Teaching Secondary Mathematics - Module 4: Conducting Practical and Collaborative Work - Focus on Contours

From Term 1 2017, Victorian government and Catholic schools will use the new Victorian Curriculum F-10. Curriculum related information is currently being reviewed and may be subject to change.

For more information on the curriculum, see:
The Victorian Curriculum F–10 - VCAA

This module focuses on conducting practical and collaborative work through the mathematical theme of contours. This module has been developed from the examples provided in the indicator of progress ‘Understanding Contour Lines 5.0’ which is found on the Mathematics Developmental Continuum P–10.  This module illustrates how teaching can give students an opportunity to work with three-dimensional models. Connecting mathematics learning in schools with the student’s own world will support each student’s growth as a community member as well as raise their achievement in mathematics.

Key messages

  • Practical work can support students in moving to abstract understanding, but only if it is well designed to focus on the mathematical ideas and to encourage student thinking
  • Productive mathematical collaboration includes clear mathematical communication, the expectation to justify ideas within a group as well as peer teaching and learning. With these components, group work assists in developing mathematical reasoning skills
  • Teachers need to value both effort and correctness, and to help students deal productively with errors
  • Practical work and collaborative work can improve students’ experiences of learning mathematics. It can connect with communities and practices beyond the classroom, help in learning to work with others and assist in providing each student with activities that are extending but attainable
  • Conducting practical work requires skills of classroom organisation and school support
  • Using 3-dimensional models enables students to see easily many mathematical relationships that are difficult to observe on a 2-dimensional representation (in this case, a map, weather chart, etc)

The module contains:

  • Examples from Mathematics Developmental Continuum P–10, indicator of progress Understanding Contour Lines 5.0
    • Potato Mountains (Mt. Spud)
    • Model It
    • Match the Views
    • What Terrain is This?
    • Imaginary Bushwalks.
  • Links between the activities and the Victorian Essential Learning Standards and Principles of Learning and Teaching P–10
  • Conducting practical and collaborative activities in mathematics classrooms.

Download Module 4 workshop booklet and presentation

To use Module 4, first save the booklet and PowerPoint presentation to your computer.


Links to the Principles of Learning and Teaching P–12

  • Principle 1: The learning environment is supportive and productive where effort is valued and satisfactory effort is fostered.
  • Principle 2: The learning environment promotes independence, interdependence and self motivation. The teacher uses strategies that build skills of productive collaboration. This is illustrated by tasks being conducted in pairs and small groups and where collaboration and discussion are encouraged.
  • Principle 6: Learning connects strongly with communities and practice beyond the classroom.  The topic of contours has obvious practical implications and contributes to an understanding of local environment.

Links across the Victorian Essential Learning Standards

This module explores the Interpersonal Development and Personal Learning domains of the Physical, Personal and Social Learning Strand, whereby students are encouraged to:

  • work with others
  • acquire self knowledge and dispositions that support learning
  • take greater responsibility for their own learning

Additional resources needed for this module



  • clean (not waxy) potatoes cut in half
  • permanent markers
  • rulers
  • newspapers
  • topographic map which includes:
    • cliffs
    • caves (not essential)