Geometry and Spatial Reasoning

Identifying 2D Polygons

Today we will learn about 2D polygons. A 2D shape is a flat shape. You can draw it on paper.

A polygon is a flat shape that is made with straight sides. The sides are joined together to make a closed shape. That means there are no openings.

Polygons do not have curved sides. A circle is not a polygon because it is curved. An open shape is not a polygon because its sides do not close.

Main Ideas to Remember

• A polygon is a flat, closed shape.
• It has only straight sides.
• The corners are where two sides meet.
• We can name polygons by counting their sides.

Let’s learn the names of some important polygons.

• Triangle: 3 sides and 3 corners
• Quadrilateral: 4 sides and 4 corners
• Pentagon: 5 sides and 5 corners
• Hexagon: 6 sides and 6 corners

You can think of it like this:

$$ \begin{aligned} 3\text{ sides} &\rightarrow \text{triangle}\\ 4\text{ sides} &\rightarrow \text{quadrilateral}\\ 5\text{ sides} &\rightarrow \text{pentagon}\\ 6\text{ sides} &\rightarrow \text{hexagon} \end{aligned} $$

How to Identify a Polygon

1. Check if the shape is flat.
2. Check if all the sides are straight.
3. Check if the shape is closed.
4. Count the sides.
5. Name the shape.

Let’s look closely at each shape.

Triangle

A triangle has 3 straight sides and 3 corners. Triangles can look different. Some are tall, some are wide, and some may lean to one side. If it has 3 straight sides and is closed, it is still a triangle.

Quadrilateral

A quadrilateral has 4 straight sides and 4 corners. Squares and rectangles are both quadrilaterals because they each have 4 sides.

Pentagon

A pentagon has 5 straight sides and 5 corners. It may not always look the same, but if it has 5 sides, it is a pentagon.

Hexagon

A hexagon has 6 straight sides and 6 corners. Some hexagons look very even, and some do not. They are still hexagons if they have 6 straight sides and are closed.

Worked Example 1

A shape has 3 straight sides and is closed. What is its name?

Step 1: Count the sides: \(3\)

Step 2: Match the number of sides to the name.

$$3\text{ sides} = \text{triangle}$$

Answer: It is a triangle.

Worked Example 2

A shape has 4 straight sides. It looks like a rectangle. Is it a polygon, and what is its name?

Step 1: Are the sides straight? Yes.

Step 2: Is the shape closed? Yes.

Step 3: Count the sides: \(4\)

$$4\text{ sides} = \text{quadrilateral}$$

Answer: Yes, it is a polygon. It is a quadrilateral.

Worked Example 3

A shape has 5 straight sides, but one side is longer than the others. Is it still a pentagon?

Step 1: Count the sides: \(5\)

Step 2: Check that the sides are straight and the shape is closed.

Step 3: The side lengths do not have to be the same.

$$5\text{ sides} = \text{pentagon}$$

Answer: Yes, it is still a pentagon.

Worked Example 4

A shape has 6 sides, but one part is open. Is it a hexagon?

Step 1: Count the sides: it may look like \(6\).

Step 2: Check if it is closed.

Step 3: The shape is open, so it is not a polygon.

Answer: No. It is not a hexagon because a polygon must be closed.

Things to Watch Out For

• Do not name a shape just by how it looks at first. Count the sides.
• A shape can be turned or tilted and still be the same shape.
• If a shape has a curve, it is not a polygon.
• If a shape is open, it is not a polygon.

Quick Practice

Try these by counting the sides:

• 3 sides = triangle
• 4 sides = quadrilateral
• 5 sides = pentagon
• 6 sides = hexagon

Ask yourself these questions:

1. Is it flat?
2. Are all the sides straight?
3. Is it closed?
4. How many sides does it have?

Summary

A polygon is a flat, closed shape with straight sides. We identify polygons by counting their sides. A triangle has 3 sides, a quadrilateral has 4 sides, a pentagon has 5 sides, and a hexagon has 6 sides.

If you are not sure, remember: straight sides, closed shape, count the sides, name the shape.

Defining vs. Non-Defining Attributes

Shapes can look different in many ways. They can be big or small, red or blue, standing up or turned sideways.

But some things about a shape really matter when we name it, and some things do not matter.

In this lesson, we will learn the difference between defining attributes and non-defining attributes.

What is a defining attribute?

