### Purpose

To give students opportunities to recognize, describe, build, and explore shapes in many different contexts.

### Context

In this investigation, students look for examples of patterns and shapes in both the natural and designed world. This investigation uses tangrams, or pattern blocks, in many of the activities. If these resources are unavailable, see Constructing Your Own Set of Tangrams on Tom Scavo's Tangrams.

### Motivation

To begin an investigation of shapes and patterns, allow students ample time for free exploration of the tangrams. Students will naturally begin to explore the shapes and patterns that they can create. Challenge students to use the tangram shapes to create familiar images such as buildings, animals, playground objects, etc.

Allow opportunities for students to work in pairs. Have students create a shape for their partner to duplicate. Or, have one partner create a pattern for the other to continue. To make this activity more challenging, put a barrier between the students and see if they can create identical shapes or patterns based only on their partner’s verbal description.

### Development

**Building shapes**

Go to Geometry Through Art from The Math Forum website and choose activities appropriate for your students. In this series of physical activities, students use a length of rope to build everything from straight lines to polygons. Students count the number of sides and corners as they create each shape. They also calculate and compare the area of each shape by counting how many children can fit inside the boundaries of the rope.

**Shape hunt with tangram sets **

Have students select one of the tangram shapes, such as a triangle. Students should look for this shape in classroom objects, on bulletin boards, or in books and magazines. Have them create a collage by drawing and/or cutting and pasting the triangles that they find.

Discuss the following with students:

- What things did you find that were shaped like your tangram piece? Can you think of things outside of the classroom that are this shape?
- Which of the shapes that you found were made by people?
- Which are found in nature?

For older students, it may be an appropriate time to introduce the concept of solid shapes.

Tell students: *"All of the shapes mentioned above are known as geometric shapes. Geometric shapes are created by putting together a certain number of straight lines, or in the case of a circle, curved lines. (Refer back to the physical activity in which students created shapes with a rope.) You probably noticed that some of the objects you found were solid, made up of many flat or curved surfaces."*

Introduce the concept of solid shapes to students and have them locate examples of spheres, cylinders, cubes, cones, pyramids, and rectangular solids in the classroom. Many examples of these shapes can also be found in students’ snacks or lunches.

Students can count and record the number of flat faces and corners on each solid shape. Have them identify the geometric shape of the faces and the base.

**Shapes in the natural and designed world**

Have students explore the outside environment for examples of both geometric and solid shapes. Students should record their findings in their science journals, using pictures and/or words. PBS Online’s Community Geometry offers suggestions on where students can look for shapes in the buildings and objects around them.

Ask students:

- What did you find?
- How many sides does each of the shapes have?
- If the object is a solid shape, what are the shapes of the faces? The base?
- Are there any shapes that you didn’t find? What are some objects in nature that have these shapes?
- What is the difference between geometric shapes and solid shapes?

### Assessment

Ask students to build the geometric shapes using toothpicks. Have students count and record the number of toothpicks used, or the number of sides, for each figure. Have them write or draw one object that has the same shape. For older students, have them build solid shapes using toothpicks and clay.

Ask students:

- Which solid shapes can be built using toothpicks and clay?
- Which cannot? Why?
- Have students identify one example of each solid shape.

### Extensions

Have students try Determining the Relations to find the relationships between the tangram shapes—Which tangrams can be used to create other tangram shapes? How many are needed? Have students count and record the shapes that they have used.