Convert these improper fractions into mixed numbers. Comment on your steps of conversion.

Unit 6


Reading and Vocabulary

1. Match the definitions/explanations in A (1–7) with the words in B (a–g):

  A B
1 complex, difficult to do a capacity
2 remarkable or unusual things b elegant
3 central or most important part of anything c essential
4 done with care, skill and taste d complicated
5 necessary, most important e profound
6 ability to hold, contain, learn things/qualities/ideas f phenomena
7 deep knowledge g core

Read the article below and complete it with a word from the task 1 (column B).

    1. I take a course in mathematics. It has been my favorite subject since I started school. I agree with Stefan Banach that ‘mathematics is the most beautiful and most powerful creation of the human spirit’. I feel a real pleasure when I manage to solve a difficult problem or prove a 1_____ theorem, and I quite agree with the people who compare maths with poetry. Sofia Kovalevsakaya believed that it was impossible to be a mathematician without being a poet in your soul. She thought that mathematics required a great amount of imagination. Albert Einstein said, ‘Pure mathematics is, in its way, the poetry of logical ideas’.

    2. At present mathematics means the combination of pure and applied maths. Pure maths deals with logical structures. It studies them as structures themselves. Applied maths is the study of real objects by means of mathematical methods, that is, the study of structures modeling real 2_____. The 3_____ of mathematics is pure maths, its theories are beautiful and 4_____ abstract mathematical systems expressing not words, but thoughts and ideas. The results in pure mathematics are appreciated not by their practical applications, but by their completeness, rigour, consistency, and beauty. So pure maths is an abstract science but its applications can be concrete and practical.

    3. Mathematics is used throughout the world as an 5_____ tool in many fields, including natural science, engineering, medicine and social sciences. You can hardly find an area of human activities where mathematics is not used. No wonder that the great German mathematician Carl Gauss called mathematics the queen of all sciences.

    4. Unfortunately, a lot of people have a deep distaste for mathematics and even fear it often as a result of early failure and poor teaching. I want them to shake off this fear and take a liking to maths, and who can help them do this? – A good teacher of mathematics! I think almost all of us have, in our natural intelligence, a capacity for mathematical thinking which may, sadly, just have been ‘blocked off’ by unhappy early experience, and the task of a mathematics teacher is to develop this 6_____, find the way to encourage schoolchildren to do maths.

    5. To become a good teacher of mathematics you should know the subject you teach very well, be well-educated and broad-minded, and of course, you should know the methods of maths teaching. Our university course of mathematics gives us 7_____ knowledge of the subject. Besides, I’m going to take a course in psychology and pedagogics in my second and third year and I hope to eventually become a good maths teacher.


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