A defining attribute is a part of a shape that tells what shape it is.

For 2-dimensional shapes, the defining attributes are things like:

• How many sides the shape has
• How many corners the shape has
• Whether the sides are the same length or not

These are the important parts that help us say, “This is a triangle,” or “This is a rectangle.”

What is a non-defining attribute?

A non-defining attribute is something about a shape that can change, but the shape is still the same shape.

Non-defining attributes include:

• Color
• Size
• Direction or orientation (whether it is turned)

A small triangle and a big triangle are both triangles.

A blue rectangle and a green rectangle are both rectangles.

A square turned sideways is still a square.

Think about it this way:

• If a change makes it a different shape, that change is about a defining attribute.
• If a change does not make it a different shape, that change is about a non-defining attribute.

Main Idea

For many flat shapes, we can sort them by their sides and corners.

• A triangle has 3 sides and 3 corners.
• A rectangle has 4 sides and 4 corners.
• A square has 4 equal sides and 4 corners.

If we change the number of sides, we may change the shape.

If we only change the color, size, or the way it is turned, we do not change the shape.

Let’s look at examples.

Worked Example 1: Same shape, different color

You see two triangles:

• one red triangle
• one yellow triangle

Are they still the same kind of shape?

Step 1: Look at the important parts.

Each shape has 3 sides and 3 corners.

Step 2: Ask what changed.

Only the color changed.

Answer: Yes. They are both triangles.

Color is a non-defining attribute.

Worked Example 2: Same shape, different size

You see two squares:

• one small square
• one large square

Are they both squares?

Step 1: Look at the defining attributes.

Each shape has 4 sides and 4 corners.

The sides of each square are the same length.

Step 2: Ask what changed.

Only the size changed.

Answer: Yes. They are both squares.

Size is a non-defining attribute.

Worked Example 3: Same shape, turned around

Look at a square.

Now turn the square so it looks like a diamond.

Is it still a square?

Step 1: Count the sides and corners.

It still has 4 equal sides and 4 corners.

Step 2: Ask what changed.

Only the direction changed. The shape was just turned.

Answer: Yes. It is still a square.

Turning a shape does not change what shape it is.

Orientation is a non-defining attribute.

Worked Example 4: A defining attribute changes

Look at a triangle. It has 3 sides.

Now imagine a shape with 4 sides.

Is that still a triangle?

Step 1: Remember what makes a triangle a triangle.

A triangle must have 3 sides.

Step 2: Compare the new shape.

The new shape has 4 sides.

Answer: No. It is not a triangle.

The number of sides is a defining attribute.

When a defining attribute changes, the shape can become a different shape.

How to tell if an attribute is defining or non-defining

1. Name the shape.
2. Look at its sides and corners.
3. Ask: If this part changes, does the shape become a different shape?

If the answer is yes, it is a defining attribute.

If the answer is no, it is a non-defining attribute.

Let’s sort some attributes.

For a triangle:

• 3 sides → defining
• 3 corners → defining
• blue → non-defining
• small → non-defining
• turned sideways → non-defining

For a square:

• 4 equal sides → defining
• 4 corners → defining
• red → non-defining
• large → non-defining
• tilted → non-defining

Be careful!

Sometimes a shape looks different because it is turned.

Do not let that trick you.

A triangle is still a triangle when it points up, down, or sideways.

A rectangle is still a rectangle when it is turned.

A square is still a square when it looks like a diamond.

Try this thinking:

• Don’t ask, “What color is it?”
• Don’t ask, “How big is it?”
• Do ask, “How many sides does it have?”
• Do ask, “How many corners does it have?”

Quick Check

1. A green triangle and a purple triangle:

Same shape or different shapes?

Answer: Same shape. Color does not define the shape.

2. A small rectangle and a big rectangle:

Same shape or different shapes?

Answer: Same shape. Size does not define the shape.

3. A square and a shape with 3 sides:

Same shape or different shapes?

Answer: Different shapes. The number of sides is a defining attribute.

Summary

Defining attributes tell us what shape it is. These include things like sides and corners.

Non-defining attributes do not change the name of the shape. These include color, size, and the way the shape is turned.

When you name a shape, look for the parts that matter most: its sides and corners.

Analyzing Quadrilaterals

Today we will learn about quadrilaterals. A quadrilateral is a flat shape with 4 sides.

The word quad means 4. So if a shape has 4 sides, it is a quadrilateral.

