Attributes of Shapes - 1st Grade Math

SECTION 1

Where Did Shapes Come From?

People have been looking at shapes for a very, very long time! Long ago, people noticed that things in the world have different forms. A rock might be round. A door might have four sides. A slice of pizza looks like a triangle. People wanted to give these forms names and learn about them.

3000 BC • Ancient Egypt

The Egyptians built giant pyramids. They used triangles and squares to make these amazing buildings!

300 BC • Euclid Writes About Shapes

A teacher named Euclid wrote a big book about shapes. He explained what makes each shape special.

Today • Shapes Are Everywhere!

We see shapes every day — in signs, buildings, toys, and books. Now you get to learn what makes each shape unique!

Here is the big question we will answer today: What makes a shape that shape? Is a triangle still a triangle if it is blue? What if it is really tiny? Let's find out!

SECTION 2

Defining vs. Non-Defining Attributes

Every shape has things about it that we can describe. We call these things attributes. An attribute is just something you can say about a shape. Some attributes are super important. Others don't matter at all!

Defining Attributes

These are the rules a shape must follow. A triangle must have 3 sides and be closed. If it breaks a rule, it is not that shape!

Non-Defining Attributes

These are things that can change, and the shape is still the same shape. Color, size, and which way it faces do not change its name.

Closed Shape

A closed shape has no gaps. All the sides connect to each other so there is no opening.

Number of Sides

The number of sides is a defining attribute. Triangles have 3, rectangles have 4, and hexagons have 6!

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KEY TAKEAWAY

Think of it like a dog. A dog must have four legs and a tail — those are like defining attributes. A dog can be brown, white, big, or small — those are like non-defining attributes. It is still a dog no matter what color it is!

SECTION 3

See the Difference!

Let's look at a picture that shows defining attributes and non-defining attributes side by side. This will help you see what matters and what doesn't!

Look at all four triangles at the top. They are different colors and sizes. Some are tilted! But they all have 3 sides and are closed. That means they are all triangles.

In the picture, you can see four triangles. One is purple and big. One is blue and small. One is pink and tilted to the side. One is yellow and tall. They all look different! But guess what? They all have 3 sides and they are all closed. So they are ALL triangles!

SECTION 4

The Shape Rules

Each shape has its own set of rules. These rules tell you exactly what makes that shape special. Let's learn the rules for some shapes you know!

Triangle Rules

✓ It must have 3 straight sides
✓ It must be closed (no gaps)
✓ It must have 3 corners

Rectangle Rules

✓ It must have 4 straight sides
✓ It must be closed
✓ It must have 4 square corners
✓ A square is a special rectangle where all 4 sides are the same length — it follows all the rectangle rules!

Circle Rules

✓ It must be perfectly round
✓ It must be closed
✓ It has no straight sides and no corners

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Remember!

You can change the color, size, or which way a shape faces. It will still be the same shape! Those things are not part of the shape's rules.

SECTION 5

Sorting: Defining vs. Non-Defining

Let's practice sorting attributes into two groups. Look at the chart below. On one side, you see things that DO matter (defining). On the other side, you see things that DO NOT matter (non-defining).

The green column shows defining attributes — the rules a shape must follow. The pink column shows non-defining attributes — things that can change without changing the shape's name.

Look at the green side. Those are the things you must check when you name a shape. How many sides? Are they straight? Is it closed? Now look at the pink side. You can change any of those things and the shape keeps its name. A big red triangle and a tiny green triangle are both triangles!

SECTION 6

Let's Try One Together!

Imagine your teacher shows you a big, blue, tilted shape. How do you figure out what shape it is? Let's go step by step!

What Shape Is This?

1
Step 1 — Ignore the Non-Defining Attributes

The shape is big, blue, and tilted to the side. But remember — color, size, and direction don't matter! We can skip those.
2
Step 2 — Count the Sides

Let's count the straight sides. We count: one, two, three, four. It has 4 sides.

4 sides
3
Step 3 — Check if It Is Closed

Do all the sides connect? Yes! There are no gaps. It is a closed shape.

Closed ✓
4
Step 4 — Check the Corners

Are all 4 corners square corners (like the corner of a book)? Yes! All the corners are square corners.

4 square corners ✓
5
Step 5 — Name the Shape

It has 4 sides, it is closed, and it has 4 square corners. That matches the rules for a rectangle! Even though it is big, blue, and tilted, it is still a rectangle. (If all 4 sides were the same length, it would be a square — and a square is a special kind of rectangle too!)

It is a rectangle!

SECTION 7

Comparing Shapes

Let's compare some shapes! This table shows you the defining attributes of different shapes. See how each one follows its own set of rules.

Shape	Number of Sides	Closed?	Special Rule
🔺 Triangle	3	Yes	3 corners
⬜ Rectangle	4	Yes	4 square corners (a square is a special rectangle with 4 equal sides)
⬟ Hexagon	6	Yes	6 corners
⭕ Circle	0 straight	Yes	Perfectly round, no corners

Defining attributes of common shapes

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KEY TAKEAWAY

Think of shapes like cookie cutters. A star cookie cutter always makes a star — no matter if you use brown dough, white dough, big dough, or small dough. The cutter's outline is the defining attribute. The dough's color and size are non-defining attributes!

