# Visual Patterns Problem 2

I was looking through Fawn’s site and was surprised that I didn’t see a Fibonacci Sequence anywhere.  I recently talked with my class about it so I decided to snap some pictures.

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

URL: visualpatterns.orgName: __________________ 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 had to show the fourth step because students first thought that it was an alternating pattern, 2-1, 2-1.  Some students even asked why there was a color change, they wanted to replace the green cubes with orange.  With my younger students, they had a hard time with determining the pattern until one student took the shapes and lined them up like this.

They then could see the pattern for the next steps, but struggled with the equation.  The coloring of the cubes showed them the pattern for constructing the next figure, but it impeded their ability to see a connection for the formula.  2, 2+1, 2+1+2, 2+1+3, …  was all they were focused on.  Once we swapped out the numbers so that the figures were all one color, they were able to start connecting the recursive property of the series.

What is the equation for this pattern?

How many blocks in the 43rd Step?

What patterns do you notice?