E. Spatial Sense · Shapes, Position and Measurement

2D Shapes, 3D Objects and Sorting Them

E1.1About 30 minutes

Learning goals

I can name some flat (2D) shapes: circle, triangle, square, rectangle.
I can name some solid (3D) objects: cube, sphere, cylinder, cone, rectangular prism, pyramid.
I can sort shapes and objects by one attribute (one thing about them).
I can tell someone the sorting rule I used, and figure out someone else's rule.

Words to know

2D shape
A flat shape, like a drawing on paper. You can trace around it but you cannot pick it up and hold it like a ball.

3D object
A solid object you can hold. It has length, width and height, like a box or a ball.

side
A straight line that makes part of the outside of a flat shape.

vertex (corner)
A pointy corner where two sides meet. More than one vertex are called vertices.

attribute
Something about a shape you can describe, like its colour, size, number of sides, or whether it can roll.

sort
To put things into groups that are the same in some way.

sorting rule
The idea you used to make the groups, for example "shapes with 3 sides" and "shapes that are not 3 sides".

Look around your room. Shapes are everywhere! A clock may be a circle. A window may be a rectangle. A ball is a sphere. Today we will learn the names of shapes and play a sorting game, just like a detective.

A round wall clock, a red ball, a cardboard box, a tin can and a party hat on a shelf by a window. — Shape hunt! Find a circle, a rectangle, a sphere, a cube-like box, a cylinder and a cone in this room. AI-generated image

Flat shapes (2D)

A 2D shape is flat. Think of a drawing or a sticker. Here are four shapes we see a lot:

A circle, a triangle, a square and a rectangle.

Shape	Sides	Corners (vertices)	What to notice
circle	0	0	Round all the way around. No straight sides.
triangle	3	3	"Tri" means three. Three sides, three corners.
square	4	4	All 4 sides are the same length.
rectangle	4	4	2 long sides and 2 short sides (opposite sides match).

Count the sides and corners with your finger.

Fun fact

A square is a special kind of rectangle, because it has 4 sides and 4 square corners. Its sides just all happen to be the same length.

Solid objects (3D)

A 3D object is solid. You can hold it in your hands. Here are some 3D objects and things at home that look like them:

A cube, a cylinder, a cone and a sphere.

A rectangular prism and a pyramid. Can you find a 3D object in your home and name it?

3D object	Looks like...	Can it roll?	Can it stack?
sphere	a ball, an orange, a marble	yes, in every direction	no
cube	a dice, an ice cube, a toy block	no	yes
cylinder	a soup can, a roll of paper towel, a hockey puck	yes, on its side	yes, on its flat ends
cone	an ice cream cone, a traffic pylon	yes, in a circle	only on its flat bottom
rectangular prism	a cereal box, a book, a brick	no	yes
pyramid	a tent, the top of some roofs	no	on its flat bottom

What is sorting?

When we sort, we put things into groups that are the same in some way. We look at only one attribute at a time. An attribute is one thing about the shape, such as:

the number of sides (3 sides or not 3 sides)
curved or straight edges
size (big or small)
colour
for 3D objects: rolls or does not roll, stacks or does not stack

The idea we used is called the sorting rule. Good mathematicians always say their rule out loud.

Worked example

Sorting by number of sides

Sort these shapes: circle, triangle, square, rectangle, triangle, circle. Use the rule "has 4 sides" / "does not have 4 sides".

Make two groups (you can draw two big loops on paper). Label one 4 sides and the other not 4 sides.
Look at each shape and count its sides. The circle has 0 sides, so it goes in not 4 sides.
The triangle has 3 sides, so it goes in not 4 sides.
The square has 4 sides, so it goes in 4 sides. The rectangle also has 4 sides, so it goes in 4 sides.
Keep going: the second triangle and the second circle go in not 4 sides.
Check: count every shape. 2 + 4 = 6. We started with 6 shapes, so we did not miss any.

4 sides: square, rectangle. Not 4 sides: circle, triangle, triangle, circle.

Worked example

Find the sorting rule (be a detective!)

Maya sorted some objects into two groups.

