For children in kindergarten and up, geometry and spatial relationships are a part of their daily lives. Understanding an object’s position in space and learning the vocabulary to describe a position and give directions are important. Terms like **above**,** below**,** left**,** right**, or **between** enable children to orient themselves with their surroundings and describe the world around them. They can apply these same terms when describing plane and solid shapes in the classroom.

## Flat Plane Shapes

Most of the objects that we encounter can be associated with basic shapes. A closed two-dimensional, or flat, figure is called a **plane shape**. Different plane shapes have different attributes, such as the number of **sides** or **corners **(or **vertices**). A side is a straight line that makes part of the shape, and a corner, or vertex, is where two sides meet.

**Key standard:**Analyze and compare two- and three-dimensional shapes, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes. (Grade K)

Although children are familiar with the most common shapes, before kindergarten, they may not have been able to verbalize what distinguishes a square from a rectangle or a circle from a triangle. They will learn to describe shapes in terms of their sides and corners.

A **triangle** is a shape with three sides and three corners. A **rectangle** is a shape with four sides and four corners. They may notice that opposite sides are the same length.

A **square** is a rectangle in which all four sides are of equal length. A **circle** is a round shape that has no sides or corners. These attributes, as well as size, can be used to sort and classify shapes.

**Extend the Lesson**

- For students who are ready, you may want to show how the sides must be straight and the corners must be right angles for the shape to truly be a rectangle.
- For students who are ready, you may want to show how all the points of a circle must be the same distance from a center point for the shape to truly be a circle.
- Flags around the world present colorful ways to showcase all sorts of shapes and designs. What countries interest your students? Showcase their flags and have students identify the flat plane shapes they see.

## Solid Shapes

Many of the everyday objects that children are familiar with are **solid shapes.** For example, blocks are often **cubes** or **rectangular prisms**. They have six **faces**, or flat surfaces.

Other familiar solid shapes are **spheres**, which children might recognize as being shaped like balls. One shape children might not immediately recognize is a **pyramid**, which has one rectangular face and four triangular faces. They will likely, however, recognize **cylinders**, which are shaped like cans, and **cones**, like ice cream cones or traffic cones.

As with plane shapes, children will learn to describe solid shapes in terms of their attributes. For example:

- Roundness or flatness
- Ability to roll or slide
- Number of sides or corners

They will also come to see how the plane shapes comprise the faces of solid shapes. This is an important idea, as the real world around us is three dimensions and made of solid shapes! The place where people see flat plane shapes is generally on the faces of 3-D objects. Because of this, it is common to teach solid shapes first before moving on to plane shapes, which we practice in *HMH Into Math*.

Tracing around the face of solids will help a child understand a cube differs from a rectangular prism because all six of its faces are squares. This will enrich the ways in which they can describe and compare solids. For example, a child might see that although both a cylinder and a sphere can roll, a sphere has no faces and cannot slide. A cylinder, on the other hand, has two circular faces, so it can both roll and slide. (But some cylinders will slide more easily than others!)

**Extend the Lesson**

- For students who are ready, you may want to show how the faces of cubes and rectangular prisms must meet at right angles, or all the points on a surface of a sphere are the same distance from a central point.
- Does your school have access to a 3-D printer? Don’t just describe shapes like cubes or spheres—actually
*create*them! Present the 3-D printed objects to the class and have them share what they notice and wonder. - Have students identify solid shapes in the real world! Either bring objects, such as an ice cream cone, number cube, or soccer ball, for students to describe and classify, or have students look for objects outside of school to share. Consider what interests your students. Look for buildings near the school and around the world with interesting shapes or balls from sports that your students like to play.
- Origami presents an exciting way to transform a flat plane shape into a solid shape. Look online for folding ideas, such as creating a cube. You can also look for printouts that let students construct 3-D shapes or have students create cubes, pyramids, and other solid shapes using toothpicks and marshmallows.

Once children can recognize and describe the attributes that distinguish plane and solid shapes, such as those that make a triangle different from a square or a cylinder different from a cone, they can begin to create and continue patterns. When children create or find patterns, they are using the attributes of not just one but of a series of shapes to determine the order or pattern.

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*Grow student confidence in mathematics with *HMH Into Math*, our core math solution for Grades K–8.*

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