A good way to teach ratios and proportions is to show students the practical applications of these mathematical concepts, which include the fields of sports, art, architecture and many other design fields. By showing students how they will actually use these principles in their non-school lives, they will likely pay more attention to the concepts and gain a better understanding of how to apply them.
Have two students come to the front of the class. Give one a regulation-size baseball bat. Give the other a souvenir miniature baseball bat. Have both students hold the bats in a baseball stance. Ask students why the student with the small bat provokes laughter. (Answer: his bat is out of proportion.) Have students measure the two bats and take an average of the two students' height. Have them figure out how tall a person would need to be in order to be in proportion to the miniature bat.
The Shadow Knows
Explain to students that shadows are in proportion to an object's height. Outdoors, have students measure the height of one student, then measure the height of his or her shadow. Have them write the two numbers as a ratio, with the student's height in inches separated from the length of the shadow in inches by a colon. Explain that the ratio can also be written as a fraction. Have students measure the shadow of a tree. Using the ratio they have already discovered, have them calculate the height of the tree.
The Golden Rectangle
Explain that a famous ratio or proportion in mathematics and art is the Golden Rectangle, also known as the Golden Mean, Divine Section, Golden Cut and Golden Proportion. The ratio of the rectangle's width to length is 1:1.6. The ancient Greeks believed that this proportion was most pleasing to the eye. Using the 1:1.6 proportion, have students cut a golden rectangle out of a standard size sheet of copy paper. Show a picture of the Pyramid of Giza. Point out that at 481 feet tall and 756 feet wide, it fits almost perfectly inside a Golden Rectangle.
Floor Plan of Classroom to Scale
Explain to students that architects use ratios and proportions when they design buildings. Blueprints, or designs for buildings and houses, are drawn to scale, often with 1/4 inch equaling 1 foot. (Display blueprints if you have some.) Have students create a floor plan of your classroom in the scale of 1/4 inch equaling 1 foot. Provide 1/4-inch graph paper and tape measures. Students will first want to measure the dimensions of the room, then measure the objects in the room before transferring them to their floor plans.