Studio Aletheia · The Center for Quantitative Studies
6.MGSR.1.2SC 6th Grade Math
Unfolding 3D Shapes Into Nets
Lesson 31 · New Content, Nets of Prisms & Pyramids
Every three-dimensional shape can be unfolded flat, like taking apart a cardboard box. Today you'll learn to create a two-dimensional net for a prism or pyramid, seeing exactly which flat shapes make up its surface.
Learning Targets and Success Criteria
Every solid shape hides a flat pattern inside it, and today you'll learn to find it.
What I will learn
- I can identify the faces, edges, and bases of a prism and a pyramid.
- I can explain the difference between a prism and a pyramid.
- I can create a net that matches a given prism.
- I can create a net that matches a given pyramid.
What success looks like
- I can sort 3D shapes into prisms and pyramids correctly.
- I can name the number and shape of faces on a given prism or pyramid.
- I can draw a net that folds up into a rectangular or triangular prism.
- I can draw a net that folds up into a pyramid.
Create a two-dimensional net that represents a given three-dimensional prism or pyramid.
The words we'll use in today's lesson.
These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.
Net
A two-dimensional pattern that can be folded up to form a three-dimensional figure.
Prism
A three-dimensional figure with two identical, parallel bases connected by rectangular faces.
Pyramid
A three-dimensional figure with one base and triangular faces that meet at a single point.
Where this shows up in the real world.
Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.
Unfolding a Building Before It's Built
Architects and engineers use nets to plan how flat materials, like sheet metal or cardboard packaging, will fold into a finished 3D shape. Learning to see a prism or pyramid as a flat pattern is the first step toward figuring out exactly how much material a real structure will need.
Same Shape, Flattened Out
Every solid shape hides a flat pattern inside it, and today you'll learn to find it.
Picture a cereal box. If you carefully cut along its edges and lay it flat, you'd see a single connected shape made of six rectangles. That flat shape is called a netA two-dimensional pattern that can be folded up to form a three-dimensional figure., and every three-dimensional figure has one, or sometimes more than one correct net.
A cereal box is an example of a prismA three-dimensional figure with two identical, parallel bases connected by rectangular faces., a solid with two identical, parallel bases connected by rectangular faces. A pyramidA three-dimensional figure with one base and triangular faces that meet at a single point. looks different: it has just one base, with triangular faces that rise up and meet at a single point. Its net looks different too, one base shape surrounded by triangles instead of rectangles.
To create an accurate net, you have to notice the pattern in the solid: how many faces does it have, what shape is each face, and how do they connect at the edges? Get that structure right, and your net will fold back into an exact copy of the original shape.
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Scissors
- B. A 3D solid or box (if available)
- C. Grid paper or plain paper
- D. Your Data Journal
- E. A ruler
Before drawing any net: count the faces on the solid, name each face's shape, then sketch how they connect at shared edges.
Faces First
Before you can draw a net, you need to know exactly what faces make up each solid.
Build a Net
Now you'll create and test a real net for a solid of your choice.
Data Journal Entry
Accountability Checklist
How Do You Know a Net Is Correct?
Explain how you would check whether a net correctly represents a given prism or pyramid before folding it.
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