Measuring Volume 40- to 1-2 50-minute sessions ACTIVITY OVERVIEW I N V E S T 8 I O N I G AT Students develop an understanding of volume by working with six different objects. They calculate the volume of these objects by using either measurement and calculation or the water-displacement method. KEY CONCEPTS AND PROCESS SKILLS (with correlation to NSE 5 8 Content Standards) 1. Measurements and mathematics are important in all aspects of scientific inquiry. (Inquiry: 1, 2) 2. Scientists use common units of measurement to collect data. This system is known as the metric or international system (SI). (Inquiry: 2) KEY VOCABULARY cubic centimeters (cm 3 ) liter (L) metric system milliliter (ml) qualitative quantitative volume A-79
Activity 8 Measuring Volume MATERIALS AND ADVANCE PREPARATION For the teacher 1 metric ruler 1 light or dark gray bar 2 50-mL plastic graduated cylinders 1 pipette * tape * 1 permanent marker * 1 pan or beaker * supply of water 1 transparency of Student Sheet 8.1 b Using Two Methods to Measure Volume 1 Science Skills Transparency 1, Reading a Graduated Cylinder * various objects to demonstrate volume 1 Scoring Guide: UNDERSTANDING CONCEPTS (UC) For each group of four students 1 set of six metal objects in a plastic cup: 1 light gray cube 1 dark gray cube 1 light gray cylinder 1 dark gray cylinder 1 light gray bar 1 dark gray bar For each pair of students 1 pair of plastic forceps 1 50-mL graduated cylinder 1 pipette * 1 calculator * supply of water * paper towels For each student * 1 pair of goggles (recommended since identity of solids is not known) 1 metric ruler 1 Student Sheets 8.1a and 8.1b Two Methods to Measure Volume 1 Science Skills Student Sheet 1, Measuring Length (optional) 1 Science Skills Student Sheet 2, Measuring Volume (optional) 1 copy of Scoring Guide: UNDERSTANDING CONCEPTS (UC) (optional) *Not supplied in kit A-80
Measuring Volume Activity 8 Science Skills Student Sheets and Transparencies are in Teacher Resources II: Diverse Learners. In the first part of this activity, you will ask students to rank a series of objects based on their volume. Collect a variety of objects to use for this. These might include a capped 2-liter bottle of air, a 1-liter bottle of water, a sealed baggie or balloon filled with air, a beaker half-filled with water and containing a few drops of food coloring, and several small and large solid objects. Use masking tape to label the eight cups that that you will use to distribute the solids with letters A to H. In each cup place a set of the six metal objects. At the end of the activity each group of students should return its set to its original cup, so that students can use the same set in Activity 9, Measuring Mass, Calculating Density. Be sure the metal pieces are clean and dry before storing. If rust does appear, gently remove it with steel wool. SAFETY Ask students to suggest whether special precautions are necessary. After they read the procedure, they should recognize that they will be dealing with unknown solids. When working with unknown solids, students must wear goggles, minimize skin contact with the materials, and wash hands after completing the procedure. In this activity the metals are iron and aluminum, but students won t determine this until later. Until then, they should assume that the materials are hazardous and use forceps to handle them. TEACHING SUMMARY Getting Started 1. Introduce the concept of volume. Doing the Activity 2. (MATHEMATICS) Demonstrate how to use two methods to determine the volume of a bar. 3. (MATHEMATICS) Students determine the volumes of the cubes and the cylinders. Follow-Up 4. (UC ASSESSMENT) Review the methods for determining volume, and revisit students initial volume predictions. A-81
Activity 8 Measuring Volume TEACHING SUGGESTIONS GETTING STARTED 1. Introduce the concept of volume. Begin class by displaying the objects you collected, as suggested in Advance Preparation. Tell students that each object takes up a different amount of space and that scientists would say that each object has a different volume. Ask students, How would you arrange these objects from the least to the greatest volume? You might want to create small signs that say least volume and greatest volume. Ask students to discuss this in pairs. You might also ask them to write their predictions in their notebooks. Discuss their answers as a class. If you have an open container partially filled with liquid, students may ask if they should consider the volume the entire container can hold or the amount of liquid in the container. This is a good question that you should discuss with the class. It can be either, but everyone should agree on which to use for comparison. Students may also have concerns that gases, such as air or helium, do not take up space and don t have volume. Point out that the filled plastic bag or balloon does not collapse; the gas inside is taking up space. Depending on the objects you have chosen, there may be some disagreement about the order of the objects. Ask students how you should resolve the disagreements. They are likely to suggest measuring them. Refer to the table, Units of Measurement, in the Student Book. Explain that in the metric system used