Building patterns II
This task is about continuing a 3D spatial pattern.
Step 1  Step 2  Step 3 
Here are the first three models of a sequence of steps.
Each model has the faces on the front and back painted blue and all the other faces painted white.
a)

Use cubes to build the next 2 models in the sequence, i.e., Step 4 and Step 5.


b) 
Use the models to complete the table for Steps 4 and 5 only in the table below.
The first three steps have been done for you.




c)

Without using the cubes, complete the table above for Steps 6 and 7.


d)  i) 
In Step 10 how many faces would be white? __________


ii) 
Explain in words how to work out the number of white faces in Step 20.


iii)

Complete this equation for the number of white faces (w) in Step number n.
w = __________


e)  i) 
How many blue faces would there be in Step 10? __________


ii) 
Complete this equation for the number of blue faces (b) in Step number n.
b = __________
