In a circus context, in which acrobats make human towers of different shapes, students are introduced to number patterns arising from spatial patterns.

Teacher notes

  • Students predict how many acrobats are needed to form specific shaped human towers.
  • Students build up a table of data, which is also displayed as a graph.
  • Students identify and describe the relationship between different representations of spatial patterns as patterns of numbers; in tables; as graphs; in words and using symbols in mathematical formulae.
  • Students are assisted to develop multiplicative and algebraic formulae, and can progress to more complicated patterns, where formulae are presented and used.
  • Students are introduced to non-linear graphs arising from figurate numbers such as triangular and square numbers, and prisms and pyramids with triangular and square bases.

Learning objects

Circus Towers picture.

Circus towers: square stacks
They start by building a square tower with four acrobats: two acrobats in the base layer and two acrobats standing on their shoulders. The formula used is n squared, where n is the number of layers.