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2I Spatial patterns

Learning intentions for this section:

• To know that a spatial pattern begins with a starting design and has a repeating design

• To understand how spatial patterns are related to number patterns

• To be able to continue a spatial pattern given the first few shapes

• To be able to describe and use a rule relating the number of shapes and the number of objects required to make them

Past, present and future learning:

• This section consolidates and extends Stage 3 concepts which are used in Stage 4

• It prepares students for future work in Linear Relationships in Stage 4 and beyond

• Expertise with these concepts may be required in non-calculator examinations such as NAPLAN and industry aptitude tests

Patterns can also be found in geometric shapes. Mathematicians examine patterns carefully to determine how the next term in the sequence is created. Ideally, a rule is formed that shows the relationship between the geometric shape and the number of objects (e.g. tiles, sticks, counters) required to make such a shape. Once a rule is established it can be used to make predictions about future terms in the sequence.

Lesson starter: Stick patterns

Materials required: One box of toothpicks or a bundle of matchsticks per student.

• Generate a spatial pattern using your sticks.

• You must be able to make at least three terms in your pattern. For example:

• Ask your partner how many sticks would be required to make the next term in the pattern.

• Repeat the process with a different spatial design.