## Geoboards

Students use appropriate vocabulary to describe shapes to their classmates. Students focus on the properties of shapes to develop mental images of objects from descriptors. They create multiple representations of triangles using geoboards, string, and crayons and paper.

Review the previous lesson by having students share their homework drawings of objects found at home that include triangles. Emphasize geometry vocabulary such as sides, edges, and angles. Next give the students brown paper bags that contain objects with distinctive geometric properties.

Have students take turns placing their hands into their bags and selecting one of the objects to describe (without removing the object from the bag). Other students pose questions with “yes” or “no” answers to elicit additional clues from the student holding the shape. After several cluse have been provided, call on a student to guess the shape.

Discuss with students the vocabulary that helped them identify the shapes. Their answers should include “sides,” “edges,” “corners,” “angles,” “triangle,” and so forth. Post these words in the room for future reference.

Before distributing geoboards strung with three different-colored rubber bands, establish rules the class will follow when using them. For example, geobands are only to be used for constructing shapes on the geoboards. Give students time to do free exploration with the geoboards. It may be helpful to demonstrate using an overhead geoboard.

Display triangles and non-triangles, as shown below. Ask students to identify the triangles you have created.

Distribute geoboards strung with three different colors of rubber bands. Ask students to make triangles using the three different colors of rubber bands for the sides of their triangles and draw pictures of them using the same color crayon as the rubber band. (Make sure the students' concrete and pictorial representations have straight sides and closed corners.) For drawing the pictures, you may want to use the Geoboards Activity Sheet.

- Brown paper bags
- Geoboards and geobands
- Objects with distinct geometric properties, such as attribute or pattern blocks
- Geoboards Student Activity Sheet

Assessment Options

- Record information about what students know, are in the process of learning, and need to know using the teacher resource sheet Class Notes.
- Photograph students with their geoboard triangles and place these photographs in their portfolios.

**Extensions**

- Place the students into groups of three or four. Provide each group with a string of yarn tied together at the ends to form a circle. Ask students to hold the yarn in front of them and form triangles of different sizes and “shapes” (triangles in different orientations and with different angles). The [Geometry Standard for Grades Pre-K-2 includes a picture of students using yarn to make triangles (figure 4.17).] Students could also make triangles with their fingers.
- Move on to the last lesson,
*Making Virtual Triangles*.

**Questions for Students**

1. How many sides does each triangle have?

[Three.]

2. Please make a triangle that is different from the one you made. Where are other triangles with the same “shape” as yours?

[Student responses may vary.]

3. Would you practice drawing a triangle in the air by watching me draw one in the air?

[Observe students as they follow along with you.]

4. What number do you use most often when you are describing a triangle?

[The number three.]

5. When you draw a triangle without tracing, what do you need to remember?

[A triangle’s sides are straight. A triangle has 3 sides and three corners.]

### Three Sides

### Tracing and Drawing

### Making Virtual Triangles

### Learning Objectives

Students will:

- Identify and recognize triangles using multiple representations.
- Locate triangles in their environment.
- Construct triangles.

### NCTM Standards and Expectations

- Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.

- Recognize and represent shapes from different perspectives.

- Recognize geometric shapes and structures in the environment and specify their location.

### Common Core State Standards – Mathematics

-Kindergarten, Geometry

- CCSS.Math.Content.K.G.A.2

Correctly name shapes regardless of their orientations or overall size.

-Kindergarten, Geometry

- CCSS.Math.Content.K.G.A.3

Identify shapes as two-dimensional (lying in a plane, ''flat'') or three-dimensional (''solid'').

-Kindergarten, Geometry

- CCSS.Math.Content.K.G.B.4

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).

-Kindergarten, Geometry

- CCSS.Math.Content.K.G.B.5

Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Grade 1, Geometry

- CCSS.Math.Content.1.G.A.1

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

Grade 2, Geometry

- CCSS.Math.Content.2.G.A.1

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.