Text 1 

Mathematics has a language of its own, which uses numbers and symbols instead of words and punctuation. The earliest recorded numbers were marks made on a stick. These marks were made in small groups of, for example, two or five. Eventually these groups were given symbols of their own (2,5, etc.) and a system of arithmetic developed. Mathematicians introduced special symbols to replace words such as «plus» and „equals“. They also introduced special words to express new ideas. Terms such as „triangle“ and „square“, for example, were applied to figures that are geometrically defined.

Text 2 

The ancient Egyptians were using special symbols, known as pictographs, to write down numbers over 3,000 years ago Later the Romans developed a system of numerals that used letters from their alphabet rather than special symbols. Today, we use numbers based on the Hindu-Arabic system. We can write down any number using combinations of up to 10 different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9).

Text 3 

Calculations that involve the repeated multiplication of a number can be written down in a simpler form. An easier way of writing 2×2×2×2 is to place a small 4 above the number 2. This indicates the number of twos that are to be multiplied together Mathematicians would say that we have multiplied the number 2 to the 4th power. Take care to remember that the two the 4th power is not the same thing as 2×4.       

Text 4 

A mathematical sequence follows a particular rule. For example, 2, 4, 6, 8 is a sequence of even numbers. Any sequence of numbers that increase by the same amount each time is called an arithmetic sequence. Sequences often occur in nature. For example, when single-celled organisms reproduce by splitting into two parts, then four, and so on, they are following a pattern known as a geometric sequence (1, 2, 4, 8, 16, 32, etc.).

Text 5 

A fraction is a part of a whole. If we divide a cake into five equal-sized pieces, we are dividing it into fifths. One piece of our cake is a fifth of the whole. This is a fraction, and mathematicians would write this fraction as 1/5. This way of writing down fractions tells us two important things. The number at the bottom of the fraction tells us into how many parts the cake (the whole) has been divided. In this case, the cake has been divided into fifths. The number at the top of the fraction tells us how many of the slices of the whole we have.