Lobsco, Michael L. “Form Any Shape On This GeoBoard, and Find Its Area By Magic.” Mental Math Workbook, Scholastic Inc, 1998. Pages 75-77. (ISBN # 0-439-14863-4)
Mathematical Concept: Using a Geoboard, Calculating Area
Grade Levels: 6th – 8th
NCTM Standards and Principles of School Mathematics:• Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Use geometric models to represent and explain numerical and algebraic relationships.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.
Piece of Wood 10 in x 10 in (25 cm x 25 cm) x ¼ inch (1.9 cm) thick
Linseed oil, Shellac, or paint (optional)
With this common grid of nails, you can do more than form many geometric shapes and symmetrical designs. You can perform the spectacular feat of finding the area of regular or jagged intricate shapes using the magical formula learned in this activity. With this secret formula you can actually do what appears to be impossible. Have a friend make the most complicated shape on the board with a rubber band. You can relay how large it is in less than a minute!
1. Photocopy the pattern attached and place it on top of the square board. Be sure you enlarge the photocopy to 300%.
2. Tape the corners of the sheet onto the board to keep it in place.
3. Nail nails on the dots into the board so that each protrudes ½ in (1.3 cm) above the surface. Remove the paper.
4. Sand the board and finish with shellac, oil, or paint. Dry completely.
1. Work through Activities One and Two in class.
2. Once activities are completed, divide class into working partners.
3. Have each partner form an intricate figure on the geoboard.
4. The other partner should us Pick’s Formula to Solve the Area.