Help your students take finding the area of a geometric shape one step further by teaching them to figure out the surface area of a cube. Teach them how to build a cube out of graph paper using a template. Once the cubes are glued together, the area of one side may be discovered by counting the number of squares it is in length and width. After multiplying those numbers to get the surface area of one side of the cube, the answer is multiplied by six to learn the total surface area of all six sides of the cube.
Using graph paper is an easy way to teach students to figure out the area of any shape. They can figure out the area of any shape, from a triangle to a circle and beyond, by drawing it on graph paper and counting the number of squares contained inside. This illustrates to students that while squares and rectangles are easy to figure area for with multiplication, the same principles apply to all shapes. They can then figure out what the area of the shape would be if the graph paper and the shape were enlarged or made smaller.
This is a fun activity that illustrates how the area of a circle can be drawn out into a much larger space. Bring a piece of 8- by 11-inch paper to class and cut the largest circle you can from. Cut a hole in the center of the circle, making a ring large enough to put your arm through. Ask your students if they believe that you can expand the surface area of the ring until you can fit one of them through it. Cut slits around the inner and outer rims of the ring, alternating starting on the outside with starting on the inside, stopping each cut 1/2-inch from the opposite edge. The ring will open into a large circle that a student, or even you, could step through. This is a good illustration of how different shapes can have the same area.
Prove to your students that the easiest way to figure out the area of a triangle is by knowing the area of a rectangle or square by providing them with rectangular and square pieces of construction paper and challenging them to cut the pieces into two equal triangles. Have them figure out the area of the square or rectangle first, then show them how the area of each triangle is exactly half the area of a triangle.