With this project we will improve our skill in problem solving in different contexts.
Activity 1: Math Prehistory
Solve problems 1 to 5 and hand in the sheet. (Answers must be in Spanish and English)
Los primeros humanos utilizaban los números para contar cosas cotianas como los animales que tenían o el paso del tiempo. Prueba de ésto lo podemos encontrar en las pinturas rupestres y en los restos arqueológicos encontrados. Los primeros humanos del paleolítico y neolítico formaban grupos que eran nómadas y para alimentarse cazaban animales y recogian frutos y granos.
Esta pintura rupestre se encontró en la Cueva de la Pileta, en Málaga, y fue pintada por los humanos del Paleolítico (40.000 aC) que habitaron en esta cueva.
La vasija de la imagen se encontró en el yacimiento de Nuzi, en Irak. Está fechada en el año 1500 a.C. Tiene la siguiente inscripción: 21 ovejas que han parido corderos, 6 ovejas, 8 carneros, 4 corderos, 6 cabras, 1 macho cabrío, 2 cabritos.
Con el paso del tiempo los humanos se asentaron en poblados y empezaron a dedicarse a la agricultura y a la ganadería.
En Almería tenemos restos arqueológicos de dos culturas de la Edad de los Metales: Los Millares y El Argar.
Se calcula que en el poblado de Los Millares, 2700 aC, llegaron a vivir 1.000 personas. Si el 15% de ellos eran niños y el 25% mujeres,
Los habitantes del Argar, 2200 aC., se dedicaron a la agricultura. De los 33.000 km² de territorio que ocupaban, el 33% se dedicaba al cultivo de la cebada.
En Almuñécar, Granada, existe un yacimiento arqueológico que data del 800 a.C. La ciudad recibía el nombre de Sexi y fue un importante centro comercial en la eṕoca fenicia.
Las vasijas de alabastro tenían en su interior restos de aceite de oliva.
Si la vasija B tiene un cuarto de la capacidad de la vasija A; la vasija C tiene la mitad de capacidad que la vasija A y la vasija D tiene un tercio de capacidad que la vasija A,
Activity 2: Number Systems
A) Egyptian System
It is thought that the Egyptians introduced the base 10 numeration system at least as early as 2700 BCE (and probably much earlier). The number system was called hieroglyphics.
This system made possible to carry out a record of the number of men available for work or military campaigns, to keep control of the grains and taxes, to distribute the land after the periodic floods of the Nile or to draw calendars and the construction of buildings.
Examples:
B) Chinese System
The Chinese number system, also known as the rod system, consists of these symbols for the numbers 1 to 9.
As the image shows, each symbol has a horizontal representation (hengs) and a vertical representation (tsungs). This is because depending on the position of the symbol in the number they were written horizontally or vertically. Thus, if 1 occupies the place of the units, hundreds or tens of thousands, it was written vertically. And if it occupied the place of tens or thousands, it was written horizontally. To symbolize zero, they left a blank space or wrote a circle.
Examples: The positive numbers were written in red. Look at the number 231 and 5089. The negative numbers were written in black.
C) Roman System
The Roman numeral system is still used today, when writing a century, on monuments, in the names of kings and popes.
This system, based on the Etruscan numbering system, was developed in Ancient Rome. It is made up of capital letters that have different values and is additive, that is, to know what number it is, you have to add the value of each symbol.
| 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
| I | V | X | L | C | D | M |
The roman number system has the following rules
- The letters I, X, C, M can be repeated only three times:
- III = 3
- XX = 20
- CCC = 300
- M = 1000
- V, L y D can not be repeated
- A letter with a minor value written at the right side of other add its value:
- XI = 10 + 1 = 11
- If it is written at the left side we subtract the value
- IX = 10 – 1 = 9
D) Babylonian System
The Babylonian civilization was located in what is now Iraq. They were great mathematicians and astronomers.
This numbering system appeared around 1800 BC. It is a positional number system, that is, the value of a symbol depends on its position in the number. It is a base sixty system, that is, they had symbols for the numbers from 1 to 59, although they only used two symbols to write all those numbers:
To write numbers larger than 59, each symbol was 60 times larger than the previous symbol, that is,
The Babylonians did not have the concept of zero as we know it today, but they did have a symbol that they used to indicate that an intermediate order was missing in a number.
E) Diferentes formas de representación
Actividad para entregar
Escribe en una hoja tu nombre y escribe los siguientes números en los diferentes sistemas de numeración (egipcio, romano, chino y babilonio). ¿Se pueden escribir esos números de otras maneras? (Piensa en la descomposición de factores primos, como sumas o multiplicación de otros números, como fracciones, etc)
a) 25
b) 121
c) 84
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