Liquid Volume Robert Foote Disney Magnet School 4140 N. Marine Drive Chicago IL 60613 (312) 534-5844 Objective: Students will learn and use formulas for the volume of a rectangular prism and volume of a cylinder. Students will see the relationship between cubic centimeters and milliliters. Students will compute formulas with and without calculators. This lesson is designed for a junior high classroom. Materials: Depending on how many students you will use for this project, the amount of materials vary. If you break students up into small groups, you should use one of each of these materials in each group. 1.Plastic graduated cylinder measuring milliliters 2. Different size cylindrical containers such as coffee cans, Pringles potato chip cans, cookie tins, and the like. (Make sure these are made of a durable material that can hold water without falling apart. Cardboard is not good.) 3. Different size rectangular prism containers such as plastic storage containers, tins, and the like. Make sure the base is either square or rectangular. 4. Water 5. Food dye (Optional) 6. Rulers or tape measures 7. Calculators (optional) Strategy: At the beginning of the class, go over the formulas for finding the volume of a rectangular prism; that is base times height or length times width times height. Explain that the basic formula (base times height) also applies to the volume of a cylinder, except that the base is now a circle so the formula for the base is Pi multiplied by radius squared. Then multiply the base times the height. Once students are comfortable using these formulas, take one of the smaller rectangular containers and have students measure the length, width and height in centimeters of the container using tape measures. (DO NOT TELL THEM HOW TO MEASURE. THIS WILL Lead TO INTERESTING DISCUSSION.) Once they have measured the sides, compute the volume. Your answer will be in cubic centimeters. This is the same as milliliters since there are 1000 cubic centimeters in a liter and 1000 milliliters in a liter. Once the volume is computed, measure the water in milliliters to see how it compares to the computed volume. If all is done correctly, you should have a close match. If the water overflows or the container is not completely full, a mistake was made. Elicit a discussion with your students to see why this happened. After showing how to do one to the class as a whole, then break up the class into groups and have them do two containers per group (One cylinder and one rectangular prism). After they have measured and calculated as a group the volume of their containers, let them check the volume with water. Observe as they measure and pour to determine accuracy of calculations and measurement. First calculate using the formula, then check using water. At the end of the class, discuss each of your findings and any problems you may have had. To more clearly see and measure the water used in this lesson, you may elect to use drops of food dye in the water. Performance Assessment: As a performance assessment for this lesson, give a child a container of each type to calculate the volume. Then have the child measure and pour the water into the containers to check his or her work. This lesson in itself is a performance assessment. Conclusions: Students should conclude in the end of this lesson that the formula for volume in cubic centimeters comes very close to the actual volume of the container in milliliters. They should also be able to detect what went wrong if a mistake occurs. References: The Only Math Book You’ll Ever Need by Stanley Kogelman, Ph. D. and Barbara R. Heller, M. A., 1993, revised edition, page 143.