In this lesson, students will study the water displacement method for determining solid volumes. Students will: 
- calculate the volume of an irregular solid using water displacement. 
- convert between milliliters, cubic centimeters, and liters. 

- When is it appropriate to estimate versus calculate?
- What makes a tool and/or strategy suitable for a certain task? 
- Why does "what" we measure affect "how" we measure?
- In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted?
- How precise should measurements and calculations be?

- Cubic Unit: A unit for measuring volume. 
- Customary System: A system of weights and measures frequently used in the United States. The basic unit of weight is the pound; the basic unit of capacity is the quart. 
- Measurement Unit: A specific quantity used as a standard of measurement. 
- Metric System: A system of measurements used throughout the world based on factors of 10. It includes measures of length, weight, and capacity. 
- Volume: The amount of space enclosed in a solid (3-dimensional) figure. Volume is measured in cubic units.

- two containers, one that holds a liter and one that holds a quart of liquid (e.g., a liter of bottled water, a quart of milk)
- graduated cylinders (mL)
- two identical, clear containers
- water
- cubic-centimeter blocks (the unit cubes in base-ten blocks are usually this size)
- small objects (marble, rock, small bolt, nickel, lump of clay) for each group
- copies of Does 1 Cubic Centimeter = 1 Milliliter? activity (M-5-1-3_Displacement Activity)
- copies of Volume of Objects Using Water Displacement (M-5-1-3_Volume of Objects Using Water Displacement)
- one copy of the In a Flash Review cards (M-5-1-3_In a Flash Review and KEY)
- one copy of the Volume of Regularly and Irregularly Shaped Objects Observation Checklist (M-5-1-3_Volume Observation Checklist)
- copies of the Lesson 3 Exit Ticket (M-5-1-3_Lesson 3 Exit Ticket and KEY)
- copies of the Estimating Volume with Regularly and Irregularly Shaped Objects worksheet (M-5-1-3_Extension and KEY)

- Use the Volume of Regularly and Irregularly Shaped Objects Observation Checklist to evaluate and track students' progress. 
- The In-a-Flash Review cards can be used to quickly assess student mastery of basic lesson concepts. 
- Use the Lesson 3 Exit Ticket (M-5-1-3_Lesson 3 Exit Ticket and KEY) to assess students' grasp of finding the volume of objects using water displacement and converting cubic centimeters to milliliters.

Scaffolding, Active Engagement, Modeling, Explicit Instruction 
W: The lesson focuses on utilizing water displacement to measure object volumes. The lesson also discusses the relationship between a cubic centimeter and a milliliter. 
H: Engage students by offering irregularly shaped things. Challenge them to think of ways to calculate the volume of these objects. Ask them if the formulas from prior lessons work. Announce that they will use water and a procedure known as water displacement to determine the volume of these objects. 
E: Engage students with a displacement activity to demonstrate that 1 \(cm^3\) = 1 mL. Encourage students to estimate the volume of objects using water displacement. 
R: Students will review topics by completing the Volume of Objects Using Water Displacement exercise worksheet. 
E: The Volume of Regularly and Irregularly Shaped Objects Checklist will be used to assess student performance in the water displacement activity. In-a-Flash Review cards will be used to assess students' grasp of the lesson's key concepts. The Lesson 3 Exit Ticket will also be used to evaluate each student's ability to calculate the volume of an item using water displacement. 
T: Use the Extension section to customize the lesson to match the needs of the students. The Routine section provides strategies for reviewing lesson concepts throughout the year. The Small Groups section provides suggestions for students who could benefit from more practice or training. The expansion section offers additional options for students who are willing to go beyond the criteria of the standard. 
O: This lesson focuses on measuring the volume of both regular and irregularly shaped objects using the displacement method. It also aims to increase students' comfort with the metric system. This lesson is meant to teach students that it is feasible, and sometimes even required, to calculate volume without using a formula. 

Explain the lesson's purpose to the class. 

"In this lesson, we'll use water displacement to measure the volumes of various irregularly shaped objects. First, we must understand the relationship between measuring volume in cubic centimeters and measuring liquids in liters and milliliters." 

Display a liter bottle to students. Show a container that can hold one quart of liquid. (Make sure both containers are filled with liquid.) Ask students to compare a liter to a quart. "Which do you think is larger, 1 liter or 1 quart?" Ask students to make their best predictions.

Now, pour the liquids from the liter bottle and quart container to two identical clear containers. This is an important image because it allows students to determine how similar the measures are. (1 liter equals approximately 1.0567 quarts, making it slightly larger than a quart.)

Remind students that there are two measurement systems: the customary English system of measurement and the metric system of measurement. “The metric system is the most widely used measurement system in the world. The United States is one of the few countries that mainly uses the customary English system. As a result, products in US retailers are labeled using both measuring systems. A quart is a customary English measuring unit, whereas a liter is a metric measurement unit. 

"Pints, cups, tablespoons, and teaspoons are the smaller liquid measurement units in the customary English system. Milliliters are smaller liquid measurement units in the metric system, which we will learn about today."

Also, explain how the metric system of measuring is based on the number 10 and uses prefixes. "The prefix 'milli' represents one thousandth. So a milliliter equals one thousandth of a liter. Another way to express this is that 1000 milliliters equals one liter. So one liter of bottled water has 1000 milliliters. The milliliter is an important unit for understanding the link between volume measurements in cubic centimeters and liquid measurements in liters and milliliters."

"In previous lessons, we were using cubic centimeters to find the volume of rectangular prisms." (Hold out 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 fit exactly.) "As you might expect, there are many solids that are not rectangular prisms, or even right prisms, but we still need a means to calculate their volume. To do so, we can utilize the water displacement method, which involves measuring the volume of an object by determining how much water it holds. This means that instead of cubic centimeters, we should use a liquid amount measurement like milliliters. 

