Measurement. Sizing Up the Cube. Activity:

Transcription

1 Measurement Activity: TEKS: Sizing Up the Cube (4.11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass. The student is expected to: (A) estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary; (C) use concrete models of standard cubic units to measure volume; (D) estimate volume in cubic units; Note: Portions of this lesson address TEKS at other grade levels as well; however, the intent of the lesson fits most appropriately at the grade level indicated. Overview: Materials: Grouping: Time: Students will reinforce their knowledge of attributes of the centimeter cube and meter cube, then use that knowledge to construct a decimeter cube. Next, the relationship between volume and capacity will be investigated in a hands-on setting using models for the cubic centimeter and cubic decimeter. Centimeter cubes Model for cubic meter (see Skeletons in the Closet lesson) Meter stick, 1 per group Centimeter grid paper on cardstock, at least 4 sheets per group Scissors, 1 pair per person Tape, 1 roll per group Plastic decimeter cube model (with masking tape over the labels), 1 per group 1-liter water bottle, 1 per group Paper towels Beach towel for each table to absorb any spills Graduated cylinder set, 1 per group Dishpan, 1 per group Sizing Up the Cube Recording Sheet Groups of 2 students each minutes Lesson: Sizing Up the Cube Page 1

2 1. Ask students to recall the attributes of a centimeter cube. 12 edges with length of 1 centimeter each 6 faces with area of 1 square centimeter each 1 cube with volume of 1 cubic centimeter 2. Next, ask students to recall the attributes of the model for a cubic meter (see Skeletons in the Closet lesson). 12 edges with length of 1 meter each 6 faces with area of 1 square meter each 1 cube with volume of 1 cubic meter 3. Give each group a meter stick. Since the metric system is based on a foundation of powers of ten, when we get ten of a unit, we can bundle those ten units and call it one of the next larger size unit. Consider the attribute of length. When we have 10 centimeters, what unit do we have? A decimeter What are some benchmarks to help us remember the length of a decimeter? Width of palm, cd jewel case, base-ten long, etc. 4. Give each group several sheets of centimeter grid paper on cardstock. Ask them how many square decimeters they can get out of one sheet of centimeter grid paper. Have each group cut out a square decimeter from the centimeter grid paper. What are some attributes for this square decimeter? Length and width of the square is 1 decimeter each (or 10 centimeters each) Remember to be cautious when copying grid paper on the copy machine. The copy machine may distort the grid measurements. Printing grid paper directly from the websites referenced in the Materials List works well; however, be sure to turn the scale to fit page feature off before printing. Sizing Up the Cube Page 2

3 Area is 1 square decimeter (or 100 square centimeters) 5. What attributes would a decimeter cube possess? 12 edges with length of 1 decimeter each 6 faces with area of 1 square decimeter each 1 cube with volume of 1 cubic decimeter 6. Have each group cut out 5 additional squares that measure 1 decimeter by 1 decimeter. Lay them out (grid side down) on the table and tape together while flat to form a net for a cube. One possible arrangement of squares to form a net for a cube is as follows: Remind students that a net for a cube is an arrangement of squares that would fold up to make a cube. Fold the net into a cube and tape it closed. Each group will make 1 decimeter cube. 7. How many cubic centimeters will fit inside the cubic decimeter? 1000 cubic centimeters will fit inside the cubic decimeter What attribute are we measuring when we find the number of cubic centimeters that will fit inside the cubic decimeter? We are finding the volume of the cube Use a base-ten long to frame the length, width, and height on the outside of the plastic decimeter cube model to show 10 cm 10 cm 10 cm = 1000 cubic cm So we have alluded to two different ways to express the volume of the decimeter cube What are they? The volume of the decimeter cube is 1 cubic decimeter or 1000 cubic centimeters. Sizing Up the Cube Page 3

