Explain the purpose of the lesson to the class.
“In today’s lesson, we are going to measure the volumes of some irregularly-shaped objects using water displacement. First we must learn about the relationship between the measurement of volume in cubic centimeters and the measurement of liquids using liters and milliliters.”
Show a liter bottle to students. Show a container that holds one quart of liquid. (Be sure both containers are full of liquid.) Ask students to compare a liter and a quart. “Which do you think is larger, 1 liter or 1 quart?” Ask students to make their best guess.
Now pour the liquids from the liter bottle and the quart container into two identical clear containers. This is an important visual because it gives students an opportunity to identify just how similar these measurements are. (1 liter is approximately 1.0567 quarts, so a liter is slightly larger than a quart.)
Remind students that there are two different systems of measurement, the customary English system of measurement and the metric system of measurement. Most of the world uses the metric system of measurement. “The metric system is considered the international system of measurement. The United States is one of a few countries that predominantly use the customary English system. For this reason, products in stores in the United States are labeled with both systems of measurement. A quart is a unit of measurement from the customary English system; a liter is a unit of measurement from the metric system.
“Smaller units of liquid measure in the customary English system are pints, cups, tablespoons, and teaspoons. Smaller units of liquid measure in the metric system include milliliters, and we will learn about them today.”
Also explain that the metric system of measurement is based on the number 10 and uses prefixes. “The prefix ‘milli’ means one-thousandth. So a milliliter is one-thousandth of a liter. Another way to say this is 1000 milliliters equal one liter. So in one liter of bottled water, there are 1000 milliliters. The milliliter is an important unit in helping to understand the relationship between the measurement of volume in cubic centimeters and the measurement of liquids using liters and milliliters.”
“In previous lessons, we were using cubic centimeters to find the volume of rectangular prisms.” (Hold up a cubic centimeter to remind students.) “What needs to be true about a solid, however, if we are going to use this method to find the volume?” (The solid must be a rectangular prism, so that cubes can fill it exactly.) “As you might imagine, there are plenty of solids that are not rectangular prisms, or even right prisms, and yet we still need a way to determine the volume. To do so, we may use the method of water displacement in which we measure the volume of an object by determining the volume of water that fills it. This means we need to use a measure of liquid quantity, such as milliliters, instead of cubic centimeters.
“Now we will investigate how many milliliters are equivalent to one cubic centimeter. In other words, if we were able to fill up the cubic centimeter with water, how many milliliters would fit inside the cubic-centimeter block?”
The following displacement activity will show students the relationship between one cubic centimeter and one milliliter. “In a small group, follow the steps outlined on the Displacement Activity (Does 1 Cubic Centimeter = 1 Milliliter?) Guide” (M-5-1-3_Displacement Activity.doc).
Students will follow the procedure listed on the activity sheet:
- Fill the graduated cylinder halfway with water. You will notice that the water level does not go straight across. The water level is concave and is referred to as the meniscus. When you are reading the water level in a graduated cylinder, you want to be sure to read it in the center of the meniscus at eye level.
- Record the level of the water on the chart. The units are milliliters (mL). (Make sure the meniscus is exactly atop the intended milliliter mark, not between
two milliliter marks.)
- Carefully lower the centimeter cube into the graduated cylinder.
- Read the new water level. Be sure to view it at eye level.
- Record the new water level on the chart.
- Repeat steps 3−5 until you have established a pattern.
As students begin to see what happens to the water level after they place the centimeter cube in the water (the sides curve up), reinforce the correct manner to read the water level by looking at the center of the meniscus, or the concave surface of the water, at eye level.
While students are working, monitor their interactions and dialogue. Be sure students are reading the water level correctly. If a group’s results are not accurate, have them repeat the process while you guide the group and monitor their understanding. It is very important to monitor groups for accuracy while they evaluate the volume of a cubic centimeter and to ask groups to repeat the process if they did not determine the correct answer. This should rectify any misconceptions a group may have before going into the more in-depth activity of measuring the volume of different objects. Small-group work and student responses to questions can be used as informal assessments. Based on the Volume of Regularly and Irregularly Shaped Objects Observation Checklist, you can identify who is not proficient in determining the volume of regularly and irregularly shaped objects and provide them extra support.
