The Arch Villain Problem / The Straight and Narrow Problem. The Arch Villain Problem When the Arch Villain wreaks havoc on the city of Mathtropolis by turning everything into arches, Super Peg and Cat Guy come to the rescue. Primary Learning Goal: Arches, finding arches in other shapes. Secondary Learning Goal: Counting backwards from 9, counting by threes. / The Straight and Narrow Problem When the Arch Villain renounces arches and embraces the straight and narrow, shapes shift all over town and Super Peg and Cat Guy are back in action. Primary Learning Goal: Understanding straight, narrow, curved. Secondary Learning Goal: Counting sides to determine shapes (rectangles, triangles, squares), counting by tens to 100.