We can look closely at a quadrilateral and ask:

• Does it have 4 sides?
• Does it have 4 corners?
• Does it have corners that make a square corner, called a right angle?
• Are some sides the same length?

These clues help us decide what kind of quadrilateral we see.

Main Idea: All of these shapes have 4 sides

Many different shapes can be quadrilaterals. Some look tall, some look wide, and some look slanted. If a shape has 4 straight sides, it is a quadrilateral.

• A rectangle is a quadrilateral with 4 right angles.
• A square is a quadrilateral with 4 equal sides and 4 right angles.
• Some quadrilaterals are not rectangles or squares. They still have 4 sides.

Let’s learn the special parts

1. Sides

A quadrilateral has exactly 4 sides. We can count them: \(1, 2, 3, 4\).

2. Corners

A quadrilateral also has 4 corners. Corners are where two sides meet.

3. Right angles

A right angle is a corner like the corner of a book or a sheet of paper. It makes a square corner.

If a shape has 4 right angles, it could be a rectangle or a square.

4. Equal sides

Equal sides means sides that are the same length.

A square has 4 equal sides. A rectangle has 2 long sides and 2 short sides, but all 4 corners are right angles.

How to tell shapes apart

1. Count the sides. If there are not 4 sides, it is not a quadrilateral.
2. Look at the corners. Are they right angles?
3. Look at the side lengths. Are all 4 sides equal, or only some?
4. Name the shape.

Important fact

A square is also a quadrilateral because it has 4 sides.

A rectangle is also a quadrilateral because it has 4 sides.

A square is also a rectangle because it has 4 right angles. It is a very special rectangle because all of its sides are equal.

Worked Example 1: Is this shape a quadrilateral?

A shape has 4 straight sides and 4 corners.

Step 1: Count the sides. There are \(4\) sides.

Step 2: Count the corners. There are \(4\) corners.

Answer: Yes, it is a quadrilateral.

Worked Example 2: Rectangle or not?

A shape has 4 sides. Its corners are all square corners. Two sides are long, and two sides are short.

Step 1: It has \(4\) sides, so it is a quadrilateral.

Step 2: It has \(4\) right angles.

Step 3: The sides are not all the same length, so it is not a square.

Answer: It is a rectangle.

Worked Example 3: Square or rectangle?

A shape has 4 sides. All 4 sides are equal. All 4 corners are right angles.

Step 1: It has \(4\) sides, so it is a quadrilateral.

Step 2: It has \(4\) right angles, so it is a rectangle.

Step 3: All \(4\) sides are equal, so it is a square.

Answer: It is a square. It is also a rectangle and a quadrilateral.

Worked Example 4: A different quadrilateral

A shape has 4 sides, but it does not have 4 right angles.

Step 1: Count the sides. There are \(4\) sides.

Step 2: It is a quadrilateral.

Step 3: It does not have \(4\) right angles, so it is not a rectangle or a square.

Answer: It is a quadrilateral, but not a rectangle or square.

Let’s compare shapes

• Square: 4 sides, 4 right angles, all sides equal
• Rectangle: 4 sides, 4 right angles, not always all sides equal
• Other quadrilateral: 4 sides, but not 4 right angles

Quick check questions

Ask yourself these when you see a shape:

• Does it have exactly \(4\) sides?
• Does it have exactly \(4\) corners?
• Are the corners right angles?
• Are all the sides equal?

Try thinking about these

• If a shape has \(3\) sides, is it a quadrilateral? No.
• If a shape has \(4\) sides and \(4\) right angles, could it be a rectangle? Yes.
• If a shape has \(4\) equal sides and \(4\) right angles, is it a square? Yes.
• If a shape has \(4\) sides but no square corners, is it still a quadrilateral? Yes.

Summary

A quadrilateral is a shape with 4 sides and 4 corners.

To analyze quadrilaterals, count the sides, look at the corners, and check whether sides are equal.

A rectangle has 4 right angles. A square has 4 right angles and 4 equal sides.

When you look carefully at sides and corners, you can tell what kind of quadrilateral a shape is.

Identifying 3D Solids

Shapes can be flat or solid. Flat shapes are 2D shapes, like squares and circles. Solid shapes are 3D solids. That means they are not flat. They have length, width, and height.

You can hold a 3D solid in your hand. A box, a ball, and a can are all 3D solids.

