Grade 2 · Geometry · MAT-02-GEO-004
Describe and Build 3D Shapes
Describe common 3D shapes using faces, edges, and vertices.
Learning objectives
What you should be able to do
- Describe common 3D shapes using faces, edges, and vertices.
- Build and compare cubes, rectangular prisms, cylinders, cones, and spheres using models.
- Distinguish 2D faces from whole3D solids.
Prerequisite check
Make sure the foundation is ready.
Checks shape-recognition foundation.
Learn
Build the idea from meaning, not memorization.
3D shapes occupy space
Unlike flat2D figures, three-dimensional solids have length, width, and height. They can be viewed and rotated from different directions.
Faces, edges, and vertices describe solids
A face is a flat surface, an edge is where faces meet, and a vertex is a corner where edges meet. Curved surfaces require careful language because not every solid has flat faces/edges in the same way.
Cubes and rectangular prisms are related
A cube has six square faces. A rectangular prism has six rectangular faces; squares are special rectangles, so a cube can be viewed as a special rectangular prism.
Curved solids behave differently
Cylinders have two circular flat faces plus a curved surface; cones have one circular flat face and a curved surface ending at a point; spheres have only a curved surface.
Interactive math lab
Change it. See what stays true.
Geometry Explorer
- rotate solid
- count features
- match real object
- assemble faces
Worked examples
Twenty different ways to see the concept work.
Cube faces.
6 square facesSolid attribute.
Cube vertices.
8Corners.
Cube edges.
12Face intersections.
Rectangular prism faces.
6Rectangular faces.
Sphere flat faces.
0Only curved surface.
Cylinder circular faces.
2Top/bottom.
Cone circular faces.
1Base.
Cone point.
1 apexCurved surface narrows.
Rolls easily sphere?
YesCurved all around.
Cube stacks?
YesFlat faces.
Cylinder can roll and stack?
YesCurved side rolls, flat ends stack.
2D square vs cube.
square is flat face; cube solidDimension difference.
Circle vs sphere.
circle2D,sphere3DNot same object.
Rectangle vs rectangular prism.
2D vs3DFace vs solid.
Rotate cube.
still cubeOrientation irrelevant.
Build cube from square faces.
6 squaresNet-like construction.
Which solids have circular faces?
cylinder,coneFlat circle bases.
Which has no vertices?
sphere and cylinderIn elementary conventional counting.
Which has8 vertices?
cube/rectangular prismBox-like solids.
Describe cylinder.
2 circular flat faces + curved surfaceAttribute description.
Practice
Guided practice with hints
01Sphere faces?
Hint: Think flat surfaces.
Answer: 0
02Cylinder circles?
Hint: Top/bottom.
Answer: 2
03Cube vertices?
Hint: Count corners.
Answer: 8
04Square vs cube?
Hint: Dimension.
Answer: 2D vs3D
05Why cube stacks?
Hint: Flat faces.
Answer: Stable contact
06Rotate prism changes name?
Hint: Attributes unchanged.
Answer: No
Practice
Independent practice
01Cube faces
Answer: 6
02Cube edges
Answer: 12
03Cube vertices
Answer: 8
04Cylinder circular faces
Answer: 2
05Cone circular faces
Answer: 1
06Sphere flat faces
Answer: 0
07Square dimension
Answer: 2D
08Cube dimension
Answer: 3D
Common mistakes
Learn to catch the error, not just the answer.
A face is one flat surface of a solid.
Circle is2D; sphere is3D.
Use precise terms: flat face versus curved surface.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Identify packaging, balls, cans, and cones by solid shape.
- Build models from blocks or paper nets.
Challenge problems
Why cube special rectangular prism?
All square faces are rectangles and it meets prism structure.
Which solid both rolls and stacks?
Cylinder
Why sphere doesn't stack well?
No flat face.
Can same solid look like different2D shapes from viewpoints?
Yes; views/projections differ.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Solid Shape Lab
Identify and describe3D solids from attributes and rotations.
Practice
Mastery check
01Cube vertices
Answer: 8
02Cube edges
Answer: 12
03Cylinder circular faces
Answer: 2
04Sphere flat faces
Answer: 0
05Circle vs sphere
Answer: 2D vs3D
06Face definition
Answer: Flat surface.
07Does rotation change class?
Answer: No
08Solid that rolls+stacks
Answer: cylinder
Terminology
Words to know
- face
- A flat surface of a3D solid.
- edge
- A line where flat faces meet.
- vertex
- A corner point where edges meet.
- solid
- A three-dimensional shape occupying space.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade2 geometry attributes
Describe and reason about shape attributes, extended with foundational solid geometry.