- For any polyhedron, what is the relationship between the number of faces, vertices, and edges?
Description of Learning Activity
For lower elementary students, this applet could be used to explore and identify the various 3D figures and the 2D figures that make them up. They could also practice counting the number of 2D shapes and relating that to the name for the 3D figure.
1. Learning Activity Types
- LA-Present - (read or attend to) presentation of new content/ideas
- LA-Present-Demo - This tool could be used by a teacher to demonstrate what a net is in relation to a 3D figure.
- LA-Explore - This tool is particularly useful for helping students to explore the various relationships between 2D and 3D figures at any level.
2. What mathematics is being learned?
PS-conceptual understanding Students develop a conceptual understanding of the 2D relationships to 3D models through experimenting and visualization with this tool
- PS-strategic competence Students build strategic competence through their continual trial and error with the creation of nets that create 3D figures.
- PS-adaptive reasoning Students' reasoning is likely to adapt as they continue to explore various combinations of polygons that create nets of 3D figures.
- PS-productive disposition Students will likely struggle with net creation at first, but as they print out and examine more nets from the program, they will become better at creating nets for 3D figures.
Additional comments on what is being learned
3. How is the mathematics represented?
4. What role does technology play?
Affordances of Technology for Supporting Learning
- Representing Ideas & Thinking - This tool enables the user to manipulate the way the 3D figure is being represented as they explore the relationships between 2D & 3D figures.
- Capturing & Creating - This tool allows the student to create their own nets in an attempt to create a net of a solid figure.
5. How does the technology fit or interact with the social context of learning?
6. What do teachers and learners need to know?
Users should be comfortable with basic mouse control and should be familiar with the terms: face, edge and vertices when using this applet. Users should also be provided access to a printer to get the most out of their experience and explorations with the applet.
How it Supports & Supplements PBL/PrBL
The various representations of 2D/3D figures comes up quite often in my projects in the geometry classroom, as students are often sketching buildings, bridges, sculptures and other designs and trying to determine how to best construct them. This applet is useful in the classroom because it allows students to get a good visual representation of the way in which the two models are related to one another. I've given students what I consider simple nets before, and they've had no idea what it would become. This applet helps those students to see the changes that happen in a net to see how it maps onto a 3D figure. After getting a conceptual understanding here, students can practice and implement the relationship in their projects.