In this activity, you will create a fractal pattern with straws. Select one straw and cut it so that the length is 27 cm (you may need to tape two straws together). Tape the straw lengthwise onto a sheet of paper. Label this Stage 0. For Stage 1, select another straw and cut it to a length of 27 cm. Divide this straw into 3 equal-length sections. Tape the straw to the paper directly under the Stage 0 straw. Remove the middle section. Label this Stage 1. For Stage 2, cut two straw sections that are the same length as each of the straw sections in Stage 1. Tape the straw sections directly under the sections for Stage 1. Divide each of the two sections into 3 equal-length sections and remove the middle section from each. Label this Stage 2.

Now, examine the lengths of the straws. On a separate sheet of paper, list the length of the straws for each stage of the fractal and answer the following questions.

1. What fraction can you multiply the length of Stage 0 by to get the total length of Stage 1?
2. What fraction can you multiply the length of Stage 1 by to get the total length of Stage 2?
3. Make a conjecture about finding the total length of straw for any stage. Use your conjecture to estimate the length of Stages 3, 4, and 5. Measure and cut straws to check your answer.