Show your students that there is no correlation between surface area and volume with two 12-by-18 pieces of heavy paper and bird seed. Make a tube out of each of the papers. One tube should be rolled "portrait" style and the other rolled "landscape" style. Tape the tubes, making sure not to overlap either of them. Place the longer tube inside the landscape tube. Stand up both of the tubes inside a plastic tub. Hold the tube securely and pour bird seed into the longer tube, filling it to the top. Remind the students that you used the same size paper for both tubes. Both tubes possess the same surface area. Ask the students to predict if the bird seed will fill up the landscape tube. Slowly pull the portrait tube up, spilling the bird seed from underneath into the landscape tube. The students will amazingly observe that the bird seed did not fill up the tube rolled an alternative way. Discuss the relationship, or lack of relationship, between surface area and volume.
Provide your students with opportunities to explore liquid volume. Place many different-sized containers on a counter. Instruct the students to place the containers in order from the container with the least volume to the container with the greatest volume. After they have them in their preferred order, ask them to fill up each container with water. The students should use a liter pitcher to fill up each container and record the amount of liquid each container holds. The students can make adjustments to their predictions and compare their volume lineup with the actual lineup.
Collect many different-sized boxes from your pantry for the students to explore volume. Pass out a box to each student. Identify the faces, edges and vertices of the boxes with your students. Ask the students to find the volume of their box by measuring the length, height and depth of their box. They can write the measurements on the box. To find the volume of the rectangular prism pantry boxes, multiply length x height x depth. Make sure that students use the same unit of measure for each measurement. The answer will be a cubic measurement, centimeters cubed. After the students have found the volume, ask them to trade boxes with a classmate to verify their calculations.
"Nets are two-dimensional patterns that you can fold into three-dimensional shapes," according to School Improvement in Maryland. Provide students with a selection of nets on a teacher-generated worksheet. Ask them to identify the rectangular prisms, cylinders, pyramids and triangular prisms by looking at the nets. If they cannot determine the outcome of the net, ask them to cut it out and tape it together. Provide a rectangular prism net with a volume of 24 centimeters cubed. The students should measure and record their measurements to verify that their net is 24 centimeters cubed. Ask the students to make the prism by cutting out the net and taping the edges together. Distribute centimeter cubes. The students should place the cubes inside the net. Twenty-four centimeter cubes fit neatly into the prism, which verifies their measurements.