Squares and matches
This task is about rules for spatial patterns.
Shape 1  Shape 2  Shape 3 
Petra made these shapes out of matches.
The rule for the number of squares can be written as an equation like this:
The rule for the number of squares can be written as an equation like this:
s_{n} = 2n^{2} – 2n + 1 
where n represents the shape number,
and s_{n} represents the number of squares in shape n.

a) 
How many squares will there be in 

i)
ii)

shape 6? __________
shape 10? ___________

The rule for the number of matches in a shape can be written in words as:

b) 
Use this rule to work out how many matches would be needed to make 

i)
ii)

shape 5? __________
shape 20? __________

c) 
Write the rule for the number of matches as an equation.

Use n to represent the shape number, and
Use t_{n }torepresent the number of matches in shape n.
Complete this equation for the number of matches needed for shape n.
t_{n }= ____________________
