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.

Circus Towers picture.

Circus towers: triangular prisms
They start by building a triangular prism with six acrobats: three acrobats in the base layer and three acrobats standing on their shoulders. The formula used is n x 3, where n is the number of layers.

Circus Towers picture.

Circus towers: rectangular prisms
They start by building a triangular pyramid with twelve acrobats: six acrobats in the base layer and six acrobats standing on their shoulders. The formula used is n x 6, where n is the number of layers.

Circus Towers picture.

Circus towers: triangular towers
They start by building a triangle with three acrobats: two acrobats in the base layer and one acrobat standing on their shoulders. The formula used is (n x (n + 1))/2, where n is the number of layers.

Circus Towers picture.

Circus towers: square pyramids
They start by building a square pyramid with five acrobats: four acrobats in the base layer and one acrobat standing on their shoulders. The formula used is 1/6 x n (n +1) (2 x n + 1), where n is the number of acrobats in the side length of the base (or the number of layers). Students will need a calculator for the harder sums.