In this lesson, we will learn to name these 3D solids:

• cube
• rectangular prism
• cone
• cylinder
• sphere

How to Tell 3D Solids Apart

When we look at a solid shape, we can ask:

• Does it have flat faces?
• Does it have a curved surface?
• Can it roll?
• Can it stack?
• Does it have a point?

These clues help us identify the shape.

1. Cube

A cube is a solid shape with flat faces that are all the same size and shape. Each face is a square.

A cube has:

• only flat faces
• faces that are all squares
• equal sides

A cube does not roll easily because it has flat faces.

Real-life examples of a cube:

• a dice
• a toy block
• an ice cube

2. Rectangular Prism

A rectangular prism is a solid shape with flat faces. Its faces are rectangles.

A rectangular prism has:

• only flat faces
• faces shaped like rectangles
• a box-like shape

Some rectangular prisms look long. Some look short. They are not all the same in every direction like a cube.

A rectangular prism does not roll easily because it has flat faces.

Real-life examples of a rectangular prism:

• a cereal box
• a tissue box
• a brick

Cube or Rectangular Prism?

A cube is a special kind of box shape. All its faces are squares. A rectangular prism is also a box shape, but its faces are rectangles. If all the faces are equal squares, it is a cube. If not, it is a rectangular prism.

3. Cone

A cone has:

• one flat circular face on the bottom
• one curved surface
• one point at the top

A cone can roll because it has a curved surface. It can also stand on its flat bottom.

Real-life examples of a cone:

• an ice cream cone
• a party hat
• a traffic cone

4. Cylinder

A cylinder has:

• two flat circular faces
• one curved surface
• no point

A cylinder can roll on its curved surface. It can also stand on one of its flat circular faces.

Real-life examples of a cylinder:

• a soup can
• a paper towel tube
• a candle

5. Sphere

A sphere is a solid shape that is round all over.

A sphere has:

• no flat faces
• only a curved surface
• no point

A sphere rolls very easily because it is curved all over.

Real-life examples of a sphere:

• a ball
• an orange
• a marble

Quick Clue Chart

• Cube: flat faces, all faces are squares
• Rectangular prism: flat faces, faces are rectangles
• Cone: 1 flat circle, 1 curved surface, 1 point
• Cylinder: 2 flat circles, 1 curved surface, no point
• Sphere: no flat faces, curved all over

Worked Example 1

Question: Mia sees a ball on the playground. What 3D solid is it?

Think: A ball is round all over. It has no flat faces and no point.

Answer: The ball is a sphere.

Worked Example 2

Question: Ben has a can of beans. What 3D solid is the can?

Think: A can has two flat circular ends and one curved surface.

Answer: The can is a cylinder.

Worked Example 3

Question: Ava is holding a toy block. All the faces are squares. What 3D solid is it?

Think: A shape with flat faces that are all squares is a cube.

Answer: The toy block is a cube.

Worked Example 4

Question: Leo sees an ice cream cone. What 3D solid is it?

Think: It has one flat circular bottom, one curved surface, and one point.

Answer: It is a cone.

How to Choose the Correct Name

1. Look to see if the shape is flat or solid.
2. If it is solid, check for flat faces and curved surfaces.
3. Look for a point.
4. Think about real-life objects that match the shape.
5. Name the solid: cube, rectangular prism, cone, cylinder, or sphere.

Let’s Compare

Cone and Cylinder

• Both have a curved surface.
• A cone has 1 flat circular face and 1 point.
• A cylinder has 2 flat circular faces and no point.

Cube and Rectangular Prism

• Both have only flat faces.
• A cube has faces that are all squares.
• A rectangular prism has faces that are rectangles.

Cylinder and Sphere

• Both can roll.
• A cylinder has 2 flat faces.
• A sphere has no flat faces.

Try to Remember

• Cube = like a small block
• Rectangular prism = like a box
• Cone = like an ice cream cone
• Cylinder = like a can
• Sphere = like a ball

Summary

3D solids are shapes that are not flat. They take up space and can be held.

You can identify 3D solids by looking at their flat faces, curved surfaces, and points.

Remember these important names:

• cube
• rectangular prism
• cone
• cylinder
• sphere

When you see an object, ask yourself: Does it look like a block, a box, a cone, a can, or a ball? That will help you name the 3D solid.