Once most students are finished, bring the class together. Explain to students that this activity shows that objects will displace the amount of water equivalent to their volume. When an object is immersed in water, the water level will rise by an amount equivalent to the volume of the object. Have students share their results. Be sure students understand that one cubic centimeter is equivalent to one milliliter. “This method of finding volume is called the water displacement method.”
Remind students that an object will displace the amount of water equivalent to its volume. Their task during this part of the activity is to measure the volume of regularly and irregularly shaped objects. To do this, students will follow the same procedure as earlier. Now that students have some experience with volume using this method, have them estimate the volume before placing the objects into the water. Estimations will be recorded on the activity guide. Each object will be carefully placed into a graduated cylinder half filled with water. A water level reading is taken before the object is placed in the graduated cylinder, and a water-level reading is taken afterward. Once students understand their task, hand out the Volume of Objects Using Water Displacement sheet (M-5-1-3_Volume of Objects Using Water Displacement.docx). Explain to students that when measuring the lump of clay, they should use all the clay. When they complete the last row in the chart, the entire lump of clay should be reshaped.
While students are working, monitor their interactions and dialogue. Be sure students are reading the water level correctly by taking a reading at eye level. If students’ results are not accurate, have them repeat the activity while you monitor their procedure. A Volume of Regularly and Irregularly Shaped Objects Observation Checklist can be used to help record observations (M-5-1-3_Volume Observation Checklist.docx). Asking the following questions can help clarify students’ levels of understanding:
- “What are you measuring during this activity?” (volumes of regularly and irregularly shaped objects)
- “Why is it necessary to read the water level at eye level?” (The water level is concave, and it is important that you measure the water level at the center of the meniscus. Water adheres to the sides, and, if you read from that level, you will over calculate the volume.)
- “How does placing a regularly or irregularly shaped object in a graduated cylinder of water tell you the object’s volume?” (The amount of water an object displaces when placed in a container of water is equivalent to the object’s volume.)
- “How can you estimate the volume of an object before completing the displacement method? What if you wanted to estimate the volume of a sphere?” (If you know the volume of a similar object, you can estimate it based on that knowledge. If you measure an object’s height, width, and length, you can find an estimate of its volume. The estimate, however, would only be accurate if the object is a rectangular prism.)
- “What do you notice about your estimated volumes and the actual volumes of the objects?” (Answers will vary. Some may say their estimates are too high or too low. Encourage students to look at the actual volumes and make generalizations about how they would make future estimations. What have they learned about the objects’ attributes that contribute to volume?)
- “So far, which object has the greatest volume? How do you know?” (Answers will vary. Reasoning should be based on how much water was displaced.)
- “What is one mL equivalent to?” (one cubic centimeter.)
Extension:
- Routine: In-a-Flash Review is an activity that can be used to review previously taught material. In this lesson, different forms of liquid measurement, prefixes, and conversions are introduced. In 5 minutes or less, review some of these key ideas using In-a-Flash Review cards (M-5-1-3_In a Flash Review and KEY.docx). This activity can help identify which students are retaining the information taught in the lesson and which students may need small-group work to strengthen the key ideas.
- Small Groups: Students who need additional practice may by pulled into small groups to work on finding the volume of objects using water displacement. The focus should be on asking the key questions identified in the lesson. Ask students to state each step in the process, as you proceed from step to step. Ask each student to read the water levels and record these measurements. Discuss the differences in measurements and why these might be occurring. To better understand displacement, use a bathtub or swimming pool as an example. Ask students what would happen if they fill a bathtub or small swimming pool up to the very top before getting in. Students will likely have more intuition about these situations. Link their experiences of their body displacing water to the objects displacing water.
- Expansion: Students who are prepared for a challenge beyond the requirements of the standard may estimate the volume of other objects. Students should base their estimates on the volumes of the objects used in the Volume of Objects Using Water Displacement activity. After predictions are made, students can use a graduated cylinder and water to determine the volume of each object by completing the Estimating Volume with Regularly and Irregularly Shaped Objects worksheet (M-5-1-3_Extension and KEY.doc). Challenge these students to also develop a method to find the volume of larger irregularly shaped objects that do not fit in the graduated cylinder, such as a hammer or a baseball.
