Standard: 5.MD.C5c – Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Grade level: Grade 5
Subject: Mathematics
Domain: Measurement & Data
Teacher Overview
This standard focuses on recognizing volume as an additive property and solving problems involving the volume of composite figures. It is important because it builds on students’ understanding of volume and prepares them for more complex geometric concepts. Students should understand the basic concept of volume and know how to calculate the volume of a single right rectangular prism. They should also be comfortable with addition and multiplication.
Students will be able to apply their understanding of volume to more complex figures and real-world problems. They will also be ready to explore surface area and other geometric properties.
Common Misconception 1
Some students may believe that the volume of composite figures cannot be determined by adding the volumes of individual parts. This is incorrect because the volume of a composite figure is simply the sum of the volumes of its non-overlapping parts.
Intervention 1
Use visual aids and manipulatives to demonstrate how the volumes of individual parts combine to form the total volume. Encourage students to build composite figures and calculate the volume of each part before adding them together.
Common Misconception 2
Students might confuse volume with surface area, thinking they are the same. This misconception arises because both concepts involve measuring three-dimensional figures, but they are fundamentally different.
Intervention 2
Provide clear definitions and examples of volume and surface area. Use diagrams and physical models to show the difference, emphasizing that volume measures the space inside a figure while surface area measures the exterior.
Prerequisite Knowledge
Students should be familiar with the concept of volume, understanding it as the amount of space an object occupies. They should know how to calculate the volume of a single right rectangular prism using the formula length × width × height.
Subsequent Knowledge
After mastering this standard, students will be able to apply their understanding of volume to more complex three-dimensional figures and solve more intricate real-world problems involving volume. They will also be prepared to explore surface area and other geometric properties.
Instructional Activities
- Create composite figures using building blocks and calculate their volumes.
- Solve real-world problems involving the volume of multi-part containers.
- Use graph paper to draw and label composite figures, then calculate their volumes.
- Engage in group activities where students design their own composite figures and challenge peers to find the volumes.
