Visual Patterns Problem

OK, so I keep thinking of so many things that many come and go with how hectic my past year has been.  I am WAY behind on posts I have simmering in my mind, so I want to get this one knocked out….

Fill out the following form from Fawn’s site by observing the pattern shown in the following series of pictures:

URL: visualpatterns.org

Name: __________________ Pattern #: _____

1.     Draw the next step:

2.    Complete this table:

 Step n # of _______________ 1 2 3 4 5 6 10 37

3.    What do you notice? What do you wonder?

4.    Write the equation:

5.    Graph the relationship below.

I typically do not show them the following pictures until there arises a discussion on how to do #1.  I want to see how students visualize the next step and it creates some interesting discussions when they start talking 4D and 5D.  I stress that this isn’t the only possibility, just one that my mind visualizes when I try to make sense out of patterns of this nature.

What is the equation for this pattern?

How many blocks in the 43rd Step?

What patterns do you notice?