Guided Lessons

# Calculating Volume Using the Formula (L x W x H)

Students will begin to calculate volume of different rectangular prisms using base ten cubes and then transition to using the formula V = L x W x H. Students will then practice using the legendary fifth grade activity, Cootie Catchers.

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Students will be able to calculate volume of rectangular prisms using the formula V = L x W x H.

(5 minutes)
• Show students a rectangular prism.
• Ask, if they were to find the volume of this figure (or, how much space can fit inside it) how might they do that? Entertain suggestions, reminding students cubic units are used to measure volume.
• Lead students to the idea that we would need to find out how many cubes would fit inside of it.
(10 minutes)
• Explain that you could fill it neatly with cubes and count them. Ask students, if they were to come up with a shortcut for finding volume, without counting blocks, how might they do that?
• Distribute a handful of base ten blocks to each student or pair. Have them create a rectangular prism and count the squares.
• Now instruct them to write the dimensions of their prism. Examine the prism, the dimensions, and the volume. Challenge them to find a shortcut.
(10 minutes)
• Using a ruler with the same unit as the cubes, you could measure each side of the top (or bottom) to determine how many cubes would fill that layer, then measure the height which tells you how many layers there are. Then multiply how many cubes are in one layer by how many layers there are. This can be illustrated using a drawing on the board, their base ten block figure or the video recommendation in the supplement section of this lesson.
• Students will notice that the volume is equal to the length times the width times the height, the three dimensions of a rectangular prism. Explain that this kind of shortcut is called a formula.
• Instruct students to make another rectangular prism and test the formula.
• Now, write three dimensions on the board without rectangular prism and have students calculate the volume using mental math. Keep the dimensions simple, such as 5 x 6 x 2 or 10 x 20 x 3, so that students can do them mentally.
(15 minutes)
• Group students in pairs.
• Distribute a copy of Practice Calculating the Volume of Rectangular Prisms with Cootie Catchers to each pair of students.
• Have students follow the directions to cut out and fold the cootie catchers. Then, instruct them to work in their pairs to practice calculating the volume using their cootie catchers.
• Have any students who already know how to make these assist their classmates.

Support

• Have students review the concept using the videos in the Suggested Media section.
• Encourage students to create more figures using base ten blocks and use the strategy of calculating the volume of one layer. Then, have them multiply that by the number of layers.

Enrichment

• Give students different three-dimensional prism shapes (hexagonal prism, triangular prism) and instruct them to make a hypothesis about the formula for finding the volume of these figures.
• Allow students to create their own cootie catchers using their own rectangular prism shapes and dimensions.
(5 minutes)
• Draw a simple rectangular prism on the board with dimensions labeled and ask students to calculate the volume. Circulate the room to see which students need additional help.
(5 minutes)
• Discuss the following questions with your class: Why do we have mathematical formulas? How do they assist us?