Solids have faces, edges and vertices. The faces are the flat surfaces of solids. The edges are the places where two faces meet. The vertices are the corners. Singular vertex, plural vertices.
Solids are three-dimensional shapes. A prism is a solid, with two parallel faces called bases. The other faces are always parallelograms. The prism is named by the shape of its base. A solid is a pyramid if it has 3 or more triangular faces sharing a common vertex. The base of a pyramid may be any polygon. An edge is formed where two faces meet. A vertex is the point where three or more faces meet.
3-D means three
dimensional (length, breath, depth). They can be regular or irregular.
A polyhedron is a 3-D
solid with flat faces and straight edges or polygonal faces. Some examples
include prisms and pyramids. Cylinder and cone are not polyhedrons or
polyhedral. This is so because their faces are not all polygons.
Singular
polyhedron- Plural polyhedral
Polyhedron can be
considered regular or irregular. For
them to be regular, all their faces must be equal /congruent example the
cube. ( It has six equal faces and is called a hexahedron) The triangular
pyramid is also a polyhedron as it has
four equal/congruent faces. (It is called a tetrahedron). Examples of irregular
polyhedron are rectangular prism. (all the faces are not the same, neither are
they congruent).
Students will review what nets are and complete an oral exercise by identifying the solids that the nets shown represent and vice versa.
Tell what they think a polyhedron is. In groups they will try to find a working definition for same.
Students will complete the table below in groups. Make a [ΓΌ] for columns 3 and 4.
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SOLIDS |
Name |
Example of Polyhedron |
Not a Polyhedron |
Justification |
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Cube |
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Square based pyramid |
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Sphere |
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Triangular prism |
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Triangular pyramid |
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Cylinder |
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EVALUATE
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Solids |
Same |
Different |
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cone, cylinder |
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Cube, cuboid |
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Cube, square-base prism |
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Square base prism, sphere |
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3. Use the words below to complete the short paragraph.
congruent polygonal
irregular equal faces
dimension
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A polyhedron is a
solid with flat ______________ and straight edges. All the faces of a
polyhedron are______________. Polyhedra with all faces equal or ___________
are called regular polyhedra. __________ polyhedra have faces that are not
__________ or congruent. |
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Regular
Polyhedron |
Irregular
Polyhedron |
Not
a Polyhedron |
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STATEMENTS |
TRUE |
FALSE |
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A polyhedron can be a prism as well as a pyramid |
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For a solid to be considered as a polyhedron, then all the faces must be a polygon |
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A sphere is a polyhedron |
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The cube is a hexahedron because it has 6 faces |
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If all the faces of a solid are the same size, then the faces are also considered congruent |
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7. Which of the following does not name the diagram below?
(a) square (b) cube (c) polyhedron (d) solid
Justify your answer. ____________________________________________________________
8. (a) Dwayne identified all the following solids as polyhedra. Do you agree with Dwayne? YES/NO
(b) Justify your reason for your answer above. _____________________________________________
___________________________________________________________________________________________
Lesson Plan
Subject: Mathematics
Grade: 6
Topic: Properties of Geometric Shapes (2D’s and 3D’s)
Focus Question: How are the characteristics of geometric solids similar and different?
Duration: 1 Hour
Objectives:
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Draw and describe nets of prisms.
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Identify and create solids that are polyhedral (tetrahedron, hexahedron, and octahedron).
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Classify solid shapes (prisms, pyramids, and polyhedra) according to their properties.
5E Instructional Model
Engage (5 minutes)
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Teacher displays a cube, pyramid, and cylinder (real objects or 3D models).
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Ask: “What do you notice about these shapes? How are they alike? How are they different?”
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Show a short 2-minute animation (or digital model) of nets folding into 3D solids.
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Record students’ initial ideas on the board.
Explore (15 minutes)
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Students work in small groups with nets of different solids (cube, rectangular prism, pyramid, tetrahedron, octahedron).
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Task: Cut, fold, and build the nets into 3D shapes using card stock or paper.
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Groups observe and discuss: “How many faces, edges, and vertices does each shape have?”
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Teacher circulates, prompting with questions such as:
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“What polygons make up the faces?”
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“Which solids are polyhedra? Why?”
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STEM Connection: Students use geometric modeling (math) and hands-on engineering (building nets → structures). Link to real-world: architects and engineers use nets and models to design buildings.
Explain (10 minutes)
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Each group shares findings: differences between prisms, pyramids, and polyhedra.
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Teacher introduces and clarifies definitions:
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Prism: 2 parallel, congruent bases + rectangular faces.
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Pyramid: 1 base + triangular faces meeting at a point.
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Polyhedron: solid with flat polygonal faces (tetrahedron, hexahedron, octahedron).
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Reinforce Euler’s formula (V – E + F = 2) as a property of polyhedra.
Elaborate (20 minutes)
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Activity:
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Groups classify solids provided (cube, prism, tetrahedron, octahedron, pyramid, cylinder, cone, sphere) into prisms, pyramids, polyhedra, or non-polyhedra.
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Students explain reasons for classification.
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Extension: Challenge students to design their own net for a new prism or pyramid and predict the 3D solid it would form.
Differentiated Learning:
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Tier 1 (Support): Work with pre-drawn nets, teacher guidance.
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Tier 2 (On Level): Draw and build their own nets with minimal guidance.
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Tier 3 (Advanced): Apply Euler’s formula to verify solids and create irregular nets.
Evaluate (10 minutes)
Three-Tier Evaluation:
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Tier 1 (Recall / Identify):
Match given nets to their correct 3D solids (cube, rectangular prism, pyramid). -
Tier 2 (Application):
Draw and describe the net of a triangular prism or square pyramid. -
Tier 3 (Reasoning / Extension):
Use Euler’s formula (V – E + F = 2) to prove whether a given solid is a polyhedron.
Students present answers orally or in writing.
Closure (5 minutes)
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Revisit focus question: “How are the characteristics of geometric solids similar and different?”
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Emphasize: All solids have faces, edges, and vertices, but their arrangement and types of faces classify them.
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Quick reflection: “Which solid would you use if you were an architect designing a roof? Why?”
✅ This plan balances hands-on exploration, STEM integration, real-world connections, and differentiation while hitting all three objectives.
