# What Are Shapes? A Guide For Teachers & Students

**Shapes are a part of the geometry domain throughout the early elementary grades. Students learn how to define math shapes, learn the attributes of basic shapes, categorize math shapes by attribute and eventually learn to measure various math shapes.**

This blog post covers an overview of math shapes taught in the elementary grades with helpful charts and diagrams with visual models for teachers and students.

## What are shapes?

Shapes are outlines or the outer surface of objects. They can be classified as 2D shapes and 3D shapes. Two-dimensional shapes are measured in two dimensions, length and height. Three-dimensional shapes are measured in three dimensions, length, width and height.

Often, people use shape to describe objects in the real world. For example, someone might say â€˜the ball is in the shape of a sphere,â€™ or â€˜the stop sign is an octagon.â€™

Types Of Quadrilaterals Worksheet

Types Of Quadrilaterals worksheet for 4th and 5th Graders. Includes 10 skills based practice questions, 5 applied questions, answer key and links to the common core state standards.

Download Free Now!### Basic shapes

Students learn about basic shapes in elementary school. Some of the most common basic shapes students learn about in the elementary grades are circles, squares, rectangles, pentagons and hexagons.

Basic shapes are often thought of as two-dimensional shapes. They are usually closed shapes and can have curved sides or straight sides with measurable line segments.

The following list highlights some of the most basic shapes, the shape definition or the properties of shapes that students learn about in the elementary grades.

Teachers can use tools such as tangrams or pattern blocks to help students learn about the properties of shapes. These blocks are a great hands-on way for students to be able to recognize the number of sides and vertices as well as find similarities and differences between shapes. They can also use pattern blocks to compose larger shapes from smaller shapes.

Additionally, teachers may use a shapes song or flashcards to develop students’ foundational understanding of shapes and their properties.

### Triangles

Triangles are three-sided closed shapes with sides that are straight line segments. These polygons are two-dimensional and have three interior angles with a combined measure of 180 degrees. In higher grades, missing triangle lengths are measured using the Pythagorean Theorem.

Triangles are everywhere in the real world and are commonly used in engineering and architecture design for stability.

IMAGE OF PIZZA SLICE, TRAFFIC SIGN, SAILBOAT SAIL, TRIANGLE BUILDING

Beginning in fourth grade, students learn the different types of triangles. They learn to categorize triangles by side length and by angle. The following chart of triangles is categorized by side length.

Regardless of the type of triangle, the Triangle Inequality Theorem states that the sum of two sides of a triangle is greater than, or equal to the length of the third side. This becomes important as students learn to measure side lengths in fourth grade and beyond.

Often, triangles are also categorized by angle measure. Sometimes, angle measure and side length categories can overlap. For example, an equilateral triangle is always an acute triangle because interior angles measure 60Â° which is less than 90Â°. However, isosceles triangles and scalene triangles can be acute, obtuse or right.

### Different types of shapes

Many different types of shapes make up objects in the world. One of the most common ways to categorize different types of shapes is whether they are polygons and non-polygons.

Polygons are two-dimensional closed shapes with straight side lengths. This means that all sides are straight and connect at a vertex. Non-polygons can either have curved side lengths, or be open shapes where not all sides connect at vertices.

Hereâ€™s a classification of some of the most common polygons and non-polygons that students learn about in the elementary grades:

Within each polygon category, there are regular and irregular shapes. Regular polygons have congruent sides that are all the same length. Irregular polygons have different side lengths.

### Dimensional shapes

Elementary students learn about a variety of 2D shapes and 3D shapes. Three dimensional shapes are measured in three dimensions: length, height and width. If a 3D shape is small enough, it can be held in your hand, as opposed to a 2D shape which is flat. For example, a two-dimensional shape such as a circle can only exist on a flat surface and be measured using two dimensions, length and height.

A cone is a three-dimensional shape measured using three-dimensions: length, height and width. Some three-dimensional shapes are small enough to hold, such as a can of beans shaped like a cylinder. Others are too large to be held. For example, the earth is a sphere and the pyramids of Giza are square-based pyramids.

Here are the most common three-dimensional shapes:

Teachers can support students in building an understanding of two-dimensional vs. three-dimensional shapes by using play-doh, or any other type of modeling dough. Teachers can have students draw a two-dimensional shape, such as a circle, in a flat piece of dough using a pencil or stick. Then they can create a sphere by rolling the dough in their hands. This helps students to understand the difference between flat shapes and shapes that have three dimensions.

### Geometric shapes

Geometric shapes are everywhere in our environment. These shapes are commonly referred to as two-dimensional geometric shapes and are created using points, line segments, and curves.

The sides of geometric shapes meet at vertices which create angles. Geometric shapes have length and height. They also have measurable area. There are many geometric shapes that are simple shapes. There are also some that are more complex.

