Manipulatives for counting were found throughout the ancient world. Counting boards made from clay and wood were used in Southwest Asia for taking inventory. Forms of abacus, comprising beans or stones on a stringed board, was used in ancient Rome and China. The Mayans and Aztecs placed corn kernels on a string for counting, while the Incas knotted strings. All of these tools were used for counting and number calculations.
Modern day geometry classes utilize tangrams to develop spatial reasoning skills. Tangrams date back to 2000 B.C. in the Orient, as described in the Seven Boards of Tan which consists of over 1000 puzzles using various shapes. The ancient Chinese tangram puzzle consisted of seven shapes for use in constructing larger shapes. The shapes, five triangles, one square and one parallelogram, fit together to form a square. The size relationships allow them to be used to create an assortment of figures. Today's students continue to use the tangrams for geometry lessons.
Magic squares are arrays of digits that when added across, up and down or diagonally, have the same sum. A typical magic square has three rows and three columns. When the digits one through nine are placed on the squares in a specific arrangement, all of the sums are equal to 15. The origin of the magic square dates back to 2800 B.C. in ancient China with the story of Lo Shu Square. According to the story, the square was discovered on the shell of a turtle.
Sundials originated in Ancient Egypt as a method of telling time using the sun's shadow. Originally called the shadow stick , gnomom or obelisk, the sundial was set on the ground. As the sun's shadow was viewed, observers would estimate the time of day based on the position and length of the shadow. To account for changes due to the Earth's axis, the stick was repositioned on an angle facing north to ensure accuracy from day to day. Smaller versions of the sundial were created to make them portable; the idea of placing a portable sundial on the wrist led to the idea of watches.