SECTION 8

Building and Drawing Shapes

Now that you know the rules, you can build and draw shapes yourself! When you draw a shape, you use its defining attributes as your guide. Let's practice drawing a triangle and a rectangle step by step.

How to Draw Shapes Using Defining Attributes

1
Drawing a Triangle — Step 1: Know the Rules

A triangle must have 3 straight sides and be closed. Remember: it can be any color, any size, and face any direction — those don't matter!
2
Drawing a Triangle — Step 2: Draw the First Side

Put your pencil on the paper and draw one straight line. This is your first side. Count it: that's 1!

1 side drawn ✓
3
Drawing a Triangle — Step 3: Draw the Second Side

From the end of your first line, draw another straight line going in a different direction. Count it: that's 2!

2 sides drawn ✓
4
Drawing a Triangle — Step 4: Close the Shape

Now draw a third straight line that connects back to where you started. Check: are all 3 sides connected with no gaps? If yes — you drew a triangle! ✓

Triangle complete! 3 sides, closed ✓
5
Drawing a Rectangle — Step 5: Know the Rules

A rectangle must have 4 straight sides, 4 square corners, and be closed. A square corner looks like the corner of a book — it does not tilt or lean.
6
Drawing a Rectangle — Step 6: Draw and Close

Draw a straight line going across (left to right). Then, at each end, turn and draw a straight line going down — make sure each turn makes a square corner (like the corner of this page). Finally, draw a line across the bottom to close the shape. Check: 4 sides? 4 square corners? No gaps? If yes — you drew a rectangle! ✓

Rectangle complete! 4 sides, 4 square corners, closed ✓

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Check Your Work!

After you draw a shape, check it against the rules! Count the sides. Check for gaps. Look at the corners. If your shape follows all the defining attributes, you did it right — no matter what color or size it is!

What You Know Now	What You'll Learn Next
Name shapes by their defining attributes	Sort shapes into different groups
Tell which attributes don't matter	Cut shapes into halves and fourths
Draw shapes with the right number of sides	Build 3D shapes (cubes, cones)

Your geometry journey

In second grade, you'll learn about 3D shapes like cubes and spheres. You'll also learn to split shapes into equal parts. The rules you learned today will help you with all of that! You're already becoming a shape expert.

SECTION 9

Practice Problems

Now it's your turn! Try these five questions. Think about what makes a shape that shape. Remember to focus on the defining attributes!

Question 1: CONCEPTUAL

Maria says, "That shape is not a triangle because it is green. Triangles are supposed to be red!" Is Maria right or wrong? Why?

Show answer

Maria is wrong! Color is a non-defining attribute. It does not matter what color a triangle is. A triangle can be green, red, blue, or any color. What makes it a triangle is that it has 3 straight sides and is closed. As long as it follows those rules, it is a triangle no matter what color it is!

Question 2: BASIC IDENTIFICATION

A shape has 4 straight sides and 4 square corners. It is closed. What shape is it?

Show answer

This shape is a rectangle! A rectangle has exactly 4 straight sides, 4 square corners, and is closed. Those are its defining attributes. It doesn't matter how big or small it is, what color it is, or which way it is turned. If it follows all three rules, it is a rectangle. (If all 4 sides are also the same length, then it is a square — and a square is a special kind of rectangle!)

Question 3: INTERMEDIATE

Look at these two descriptions: Shape A has 3 sides, is closed, and is red. Shape B has 3 sides, is closed, and is blue. Are these the same type of shape or different? Explain which attributes you used to decide.

Show answer

Shape A and Shape B are the same type of shape — they are both triangles! Both have 3 sides and both are closed. Those are the defining attributes of a triangle. The only difference is their color (red vs. blue). Color is a non-defining attribute, so it does not change what kind of shape it is. We only used the number of sides and whether it was closed to decide.

Question 4: APPLIED

Your friend draws a shape with 3 straight sides, but one side does not connect to the others — there is a gap. Your friend says it is a triangle. Is your friend correct? Why or why not?

Show answer

Your friend is not correct! Even though the shape has 3 sides, it has a gap. That means it is not closed. Being closed is a defining attribute of a triangle. All the sides must connect with no openings. Since there is a gap, this shape does not follow all the rules for a triangle. Your friend should close the gap so all sides connect!

Question 5: CRITICAL THINKING

Can you name two defining attributes and two non-defining attributes of a rectangle? Then explain: if you change one defining attribute, what happens to the shape?

Show answer

Two defining attributes of a rectangle are: (1) it has 4 straight sides and (2) it has 4 square corners. Two non-defining attributes are its color and its size. If you change a defining attribute — for example, if you change the number of sides from 4 to 3 — it is no longer a rectangle! It would become a different shape (a triangle). Defining attributes are the rules that make the shape what it is, so changing them changes the whole shape.

SUMMARY

What Did We Learn?

Summary

Today you learned about attributes of shapes. Every shape has defining attributes — the rules it must follow, like the number of sides, being closed, and the number of corners. Shapes also have non-defining attributes like color, size, and orientation — these can change and the shape keeps its name.

A triangle always has 3 sides and is closed. A rectangle always has 4 sides and 4 square corners — and a square is a special rectangle where all 4 sides are the same length. A circle is always perfectly round with no corners. Now you can look at any shape, check its defining attributes, and name it — and you can build and draw shapes by following the right rules. Great job, shape detective!