The most common 2d geometric shapes are:

- Circles
- Ellipses
- Squares
- Rectangles
- Trapezoids
- Rhombuses
- Parallelograms
- Pentagons
- hexagons
- Octagons
- Decagons

The shape name of many geometric shapes describes the number of sides the shape has. For example, the prefix tri- means â€˜threeâ€™ so a triangle has three sides. Similarly the prefix oct- means â€˜eightâ€™ so an octagon has eight sides. Elementary students usually learn about the shapes listed above, however it should be noted that heptagons, nonagons, decagons, hendecagons and dodecons are geometric shapes as well.

### Closed shapes

Closed shapes are shapes where the beginning point and the ending point of the shape outline are at the same point. This means that the lines connect in a continuous path, as opposed to starting and ending at different points or having openings in the shape.

The perimeter of a closed shape is measurable. Closed shapes can have curved sides such as a circle. They can also have straight sides such as the line segments in a square. Closed shapes can be organic shapes or can be more rigid shapes with straight side lengths such as polygons.

### Line segments, vertices and edges

A line segment in geometry is a line that has two distinct endpoints. Line segments can stand alone or can be parts of other, longer lines or shapes.

Vertices are the places where two or more curves, lines or edges meet/intersect. The vertex where two lines meet forms a measurable angle. An edge is the place where two or more faces in a shape meet. They can also be described as the line segments that join one vertex to another.

Line segments, vertices and edges can be identified in 2d and 3d shapes. For example, a square has 4 vertices, 4 line segments and 1 face. A cube has 6 flat faces, 12 edges and 8 vertices.

### Solid shapes

Solid shapes are also known as three-dimensional geometric shapes. They are shapes that take up space in three dimensions. The three dimensions of a solid shape that can be measured are length, height and width.

A solid shape has volume. Solid shapes are composed of other 2d shapes creating line segments, faces, vertices and edges. Some examples of solid shapes include:

- Cube
- Pyramid
- Cone
- Sphere
- Prism

### Curved lines and curved shapes

Curved lines are lines that are not straight. In other words, lines that bend or are not composed of straight line segments are considered curved lines. The arched shape of a rainbow or a parabola are examples of curved lines.

Curved shapes are composed of continuous curved lines. For example, a circle, ellipse and oval are all curved shapes. Curved shapes have no fixed sides or vertices, and have a radius of curvature at each point around the shape.

Curved shapes contrast with straight shapes, which are shapes composed of straight line segments. Straight shapes have vertices where line segments meet, and an internal angle measure at each vertex. Curved shapes by definition do not have vertices. In the elementary grades, the main curved shapes that students learn about are:

- Cicles
- Ovals
- Ellipses

### Symmetry and equal sides

Many shapes have sides that are congruent. Congruent means the same measure. In geometry, these are often called regular polygons. Shapes with all equal sides also have internal angles that are congruent. Some examples of polygons with equal side lengths include:

- Equilateral triangle
- Square
- Regular pentagon
- Regular hexagon
- Regular octagon

This concept is challenging for students at first, so teachers can support students in understanding symmetry by doing various paper folding activities. First, instruct students to draw a regular polygon. Alternatively, the teacher can provide a printed copy of one. Then, students fold the paper in half to see that both halves are mirrors of each other. This is symmetry. It is also helpful to try this with shapes that have no lines of symmetry, or to have students fold it in a different way to see how the sides do not match in shapes that do not have lines of symmetry.

Shapes with equal side lengths have more lines of symmetry than shapes with varying side lengths. A line of symmetry occurs when a shape is divided directly in half either by folding, cutting or drawing a line and each half is a mirror image of the other half. For example, when a square is cut directly in half, it has two identical halves that are mirror images of each other.

The number of lines of symmetry of a regular polygon is equal to the number of sides of the polygon. For example, an equilateral triangle has 3 lines of symmetry and a square has 4 lines of symmetry. The chart below shows more examples of lines of symmetry in regular polygon:

### When do students learn about shapes?

Student understanding of math shapes develops across a progression of skills throughout the elementary grades. The progression begins with identifying shapes, then progresses to categorizing shapes, and then builds towards measuring shapes.

The skills that elementary students learn related to shapes are primarily in the Geometry and Measurement & Data domains of the common core state standards. The following shows the progression in more detail.

**Kindergarten and first grade**

- Identifying basic shapes
- Differentiating between 2d and 3d shapes
- Learning the defining attribute of shapes (and contrasting this with non-defining attributes such as size, color and orientation).

