Shapes All Around

What you will learn

• Name the common flat shapes and count their sides and corners.
• Name the common solid shapes and count their faces, edges and vertices.
• Sort shapes into groups using a rule you can explain.

Before you start: you only need to be able to count to $12$. This is the first shapes lesson, and it leads on to Position, Direction and Turns and Recognising 3D Shapes.

The idea

Look around the room. A window is a rectangle. A clock face is a circle. A slice of toast cut corner to corner makes two triangles. Shapes are everywhere, and once you know their names you start spotting them in everything.

There are two big families of shape. Flat shapes can be drawn on paper. Solid shapes take up space and can be picked up.

Flat shapes

A flat shape made of straight sides is called a polygon. You can name most polygons just by counting their sides.

• A triangle has $3$ straight sides and $3$ corners.
• A square has $4$ sides that are all the same length, and $4$ square corners.
• A rectangle also has $4$ sides and $4$ square corners, but only the opposite sides match in length.
• A pentagon has $5$ sides.
• A hexagon has $6$ sides.

A circle is a flat shape too, but it is not a polygon. It has one curved side that goes all the way round, and no corners at all.

Sides and corners

A side is one straight edge of a flat shape. A corner is where two sides meet. In maths, a corner is often called a vertex, and more than one are vertices.

Here is a handy fact. A polygon always has the same number of corners as sides. Three sides, three corners. Six sides, six corners. If you lose count of the sides, count the corners instead.

Square corners

Some corners are a special sharpness: the corner of a page, the corner of a door, the corner of a tile. These are called right angles, or square corners. A square and a rectangle have four of them. You can check a corner by fitting the corner of a piece of paper into it. If it fits exactly, it is a right angle.

Solid shapes

Solid shapes have three parts to count.

• A face is a flat surface you could lay a sheet of paper on.
• An edge is a line where two faces meet.
• A vertex is a point where edges meet. It is the pointy bit.

The common solid shapes are:

• A cube, like a dice. Six square faces, $12$ edges, $8$ vertices.
• A cuboid, like a cereal box. Six rectangular faces, $12$ edges, $8$ vertices.
• A sphere, like a ball. One curved surface, no edges, no vertices.
• A cylinder, like a tin of beans. Two circle faces, one curved surface, two curved edges, no vertices.
• A cone, like a party hat. One circle face, one curved surface, one curved edge, one vertex at the top.
• A pyramid with a square bottom, like the ones in Egypt. One square face, four triangle faces, $8$ edges, $5$ vertices.

Sorting shapes

Shapes can be sorted into groups by what they share. All the shapes with four sides. All the shapes with a curved part. All the solids that roll. There is often more than one right way to sort, as long as you can say what your rule is.

Worked examples

Example 1: Naming a flat shape

A road sign has $8$ straight sides, all the same length. What shape is it, and how many corners does it have?

1. Count the sides: $8$.
2. Sides and corners match on a polygon, so there are $8$ corners too.
3. A polygon with $8$ sides is called an octagon. “Oct” means eight, like an octopus with its eight arms.

Answer: An octagon, with $8$ corners.

Example 2: Counting the parts of a solid

Lena has a cuboid-shaped shoe box. Without a label, how can she count its faces, edges and vertices?

1. Faces: count the flat surfaces. Top, bottom, front, back, left, right. That is $6$.
2. Edges: count the lines where two faces meet. $4$ around the top, $4$ around the bottom, $4$ standing up at the corners. That is $12$.
3. Vertices: count the pointy corners. $4$ on the top, $4$ on the bottom. That is $8$.

Answer: $6$ faces, $12$ edges and $8$ vertices.

Example 3: Sorting by a rule

Sort these into two groups: ball, dice, orange, cereal box, marble, brick. What rule did you use?

1. Try the rule “it can roll”. Ball, orange and marble all roll because they are spheres with no flat faces.
2. Dice, cereal box and brick cannot roll. They have flat faces and sit still.
3. Check that every object is in exactly one group. It is.

Answer: Rollers: ball, orange, marble. Non-rollers: dice, cereal box, brick. The rule was “it can roll”.

Turning a shape does not change what it is. A square tipped onto one corner is still a square, even though people sometimes call it a diamond. Count its sides and check its corners instead of trusting how it happens to be sitting.

Why it matters

Shape names let you describe the world quickly and clearly. A builder orders rectangular tiles, a baker uses a round tin, and a footballer kicks a sphere. Knowing that a cube has six faces tells you how many stickers you need to cover a dice. Spotting right angles helps you hang a picture straight or fold a paper aeroplane. Later in geometry you will measure the sides and angles of these same shapes, so learning their names now is the first step.