Lesson Summary: The teacher will begin by asking students to predict how many 1-inch cubes are needed to fill an object shaped like a rectangular prism. Students will then learn the definition of volume and use snap cubes to build figures and find the volume of them. Students will then learn the formula for volume and how to utilize it. Advanced learners will find the volume of a few irregular figures in addition to rectangular prisms. Struggling learners will complete a performance assessment with the teacher in which they will build figures in order to find their volume.
Lesson Objectives:
The students will know…
- How to find the volume of rectangular prisms.
- Use a picture or model to find the volume of rectangular prisms.
- Use a formula to find the volume of rectangular prisms.
Learning Styles Targeted:
Visual / Auditory / Kinesthetic/Tactile
Pre-Assessment: Hold up a rectangular prism (a shoe box or emptied box of tissues) for students to see. Students need to be able to see inside the box, so make sure the lid or top is removed if there is one. Then, hold up a 1-inch cube or snap cube for students to see. Tell students that you want to make a prediction about how many 1-inch cubes will be needed to completely fill the box. Have students record their predictions on a piece of scratch paper. Ask several students to share their predictions as you record them on the board. After eliciting several predictions from students, use the 1-inch cubes to cover the bottom layer of the box. Walk around and show students the cubes or use the document camera to project it for students to see. Count how many cubes layer the bottom of the box, and tell students how many it took. Ask students if any of them want to change their predictions about how many cubes it will take to fill the box. If so, allow them to revise their predictions. Have students share their predictions. Ask answering students to explain why/how they changed their predictions. Then, fill the remainder of the box with cubes. Fill it layer by layer so that students can begin thinking about the cubes’ organization within the rectangular prism.
Whole-Class Instruction
Materials Needed:1 piece of chart paper, Example Graphic Organizer* for teacher reference, 1 copy of the Guided Practice* to project under a document camera, a document camera connected to a projector, 45 snap cubes per student, writing utensils, 1 copy of the picture and problem from Example Graphic Organizer*, 1 bottle of glue or glue stick, 1 copy of the Independent Practice* per student, writing utensils
Procedure:
1)Explain to students that placing the cubes inside the rectangular prism was actually a form of measurement. Post a piece of chart paper on the board and divide it into 4 sections like the Example Graphic Organizer in supplemental resources. Write “Volume” in the first section, and tell students that volume measures how much space a 3-dimensional object takes up. Record the definition in the second section of the chart paper. Leave the remaining two sections blank for now.
2)Project a copy of the Guided Practice under a document camera. Give each student a set of 45 snap cubes. Tell students that they will be finding the volume of the figure shown, or how many cubes needed to build the figure. Point out to students that not all the cubes are shown, so it’s not possible just to count them. Ask students to use the snap cubes to build the figure. Walk around the room, observing the strategies used by students to build it. After students have built the figure, ask students to share how they built the figure. Lead a discussion about how you built the figure. You might say, “I noticed that there were 4 cubes on top, so I put 4 cubes together. Then, I noticed that there were two layers of cubes, so I put another 4 cubes together in the same way. Then, I played the two layers of cubes together.” Ask students how many total cubes were used. Elicit responses until a student says, “8.” Prompt the answering student to explain how s/he knew the answer was 8. Lead a discussion about how you know the answer is 8. You might say, “I know I used 4 cubes for the top layers, and I used 4 cubes for the bottom layer. Therefore, I used 8 cubes because 4 + 4 = 8.” Record “8 cubic units” on the projected copy of the Guided Practice.
3)Repeat this building and discussion process for the remaining two figures on the Guided Practice.
4)Cut out a copy of the picture from the Example Graphic Organizer, and paste it to the third section of the chart paper. Number the 4 blocks on the top layer as shown on the Example Graphic Organizer. Bracket the 2 layers, and write “2” beside it to show that it has 2 layers. Record the volume underneath the picture. See the Example Graphic Organizer, if necessary.
5)Tell students that there is another way to find volume when you don’t have the cubes to refer to. Explain to students that there is a formula used by mathematicians to determine the volume of a rectangular prism. Write “volume = length x width x height” on the chart paper in the fourth section. Explain to students that they can simply multiply the dimensions of a rectangular prism to find its volume. Cut out a copy of the problem from the Example Graphic Organizer, and paste it in the fourth section of the chart paper. Read the problem aloud to students, and show them how to multiply 3 x 2 x 2 to find the volume.
6)Leave the chart paper posted for students to refer to, and take up snap cubes from students. Give each student a copy of the Independent Practice, and allow them to work independently.
Advanced Learner
Materials Needed:1 copy of the Advanced Learner Independent Practice* per student, writing utensils
Procedure:
1)Give each student a copy of the Advanced Learner Independent Practice, and explain the directions. When students understand what to do, allow them to work independently.
Struggling Learner
Materials Needed:60 snap cubes per student, 60 snap cubes for the teacher, 1 copy of the Struggling Learner Activity* to project under a document camera, a document camera connected to a projector
Procedure:
1)Gather struggling learners together, and project a copy of the Struggling Learner Activity. Have students look at figure A, and give each student a set of 60 snap cubes. Tell students that they are going to build the figure shown in the picture in order to find the volume of it. Ask students to imagine figure A as a layered cake. Tell them that they will build the figure one layer at a time. Point out how the top layer of figure A is 5 cubes wide and 4 cubes deep. Lead students through using the snap cubes to build only the top layer. Check students work, and discuss with them the number of cubes used to build the top layer (20).
2)Ask students to look at figure A again and see how many layers it has. Elicit responses until a student says, “2.” Use the picture to show students the 2 layers. Show students how some of the cubes are hidden in the picture. Explain to students that the top layer is the same as the bottom layer, so they should build another layer identical to the one they already built. Build one with your snap cubes as students build theirs. Check their work, and ask students how many cubes were used to build the bottom layer. Elicit responses until a student says, “20.” Make sure students understand that the layers are identical. Show students how to place the layers on top of one another, and have them do it as well. Ask students how many total cubes were used to build figure A. Elicit responses until a student says, “40.” Make sure students understand why 40 is the volume.
3)Repeat this process for figures B, C, and D.
*see supplemental resources
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