Arithmetic

Arithmetic is a branch of mathematics commonly considered a separate branch but in actuality a part of algebra. Conventionally the term has been most widely applied to simple teaching of the skills of dealing with numbers for practical purposes, e.g. computation of areas, proportions, costs and the like. The four fundamental operations of this study are addition, subtraction, multiplication, and division. The older teaching arbitrarily divided arithmetic into elementary arithmetic and higher arithmetic. In advanced study the concept of number is greatly generalized to include not only complex numbers, but also quaternions, tensors, and abstract entities with no other meaning than that they obey certain laws. This division of arithmetic into the practical and the theoretical dates back to classical Greek times, when the term logistics referred to elementary arithmetic and the term arithmetic was reserved for the theory. The basic operations of arithmetic were formerly learned largely or even entirely by rote. In the early 20^th century, however, new and more practical methods were adopted, and late in the 1950s there was a turn in elementary education toward utilizing the methods developed by higher mathematics and by use of computers. For the ordinary purposes of practical figuring the old method survives.

3. Answer the questions.

1. What is arithmetic?

2. What are fundamental operations of this study?

3. What is the division of arithmetic? To what times does this division date back?

4. What did logistics mean?

5. How did people learn the basic operations of arithmetic?

6: When were new and more practical methods adopted?

4. Find the English equivalents to the words and word combinations given below. Be ready to write dictation.

алгебра додавання вища математика

обчислення віднімання математична логіка

площа множення теорія

пропорція ділення практичні методи

використання

Практичне заняття №2

Тема: Реєстрація в аеропорту (на вокзалі, в порту). Митний контроль

І. Граматичний матеріал (повторення: Simple and Continuous Tenses)

Ознайомтеся з таблицею та пригадайте правила утворення та вживання Present/Past/Future Simple; Present/Past/Future Progressive. Зведена таблиця часових форм англійського дієслова активного стану

	Present	Past	Future
Simple (Indefinite)	V ( + -s/-es) Повторювана або постійна дія в теперішньому часі. 1.Students pass exams every semester. Do students pass exams every semester? Students do not pass exams every month. 2.My neighbour always listens to loud music. What music does your neighbour always listen to? My neighbour does not listen to loud music.	V + -ed or V2 Одноразова, постійна або повторювана дія в минулому; ряд послідовних дій у минулому. 1. She opened the window a minute ago. When did she open the window? She did not open the window. 2. My friend bought a new camera last week. What did your friend buy? My friend did not buy anything.	will (shall) + V Дія, що відбудеться у майбутньому. 1. Jack and I shall take part in the competition next time. Shall we take part in the competition next time? We shall not take part in the competition next time. 2. The President will pass a new bill next month. Will the President pass a new bill? The President will not pass a new bill.
Progressive (Continuous)	am/is/are + V + -ing Дія, що відбувається в момент мовлення або в певний період теперішнього часу. Look! Someone is running towards us. Where is that man running? He is not running towards us.	was/were + V + -ing Дія, що відбувалась, тривала в певний момент або протягом якогось періоду часу в минулому. The band was playing the whole night yesterday. Was the band playing last night? The band was not playing the whole night.	will (shall) + be +V + -ing Дія, що відбуватиметься в якийсь момент або період часу в майбутньому. The workers will be attending the courses for two weeks. How long will the workers be attending the courses? The workers will not be attending the courses.
Perfect	have/has + V3 Дія, яка відбулась до моменту мовлення, і той, хто говорить, має на увазі результат цієї дії. I have already seen this film. Have you seen this film? I have not seen this film yet.	had + V3 Дія, що вже закінчилась до іншої минулої дії або до певного моменту в минулому. The teacher had corrected our works before the holidays began. Had the teacher corrected your works before the holidays? The teacher had not corrected our works.	will (shall) + have + V3 Дія, що закінчиться до певного моменту або до початку іншої дії в майбутньому. The clock will have struck twelve by the time you come. Will the clock have struck twelve? The clock will not have struck twelve.
Perfect Progressive (Continuous)	have/has + been + V + -ing Дія, що почалася в минулому і тривала протягом певного періоду і або все ще продовжується в цей момент, або щойно закінчилася. The participants have been waiting for the decision of the judges since 5 p.m. Have the participants been waiting long? The participants have not been waiting since 5 p.m.	had + been + V + -ing Дія, яка почалася до якогось моменту в минулому і або продовжувалася в цей момент, або закінчилася безпосередньо перед ним. He had been keeping this book for two months before I asked him to return it. Why had he been keeping this book? He had not been keeping this book for two months.	will (shall)+ have + been + V + -ing Майбутня дія, що, розпочавшись у майбутньому, триватиме протягом певного періоду часу до настання іншої, більш пізньої майбутньої дії або моменту. You will have been studying English for five years by the next spring. How long will you have been studying English by the next spring? You will not have been studying English for six years by the next spring, will you?

