Design your own pattern make of dots or toothpicks.

1. Draw the first three figures of your pattern.

   Hint (a):

   Everyone's dots will look different, but make sure there is a pattern. Sharon's first three figures are below.

   

2. Show how you can predict how many tiles or toothpicks will be in the 30^th figure.

   Hint (b):

   For each figure of Sharon's pattern, there are $1+ 3x$ dots, where $x$ is the figure number.
   In the 30th Figure, there are $91$ dots, since $1+3\left(30\right) = 91$.
   Try writing a similar expression for the number of dots in your pattern.