Colour of lunch boxes

Colour of lunch boxes

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about commenting on statements about what a dot plot shows.

Question

Here is a graph that shows the colour of lunch boxes of all the children in Room 3. Some children have no lunch box.
 
Colour of lunch boxes of children in Room 3
Colour-of-lunch-boxes-dot-plot.png
 
Colour-of-lunch-boxes-speech-bubbles.png
a)  Which person said something that was not correct?

    • Emma

    • Jack

    • Maya

    • Noah

    • They all made correct statements.

b) Explain why you decided on your answer.
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Level:
2
Curriculum info: 
Maths, Statistics, Statistical literacy
Key Competencies: 
Using language, symbols, and texts
Keywords: 
graph interpretation, distribution, dot plots
Description of task: 
Students decide which statement about a dot plot is incorrect and explain their reasoning.
Curriculum Links: 
This resource can be used to help to identify students' understanding of identifying a correct statement about a data display.
 
Key competencies
This resource involves interpreting a graph, and explaining which person has a correct interpretation of the graph. This relates to the Key Competency: 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, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y4 (06/2009)

a)

b)

D and

Any 1 of:
  • An explanation that fewer than half had no lunch boxes;
  • An explanation that more than half had lunch boxes;
  • An explanation that they counting all the dots, regardless of whether any actual numbers given;
  • Counts 17 coloured boxes out of 26 (more than half); or
  • Counts 17 coloured boxes and only 9 with No Lunch Box.

[Do not give credit if the student responds with D but reasons"A, B, and C are correct, so D must be wrong."]

Both correct - very difficult
Based on a representative sample of 163 students.
Diagnostic and formative information: 
A selection of correct responses

  • Because … there were 9 in that column and 17 in the other columns.
  • Because I added the dots and colours [of the lunch boxes and these] had more than people with no lunch boxes.
  • Because 5, 6, 4 and 2 add up to more than 9
  • Because there are 26 children in the class and half of 26 is 13 and only 9 children had no lunch box.
  • Because I counted the number of coloured boxes and I counted the number of people that hadn't bring (sic) their lunch box and the numbers weren't equal.
  • ... because I counted no lunch boxes, then I counted green, yellow, blue, and red and there were more lunch boxes.
  • Because if you stacked up all the other colours but no lunch box the colour would be taller.
  Common error Likely misconception
a) Emma

 

All correct
Confuses "Most common" with "More than half"
Sees "No lunch boxes" as the most common, rather than blue or that blue is the second most common colour.

Sees that blue as the most common colour (a correct conclusion), but then thinks that "No Lunch Boxes" is more than half because it is the most common frequency.
a)
b)
 Noah and "Emma, Jack, and Maya correct so D must give an incorrect statement."
Difficulty finding a half & the sample size from graph
Uses the information on the individual bars of the graph for Emma, Jack, and Maya, but not for Noah.
a)
b)
 Noah  Any 1 of

  • Wrote down what the student they selected said;
  • Wrote "I looked at the graph"; or
  • Other statements that are true by definition.
Cannot write down their reasoning
The student may be able to correctly select Noah, but cannot write down a reason.
Next steps: 
Confuses "Most common" with "More than half"
The students need to see where the biggest chunk of the data is. Get them to put a circle around the part of the graph which has most of the data (i.e., red, blue and yellow).The student needs to see that blue is the most common colour of lunch box.
  • You could ask "What colour is more common that blue?" Students may respond "No lunch box." You could then respond "What colour is that?"
  • You could ask "Which is more common, having a lunch box, or not having a lunch box?" This can be done visually (estimating), or by counting.
  • Students may then need to explore if Noah is correct or not. This needs them to understand "half" and how to find the sample size on a dot plot.
If the student does not understand dot plots, then they need to be introduced to the idea, and then given simple dot plots to construct.
Click on Waiting time or Marine fish for examples.

Difficulty finding a half & the sample size from graph

  • Ask the student(s) "How many students were in the class?"

If they cannot do this, then they will need experience in constructing and understanding dot plots. Click on the link or use the keyword, dot plots.

  • If they can answer the question (i.e., "There are 26 students), then ask them:

-  "How many have lunch boxes?" or "How many do not have lunch boxes?"-  "Is this more than half?" or "Is this less than half?"If they cannot answer this, then they need to work on recognising fractions greater than or less than a half.