Have students compare different sizes of containers to figure out which ones hold more liquid. This introduces the concept of volume in a hands-on way. Give students a wide variety of containers, including some that are short and wide and others that are tall and thin. Have students pour measured amounts of water into different containers and sort the containers according to how much water they hold.
Roll something with known measurements, such as a sheet of paper, into the shape of a cylinder. Roll another sheet of paper into a cylinder with different dimensions. Have students use the formula for volume of a cylinder (V= area of base x height) to calculate and compare the volume of each paper cylinder. Have students cut and fold sheets of paper into cubes and find the volume of the cubes compared to that of the cylinders.
Have students cut out a variety of geometric shapes and glue them to a sheet of paper. They can cut circles, triangles, squares and other polygons. Use a calculator and the correct formula to figure out the area of each shape. Have students draw their own shapes and figure out the area of each shape. Students can draw regular or irregular shapes and calculate the area of each shape. This project is a bit easier if students draw their shapes on graph paper since it makes it easier to keep the sides of the shapes even.
For a larger project, give students a tape measure and have them try to figure out the area and volume of the classroom. If the classroom is a regular square or rectangular the most difficult part of this assignment is getting the measurements. If the classroom is an irregular shape then figuring out the area and volume can be more difficult but with careful measuring your students should be able to do it.