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7 Which rule correctly describes this spatial pattern of ‘hats’?

A Number of sticks = 7 × number of hats

B Number of sticks = 7 × number of hats + 1

C Number of sticks = 6 × number of hats + 2

D Number of sticks = 6 × number of hats

8 Which rule correctly describes this spatial pattern?

A Number of sticks = 5 × number of houses + 1

B Number of sticks = 6 × number of houses + 1

C Number of sticks = 6 × number of houses

D Number of sticks = 5 × number of houses

Reasoning

9 Design a spatial pattern to fit each of the following number patterns.

a 4, 7, 10, 13, b 4, 8, 12, 16, c 3, 5, 7, 9, d 3, 6, 9, 12, … e 5, 8, 11, 14, … f 6, 11, 16, 21, … a How many sticks are required to make one window? b How many sticks are required to make 10 windows? c How many sticks are required to make g windows? d How many windows can be made from 65 sticks?

10 A rule to describe a special window spatial pattern is written as y = 4 × x + 1, where y represents the number of ‘sticks’ required and x is the number of windows created.

11 a How many pieces of timber are required to make one panel? b What does m represent? c Draw the first three terms of the fence spatial pattern for m = 4 and n = 1.

A rule to describe a special fence spatial pattern is written as y = m × x + n, where y represents the number of pieces of timber required and x represents the number of fencing panels created.