Incorporate angles into a science project such as building a bridge. Instruct students to write a scientific report detailing the proper procedure for measuring an angle with a protractor.
Teach students about angles while explaining perspective drawings in art class. Draw three-dimensional cubes and have students measure and mark the angles of the forms. Discuss how obtuse and acute angles affect the angle of the cube.
Research the use of catapults in medieval warfare. Discuss the main types of catapults such as trebuchets, ballistas and mangonels. Build model catapults with plastic spoons and popsicle-stick frames. Measure the angle of the spoon to the ground and determine how the angle relates to the distance projectiles travel.
Read a book about treasure hunting such as "Treasure Island," and then use the book as inspiration to make your own treasure maps of your classroom or the school. Describe the directions to the treasure in terms of angles and feet. For example, "Stand in the doorway and walk 5 feet, then turn 90 degrees to the south and walk another 10 feet."
Incorporate angles into a lesson about simple machines and the physics of work. Examine how the angle of your machine or pulling force changes the amount of work. For example, pulling a pulley straight down at a 0-degree angle places twice the force of the object's weight on the pulley from the object itself and your efforts to lift the object. The force on the pulley decreases as the angle between you and the pulley changes.
Have students make sand paintings using geometric shapes. Instruct students to exchange paintings randomly and describe the painting of another student in mathematical terms discussing specific shapes and angles.