Teacher Guide. V= r 2 (h) V=lwh
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1 Log Truck Math Authors: Erika Pitman & Shirley Webb Grade Level: 7 th & 8 th Written as part of the BITL IV grant funded by the Officer of the Commissioner of Higher Education in Montana Abstract: The purpose of this activity is to introduce the concept of volume and compare the volumes of a cylinder and a rectangular prism. In Western Montana, logging trucks are a common site on the highways. Though trees aren t perfect cylinders, being able to see the real life shape will help a student to visualize volume. Students will be able to compute the cubic feet of one log depending on it s diameter and length. Then, the students can add their calculations to find the total cubic feet of the log load. Students can compare this calculation to the volume of a log truck trailer 8 x8 x36 (approx). Objectives: Students will determine the total cubic feet of a "standard load of logs" on a logging truck Students will understand how logs could be modeled by cylinders Students will demonstrate relationships between formulas and procedures for determining volume MT Content Standards: Content Standard 1 - Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications. Content Standard 2 - Students demonstrate understanding of and an ability to use numbers and operations. Content Standard 5 - Students demonstrate understanding of measurable attributes and an ability to use measurement processes. Materials: Pencil, Calculator, standard/metric conversion table (if necessary), log load picture, optional student practice worksheet Time Req d: One 50 minute class period
2 Teacher Guide If at all possible, try to arrange to have a logging truck driver come to your school with a load of logs. The students could then count the logs on the truck, measure lengths and diameters and estimate the total cubic feet of the load. This would give the students a great visual! Another idea would be to take a picture of a load from the rear. You could then print out 8 x10 pictures for each student and they could write the diameters on the ends of the logs. You would need to give them a length to go by. On a long load truck, the standard length of a log is 33 feet. You may even be able to get lengths for a short load truck and even lengths for pup trailers. There are many different ways to haul logs to mills and this can turn into a terrific discussion for the class. Introduction: -Show a picture (one you have taken or one from the internet) of a load of logs to the students. -Tell your students that they will be learning to calculate volume. They should already know what the term volume means the space inside a 3-D object. They should also know what a cylinder and rectangular prism are. Have a short discussion on these terms. Ask your students if they recognize any of these shapes around the classroom or outside. -Ask if any of your students know the formula to find volume. Many have probably seen it, but haven t had much experience and will need to be reminded. To find the volume of a cylinder: V= r 2 (h) To find the volume of a rectangular prism: V=lwh -In this case, the height (h) is the length of the log. -Students may need to be reminded that the diameter is given in inches and the length is in feet so they will have to convert the inches to feet. (for example: 10 in is 5/6 ft ) -You could start the students out with some simple calculations. V= A pop can is 5 tall and is 2 in diameter. V= (1 2 )(5) = (5) in 3 -Now, give them each a picture of the log load that you took. Have them write the diameters and lengths on the ends of the logs (these measurements can be made up by the teacher). You can give them different diameters and lengths or have them assume that all the logs are the same diameter (use 10in) and length (use 33ft). Giving them different measurements for each log will be more challenging and may be more real. -First have your students find the volume of the trailer. This may be hard to visualize for some students because the trailer is open. So a model of a rectangular prism may need to be drawn on the board for the students. The normal bunks on a long log trailer are 8ft
3 wide, 8ft high, and can haul logs up to approximately 33 feet. Use the same length that you will give them for the log length in the above step of writing on the picture (33ft). -Having the students compute the volume of the rectangular prism will allow them to compare the calculations to the actual log load cubic feet. The students will be able to see that logs are round and cannot use up all the space in the trailer. There will be wasted space. How much wasted space is there? This can be found if you compare the calculations. -Now have your students find the total cubic feet of the log load. They will need to find the volume of each log and add the measurements together for the total cubic feet. -The students should now be ready to view an actual load of logs and start measuring! (This step is only possible if you were able to arrange for a load to come to your school) The student worksheet can be given once the students are comfortable with the calculations or can be given as a homework assignment.
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5 Optional Student Practice Name: Date: 1. Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. How many cubic inches of soda are contained in a full can? (Round answer to the nearest tenth of a cubic inch.) cubic inches of soda 2. Pringles Potato Chips come in a can shaped like a. If the can measures 10 inches in height 2.5 inches in diameter, how many cubic inches are contained in the can? Cylinder, cubic inches 3. Jacob brought a Tupperware to school for his soup. The Tupperware is 16cm in height, 16cm in width, and 16cm in length. How many cubic inches of soup can Jacob pour into his Tupperware container? 16cm = 6.24 in, so 6.24x6.24x6.24= cubic inches
6 4. Hailey has purchased a new water tank. It will be used to water her horses. It is a cylinder shaped metal container that is 2.6 feet tall. The area of the bottom of the tank is 9.3 square feet. How many cubic feet of water can the tank hold? cubic feet of water 5. If the horses drink 204 cubic feet of water a day, how many times per day will the tank have to be filled? 8.44 times, so Hailey should fill her tank 9 times!!! 6. Should Hailey buy a bigger tank? UH HUH!!! 7. Luke has a secret drawer hidden in his closet. The inside dimensions of the drawer are 2 ft long, 18 inches deep, and is 8 inches tall. Luke fills the drawer with boxes of candy. If one box of candy measures 1.5 inches in height, 1.5 inches wide, and 4 inches long, How many boxes of candy could Luke store in his drawer? 384 boxes!!!!
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