1. Put the verb in the Present Continuous (I am doing) or Present Simple (I do).

Model: Excuse me, do you speak (you/speak) English?

Tom is having (have) a shower at the moment.

1. They__________ (not/watch) TV very often.

2. Listen! Somebody_________(sing).

3. She is tired. She ___________(go) home now.

4. How often _________________(you/read) a newspaper?

5. “Excuse me, but _____________(you/sit) in my place.” – “Oh, I am sorry!”

6. “I am sorry, I_______________(not, understand). Please speak more slowly”.

7. “Where are you, Roy?” – I am in the sitting room. I ______________(read).

8. What time __________(she/finish) work every day?

9. You can turn off the radio. I ____________________(not/listen) to it.

10. He ______________(not/usually/ drive) to work. He usually __________(walk).

2. Open the brackets using the verbs in the form of Past Simple, Past Continuous or Present Perfect.

1. I ____________(to write) this exercise at this time yesterday.

2. I ____________(to go) to the cinema yesterday.

3. (You/ to see)___________any good movie recently?

4. (Mark/to read) ___________this book already?

5. The cat ___________(to take) a peace of fish and (to run) away.

6. At this time yesterday___________________I (to sit) at the theatre.

7. He (to come) back to London on the 15^th of January.

8. When I ___________(to come) home yesterday, my little sister (to sleep).

9. When I (to see) my friends), they _____________________(to play) football.

10. The boy _______________(to hurt) himself while he ____________(to skate).

11. While we ________________(to wait) , we ___________(to do)crossword puzzles

3. Open the brackets using the necessary forms of the verbs below.

1) We _______________________ TV when it started to rain. (to watch)

2) I ____________to visit you yesterday, but you _____not at home.(to want) (to be)

3) Look! It ______________,so we can't ___________to the beach. (to rain) (to go)

4) There are a lot of clouds! It _________________ soon. (to rain)

5) The sun _________________________ in the East. (to rise)

6) Since 2003 they ___________________their son every year. (to visit)

7) I __________________________for my girlfriend for two hours. (to wait)

9) After Larry _______________ the film on TV, he decided to buy the book. (to see)

10) Wait a minute, I __________________________this box for you. (to carry)

ІІ. Робота над текстом за темою заняття.

1. Read the following dialogue and translate it into Ukrainian.

2. Write out the new words and word combinations and translate them with the help of a dictionary.

3. Fill in the gaps with appropriate words/word combinations given bellow.

Booking a ticket for a train

1. Do you have________________ for the seven-twenty-five (train) to Sochi tomorrow?

2. How many____________?

1. Two, please.

2. ________________. Let me see…Well, I can offer you two tickets but the __________are in different _____________Will that do?

1. I am afraid not. What about the day after tomorrow?

2. Yes, we have some _________________ in a compartment car, if you like,

1. We will not have to _____________________trains, I hope.

2. No, it is a through train.

A. Ok, I will take the tickets.

B. Here you are.

A. I’ve got a question. My son is _____________with us. He is just four. Shall ________for him?

B. No, children under five may travel ________. Anything else?

A. How long does it take to get to Sochi, please?

B. I am not quite sure. I think something like seventy hours. Ask at the _____________over there. They will give you all the ______________you want.

A. Thank you.

_________________________________________________________

Free, to change, just a minute, carriages, to pay, tickets, upper berths, inquiry office, tickets, to travel, information, seats.

4. Learn the dialogue by heart.

***

1. Read the dialogues in pairs.

2. Translate the dialogue.