Activity I: The Abacus (Grades 4  6)

The Abacus | Tangrams and Fractions | Take A Trip| Career Connections | More Math Concepts

Objectives:

• Students will be introduced to the Chinese and Japanese abacus.
• Students will learn to use the abacus to display numbers and calculate sums of whole numbers.
• Students will compare the abacus, the calculator and mental computation to determine the tool that produces the fastest correct answer.

Standard 1: Number and Operation

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another
• Compute fluently and make reasonable estimates

Standard 10: Representation

• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems
• Use representations to model and interpret physical, social, and mathematical phenomena

Introduction to the Chinese and Japanese Abacus

The abacus is an ancient device used in China and other Asian countries. It is a counting device and can be used to add, subtract, multiply, and divide. There are many types of abaci, but they all work on the same principle. A simple Chinese abacus consists of 13 columns of beads. A horizontal beam separates the frame into two sections. These are called the upper deck and the lower deck. Each bead in the upper deck has a value of FIVE. Each bead in the lower deck has a value of ONE. When you display a number, beads are moved towards the horizontal beam that separates the two decks. The first column on the right is the ONES column and represents numbers 0 to 9. The next column to the left is the TENS column and represents 10  90. The third column is the HUNDREDS column. The place value continues to the last column that represents trillions.

Three of the most used abaci are from China and Japan. They differ in the number of beads that are in the lower deck. The Chinese abacus before 1850 had five beads on the lower deck and two beads on the upper deck (See Figure 1). The Chinese abacus after 1850 has five beads below and one bead on the upper deck (See Figure 2). The Japanese abacus has four beads in the lower deck and one bead on the number deck (See Figure 3).

Figure 1: Chinese Abacus Prior to 1850

Figure 2: Chinese Abacus After 1850