Off-the-shelf Masterclass: Being systematic

Investigate how many squares there are on a chessboard (hint: not 64) and extend this reasoning to cubes, triangular grids, and more.

chess board with chess pieces made out of wood
Image credit: Balaji Malliswamy via Unsplash

About this Masterclass

The ability to work systematically, recognise patterns and extend observations to create general rules are all important skills for everyday life as well as being cornerstones of mathematical endeavour.

The aim of the Masterclass is for students to develop their skills in being systematic. They will conduct a mathematical investigation by counting squares in a chessboard, spot patterns and conjecture a rule for a chessboard of any side-length. Thinking systematically will enable them to be sure that they have counted all possible squares without missing any out or double-counting. They will extend their thinking to three dimensions by investigating cubes, starting with a 3x3 cube and developing a rule for cube of any side-length. In a longer Masterclass they will explore other two-dimensional shapes.

Length: 2 hours (see the session leader notes for ideas on how to shorten the Masterclass).

Resources needed

  • 'Being Systematic' presentation (download from "Supporting documents")
  • Student worksheets (download below)
  • Paper and pencils
  • Coloured pencils
  • Multi-link cubes
  • Tracing paper
  • Supporting notes (download below)
  • Computer and data projector
  • Further details of quantities etc. can be found in Session Leader Notes

Worksheets

01 Counting squares worksheet 02 Results Tables 03 Extra counting squares activity 04 Counting cubes 3x3x3 worksheet 05 Counting cubes 4x4x4 worksheet 06 Extra activity counting triangles

Supporting documents

Session leader notes Helper notes "Being Systematic" presentation

Support for this Masterclass

All supporting notes, worksheets and solutions can be downloaded from this page along with the Powerpoint presentation.

The Session Leader Notes offer full notes on the activities and a detailed list of resources, including quantities needed. 

The Session Helper Sheet can be distributed amongst helpers so they can better support the students.

Ask the Ri

You can collect any student questions and email them to the Ri Masterclass team at masterclasses@ri.ac.uk - we will endeavour to answer them before the next Masterclass in your series.

Masterclass series support

For more information on running a Masterclass series and the support, templates and other resources available to you, please get in touch via masterclasses@ri.ac.uk.

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