E. Spatial Sense · 3D Objects, Directions and Measurement

3D Objects: Faces, Edges and Vertices

E1.1About 35 minutes

Learning goals

I can name cubes, prisms, pyramids, cylinders and cones.
I can count the faces, edges and vertices of a 3D object.
I can describe the shapes of the faces of a 3D object.
I can tell if the faces of a 3D object meet in square corners.

Words to know

three-dimensional (3D) object
A solid object that has length, width and height, like a box or a can. You can hold it in your hands.

face
A flat surface of a 3D object. The faces of a box are rectangles.

curved surface
A surface that is not flat, like the side of a soup can. It can roll.

edge
The line where two faces (or a face and a curved surface) meet.

vertex (plural: vertices)
A corner point where edges meet. The tip of a cone is also a vertex.

base
The face that a prism or pyramid is named after. A triangular prism has triangle bases.

prism
A 3D object with two matching bases joined by rectangle faces.

pyramid
A 3D object with one base and triangle faces that meet at one vertex at the top.

Remember from Grade 2

In Grade 2 you studied 2D shapes (flat shapes) like triangles, squares and hexagons. You counted their sides and vertices (corners).

This year we study 3D objects. A 3D object is solid. You can pick it up, turn it around and look at it from every side.

Let's start with a hunt

Open your kitchen cupboard. You might see a cereal box, a soup can, a number cube from a board game and an ice cream cone. These are all 3D objects!

Mathematicians give each kind of 3D object a name. Here are the ones we will learn about.

A cardboard box, a metal can, a wooden cube and an ice cream cone in a glass on a kitchen counter. — A cupboard hunt: a box (rectangular prism), a can (cylinder), a cube and a cone. Which ones have flat faces, straight edges and pointy vertices? AI-generated image

Three objects with only flat faces: a cube, a rectangular prism and a triangular prism.

A square-based pyramid, a triangular pyramid, a cylinder and a cone. The cylinder and cone have curved surfaces.

The parts of a 3D object

A face is a flat surface. A cube has square faces.
An edge is where two faces meet. Run your finger along it. It feels like a line.
A vertex is a corner point where edges meet. It feels pointy. Two or more are called vertices.

In our drawings, a dashed line shows an edge that is hiding at the back. You could see it if you turned the object around.

A cube. The front square is one face. An edge is where two faces meet. A vertex is a corner where edges meet.

Count carefully

Counting edges is tricky because some hide at the back. Use the top, bottom, sides trick for a box:

4 edges around the top
4 edges around the bottom
4 edges going up and down

4 + 4 + 4 = 12 edges. With a real object, you can put a small sticky note on each part as you count it.

Object	Faces	Edges	Vertices	At home
cube	6 (all squares)	12	8	🎲 number cube
rectangular prism	6 (rectangles)	12	8	📦 box
triangular prism	5 (2 triangles, 3 rectangles)	9	6	a tent shape
square-based pyramid	5 (1 square, 4 triangles)	8	5	some roof tops
triangular pyramid	4 (all triangles)	6	4	a 4-sided game die
cylinder	2 flat circle faces + 1 curved surface	2 curved edges	0	🥫 can
cone	1 flat circle face + 1 curved surface	1 curved edge	1	a traffic cone

Faces, edges and vertices of 3D objects. A cube is a special rectangular prism: all of its faces are squares.

Worked example

Example 1: A triangular prism

How many faces, edges and vertices does a triangular prism have?

Faces: there are 2 triangle faces (the front and the back) and 3 rectangle faces joining them. 2 + 3 = 5 faces.
Edges: 3 edges around the front triangle, 3 around the back triangle, and 3 long edges joining them. 3 + 3 + 3 = 9 edges.
Vertices: 3 corners on the front triangle and 3 on the back. 3 + 3 = 6 vertices.

A triangular prism has 5 faces, 9 edges and 6 vertices.

Worked example

Example 2: A square-based pyramid

Count the faces, edges and vertices of a square-based pyramid.

Faces: 1 square base on the bottom and 4 triangles that lean in to the top. 1 + 4 = 5 faces.
Edges: 4 edges around the square base and 4 slanted edges going up to the top. 4 + 4 = 8 edges.
Vertices: 4 corners on the base, plus 1 at the very top. 4 + 1 = 5 vertices.