Faces, Edges, and Vertices

Today we will learn about parts of 3D shapes. A 3D shape is a shape that is solid. It is not flat. You can hold it in your hand.

Some 3D shapes are like objects you see every day. A box is a 3D shape. A can is a 3D shape. A ball is a 3D shape.

When we study 3D shapes, we can look for three important parts: faces, edges, and vertices.

What is a face?

A face is a flat surface on a 3D shape. If you put a shape down on a table, one flat part touching the table can be a face.

A cube has flat sides, so it has faces. A rectangular prism also has faces. A sphere, like a ball, does not have any flat faces.

What is an edge?

An edge is where two faces meet. It looks like a line on the shape.

If a shape has flat faces, you can often trace an edge with your finger. A cube has many edges because all of its faces meet along lines.

What is a vertex?

A vertex is a corner of a 3D shape. It is the point where edges meet.

The plural of vertex is vertices. That means more than one corner.

Let’s remember:

• Face = flat surface
• Edge = line where two faces meet
• Vertex = corner where edges meet

Common 3D Shapes

Here are some shapes you may know:

• Cube — like a dice or a small box
• Rectangular prism — like a cereal box
• Sphere — like a ball
• Cylinder — like a can
• Cone — like an ice cream cone

Some of these shapes have many faces, edges, and vertices. Some have only a few. Some have none.

How to count faces, edges, and vertices

1. Hold the shape or picture still.
2. Find the flat faces first.
3. Then count the edges where faces meet.
4. Last, count the vertices, or corners.
5. Count slowly so you do not count the same part twice.

It can help to touch each part as you count it.

Shape facts to know

• A cube has 6 faces, 12 edges, and 8 vertices.
• A rectangular prism has 6 faces, 12 edges, and 8 vertices.
• A sphere has 0 flat faces, 0 edges, and 0 vertices.
• A cylinder has 2 flat faces, 2 curved edges, and 0 vertices.
• A cone has 1 flat face, 1 curved edge, and 1 vertex.

For a cylinder and a cone, some parts are curved. That is why they are a little different from cubes and prisms.

Worked Example 1: Cube

Let's look at a cube.

First, count the flat faces. A cube has a front, back, left, right, top, and bottom.

So the number of faces is:

$$6$$

Now count the edges. A cube has 12 edges.

Now count the corners. A cube has 8 vertices.

Answer: A cube has 6 faces, 12 edges, and 8 vertices.

Worked Example 2: Rectangular Prism

Now look at a rectangular prism, like a cereal box.

It has 6 flat faces.

It also has 12 edges where the faces meet.

And it has 8 vertices, or corners.

Answer: A rectangular prism has 6 faces, 12 edges, and 8 vertices.

Worked Example 3: Cone

Now think about an ice cream cone shape.

It has 1 flat face on the bottom.

It has 1 edge around the circle where the flat face meets the curved side.

It has 1 point at the top. That point is a vertex.

Answer: A cone has 1 face, 1 edge, and 1 vertex.

Worked Example 4: Sphere

Now think about a ball.

A ball is a sphere. It is round all over.

It has no flat faces.

It has no edges because no flat faces meet.

It has no vertices because it has no corners.

Answer: A sphere has 0 faces, 0 edges, and 0 vertices.

Tips to help you remember

• Faces are flat.
• Edges are lines where faces meet.
• Vertices are corners.
• If a shape is round like a ball, it may have no faces, no edges, and no vertices.
• If a shape looks like a box, it usually has many faces, edges, and vertices.

Let’s compare some shapes

A cube and a rectangular prism are alike because they both have:

• 6 faces
• 12 edges
• 8 vertices

A cone and a cylinder are different.

• A cone has 1 vertex, but a cylinder has 0 vertices.
• A cylinder has 2 flat faces, but a cone has 1 flat face.

Quick check

• How many vertices does a cube have? 8
• How many faces does a sphere have? 0 flat faces
• What do we call the lines where two faces meet? Edges
• What do we call corners on a 3D shape? Vertices

Summary

3D shapes have different parts that help us describe them.

Faces are flat surfaces. Edges are where faces meet. Vertices are corners.

When you look at a 3D shape, count the faces first, then the edges, and then the vertices. This will help you describe and compare shapes correctly.

Composing Complex Shapes means putting smaller shapes together to make a bigger shape. It is like building with shape pieces. When we join shapes, we can make new pictures and new larger shapes.