4 8. Give each group a plastic decimeter cube model (with masking tape over the labels) and a bag of centimeter cubes. Ask each group to make an estimate for how much water the decimeter cube will hold. Then have each group check their estimate using the water from the water bottles. Students should pour into the graduated cylinder, read the measurement, then transfer the water into the decimeter cube, keeping track of how much water they have transferred. Repeat the process until the decimeter cube is full. Each group will have their own paper version for a reference, but the plastic model will be sturdier for the remainder of the investigation. Remind students to pour over the dishpans to catch any spills. 9. After the investigation. How much water did it take? It took 1000 milliliters of water to fill the decimeter cube. Is there another way to say 1000 milliliters using another metric unit? Yes.1000 milliliters is the same as 1 liter. 10. Think back to the previous lesson My Tub Runneth Over. Can you justify your answer that it took 1000 milliliters of water (or 1 liter of water) to fill the decimeter cube based on our results from that lesson? Yes in that lesson, we discovered that each centimeter cube (volume of 1 cubic centimeter) displaced 1 milliliter of water. So, if the decimeter cube will hold 1000 centimeter cubes (volume of 1000 cubic centimeters), then the 1000 centimeter cubes would have displaced 1000 milliliters (or 1 liter) of water. When students measure 1000 milliliters of water, they may or may not associate this amount of water with 1 liter. If they don t, refer them to the label on the water bottles. The water bottles were 1-liter water bottles, so this fact will help the students remember the conversion that 1000 milliliters = 1 liter. This thought process may have already come up during the prediction phase of the lesson. If so, then just use this time to reinforce what we have discovered. Sizing Up the Cube Page 4

5 11. Now we want to reconnect the ideas of capacity and volume from the beginning of this series of lessons. What is volume? Volume is the amount of space that a solid object occupies. If the object is hollow, then the volume of the object is the amount of space that is enclosed by its outer boundary. What is capacity? The capacity of a container refers to the amount of space in the container that could be filled with dry, pourable material or with liquid. This material is referenced in the Background Section in the Full to Capacity lesson. See Tierney, Singer, Kliman, & Murray, (1998) and Encyclopedia Britannica Educational Corporation (1998). How are volume and capacity related? Since capacity is a description of the maximum amount of material a container can hold, capacity refers to the maximum volume of the container. What are some typical units for measuring volume? Typical units for measuring volume are cubic centimeters and cubic meters in the metric system, or cubic inches and cubic feet in the customary system. This lesson has dealt with the volume unit of a cubic decimeter in the metric system. What are some typically units for measuring capacity? Liters and milliliters are standard capacity units in the metric system, whereas ounces, cups, pints, quarts, and gallons are standard capacity units in the customary system. Both capacity and volume refer to the amount of space that is being occupied by an object. So, we can describe the amount of space being occupied using cubic units or using capacity units. Sizing Up the Cube Page 5

6 12. Let s summarize the relationships we have discovered between volume and capacity on the Sizing Up the Cube Recording Sheet. Give groups a few minutes to complete the chart, then go over the chart as a large group. It is possible that someone may reply that 1 cubic centimeter = 1 milliliter = 1 gram. This relationship is true IF the substance is water under certain conditions. The relationship of 1 cubic centimeter = 1 milliliter is true for any fluid, not just water. Assessment: Extensions: Resources: Assessment is done through questioning throughout the lesson. In addition, the summary on Sizing Up the Cube Recording Sheet serves as a summative assessment at the end of the lesson. Students could determine the volume and capacity of other units such as the cubic meter. Littleton, P. & Jackson, R. (1995). The Incredible Cube. TEXTEAMS 3-5 Institute. Austin, TX: Texas Teachers Empowered for Achievement in Mathematics and Science (TEXTEAMS). Encyclopedia Britannica Educational Corporation. (1998). Math in context: Made to measure. Chicago: Author. Tierney, C., Singer, M., Kliman, M., & Murray, M. (1998). Investigations in number, data and space: 5 th -grade measurement benchmarks: Estimating and measuring. Menlo Park, CA: Dale Seymour Publications. Sizing Up the Cube Page 6

7 Sizing Up the Cube Recording Sheet Attribute Decimeter Cube Centimeter Cube Length of each edge on the cube Area of each face on the cube Volume of the cube Capacity of the cube Sizing Up the Cube Page 7