Data – Mystery graph

Students create displays of data using lists, tables and picture graphs and interpret them.

Verbal recording Teacher observation Individual Collaboration

Statistics and probability – Data 2

A student:

  • describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-1WM
  • supports conclusions by explaining or demonstrating how answers were obtained MA1-3WM
  • gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results MA1-17SP


  • Create displays of data using lists, tables and picture graphs and interpret them.

National Numeracy Learning Progression mapping to the NSW mathematics syllabus

When working towards the outcome MA1‑17SP the sub-elements (and levels) of Interpreting and representing data (IRD1-IRD3) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.


Teacher instructions

The purpose of this task is for students to:

  • analyse an unlabelled data display and
  • form conclusions about the graph.

Students may work independently or in small groups.

When presenting the graph, advise students that it is about a Year 2 class and encourage them to make as many observations and interpretations as they can.

Students may record their responses in writing, by video or as a voice recording. Teachers may also choose to interview students about their responses.

Student instructions

This graph was created by a Year 2 class.

What is it about?

Enabling prompt: What information is displayed?

How do you know?

What else could this graph be about?

Enabling prompt: Why would a class use these symbols?

How do you know?

How many children could be in this class? Why do you think this?

Extending prompts:

What would be a good title for this graph?

Label the parts of the graph.

How could you show that each symbol indicates more than one student?

Possible areas for further exploration

Possible misconceptions:

  • Requires support to see the significance of categories
  • Does not recognise one-to-one representation of data
  • Only recognises one-to-one representation of data
  • Interpretation based only one numerical observation for example, 3 people like skiing.

Where to next?

Involve students in the creation of human graphs based on obvious categories such as; type of shoes, long or short-sleeved shirt. Photograph these human graphs and discuss.

Jointly construct graphs of many-to-one correspondence using familiar collections and within the students’ skip counting range, for example, feet, toes

Teacher models vocabulary through think-alouds, for example, There are more bike riders than swimmers. The least popular sport is soccer.

Adapted from Sullivan P, & Lilburn, P (1997) Open-ended Maths Activities Second edition. Oxford, New York.


Please note:

Syllabus outcomes and content descriptors from Mathematics K-10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2012

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