"Now we'll see how many milliliters equal one cubic centimeter. In other words, if we could fill the cubic centimeter block with water, how many milliliters would it hold?" 

The displacement activity below will show students the link 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).

Students will follow the procedure outlined on the activity sheet. 

1. Fill the graduated cylinder halfway with water. You'll see that the water level doesn't run straight across. The water level is concave and known as the meniscus. When reading the water level in a graduated cylinder, make sure it's in the center of the meniscus and at eye level. 
2. Mark the level of the water on the chart. The units are milliliters (mL). (Ensure the meniscus is directly atop the desired milliliter mark, not between two milliliter marks.)
3. Carefully place the centimeter cube in the graduated cylinder. 
4. Check the new water level. Make sure you view it at eye level.
5. Note the new water level on the chart. 
6. Repeat steps 3–5 to build a pattern. 
As students see what happens to the water level after placing the centimeter cube in the water (the sides curve up), reiterate the proper method of reading the water level by looking at the center of the meniscus, or the concave surface of the water, at eye level. 

Keep an eye on students' relationships and dialogue while they work. Make sure students are reading the water level appropriately. If a group's results are inaccurate, have them repeat the procedure as you coach them and monitor their comprehension. It is critical to monitor groups for accuracy while evaluating the volume of a cubic centimeter and to instruct groups to repeat the process if they do not get the correct result. This should clear up any misconceptions that a group may have before proceeding to the more in-depth practice of measuring the volume of various things. Small-group work and student replies to questions can serve as informal assessments. Using the Volume of Regularly and Irregularly Shaped things Observation Checklist, you can determine who is having difficulty determining the volume of regularly and irregularly shaped things and provide them with additional support.

Once the majority of students have done, bring the class together. Explain to students that this activity demonstrates that items will displace a quantity of water equal to their volume. When an object is immersed in water, the water level rises proportionally to the object's volume. Allow students to share their outcomes. Make sure students understand that one cubic centimeter equals one milliliter. "This method of finding volume is called the water displacement method." 

Remind students that an object will displace an amount of water equal to its volume. During this part of the activity, they must measure the volume of both regularly and irregularly shaped objects. Students will follow the same procedure as earlier. Now that students have gained some experience with volume using this method, ask them to estimate the volume before placing the objects in water. Estimates will be recorded in the activity guide. Each object will be carefully placed inside a graduated cylinder half-filled with water. A water level reading is made before and after the object is placed in the graduated cylinder. Once students have grasped their task, distribute the Volume of Objects Using Water Displacement sheet (M-5-1-3_Volume of Objects Using Water Displacement). Explain to students that they should measure the entire lump of clay. When they finish the last row on the chart, the entire lump of clay should be molded.

Keep an eye on their interactions and dialogue while they work. Check that students are reading the water level correctly by taking a reading at eye level. If students' results are inaccurate, have them retake the activity while you observe their procedure. A volume of regular and irregularly shaped objects. The Observation Checklist (M-5-1-3_Volume Observation Checklist) can be used to assist you record your observations. To clarify students' levels of understanding, ask the following questions:

"What are you measuring during this activity?" (volumes of objects with regular and irregular shapes)
"Why is it necessary to read the water level at eye level?" (The water level is concave, so measure it in the center of the meniscus. Water sticks to the sidewalls; if you read from that level, you will overestimate the volume.) 
"How does placing a regularly or irregularly shaped object in a graduated cylinder of water tell you the object's volume?" (When an object is placed in a container of water, it displaces the same amount of water as its volume.)
"How can you determine an object's volume before applying 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 using that information. If you measure an object's height, width, and length, you can get an approximation of its volume. However, the estimate is only accurate if the item is a rectangular prism.)
"What do you notice about your estimated volumes and the actual volumes of the objects?" (The answers will vary. Some may argue that their estimates are too high or low. Encourage students to examine the actual quantities and draw conclusions about how they might make future estimates. What have they learnt about the objects' properties that contribute to volume?)
"So far, which object has the greatest volume? How do you know?" (The answers will vary. Reasoning should be based on the amount of water displaced.)
"What is one mL equivalent to?" (One cubic centimeter.)

Extension:

Routine: In-a-Flash Review is an activity for reviewing previously taught content. This lesson covers several liquid measurement methods, prefixes, and conversions. Review some of these essential topics in 5 minutes or less with In-a-Flash Review cards (M-5-1-3_In a Flash Review and KEY). This task can assist identify which students are remembering the information from the class and which may require small-group practice to reinforce the important topics.

Small Groups: Students who require further experience may be divided into small groups to work on determining the volume of objects using water displacement. The focus should be on asking the important questions outlined in the lesson. As you go through the procedure, ask students to state each step. Ask each student to read the water levels and note their findings. Discuss the measurement variances and why they may occur. To further comprehend displacement, consider a bathtub or swimming pool. Ask students what happens if they fill a bathtub or small swimming pool to the very top before entering. Students are likely to have stronger intuition regarding these circumstances. Connect their experiences with their body displacing water to the items displacing water.

Expansion: Students who are prepared to take on a challenge outside the scope of the standard may estimate the volume of other items. Students should estimate the volumes of the objects used in the Volume of Objects Using Water Displacement activity. After making predictions, students can use a graduated cylinder and water to calculate the volume of each object by completing the Estimating Volume with Regularly and Irregularly Shaped Objects worksheet (M-5-1-3_Extension and KEY). Challenge these students to create a system for calculating the volume of larger irregularly shaped objects that do not fit into the graded cylinder, such as a hammer or a baseball.