by scientists volume is measured in liters (L) or related units, such as milliliters (ml), one of which is equal to one one-thousandth of a liter. If appropriate, explain that a liter is equivalent to the volume of a cube 10 cm x 10 cm x 10 cm, or 1,000 cm 3. Thus 1 cm 3 is equal to one thousandth of a liter, or 1 ml. This equivalency, 1 cm 3 = 1 ml, will be important when students use two different methods to calculate density. You might further explain that in the metric system length is measured in meters (m) or fractions or multiples of a meter, such as centimeters (cm) or kilometers (km). You can use the optional Science Skills Student Sheet 1, Measuring Length, and Science Skills Student Sheet 2, Measuring Volume, to introduce or review these measurements. Read the introduction and Challenge for the activity with the class, and emphasize that students are learning about volume measurements in preparation for determining the density of their solids. DOING THE ACTIVIT Y 2. (MATHEMATICS) Demonstrate how to use two methods to determine the volume of a bar. Tell students there are two methods to determine the volume of a solid object. They will learn both and then will use their judgment to decide which method is the most appropriate to use for measuring a particular object. The first method you will demonstrate is measurement and calculation. Display and name each of the three kinds of objects students will measure in this activity a cube, a cylinder, and a bar. Check in advance whether students know how to calculate the volume of these objects. These volume calculations are commonly introduced in late elementary or early middle school. Review or explain that the formula for determining the volume of a cube or bar is l x w x h, where l = length, w = width, and h = height. For a cylinder it is πr 2 h, where r = radius and h= height. These formulas are given on Student Sheet 8.1a, Using Two Methods to Measure Volume, for students to use when needed. Demonstrate the methods for determining volume with a bar. Model how to use the ruler to measure length (l), width, (w), and height (h). You can have students use optional Student Skill Sheet 1, Measuring Length, if necessary, to review how to read a metric ruler. Use a transparency of the table to show students how to record their data on Student Sheet 8.1b Two Methods to Measure Volume. Then have them choose a formula to calculate the prism s volume; A-82
Measuring Volume Activity 8 they should choose v = l x w x h. The result should come out to about 8 cm 3. Remind them that for a cylinder the formula is v = πr 2 h. Also tell them that it might be easiest for them to measure the diameter of the cylinder and divide it by 2 to get the radius. Stress that the measurement-and-calculation method only works for objects that have these regular shapes. Use an irregular object such as a large stone or small rock to demonstrate that it isn t possible to get consistent measurements of height and either length, width, or radius for this irregular object. Next, demonstrate how to determine volume using the water-displacement method. Fill a graduated cylinder completely to the top with water. Place the graduated cylinder in a small pan or in a beaker. Ask students to predict what will happen when you put an object, like one of the bars, into the cylinder. Remind them that they know from their calculations that the volume of the prism is about 8 cm 3, and ask them how much water they think will spill out of the cylinder. Measure it with a second graduated cylinder and demonstrate that it is 8 ml. Remind them that 1 ml equals 1 cm 3. Thus the volume determined by water displacement is the same as the volume of the prism determined by calculations, with slight differences possible due to measurement errors. The prism displaced a volume of water equal to its own volume. Tell students that instead of allowing water to spill over into another container, they will measure the initial volume (v i ) and then the final volume (v f ) of water in a graduated cylinder that is partially filled and then determine the difference. Use Science Skills Transparency 1, Reading a Graduated Cylinder, to introduce how to read a graduated cylinder. Demonstrate this method with the same prism. Show them how to read the graduated cylinder by moving either himself or herself or the cylinder so that their eyes are level with the surface of the water in the cylinder. Show how the meniscus, the curved surface at the top of a column of liquid, can skew the reading of the amount present in the graduate. They can use the pipette to add or remove small amounts of water so that they begin with a convenient initial volume. 