Geoboards

Description:

Geoboards are manipulatives used for geometry. Originally, they were typically made of wood with nails driven half way in and used with elastic bands to form shapes with the nails. Now they are available in clear plastic, which allows them to be viewed from the reverse and also to lay one geoboard over the other. The are typically in a 5x5 layout or 10 x 10 layout. Geoboards are also now available that link together to form a larger working surface. This way, by linking 4 together, they can also be used for graphing with an x and y axis. Geoboards are also available in circles for working with angles and degrees.

Geoboards were invented in the 1950sby Egyptian mathematician Caleb Gattegno. He was also famous for his pedagogical books;“Words in Color” to teach reading and “Silent Way” to teach foreign languages. He popularized the use of Cuisenaire’s rods and book, “Nombres en Couleurs”(Numbers in Color), for use in mathematics.

Square Geoboards

5x5 pin square geoboard

10x10 pin square geoboard

Circular Geoboard

Purpose

Geoboards are a hands-on learning tool for a variety of mathematical investigations about area, perimeter, geometric properties of shapes, fractions, graphing of coordinates (coordinate geoboard), and measuring degrees (circular geoboard). This is a good tool to kinaesthetic learners and visual learners as they can “see and do” geometry. It enables students to make discoveries on their own, and as a jumping point for discussions, which benefits auditory learners.

Sample Activities

Activity1)Building rectangles from triangles

a)Experimenting with the geoboard, create a rectangle from 2 congruent triangles. What kind of triangles must they be?

b)Using Activity 1 sheet (attached), add a second triangle to the one pictured to create a rectangle.

c)Compare the areas of each starter triangle with the final rectangle.

d)Select one of the rectangles from b) above, and cut out the two triangles from dot paper. See if you can make a larger triangle instead of a rectangle in two different ways.

Activity 2) Rhombus

A rhombus is a diamond-shaped quadrilateral with all sides of an equal length. It is a special kind of kite.

Activity:

a)Create a rhombus on the geoboard.

b)A square is a special type of rhombus. Make a square by moving 2 corners of the rhombus you created to new positions.

c)There are only three possible different rhombus shapes on a 5x5 geoboard that are not squares. Find them and record your answers on the dot paper.

Using the design on a rhombus (Activity 2 attached)

d)Find a rhombus in the design. Show it is a rhombus by: measuring and comparing the four sides, cut out the shape on paper and place it on the design. Flip it to see if it still fits. How does this show it is a rhombus?

e)How many other rhombi in the design are congruent to the one found in a) above?

Activity 3) Area of an Isosceles Trapezoid

The area of an isosceles trapezoid can be calculated by using squares and/or rectangles. (see example in “Activity 3” handout.

a)Create 5 isosceles trapezoids with different areas on your geoboard. Calculate the area of each using the same method.

b)Create the smallest possible isosceles trapezoid on a 5x5 geoboard. Find the area.

c)Create the largest possible isosceles trapezoid on a 5x5 geoboard. Find the area.

(Above activities derived from “The Geoboard Collection: Intermediate Level” by Exclusive Educational Products)

Black Line Masters (attached)

Activity 1

Activity 2

Activity 3

Dot paper

Evaluation tools

Assignment 1 –

Building Rectanglesfrom Triangles

Assignment 1 –(cont’d)

Assignment 2 - Rhombi

Assignment 3 – Isosceles Trapezoid

Area = 3 x 2 + 1 x 3 = 9 square units

Dot Paper

Assignment 2 - Rhombi

Part 2

Using this design:

a)Find a rhombus in the design. Show it is a rhombus by: measuring and comparing the four sides, cut out the shape on paper and place it on the design. Flip it to see if it still fits. How does this show it is a rhombus?

b)How many other rhombi in the design are congruent to the one found in a) above?

Geoboard Project Evaluation Sheet

Student: ______Date: _____

Teacher: ______Grade: ____

Topic Title: ______

A. CONTENT AND PROCESS
  1. Organization of the diagrams and ideas
  2. Degree of accuracy of the data and ideas
  3. Level of understanding
  4. Appropriate use of materials
  5. Completeness of project
/ 1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
B. CREATIVITY
  1. Topic originality/Uniqueness of approach
  2. Level of difficulty of the activities
/ 1 2 3 4 5
1 2 3 4 5
C. DRAMATIC/VISUAL VALUE
  1. Interest/ideas generated by the project
  2. Overall appearance/structure/
design
  1. Delivery/Flow
/ 1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

Total ______

Additional Comments: ______

______

______

______

______

______

______

______

(taken from “The Geoboard Collection: Intermediate Level” by Exclusive Educational Products)

Joanne CoumansPage 1 of 9