Nets of 3D shapes

What a net is

A net is a flat shape that folds up into a 3-D solid, like a cardboard box before it is put together. On this page, choose one of six solids. The net is drawn flat; Fold it up animates the folding, Unfold flattens it again, and the Fold slider stops it at any point in between. Drag the picture, or use the turn buttons, to look at the solid from another side.

Below the picture, set your own counts for faces, edges and vertices, then press Check my counts to see which are right. Show me gives the answer and describes the faces, for example 1 square and 4 triangles for the square pyramid. For the cylinder and cone, the curved surface is counted as a face, as many classrooms do.

Why folding helps

Turning a 3-D shape into a 2-D one in your head, and back again, is a skill that takes practice. Watching a net fold shows which edges join up and why a cube needs exactly six squares. It also leads to surface area: the area of the net is the surface area of the solid. Common Core standard 6.G.A.4 asks students to represent 3-D figures with nets made of rectangles and triangles and use them to find surface area. Counting faces, edges and vertices on a solid you can turn builds the vocabulary younger children need.

Common mix-ups

• Counting only the faces you can see. Turn the solid around, or count the shapes in the flat net.
• Counting an edge twice. Each edge is where two faces meet, so it belongs to two faces but is only one edge.
• Thinking any six squares make a cube. Some arrangements of six squares overlap when folded; a cube has 11 different nets.
• Mixing up vertices and edges. A vertex is a corner point; an edge is a line where faces meet.

A 10-minute nets session

• Show the cube net flat. Ask the child to predict which square will be the top.
• Fold it slowly with the slider and check the prediction.
• Switch to the triangular prism. Count its faces in the net, then fold and count edges and vertices.
• Set the counts and press Check my counts.
• Finish with the cylinder and cone, and talk about curved surfaces.

Where it fits by grade

• Grade 1: compose 3-D shapes such as cubes, prisms, cones and cylinders (1.G.A.2).
• Grade 2: recognize and draw shapes with given attributes, such as a number of faces (2.G.A.1).
• Grade 6: use nets to represent 3-D figures and find surface area (6.G.A.4).
• England: Year 2 describes the properties of 3-D shapes, including edges, vertices and faces, and Year 6 recognizes, describes and builds 3-D shapes, including making nets.

Learning more

Area and perimeter are on Eurekami's skill map, and surface area builds directly on them. Daily Practice brings skills back when they start to fade, and teachers can print worksheets with answer keys.