Off-the-shelf Masterclass: Magic squares

Magic squares are squares of numbers where all rows, columns and diagonals add up to the same magic total. Find out about their history in art, sculpture and legend and learn how to create your own magic squares of different sizes.

Magic square on the façade of the Sagrada Familia in Barcelona
Image credit: Mathieu Pillard via Flickr

About this Masterclass

Magic squares are amazing things. A magic square is a square grid of numbers where each row, column and diagonal must add up to the same number. An exploration of number bonds and symmetry, magic squares capture something of the beauty and joy of manipulating numbers. They have a long and distinguished history, having fascinated mathematicians for centuries.

The aim of the Masterclass is for students to explore the properties of magic squares, developing their number sense, creativity and reasoning. They will begin with the challenge of constructing a 3x3 magic square before exploring the history of magic squares in art, sculpture and legend through three examples:

  • The magic square carved into the façade of the Sagrada Familia in Barcelona
  • The magic square depicted in the Durer painting “Melancolia”
  • The ancient Lo Shu Square from China

Students then explore the structure of magic squares by constructing their own examples, learning simple number tricks to help them.

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

Resources needed

  • 'Magic Squares' presentation (download from "Supporting documents" below)
  • Student worksheets (download below)
  • Paper and pencils
  • Scissors or pre-prepared digit cards (see worksheet 1)
  • Supporting notes; helper/session leader download from "Supporting documents" below)
  • Computer and data projector
  • Further details of quantities etc. can be found in Session Leader Notes

Worksheets

01 3x3 magic square digit cards (two sets per sheet) 02 Durer magic square (six per sheet) 03 4x4 magic squares worksheet (two per sheet) 04 Sagrada Familia magic square (six per sheet) 05 Random total magic square worksheet 06 Special date magic square worksheet

Supporting documents

Session leader notes Helper notes Additional information Worked example - special data magic square Magic Squares 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.

Back to top