**Second and Third grade**

- Drawing and identifying shapes with specific characteristics
- Learning new shapes
- Partitioning shapes
- Categorizing various polygons such as quadrilaterals
- Measuring perimeter and area of rectangles

**Fourth grade**

- Measuring angles
- Categorizing triangles by angle measure
- Identifying lines of symmetry
- Finding area and perimeter of rectangles

**Fifth and Sixth grade**

- Categorizing shapes based on a hierarchy of characteristics
- Calculating volume of three-dimensional rectangular prisms
- Drawing polygons on the coordinate plane.

At all levels of development, it is important for children to get experience with hands-on math manipulatives to learn about shape. Pattern blocks, tangrams, modeling dough as well as geoboards are all great ways for students to identify shapes, create shapes and measure shapes. This conceptual understanding is the foundation for students as they progress in their geometry understanding.

Teachers can also play games at every level such as a scavenger hunt for shapes around the room or have students make shapes with their bodies.

### Worked examples

#### 1. Grade level: Kindergarten

What is the name of the following shape? How do you know it is that shape?

**Answer:** This is a triangle because it has 3 sides. This same type of problem can be created with squares and trapezoids, as well as various 3d shapes such as cones, cylinders, spheres and cubes.

#### 2. Grade level: First Grade

Draw a picture of a square. How do you know the shape you drew is a square?

**Answer:**

Students should draw a four sided closed shape (polygon) which is a square. They should be able to identify that it is a square because it has 4 sides which meet at corners (vertices) and all sides are the same length.

#### 3. Grade level: Second Grade

What makes a square and a cube different? Explain your thinking.

**Answer:** A square is a two-dimensional geometric shape, while a cube is a three-dimensional geometric shape. A square has length and height that can be measured and is flat. A cube has length, height and width that can be measured and is three dimensional. A square has one face, four line segments and four vertices. A cube has six faces, twelve edges and eight vertices.

#### 4. Grade level: Third Grade

Which of the following quadrilaterals is also a rectangle?

- Square
- Trapezoid
- Rhombus
- Parallelogram

**Answer:** A square is also a rectangle because it has square corners. In other words, its vertices meet at 90 degree angles. The only thing that makes a square more unique than a rectangle is that its sides are all the same length. A square is a rectangle. A trapezoid, rhombus and parallelogram by definition are not.

It should be noted that a parallelogram can be a rectangle, but it is not always a rectangle. It is only a rectangle if all four angles are 90Â°.

#### 5. Grade level: Fourth Grade

Is the following triangle equilateral, isosceles or scalene? How do you know?

**Answer:** This is a scalene triangle because all three sides are different lengths.

#### 6. Grade level: Fifth Grade

What is the volume of the rectangular prism?

**Answer:** Volume can be calculated by using the formula length x width x height. In this case 8 x 2 x 3 = 48 cubic units.

### Practice problems

Shapes are everywhere in real life. In our environment, everything has shape. So it is important that students can identify various shapes and their attributes. Bringing in real-world examples can also increase engagement and make lessons more fun. These word problems are examples of shapes in the real world.

#### Grade level: Kindergarten & First grade

Mr. Newsom saw three street signs while he was driving his car. Which street sign is a circle?

**Answer:** The railroad crossing sign is a circle. The outline of the shape has one continuous curved line. The yield sign is a triangle, the stop sign is an octagon and the dead end sign is a rotated square/diamond.

#### Grade level: Second & Third grade

Lorelai wanted to build a fence around her yard. Her yard is a rectangle that is 24 feet long and 18 feet wide. How much fencing will Lorelai need to cover the perimeter of her yard with fencing?

**Answer:** The perimeter of the yard is 84 feet.

#### Grade level: Fifth grade

The moving company has two different sized boxes. Both boxes are shown below. Which box has a larger volume? Explain.

**Answer:** Box B has a larger volume 17,576 cubic inches. Box A has a volume of 15,522 cubic inches.

### Shapes worksheets & resources

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Sessions cover the full range of standards, including Geometry. Tutors personalize lessons and work at a pace and pitch to suit the student.

#### Shapes FAQs

##### 1. what are 20 shapes?

The following is a list of shapes:

- Circle
- Square
- Triangle
- Rectangle
- Pentagon
- Hexagon
- Heptagon
- Octagon
- Nonagon
- Decagon
- Sphere
- Cone
- Cylinder
- Cube
- Triangular pyramid
- Rectangular pyramid
- Hexagonal pyramid
- Triangular prism
- Rectangular prism/cuboid
- Hexagonal prism

##### 2. What are basic shapes of the universe?

The most basic shapes of the universe are shapes seen in everyday life. A sphere is the shape of all the planets in our solar system and is seen in everyday life in balls of various sizes

##### 3. What is the most popular shape in the world?

It can be argued that a circle or a square are the most popular shapes in the world. Both circles and squares are the shapes seen most commonly in objects in daily life.

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