Building patterns

This task is about continuing a spatial pattern and writing a rule.
Shape 1 Shape 2 Shape 3

Here are the first three shapes in a pattern.
a)
b)		 Use the cubes to build Shape 4.
Complete the table below for Shape 4.
  

Shape number (n)

1

2

3

4

Number of cubes (c)

1

4

9

 
   

Check with your teacher if your model is correct, and your table is correct for Shape 4.
 
c)
 
How many cubes would be needed to build
 
 
i)
 
ii)
 
iii)
 
Shape 5? __________
 
Shape 6? __________
 
Shape 20? __________
 
d)
Explain in words or symbols how to get the answer for shape 20 above.
 
 
 
 
 
e)
Use your model of Shape 4 to show your teacher how this works.