Look at the triangle you made in Step One. What fraction of the triangle did you NOT shade?
What fraction of the triangle in Step Two is NOT shaded?
What fraction did you NOT shade in the Step Three triangle?
Do you see a pattern here? Use the pattern to predict the fraction of the triangle you would NOT shade in the Step Four Triangle. Confirm your prediction and explain.
CHALLENGE: Develop a formula so that you could calculate the fraction of the area which is NOT shaded for any step.
Write the fractions in the above questions in order from least to greatest. Write a statement about how their order connects to the shading out process.
Find another interesting pattern in the fractal called the Sierpinski Triangle. Write a paragraph descibing this pattern.
Math Questions On Sierpinski's Triangle