Group 1: ball, soup can, orange, marble
Group 2: cereal box, toy block, book

What was her sorting rule?

Look at Group 1. What is the same about all of them? A ball, a can, an orange and a marble can all roll.
Look at Group 2. A box, a block and a book do not roll. They slide.
Check that the rule works for every object. It does!

Maya's rule was "objects that roll" and "objects that do not roll".

Remember

There can be more than one correct way to sort the same things. Sorting by colour and sorting by shape are both fine. What matters is that you can explain your rule.

Just for fun

Why is a sphere so bad at hide and seek?

It always rolls out of its hiding spot!

Hands-on activity

Shape hunt and sorting party

Go on a shape hunt around your home. Collect 8 to 10 safe objects, such as a cereal box, a can of soup, a ball, a block, a cup, a toilet paper roll and a tissue box.
Name each object: is it a sphere, cube, cylinder, cone, rectangular prism or pyramid?
Sort your objects into two groups. Choose your own rule, like "rolls / does not roll" or "has flat parts / no flat parts".
Ask a grown-up to guess your rule. Then swap: the grown-up sorts, and you guess their rule!
Bonus: cut out paper circles, triangles, squares and rectangles in different colours and sizes. Sort them three different ways: by shape, by colour, then by size.

Your turn!

How many sides does a triangle have?

I am a flat shape with 4 sides that are all the same length. What am I?

I am a solid object shaped like a soup can. What am I called?

Which of these is a 2D shape: a ball, a circle, or a can?

Sort these into "curved" and "straight sides only": circle, square, triangle, oval.

Ben put a dice, a cereal box and a book in one group. He put a ball and an orange in another group. What could his rule be?

A rectangle has how many corners?

Name something at home shaped like a cone.

More practice: warm-up

How many sides does a square have?

True or false: a circle has corners.

Which one is a 3D object: a ball, or a triangle drawn on paper?

Fill in the blank: a flat shape with 3 sides and 3 corners is a ___.

A hockey puck looks like which 3D object: a cube, a cylinder or a cone?

More practice: on your own

Count the shapes: 🔺🔺⬜🔺⬜

How many triangles? How many squares?

I am a 3D object. I can roll on my side, and I can stack on my flat ends. What am I?

Mia turns a triangle upside down. She says, "Now it is not a triangle." Is she right? How do you know?

Sort these into rolls and does not roll: orange, cereal box, soup can, toy block, marble.

How many corners do 2 triangles have all together?

Challenge

Find the mistake! Leo sorted shapes with the rule "4 sides" / "not 4 sides".

4 sides: square, rectangle, triangle
Not 4 sides: circle

What did Leo do wrong? Fix his groups.

Sort these objects two different ways. Say your rule each time: ball, soup can, cereal box, ice cream cone.

Riddle: I am a flat shape. I have 4 sides and 4 square corners. My sides are not all the same length. What am I? How do you know I am not a square?

Check your understanding

Quiz

Which shape has 3 sides?

Which one is a 3D object?

Sam sorted shapes into two groups: {circle, oval} and {square, triangle, rectangle}. What was his rule?

Which object can roll?

How many corners does a square have?

What is a sorting rule?

For parents and teachers

What your child is learning: naming common 2D shapes and 3D objects, and sorting them by one attribute at a time, then saying the sorting rule (Ontario Grade 1, E1.1).

Common mistakes:

Mixing up 2D and 3D names, for example calling a ball a "circle" or a box a "square". Gently give the right word: "The ball is a sphere. When we trace it, we get a circle."
Thinking a triangle must point up. Turn a triangle upside down or tilt it and ask, "Is it still a triangle?" (Yes! Turning a shape does not change its name.)
Thinking a square is not a rectangle. Both have 4 sides and 4 square corners.
Changing the rule partway through sorting (e.g. starting with colour, then switching to size). Ask, "What is your rule? Does this one follow it?"

How to help: play "Guess my rule" often with toys, socks, cutlery or laundry. Ask math-talk questions such as "How do you know?", "Is there another way to sort these?" and "Which group would this go in?" Praise careful explaining more than speed.