A square-based pyramid has 5 faces, 8 edges and 5 vertices.

Looking at angles

Where edges meet, they make an angle. In Grade 2 you checked for square corners using the corner of a piece of paper.

Every corner of every face of a cube or rectangular prism is a square corner.
The triangle faces of a pyramid come to a point at the top. The angle at the top is smaller than a square corner. It is sharper.

Left: the paper corner fits the corner of a cube face exactly, so it is a square corner. Right: the top angle of a pyramid's triangle face is smaller than a square corner.

Worked example

Example 3: Mystery object

I have 2 flat faces that are circles and 1 curved surface. I have no vertices. What am I?

Only two objects on our list have circle faces: the cylinder and the cone.
A cone has only 1 flat face and it has a vertex at its tip.
This object has 2 circle faces and no vertices.

It is a cylinder, like a soup can.

Math talk

Use the words face, edge and vertex when you describe an object. Say "It has a square face", not "It has a square side". Clear words help others understand your thinking.

Just for fun

What has 6 faces but no eyes, no noses and no smiles?

A cube!

Hands-on activity

3D object hunt

You need: 5 or 6 objects from home (a box, a can, a number cube, a party hat or ice cream cone, a tissue box), paper and a pencil.

Make a chart with these columns: Object, Name, Faces, Edges, Vertices.
Pick up the first object. What 3D object is it? Write its name.
Count its faces. Put a small sticky note (or a tiny piece of tape) on each face as you count, so you don't count one twice.
Run your finger along each edge as you count it.
Touch each vertex as you count it.
Check your answers with the table in this lesson.

Math talk: "Which of your objects can roll? Which can stack? Why?"

Your turn

How many faces does a cube have? What shape are they?

Which object has 2 flat circle faces and 0 vertices?

How many edges does a rectangular prism have?

How many vertices does a cone have?

A shoebox is shaped like which 3D object?

How many vertices does a triangular pyramid have?

What shapes are the faces of a triangular prism?

More practice: warm-up

What do we call a flat surface of a 3D object?

What do we call the line where two faces meet?

Name a 3D object that has a curved surface.

How many edges go around the top of a box?

A soup can is shaped like which 3D object?

More practice: on your own

Ella says a cube has 8 edges. What did she forget?

I have 1 square face and 4 triangle faces. What am I?

Which has more faces: a triangular prism or a square-based pyramid?

Tell one way a cylinder and a cone are the same and one way they are different.

Do the faces of a cereal box meet in square corners? How could you check?

Challenge

A pentagonal prism has a pentagon (5 sides) at each end. How many faces, edges and vertices does it have?

Riddle: I have 6 faces, 10 edges and 6 vertices. One face is a pentagon. The others are triangles. What am I?

Look at the square-based pyramid (5 faces, 5 vertices) and the triangular pyramid (4 faces, 4 vertices). What do you notice? Do you think it works for every pyramid?

Check your understanding

Quiz

How many faces does a rectangular prism have?

What is a vertex?

Which object has no vertices?

How many edges does a triangular prism have?

Which object has 4 triangle faces and 1 square face?

An ice cream cone is shaped like a ...

For parents and teachers

Big idea: 3D objects are described by their faces (flat surfaces), edges and vertices, and by the shapes and angles of their faces (Ontario E1.1). Real objects are the best teaching tool: boxes, cans, dice and party hats.

Common difficulties:

Missing hidden parts. Children often count only what they can see in a picture. Let them hold a real box and turn it, marking each face with a sticky note.
Counting edges twice or missing some. Teach the "4 on top, 4 on the bottom, 4 up and down" strategy for boxes.
Mixing up 2D and 3D names. A cube is not a square; a square is one of its faces. Gently correct "square" to "cube" for the object.
Curved parts. In this lesson we call the flat circles of a cylinder or cone faces, and the rounded part a curved surface. Some books use slightly different words; what matters is that your child can describe the parts clearly.

How to help: While unpacking groceries, ask "What 3D object is this? How many faces does it have?"