The Square Garden Problem

This is the problem we have been working on in math:

You have been asked to design square garden plots for the Richmond Botanical Garden. They have requested that each garden has a square area in the center for plants. Around each garden is a border of tiles so that people can walk around to enjoy the beautiful flowers. Follow the pattern and find the designs for garden plots #4 and #5. You should use pictures to show your designs. How did you know what Garden Plot #4 looked like? After drawing the designs you should use words and numbers to explain the patterns that you notice.  Be specific so that someone else can understand the specific patterns that you noticed.

Some of the patterns we found include:

Do you see any other patterns that we missed?

Some of us are continuing the pattern much further - even on to the 50th garden plot! Because we know the patterns for the inside and outside we don't have to draw them each time. This makes the process much more efficient. We have found that looking for a pattern in math often makes things much easier to solve.