Mathematics
Grade 6
15 min
Nets of three-dimensional figures
Nets of three-dimensional figures
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1
Introduction & Learning Objectives
Learning Objectives
Identify a net as a 2D pattern that can be folded to form a 3D figure.
Match given nets to their corresponding three-dimensional figures (e.g., cube, rectangular prism, square pyramid).
Draw a net for simple three-dimensional figures like cubes and rectangular prisms.
Determine if a given 2D pattern is a valid net for a specific 3D figure.
Visualize how a 2D net folds into a 3D shape and vice versa.
Understand the relationship between the faces of a 3D figure and the parts of its net.
Have you ever flattened a cardboard box? 📦 What did it look like when it was completely flat?
In this lesson, you'll discover how three-dimensional shapes can be 'unfolded' into two-dimensional patterns called nets. Learning about nets helps us understand ho...
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Key Concepts & Vocabulary
TermDefinitionExample
NetA 2D (two-dimensional) pattern that can be folded along its edges to form a 3D (three-dimensional) figure.A flat pattern of six squares connected in a specific way is a net for a cube.
Three-dimensional (3D) FigureA shape that has length, width, and height, occupying space. Examples include cubes, prisms, and pyramids.A shoebox is a rectangular prism, which is a 3D figure.
FaceA flat surface of a 3D figure. In a net, these are the individual 2D shapes (like squares or triangles) that make up the pattern.A cube has 6 square faces.
EdgeA line segment where two faces of a 3D figure meet. In a net, these are the lines you fold along.The line where the top of a box meets its side is an edge.
Vertex (plural: Vertices)A point where three or more edges of a 3D figure meet...
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Core Formulas
Number of Faces Rule
$ ext{Number of faces in net} = ext{Number of faces in 3D figure}$
A valid net must have the exact number of individual flat shapes (faces) as its corresponding 3D figure. For example, a cube always has 6 faces, so its net must have 6 squares.
Connectivity Rule
$ ext{All faces must be connected along shared edges to form a continuous pattern}$
All parts of a net must be connected in a way that allows them to fold into a single, continuous 3D figure without gaps. Each face must have at least one edge connected to another face that it will share an edge with in the 3D shape.
No Overlap Rule
$ ext{No overlapping faces upon folding}$
When a net is folded, its faces must meet perfectly at their edges without any overlapping parts. If, when you mental...
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Challenging
A net for a cube has a star on one face, a circle on an adjacent face, and a triangle on a third face that meets the other two at a single vertex. Which option could show a correct view of that vertex when the cube is folded?
A.view where the star and circle are on opposite sides.
B.view where only the star and triangle are visible.
C.view showing the corner where the star, circle, and triangle all touch.
D.view where the star, circle, and triangle are in a straight line.
Challenging
A net for a prism has a total of 5 faces. Three of these faces are rectangles. What must be the shape of the two remaining faces (the bases)?
A.Triangles
B.Squares
C.Pentagons
D.Rectangles
Challenging
A path is drawn across a '1-4-1' net of a cube, starting from the middle of the top face, going straight down across the four middle faces, and ending on the middle of the bottom face. What does this path look like on the folded cube?
A.single small line on one face.
B.square shape around the middle of the cube.
C.zig-zag line.
D.continuous line that wraps all the way around the cube like a belt.
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