3. Students determine the volumes of the cubes and the cylinders Each pair of students should determine the volume of one bar, one cube, and one cylinder, and then exchange objects with the other half of their group. If they begin with the bar, they can verify whether they get the same results as you did in the demonstration. They should record their data on Student Sheet 8.1b. Students may choose to use either measurement and calculation or the water-displacement method to determine the volume of the cylinder. The cubes, however, will not fit into the graduated cylinder, so students will have to use the measurement-and-calculation method. If they have time to do both methods for the bars and cylinders, encourage them to do so. There should be enough space to fit both methods into their data tables, as shown in the sample answers. Students should use their data to complete volume calculations for each object. Once they have measurements for all six objects, they should compare their answers with those of the other pair in their group. Ask, Were there any differences in your results for the volumes of the different objects? What do you think caused them? Student answers should indicate that error in measurements, such as reading the ruler or graduated cylinder incorrectly, added to inaccuracy in their data. Calculation errors would add another possible source of error. The actual measurements for each of the three shapes are: 2.5 cm on each side for the cubes, and 1.2 cm x 1.2 cm x 5 cm for the bars, and 1.2 cm x 5 cm for the cylinders. Students measurements, however, are likely to vary slightly from the exact measurements, as shown in the sample answers on the following page. A-83
Activity 8 Measuring Volume Sample Results Student Sheet 8.1b, Two Methods to Measure Volume Object Method Used Measurements Formula and Calculations Volume Light gray bar Measurement and calculation 1.2 cm x 1.2 cm x 5.0 cm V = l x w x h = 1.2 cm x 1.2 cm x 5 cm = 7.2 cm 3 7.2 cm 3 Displacement v i = 30 ml, v f = 38 ml V = v f - v i = 38 ml 30 ml = 8 ml 8 ml Dark gray bar Measurement and calculation 1.3 cm x 1.3 cm x 5.0 cm V = l x w x h = 1.3 cm x 1.3 cm x 5 cm = 8.5 cm 3 8.5 cm 3 Displacement v i = 30 ml, v f = 38 ml V = v f - v i = 38 ml 30 ml = 8 ml 8 ml Light gray cube Measurement and calculation 2.5 cm x 2.5 cm x 2.5 cm V = l x w x h = 2.5 cm x 2.5 cm x 2.5 cm = 15.6 cm 3 15.6 cm 3 Dark gray cube Measurement and calculation 2.5 cm x 2.5 cm x 2.5 cm V = l x w x h = 2.5 cm x 2.5 cm x 2.5 cm = 15.6 cm 3 15.6 cm 3 Light gray cylinder Measurement and calculation d = 1.2 cm V = πr 2 h = 3.14 x (0.6 cm)2 x 5.0 cm 5.7 cm 3 (r = 0.6 cm) = 3.14 x 0.36 cm2 x 5.0 cm = 5.7 cm 3 h = 5.0 cm Displacement v i = 30 ml, v f = 36 ml 6 ml Dark gray cylinder Measurement and calculation d = 1.3 cm V = πr 2 h = 3.14 x (0.65 cm)2 x 5.0 cm 6.6 cm 3 (r = 0.6 cm) = 3.14 x 0.42 cm2 x 5.0 cm = 6.6 cm 3 h = 5.0 cm Displacement v i = 30 ml, v f = 37 ml 7 ml Note: For objects where two methods are shown separated by a dotted line, student may choose either method to measure volume. The cubes will not fit in the 50 ml graduated cylinder, so measurement and calculation is the recommended strategy to determine their volume. A-84
Measuring Volume Activity 8 FOLLOW-UP 4. (UC ASSESSMENT) Review the methods for determining volume and revisit students initial volume predictions. Have students compare their predicted ranking of the objects volumes with their final ranking based on their measurements. Emphasize the advantages of the quantitative observations using measurements over the qualitative observations made without measurements. Students may find that their measurements contradict some of their qualitative impressions. Even those students who ranked the order of the objects volumes correctly now have more information about the objects volumes. Their final ranking of the volumes should be: least volume most volume cylinders bars cubes Use Analysis Question 1 to emphasize that either method will work for the cylinders and the bars, so their choices depended on which method they preferred, or which they perceived as more accurate. However, the cube did not fit in the graduated cylinders, so measurement and calculation was the only method that worked. Make sure students understand that water displacement could be used for the cubes if they had the right equipment, such as a beaker and overflow container or a wider graduated cylinder. You may also want to discuss the fact that the measuring with the ruler and calculating method gives a result to the nearest 0.1 cm 3, while the water-displacement method is only accurate to the nearest 1 cm 3 (or ml). If students make their length measurements carefully, the volumes calculated from this method are likely to be more accurate than the ones done by the water-displacement method. Analysis Question 3 requires that students know the relationships of liters, milliliters, and cubic centimeters. They will need to know that 1 ml is equal to 1 cm 3. Analysis Question 4 is a quick check opportunity to ensure that students understand how to determine the volume of liquids and of regularly and irregularly shaped solids. When discussing the case of the child s wooden block, explain that if the object floats, it can be submerged by pushing on it with a pencil or similar instrument until it is just beneath the water s surface. The volume of water plus the object can then be read from the side of the graduated cylinder. Use additional examples to make sure students understand when each method of measuring volume is appropriate. You may use the UNDERSTANDING CONCEPTS (UC) Scoring Guide with Analysis Question 6 to assess students ability to provide simple examples to explain volume. Additional examples might include comparisons of large and small boxes of cereal, large and small rooms in a house, or different sizes of balls, such as baseballs and soccer balls. Look for examples that refer to the amount of space objects takes up, rather than their masses. SUGGESTED ANSWERS TO QUESTIONS 1. Choose one of the objects from Student Sheet 8.1b. Which method water displacement or measurement-and-calculation did you use to determine its volume? Explain why you chose that method. Answers will vary but should include an appropriate method for the object. The explanations are likely to focus on convenience, their comfort with using the rulers or graduated cylinders, their comfort with using calculations, and their perceptions of which will give the best answer. 