For example, two small triangles can be put together to make a bigger shape. A square and a triangle can be put together to make a house shape. We use our eyes to notice how shapes fit together.

In this lesson, you will learn how to:

• look at simple shapes,
• put shapes together,
• tell what bigger shape they make,
• and describe the parts of a larger shape.

First, let’s remember some basic shapes.

• Triangle: a shape with 3 sides.
• Square: a shape with 4 equal sides.
• Rectangle: a shape with 4 sides, with 2 long sides and 2 short sides.
• Circle: a round shape with no straight sides.

When we compose shapes, we join two or more smaller shapes. The smaller shapes are called parts. The new big shape is the whole.

Think about a puzzle. Each puzzle piece is a part. When the pieces fit together, they make a whole picture. Shapes can work the same way.

How to compose shapes

1. Look at the small shapes.
2. Notice their sides and corners.
3. Think about how the shapes can touch.
4. Put them together to make a new shape.
5. Name the larger shape, if you can.

Sometimes the new shape has a name, like a rectangle or a square. Sometimes it makes a picture, like a rocket or a house. Both are examples of composing shapes.

Important idea: A larger shape can be made from smaller shapes.

Here are some ways shapes can fit together:

• Two triangles can make a square or a rectangle.
• Two squares can make a rectangle.
• A square and a triangle can make a house-like figure.
• Several rectangles can make a bigger rectangle.

When shapes fit together, their sides often line up. This helps the new shape look neat and complete.

Worked Example 1

You have 2 small squares. Put them side by side.

What larger shape do they make?

They make a rectangle.

Why? Each square has 4 sides. When the two squares touch along one side, the outside edge of the whole shape looks like one long rectangle.

You can think of it like this:

$$1\text{ square} + 1\text{ square} = 1\text{ rectangle}$$

Worked Example 2

You have 2 matching triangles. Put them together along one side.

What larger shape could they make?

They can make a square.

The two triangles are the parts. The square is the whole.

This shows that small shapes can join to make a different shape.

$$2\text{ triangles} = 1\text{ square}$$

Worked Example 3

You have 1 square and 1 triangle. Put the triangle on top of the square.

What could this look like?

It can look like a house.

The square makes the bottom. The triangle makes the roof.

This is a composite shape. That means it is made of more than one simple shape.

Worked Example 4

You have 3 rectangles. Two are vertical, and one is horizontal across the top.

What picture can they make?

They can make a shape like a door frame or a big upside-down U.

Even if the new figure is not a single basic shape name, it is still a larger shape made by composing smaller shapes.

How to figure out a composite shape

Sometimes you see a big shape and need to find the smaller shapes inside it. Here is what to do:

1. Look at the whole shape carefully.
2. See if you can spot smaller familiar shapes inside.
3. Count the parts.
4. Name the shapes you found.

For example, if you see a house picture, you might say:

• “I see 1 square.”
• “I see 1 triangle.”
• “Together they make a house.”

Tips for success

• Look for straight sides that match.
• Turn shapes in your mind to see if they fit.
• Ask yourself: “What smaller shapes do I see?”
• Ask yourself: “What bigger shape can these parts make?”

Let’s compare part and whole.

If a large rectangle is made from 2 small squares, then:

• The parts are 2 squares.
• The whole is 1 rectangle.

If a large picture is made from 1 rectangle and 2 triangles, then:

• The parts are 1 rectangle and 2 triangles.
• The whole is the full picture they make together.

Try thinking about these:

• If you put 2 triangles together, what might they make?
• If you put 2 squares together, what larger shape do you get?
• If you see a big shape, can you break it into smaller shapes?

There can sometimes be more than one right way to compose shapes. The same pieces can be arranged in different ways to make different larger shapes or pictures.

Why this matters

Composing shapes helps you understand how shapes work. It also helps with puzzles, building, drawing, and seeing how parts make a whole.

When you practice, you get better at noticing sides, corners, and how shapes fit together. That is an important geometry skill.

Summary

Composing complex shapes means joining smaller simple shapes to make a larger shape or picture. We can use shapes like triangles, squares, and rectangles as parts. Then we look at the whole shape they make together.

Remember:

• Small shapes can make a big shape.
• The small shapes are the parts.
• The big shape is the whole.
• Shapes can be put together in different ways.

Keep practicing by looking at shape puzzles and asking, “What shapes do I see, and what can they make together?”