Number patterns in diagrams

A number pattern in a diagram often requires counting shapes to find the rule. Look at how the pattern grows from one term to the next.

Example

Number pattern diagrams
  • pattern {1} has {0} purple tiles and {3} blue tiles, so it has {3} tiles altogether
  • pattern {2} has {1} purple tile and {5} blue tiles, so it has {6} tiles altogether
  • pattern {3} has {2} purple tiles and {7} blue tiles, so it has {9} tiles altogether
Question

Q1. Based on the number patterns above, draw pattern {4}.

Q2. Look again at the number patterns above. Write the rule and the fourth terms for:

a) purple tiles

b) blue tiles

c) all the tiles

A1.

Number pattern diagram

Pattern {4} has {3} purple tiles and {9} blue tiles, so it has {12} tiles altogether

A2.

a) The rule for the number pattern of purple tiles is 'add {1}' and the {4}^{th} term is 3.

b) The rule for the number pattern of blue tiles is 'add {2}' and the {4}^{th} term is 9.

c) The rule for the number pattern of all tiles is 'add {3}' and the {4}^{th} term is 12.