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Key Ideas

■ A spatial pattern is a sequence of geometrical shapes that can be described by a number pattern For example:

■ A spatial pattern starts with a simple geometric design. Future terms are created by adding on repeated shapes of the same design. If designs connect with an edge, the repetitive shape will be a subset of the original design, as the connecting edge does not need to be repeated. For example:

■ To help describe a spatial pattern, it is generally converted to a number pattern and a common difference is observed.

■ The common difference is the number of objects (e.g. sticks) that need to be added on to create the next term.

■ A table of values shows the number of shapes and the number of sticks.

Number of squares 1 2 3 4 5

Number of sticks 4 8 12 16 20

■ A pattern rule tells how many sticks are needed for a certain number of shapes. For example: Number of sticks = 4 × number of shapes

■ Rules can be found that connect the number of objects (e.g. sticks) required to produce the number of designs. For example: hexagon design

Rule: Number of sticks used = 6 × number of hexagons formed