Ideas for Teaching Students About Surface Area in the Classroom
The best ideas for teaching surface area entail physical manipulatives that students can use to experience the concept of surface area for themselves. You can make your own surface area manipulatives for students to play with. Just use boxes and containers of different shapes, such as a cylindrical container of breadcrumbs, a pasta box, and a Toblerone package. Cut each of them along just a few edges so that they stay together but can be unfolded to show the different surfaces that make them up. For example, students will be able to see that the breadcrumb can is actually made up of two circles connected by a rectangle. Encourage students to calculate the actual surface area of each container, and then ask them to figure out what would happen if one variable, such as the height of the breadcrumb can or even its diameter, would change. In this way, students will figure out how each variable affects the final answer.
This type of discovery learning will help students actually engage in their learning, rather than simply listening to instruction. Once students have discovered how to calculate each shape's surface area, they will be able to apply what they have learned to other, similar shapes. They will also learn how to manipulate objects in their minds, visualizing each of the surfaces that make up the complete shape.
Sure, it might be simple for your students to simply memorize various equations for the surface area of cylinders and other objects, but this idea for teaching surface area will force them to truly think about what the term means. Instruct each student to stack a certain number of identical one-inch square blocks to make a particular formation, and then have them swap formations with a partner. The student who receives the formation needs to figure out what its surface area would be without actually measuring anything. If you'd like, you can create the block formations and have a group of students tackle each one to figure out its surface area. They can circulate from one formation to the next, writing down what they think is the surface area of each formation. When all of the groups finish, they can compare their answers and discuss any differences that they find.
The Wrapping Paper Project
These first two ideas for teaching surface area may seem contrived to many students. They may think, "Who cares about the surface area of a block tower?" To make the concept more applicable, try giving groups of students a given amount of wrapping paper and asking them how many square blocks they think they can cover with the amount of wrapping paper that they have. (They will have to tape the paper directly to the block, without any overlap.) Then ask them how many presents of various shapes and sizes (e.g., a box of puzzle pieces, a can of plastic monkeys, a round ball) they can wrap with the given amount of paper and let them test it out. This gives them a concrete activity in which surface area actually matters.