Representing 3D Objects in 2D
This lesson unit is intended to help you assess how well students are able to visualize two-dimensional cross-sections of representations of 3-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing 2-dimensional cross-sections at different points along a plane of a representation of a 3-dimensional object.
- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and difficulties. You review their solutions and create questions for students to consider, to help improve their work.
- During the lesson, students work in groups on a collaborative activity. They match representations of three-dimensional objects with two-dimensional cross-sections. Students then share their work with another group.
- In a whole-class discussion, students compare and evaluate the methods they have seen and used.
- In a follow-up lesson, students review their initial solutions and then use what they have learned to either revise the same introductory assessment task or complete a different task.
- Each student will need a copy of the two assessment tasks, Vessels of Water and Vessels of Water (revisited), a mini-whiteboard, pen, and eraser.
- Each small group of students will need the cut-up cards Flowing Water and Shape of the Surface of the Water (1) and (2), a large sheet of paper for making a poster, and a glue stick.
- There is a projector resource to support whole-class discussions.
For the introduction, a real example, such as soda bottles filled to different levels with colored water, may help students visualize the two-dimensional cross-sections.
In the collaborative activity students may also benefit from seeing real examples of the three-dimensional objects such as cones, hemispheres, cuboids, triangular prisms, and rectangular pyramids.
20 minutes before the lesson, a 75-minute lesson (or split into two shorter ones), and 20 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards: