

    • Students in Room 4 get about the same amount of money as students in Room 5.

b) Use the two graphs to explain why you choose your answer.
Task administration: 
This task can be completed with pen and paper or online (with SOME auto marking).
Level:
3
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Using language, symbols, and texts
Keywords: 
distribution, graph interpretation, dot plots, income
Description of task: 
Students compare the overall distribution of two dot plots and describe their reasons.
Curriculum Links: 

This resource can be used to provide evidence of students' ability to "Identify patterns in data" and explain their reasoning.

​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.

For more information see http://nzcurriculum.tki.org.nz/Key-competencies

Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Correct answer Y6 (10/2013)*
a) Room 4 moderate
b)

Response based on the shape of the graph
Examples:

  • Room 4s dots are clustered between 3-5 and Room 5 between 1-3.
  • Because Room 4 has more people with higher amounts of pocket money.
  • Becasue more people in Room 4 are higher than 3 and in Room 5 more people are lower than 3.

or
Response based on the mean, mode or median
Example:

  • The median for Room 4 is higher
  • The mean its bigger in the Room4 graph than the Room 5 graph.
  • In Room 4 the highest amount [mode] is $4 and in Room 5 the most [common] amount is $2.
 difficult

Based on an online sample of 68 Y6 students in Oct-Nov 2013.

Teaching and learning: 

The big idea behind this question is where most of the data in a graph lies (i.e., the shape or distribution of the graph). Interpreting statistical graphics is far more than identifying single features of a graph. 

Students need to look at what the graph is showing overall. In this case, students are asked to identify where most of the data lies, i.e. where "the biggest chunk" of the data is.

Diagnostic and formative information: 
Common error Next steps
Confuses the sample size (number of children in the class) with the amount of pocket money
Examples:
[Room 5] There were more dots on the Room 5 chart than the Room 4's chart.
[Room 5] Room 4 has 23 [dots and] Room 5 has 24.		 It may be helpful to ask these students "How many children are there in Rooms 4 and 5?".
Get them to read Jason's statement again. Help them see that the question is about the amount of pocket money, not the number of children in the class.
If students still cannot interpret the statements or the graph, they may need to construct some dot plots of their own.
Comments about individual features of the graph
Examples:
[Room 5] In Room 4 only 1 person got $6+ and in Room 5, 2 people got $6+.
[Room 5] Room 5 usually has at least two people with 6 dollars or more.		 Students need to see the "big picture" of the graph, rather than looking at individual features.
Get students to put a circle around most of the data ($3-$5 for Room 4 and $1- $3 for Room 5).
Makes no comments for Question b)
Students may feel that an explaining is not important.
Get these students to explain their answer in a small group, pairs or to you individually.
Then get them to write down their oral explanation.