Nets

Task goals

• State how many faces a named solid or a given net has, for a cube, cuboid, square pyramid, triangular prism, hexagonal prism, tetrahedron or cylinder.
• Name the 3D shape that a given net folds up into, and identify the shape of each of its faces.
• Decide whether a given arrangement of squares or polygons folds into a cube or an open box, and explain why an arrangement that looks plausible fails.
• Use a labelled or dotted cube net to work out which face ends up opposite a given face once the net is folded, including on a standard die.
• Sketch a valid net for a named solid, and produce a second, different valid net for that same solid.
• Describe the net of a cylinder as two congruent circular faces plus the rectangle formed by unrolling the curved surface, and give that rectangle's dimensions from a stated radius, diameter or height.
• Reason about the properties of faces in a net, such as which faces must be congruent, why the triangular faces of a square pyramid are isosceles, and why a cylinder has no vertices.
• Find the area of an individual face from a net, and combine face areas into a total surface area, as the bridge from nets into the separate surface area objective.