Measuring Volume of Solid Objects

Est. Class Sessions: 2–3

Developing the Lesson

Part 1. Estimating the Volume of Solid Objects

Count Centimeter Connecting Cubes. Demonstrate building a shape or cube model with centimeter connecting cubes. Display the cube model for students to view.

Ask:

How could you find the volume of this cube model? (Possible response: Count the cubes.)
What is the volume of each centimeter connecting cube? (1 cubic centimeter)
How do you know? Show us. (It is 1 centimeter long on each side. Students can measure each side of the cube with a centimeter ruler.)

Find the volume of the cube model by counting the number of cubes. Take it apart if necessary. Encourage students to build cube models and find the volumes.

Direct students' attention to the Measuring Volume of Solid Objects pages in the Student Guide. Read the vignette aloud together. The characters from the “Elixir of Youth” story, Tess and Sam, have returned to the Ancient History Museum. A startled Professor Garcia accidentally drops an artifact into a jar of water. Tess notices that the water level in the jar is higher with the object in it, and Sam introduces the concept of displacement.

After reading the vignette, but before assigning Question 1, ask:

What happened to the water level in the jar when the artifact fell into it? (The water level rose.)
How does Sam suggest they measure the volume of the artifacts? (He suggests placing them into a graduated cylinder and seeing how much the water level rises.)
What does displace mean? (to push away)
Why doesn't the professor want to measure the real artifacts using displacement? (The water will get them wet.)
How did Professor Garcia make a model of the tablet? (with centimeter connecting cubes)
Is the model going to give an exact measure of the small stone tablet's volume? (No, but it will give a good estimate of its volume.)
How did the professor find the volume of the stone tablet model? (Possible response: I think she counted the centimeter connecting cubes.)

Build Models to Estimate Volume. Assign Question 1 on the Measuring Volume of Solid Objects pages in the Student Guide to provide practice with finding the volumes of cube models. Students first build the models and then count the number of cubes. See Content Note.

When students use cube models to find volume, there is the potential to count the cubic centimeters incorrectly. Students may count the faces of the models, calling each face a cubic centimeter. Another potential error is that they do not count the centimeter connecting cubes that they cannot see or touch. It can be difficult for students to look at a model and keep track of all the cubic centimeters. Encourage students to be systematic, to look for patterns, and to think about simple addition and multiplication when counting the cubes. Students need to develop a conceptual understanding of the volume of shapes. Introducing them to a l × w × h formula at this point may impede this conceptual development of meaningful and efficient ways to measure.

After students have completed the question, ask:

How did you find the volume of the cube model in Question 1B? (Possible response: I made the model and then counted the cubes.)
Did anyone find the volume another way? (Possible response: I saw a pattern and I thought about multiplication. I knew each level of the cube had 3 rows of 3 cubes, so each level had 9 cubes. There were 3 levels. 3 levels times 9 cubes in each level equals 27 cubes in the model.)

Next show students the collection of small objects you gathered.

Ask:

How could you use centimeter connecting cubes to estimate the volume of one of these small objects? (Possible response: We could build a model that looks like the object and then count the cubes.)
Would the model give you the exact volume of the object? Why or why not? (Possible response: Probably not; we cannot make the exact shape of the object with the cubes, so we can only estimate the volume with a cube model. The objects have curvy sides, and we can't make curvy sides with the cubes.)

Estimate Volume with Models. Direct students' attention to the Measuring by Displacement section of the Measuring Volume of Solid Objects pages in the Student Guide. Read the vignette as a class to introduce how to measure the volume of objects using a graduated cylinder and the displacement method.

After the introduction, have students find the Yolanda Measures Volume by Displacement pages in the Student Activity Book. In the Estimating Volume section, read the short vignette with students to find out how Yolanda estimated the volume of a marker. She used centimeter connecting cubes to make a model about the same size as the marker. She found the volume of the model simply by counting the number of cubes.

Distribute two handfuls of centimeter connecting cubes to student groups. Have the small objects you gathered available, or have students choose items from the classroom or their desks that will fit inside the graduated cylinders. Assign Question 1. Students estimate the volume of several objects by making models as Yolanda did and recording the volume of the models in the Volume by Displacement data table. They should choose at least four objects, including a shape they build from 10 centimeter connecting cubes. There are three columns in the data table. Students should fill in just the first two columns and leave the third blank. This column will be used in Part 2 of this lesson. Students will need to use the same set of small objects for the next part of the lesson.

Assign the Measuring Volume of Solid Objects Homework pages in the Student Guide at this time. The work on these pages will prepare students for the second part of Yolanda Measures Volume by Displacement.

Use the Yolanda Measures Volume by Displacement page in the Student Activity Book and the corresponding Feedback Box in the Teacher Guide to assess students' progress toward estimating volume by counting cubic centimeters [E11]; measuring the volume of small objects using displacement [E10]; finding a strategy [MPE2]; showing work [MPE5]; and using labels [MPE6].