Math in Our World: Scratch Art

Paco colored paper 12 inches long by 8 inches wide. 1 fourth is divided into 4 triangles. 2 triangles are green and make 1 big triangle. The smaller triangles are orange and blue. 2 of the fourths are divided into 3 rectangles each. The rectangles in 1 set are vertical. The rectangles in the other set are horizontal. In both sets, the yellow rectangle is twice as big as the purple and red rectangles. The last fourth is all orange.
Paco scratched off bits of black paint in the shape of a tree. The colors below the paint show through.

Paco loves to create. He made this scratch art. First he folded a piece of paper into fourths. After unfolding, he colored every bit of the paper with crayons. Then he painted over the colors with black acrylic paint.

After the paint dried, Paco began to scratch this tree. He is still scratching leaves!

  1. What do you notice? What do you wonder?
  2. Use pictures, models, or numbers to describe this situation.
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!
  • Create a sketch that shows the crayon layer. What fraction does each part represent? How do you know?
  • How much of the paper is covered with each color?
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer!

Fold a piece of paper into fractional parts. Use 4 or more colors to cover the paper. (Make sure to completely and heavily cover the paper with color.) What fractional part did you cover with each color?

If you have acrylic or tempera paint, you can cover your crayon layer with black paint and make your own scratch art.