🔢 MathGrade 6Lesson 23
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Nets and 3D Reasoning

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Learning Objectives

  • 1Define a net as a flat pattern of faces that folds into a 3D solid
  • 2Identify the net of a cube, square pyramid, and triangular prism by counting faces
  • 3Sort 3D solids into prisms, pyramids, cylinders, and cones
  • 4Describe how the faces, edges, and vertices of a solid relate to its net
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Mini Lesson

A net is a 2D pattern of polygons that folds up into a 3D solid. If you cut a cardboard box along its edges and lay it flat, what you see is a net. In this lesson you will look at nets, count the faces inside each one, and figure out which 3D shape each net builds.

What a Net Tells You

  • A net shows every face of a 3D solid, all at once, on a flat surface.
  • The number AND shape of the polygons in the net match the faces of the solid: 6 squares fold into a cube, 1 square + 4 triangles fold into a square pyramid.
  • A face is a flat side. An edge is where two faces meet. A vertex is a corner where edges meet.
  • Solids with the same name share the same net pattern. Every cube, no matter the size, has the same net layout: 6 connected squares.

The Three Big Net Patterns to Memorize

  • Cube: 6 squares, all the same size. Often arranged in a cross or T-shape.
  • Square pyramid: 1 square (the base) + 4 triangles (the sides) that meet at the apex.
  • Triangular prism: 2 triangles (the two bases) + 3 rectangles (the sides). The two triangles are identical.
  • Rectangular prism: 6 rectangles in three matching pairs (top/bottom, front/back, left/right).
  • Cylinder: 2 circles (the bases) + 1 rectangle (the curved side rolled flat).
  • Cone: 1 circle (the base) + 1 sector of a circle (the curved side rolled flat).

Prism vs Pyramid vs Cylinder vs Cone

  • Prism: TWO identical parallel bases (top and bottom match) connected by rectangles. Named after the base shape — triangular prism, rectangular prism, hexagonal prism.
  • Pyramid: ONE flat base, all other faces are triangles that meet at a single point called the apex. Named after the base shape — square pyramid, triangular pyramid.
  • Cylinder: 2 parallel circular bases connected by a curved surface. Like a soup can.
  • Cone: 1 circular base and 1 curved surface that comes to a single apex point. Like an ice-cream cone.
Cube NetA cross-shaped cube net: a row of four squares labeled Left, Front, Right, Back, with one square labeled Top above the second square and one labeled Bottom below it.Cube Net: 6 Square FacesFold along every edge to form a cube.TopLeftFrontRightBackBottomss6 squares fold into a CUBEAll 6 faces are equal squares.A net is a 2D pattern that folds up into a 3D solid.
Cube net: six connected squares.
Pyramid and Prism NetsLeft: a square pyramid net (a central square base with four triangles attached). Right: a triangular prism net (three stacked rectangles with a triangle on top and bottom).Pyramid and Prism NetsCount the faces. Match the shapes.Square PyramidTriangular PrismBase1 square + 4 trianglesRect 1Rect 2Rect 32 triangles + 3 rectanglesCount faces to match each net to its solid.Pyramids end at a point. Prisms keep the same cross-section.
Pyramid and prism nets compared.
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Tip: to identify a 3D solid from its net, count the polygons inside the net first, then look at their shapes. 6 squares = cube. 1 square + 4 triangles = square pyramid. 2 triangles + 3 rectangles = triangular prism.

Vocabulary
net
A flat 2D pattern of polygons that folds up into a 3D solid.
face
A flat side of a 3D solid.
edge
A line where two faces of a solid meet.
vertex
A corner of a solid where edges meet (plural: vertices).
prism
A solid with two identical parallel bases connected by rectangles.
pyramid
A solid with one base whose other faces are triangles meeting at an apex.
cylinder
A solid with two parallel circular bases connected by a curved surface.
cone
A solid with one circular base and a curved surface ending at a single apex.
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← Lesson 22: Volume of Rectangular PrismsLesson 24: Geometric Problem Solving →