2. Look at the way you ordered the objects by volume in Step 3. Compare this with the measured volumes you recorded in your notebook in Step 10. Were they the same? Explain. Students answers will vary. A correct answer will contain information from both Procedure Steps 3 and 10. A-85
Activity 8 Measuring Volume 3. Copy the three lists of measurements shown below. Pay close attention to the units that follow each number. List 1 List 2 List 3 150 ml 2 ml 1 L 11 ml 801 ml 999 ml 200 ml 27 cm3 998 cm3 a. Cross out the smallest volume in each list. b. Circle the largest volume in each list. 4. How would you measure the volume of: a. a cardboard shoebox? Use a ruler to measure its length, width, and height in a single unit, such as centimeters. Multiply the three numbers to get its volume. b. a plastic pen? Fill a graduated cylinder with enough water to cover the pen and measure the amount of water in the cylinder. Drop the pen into the cylinder. Measure the final volume of the water and then subtract the initial volume of the water to get the volume of the pen. c. an irregularly shaped stone? Water displacement is the best method for an irregular object. d. a child s large wooden building block? Either method will work. If the block is made of wood it might float, so measurement of the dimensions and calculation is probably easier. e. some orange juice? Pour it into a graduated cylinder (or beaker, etc) and read its volume. f. the two unidentified solids from your mixture? One of the solids has an irregular shape, so we need to use the water displacement method. The other solid has a cylindrical shape, so we can either use water displacement or calculate the volume by measuring the radius and height and using the formula v = πr 2 h. 5. In this activity, you were working with unidentified materials. Explain the safety steps you took when working with the solids. Students answers should include using goggles, minimizing skin contact with solids by using forceps, and washing hands after the activity is completed. 6. (UC ASSESSMENT) How would you explain volume to a 10-year-old? Include at least two examples that would be familiar to a child and that would clarify your explanation. Include a diagram to help you explain your ideas. Level 3 Response Volume is a measurement of how much space something takes up. One example is a balloon. If I leave it empty and tie it, it is very small. If I blow it up part way and close it, it has a greater volume. If I blow it up all the way, it has an even greater volume and it takes up a lot more space than the empty or part-full balloon. Another example is when you go to a store to buy a soda. They ask if you want a small, medium, or large (1). The large has the greatest volume of soda, and it takes up more space, so you need a bigger cup to hold it. If you try to pour your large soda into a small cup, it won t fit (2 and 3). The volume of the soda is too much for the small cup. (1) (2) Small Medium Large Large cup (3) Small cup Large cup Small cup A-86
Name Date Two Methods to Measure Volume Record the letter of your group s cup here: Predicted volume ranking from least to greatest: Final volume ranking from least to greatest: MEASUREMENT-AND-CALCULATION METHOD FOR DETERMINING VOLUME For a cube or a bar: height width CUBE length height width BAR length Measure length (l), width (w), and height (h) to the nearest 0.1 cm with your metric ruler. Then use the following formula to calculate volume: v = l x w x h For a cylinder: R diameter height Measure the height (h), and measure the diameter (d). Determine the radius (r) by dividing d by 2: r = d. Then use the following formula to calculate volume: 2 v = r 2 h 2007 The Regents of the University of California Water-Displacement Method for Determining Volume Add water to a graduated cylinder. Use a pipette, if necessary, to adjust the volume to a level that is easy to read. Record the initial water volume, v Initial. Then add the object to the graduated cylinder and record the final water volume, v Final. Calculate the volume of the object by subtracting, as shown below: v = v Final v Initial Issues and Physical Science Student Sheet 8.1a A-87
Name Date Two Methods to Measure Volume (cont.) Object Method Used Measurements Formula and Calculations Volume Light gray bar Dark gray bar Light gray cube Dark gray cube Light gray cylinder Dark gray cylinder 2007 The Regents of the University of California Issues and Physical Science Student Sheet 8.1b A-89