A Story of NumbersClass 8 Mathematics Case Study Questions

A group of Class 8 students is creating a museum exhibit on ancient mathematics. Their focus is the Mesopotamian number system, which is a base-60 (sexagesimal) system. They learn that for numbers from 1 to 59, it uses two main symbols: '▼' for 1 and '◀' for 10. For numbers 60 and above, it uses a place value system. The position of a group of symbols determines its value. The rightmost position is for units ($60^0=1$), the position to its left is for the number of 60s ($60^1$), the next is for the number of 3600s ($60^2$), and so on.

For their exhibit, they need to translate several numbers. For example, the number 85 is broken down as $(1 \times 60) + 25$. It would be written with the symbol for 1 in the '60s' place and the symbol for 25 in the 'units' place. The symbol for 25 is '◀◀▼▼▼▼▼'.

An archaeologist is studying an ancient Egyptian papyrus that lists the inventory of a pharaoh's storeroom. The Egyptians used a base-10 system but without place value. They had unique hieroglyphs for powers of 10. The symbols are: a vertical stroke ' | ' for 1, a hobble '∩' for 10, a coil of rope '୭' for 100, and a lotus flower '𓍢' for 1000. To write a number, they simply repeated the symbol as many times as needed. For example, the number 234 would be written as ୭୭∩∩∩||||. The order of symbols did not matter, but they were often grouped for readability.

The papyrus lists '୭୭୭∩∩|||||' loaves of bread and '𓍢𓍢∩∩∩∩∩||' sacks of barley.

An architect is studying the blueprints of an ancient Roman aqueduct. All dimensions are in Roman numerals. The main channel's length is recorded as MMDCLXXV paces, and a supporting arch has a height of XLII feet. The architect needs to convert these to modern numbers to create a digital model. The Roman system uses symbols I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). It is not a base system but uses these 'landmark numbers' to build other numbers. For example, 23 is represented as XXIII ($10+10+1+1+1$), and 4 is represented as IV (1 less than 5). The architect's first task is to understand the scale of the structure.