A sample version:

The abacus is typically constructed of various types of hardwoods and comes in various sizes. The frame of the abacus has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck.

The standard abacus can be used to perform addition, subtraction, division and multiplication. The abacus can also be used to extract square-roots and cubic roots.

The abacus is prepared for use by placing it flat on a table or one's lap and pushing all the beads on both the upper and lower decks away from the beam. The beads are manipulated with either the index finger or the thumb of one hand. Each bead in the upper deck has a value of 5; each bead in the lower deck has a value of 1. Beads are considered counted, when moved towards the beam that separates the two decks. After 5 beads are counted in the lower deck, the result is "carried" to the upper deck; after both beads in the upper deck are counted, the result (10) is then carried to the left-most adjacent column. The right-most column is the ones column; the next adjacent to the left is the tens column; the next adjacent to the left is the hundreds column, and so on. Floating point calculations are performed by designating a space between 2 columns as the decimal-point and all the rows to the right of that space represent fractional portions while all the rows to the left represent whole number digits.

The abacus is one of many counting devices invented to help count large numbers. The earliest counting device was the human hand and its fingers. Then, as larger quantities (larger than ten human-fingers could represent) were counted, various natural items like pebbles and twigs were used to help count. Merchants who traded goods not only needed a way to count goods they bought and sold, but also to calculate the cost of those goods. Until numbers were invented, counting devices were used to make everyday calculations.

Step Ⅴ Homework

Ask the students to summarize what they have learnt in the unit and prepare for the next unit.

附 件

I. 语法: 过去分词作定语

1. 过去分词作定语既可以放在所修饰的词之前，作前置定语，也可以放在所修饰的词后面，作后置定语。表示被动和完成意义,其作用相当于一个定语从句。例如：

Where are the reserved seats? (=Where are the seats which have been reserved?)

预定的座位在哪里？

The injured workers are now being taken good care of in the hospital.

受伤的工人现正在医院受到很好的照料。

We needed much more qualified workers.

我们需要更多合格的工人。

My friend is a returned student.

我的朋友是个归国留学生。

2. 过去分词作后置定语可分为限制性（紧跟在所修饰的中心词之后）和非限制性（用逗号与其所修饰的中心词分开）两种，其作用分别相当于一个限制性定语从句和非限制性定语从句。例如：

The funds raised (= which have been raised) are mainly used for helping the homeless.

筹集的资金主要用来帮助那些无家可归的人。

He is a teacher loved by his students.