E. Spatial Sense · Shapes, Maps and Measurement

Polygons: Counting Sides and Vertices

E1.1About 30 minutes

Learning goals

I can tell what makes a shape a polygon.
I can count the sides and vertices of a polygon.
I can name triangles, quadrilaterals, pentagons, hexagons and octagons.
I can sort shapes by the number of sides and by their side lengths.

Words to know

polygon
A flat, closed shape with only straight sides. A triangle and a square are polygons. A circle is not.

side
One of the straight lines that make the outside of a polygon.

vertex
A corner, where two sides meet. When there is more than one, we say vertices (VER-tih-sees).

quadrilateral
Any polygon with 4 sides. Squares and rectangles are quadrilaterals.

pentagon
Any polygon with 5 sides.

hexagon
Any polygon with 6 sides.

octagon
Any polygon with 8 sides. A stop sign is an octagon.

Shape detectives

Look at a stop sign on your street. How many sides does it have? Count them: 1, 2, 3, 4, 5, 6, 7, 8. Eight sides!

In Grade 1 you learned to name circles, triangles, squares and rectangles. This year you will be a shape detective. You will look closely at shapes and count their parts.

What is a polygon?

A polygon is a flat shape that:

has only straight sides, and
is closed. That means there are no gaps. All the sides join up.

A circle is not a polygon, because it is curved. A shape with a gap is not a polygon, because it is not closed.

Only the triangle is a polygon. The others have a curve or a gap.

Sides and vertices

Every polygon has sides and vertices.

A side is a straight edge.
A vertex is a corner, where two sides meet. More than one vertex are called vertices.

Here is a shape like a house. Put your finger on each dot and count the vertices.

This house shape has 5 sides and 5 vertices (the dots).

Counting trick

Put a small mark on the side where you start counting. Then count around the shape until you come back to your mark. That way you never count a side twice or miss one.

A polygon always has the same number of sides as vertices.

Polygons get their names from their sides

We name polygons by how many sides they have. The shape can be long, skinny, tipped over or bumpy. If it has 5 straight sides, it is still a pentagon!

Polygon names: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), octagon (8).

Name	Sides	Vertices	Where you might see one
triangle	3	3	a slice of pizza, a yield sign
quadrilateral	4	4	a door, a window, a book
pentagon	5	5	the front of a birdhouse shape
hexagon	6	6	a honeycomb cell, a nut for a bolt
octagon	8	8	a stop sign

Count the sides to name the polygon.

Squares and rectangles are special quadrilaterals. A shape with 4 sides that is not a square or rectangle is still a quadrilateral.

Worked example

Example 1: Name the shape

A shape has straight sides. Sam counts 6 sides and 6 vertices. What is its name?

Check: Are all the sides straight? Yes. Is it closed? Yes. So it is a polygon.
Count the sides: 6.
A polygon with 6 sides is a hexagon.

It is a hexagon.

Looking at side lengths

Detectives also look at how long the sides are. Some shapes have sides that are all the same length. Some have a few that match. Some have no sides that match.

In drawings, we put little tick marks on sides that are the same length.

Sides with the same number of tick marks are the same length.

Worked example

Example 2: Sort by sides

Sort these shapes into two groups: square, triangle, rectangle, hexagon, pentagon, octagon. Group A: fewer than 5 sides. Group B: 5 or more sides.

Count the sides of each shape: square 4, triangle 3, rectangle 4, hexagon 6, pentagon 5, octagon 8.
Fewer than 5 sides: square (4), triangle (3), rectangle (4).
5 or more sides: hexagon (6), pentagon (5), octagon (8).

Group A: square, triangle, rectangle. Group B: hexagon, pentagon, octagon. Our sorting rule was "number of sides".

Just for fun

What do you call a parrot that flew away?

A polygon! (Polly... gone.)

Hands-on activity

Toothpick polygons

You need: toothpicks, cotton swabs or straws (all the same length), and a few balls of playdough or mini marshmallows for corners.

Make a triangle with 3 sticks. Count its vertices.
Make a shape with 4 sticks. Then make a different shape with 4 sticks. Are they both quadrilaterals? (Yes!)
Make a pentagon (5 sticks) and a hexagon (6 sticks).
Now break one stick in half. Make a 4-sided shape that has 2 short sides and 2 long sides.
Go on a home hunt. Find 3 quadrilaterals and 1 shape that is not a quadrilateral.

Math talk: "How do you know it is a hexagon?" ("I counted 6 straight sides.")

Your turn

How many sides does a pentagon have?

A shape has 4 straight sides. What kind of polygon is it?

Is a circle a polygon? Why or why not?

How many vertices does a triangle have?

A stop sign is an octagon. How many sides does it have?

Ella draws a shape with 6 straight sides. Some are long and some are short. What is its name?

Is a square a quadrilateral?

More practice: warm-up

How many sides does a hexagon have?

What do we call a corner of a polygon?

How many sides does a rectangle have?

What shape has 3 sides?

A shape has 8 vertices. How many sides does it have?

More practice: on your own

A shape has 5 vertices. What is its name? How do you know?

Which one is NOT a quadrilateral: square, rectangle, triangle, or a kite shape?

How many sides do 2 triangles have altogether?

Sort by number of sides: octagon, triangle, hexagon, square. Put them in order from fewest sides to most sides.

A rectangle has 2 long sides and 2 short sides. Does a square have long and short sides? Explain.

Challenge

Leo says, "This shape is not a hexagon because it doesn't look like a honeycomb." The shape has 6 straight sides and is closed. Is Leo right?

Mila used 18 straws (one straw per side). She made only triangles. How many triangles did she make?

You have 9 toothpicks. Can you make one quadrilateral and one pentagon, using one toothpick for each side? Will any be left over?

Check your understanding

Quiz

Which shape is a polygon?

How many sides does an octagon have?

A shape has 5 straight sides. What is it called?

What is a vertex?

Which shape is not a quadrilateral?

A hexagon has how many vertices?

For parents and teachers

Big idea: Polygons are named by the number of sides, not by how they look. A long, skinny 6-sided shape is still a hexagon. This is new compared with Grade 1, where children mostly named "typical" shapes.

Common difficulties:

Counting a side twice or skipping one. Have your child mark the starting side with a finger or pencil dot.
Thinking a tipped-over square is a "diamond". Turn the paper. The shape does not change when it is turned. ("Diamond" is not a math name.)
Thinking squares are not quadrilaterals. Squares and rectangles are special quadrilaterals.
Saying "vertexes". The plural is vertices. It is fine if this takes time.

How to help: Hunt for polygons on walks (signs, windows, tiles, floor patterns). Ask "How many sides? How many vertices? Are any sides the same length?"