- •Навчальний посібник
- •First term
- •Second term
- •Mathematics as a science
- •Mathematics
- •Task 17
- •Isaak Newton
- •Age problem
- •Self-assessment Be ready to speak on the topic "Mathematics as an independent science" using the following as a plan:
- •Check your active vocabulary on the topic:
- •Translate into English and be ready to give illustrative examples:
- •Fill in the gaps using a word from the list:
- •Arithmetic operations
- •Four basic operations of arithmetic
- •Two Characteristics of Addition
- •Self-assessment
- •Rational numbers
- •Rational and irrational numbers
- •Rational and irrational numbers
- •What is a number that is not rational?
- •Self-assessment
- •Properties of rational numbers
- •Properties of rational numbers
- •Properties of rational numbers
- •Reciprocal Fractions
- •Reducing Fractions to Lowest Terms
- •A Visit to a Concert
- •Self-assessment
- •Geometry
- •Meaning of geometry
- •Points and Lines
- •The history of geometry
- •Strange figures.
- •Measure the water.
- •Self-assessment
- •Simple closed figures
- •Simple closed figures
- •Simple closed figures
- •Problems of Cosmic and Cosmetic Physics
- •How to find the hypotenuse
- •Geometry Challenges
- •Self-assessment
- •Functional organization of computer
- •Computers
- •An a is a b that c
- •Find the numbers
- •Hundreds and hundreds
- •Tasks for self-assessment
- •Computer programming
- •Now read the description below. Do you like it? Why/Why not?
- •Instruction, instruct, instructed, instructor
- •Programming languages
- •Testing the computer program
- •Genius’s answer
- •A witty answer
- •The oldest profession
- •Tasks for self-assessment
- •Additional texts for reading
- •Read the text and summarise the main ways of expressing numbers in English.
- •Expressing numbers in english
- •Expressing millions
- •Ways of expressing the number 0
- •Fractional numbers
- •Writing full stops and commas in numbers
- •A short introduction to the new math
- •Algorithm
- •Mathematical component of the curriculum
- •Some facts on the development of the number system
- •The game of chess
- •Computers in our life
- •Is "laptop" being phased out?
- •The Main Pieces of Hardware
- •Text 10
- •Programs and programming languages
- •Text 11
- •All about software Categories of applications software explained
- •Systems Software
- •Applications Software
- •All the Other 'Ware Terminology
- •Malware
- •Greyware
- •Text 12
- •Advantages and disadvantages of the internet
- •Advantages
- •Disadvantages
- •Text 13
- •Text 14
- •Thinking about what we’ve found
- •Meta-Web Information
- •Text 15
- •Computer-aided instruction
- •Text 16
- •Teacher training
- •Іменник Утворення множини іменників
- •Правила правопису множини іменників
- •Окремі випадки утворення множини іменників
- •Присвійний відмінок
- •Практичні завдання
- •Артикль
- •Вживання неозначеного артикля
- •Вживання означеного артикля
- •Відсутність артикля перед обчислюваними іменниками
- •Вживання артикля з власними іменниками
- •Практичні завдання
- •Прикметник
- •Практичні завдання
- •Числівник
- •Практичні завдання
- •Займенник Особові займенники
- •Присвійні займенники
- •Зворотні займенники
- •Вказівні займенники
- •Питальні займенники
- •Неозначені займенники
- •Кількісні займенники
- •Практичні завдання
- •Прийменник
- •Дієслово
- •Неозначені часи indefinite tenses
- •Теперішній неозначений час the present indefinite tense active
- •Вживання Present Indefinite Active
- •Майбутній неозначений час the future indefinite tense active
- •Практичні завдання
- •Did you have a meeting yesterday?
- •I had an exam last week.
- •I didn't have an exam last week. Did you?
- •Тривалі часи дієслова continuous tenses
- •Теперішній тривалий час The present continuous tense active
- •Минулий тривалий час The past continuous tense active
- •Майбутній тривалий час The future continuous tense active
- •Практичні завдання
- •Перфектні часи perfect tenses
- •Теперішній перфектний час The present perfect tense active
- •Минулий перфектний час The perfect past tense active
- •Майбутній перфектний час The future perfect tense active
- •Практичні завдання
- •Узгодження часів sequence of tenses
- •Практичні завдання
- •Модальні дієслова modal verbs
- •Практичні завдання
- •Типи питальних речень question types
- •Практичні завдання
- •Пасивний стан дієслова passive voice
- •Практичні завдання
- •Check yourself
- •Читання буквосполучень
- •Читання голосних буквосполучень
- •Читання деяких приголосних та їхніх сполучень
- •Irregular verbs
- •Indefinite Tenses
- •Continuous Tenses
- •Perfect Tenses
- •Perfect Continuous Tenses
- •List of Proper Names
- •Sources of used materials
- •Contents
Strange figures.
The father asked his three sons to write four numbers using five odd figures so that they would equal fourteen. Can you do it?
Measure the water.
A girl was sent to the well with two jugs. One of them contained 7 litres and the other 11 litres. She had to bring back exactly 2 litres of water. How could she do it? What is the smallest number of times she had to fill and empty her jugs?
Self-assessment
Be ready to speak on the topic "Meaning of geometry" using the following as a plan:
Is geometry an old subject?
Did geometry begin in England?
Were Egyptians mostly concerned with the practical use of geometry?
Did the knowledge of Egyptians spread to Greece?
Is Euclid’s book called Elements famous ?
Does geometry include only the study of the shape and size objects?
In the idea of a point fundamental in geometry?
Can one feel, see, move or hold a point?
Has a point any dimensions?
Are points represented by dots?
Does a line segment include its endpoints?
How can you draw a straight line?
Check your active vocabulary on the topic:
Size Earth Relation Point Location Space Dimension Dot To refer to Shape
|
Geometry To define Volume To be concerned with To apply smth to To spread Intriguing Mysterious To improve on To include
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Ruler To draw A straight line Line segment Endpoint To extend Indefinitely Capital letter To mark
|
Translate into English and be ready to give illustrative examples:
Покращувати, розвивати Загадковий Геометрія Застосовувати у, до Необмежено Місцезнаходження Поширюватись Простір Кінець відрізка Вимір
|
Поширюватись Точка Відношення Визначати Земля Об’єм Розмір Форма Бути зацікавленим Включати, містити
|
Відрізок Називати Пряма лінія Намалювати, накреслити Позначити Велика літера Лінійка Крапка Інтригуючий
|
Fill in the gaps using a word from the list:
relations mysterious subject |
line segment dots space shape |
endpoints capital line point |
Geometry is a very old…
The Greeks found the ideas about geometry very intriguing and ….
Today geometry includes not only the study of the … and size of the earth and all things on it, but also the study of … between geometric objects.
The most fundamental idea in the study of geometry is the idea of a ….
A point is an exact location in … .
In writing we represent the points by ….
Points are commonly referred to by using … letters.
The … includes endpoints and all the points between them.
If we extend the segment indefinitely we will get a … .
It is impossible to draw the complete picture of such an extension because a line has no … .
MODULE 6