Find in the text modal verbs or their equivalents, define their meaning in the sentence, give possible variants for their translations.

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4. Define the following word combinations. Use them in the sentences or situations of your own:

· use math to maintain

· be good for

· enhance

· in a variety of ways

· work with

· in some ways

· component value

· in a certain order

· per million

· it is vital for smb to know

· in terms of

Scan the text again, find the part which is of special interest and great importance to you, and explain why.

Write the plan of the text and make a report, based on it. It is desirable that you should apply new terms, concepts and phrases from above.

7. Work in pairs. Make up the English-Russian glossary on the theme of the lesson. Your glossary should contain 20 – 30 (or more) lexical units. Give the sources you referred to. Exchange your version with your partner’s one, then compare them, and complete each other’s variants of the glossary, if necessary.

8. Listen to the text Charts and retell it:

http: //englishon-line.ru/chtenie-nauchnii-tekst29.html

9. Watch the video Problem Solving and Mathematical Modelling to define its main theses. Name at least 5 of them. Discuss the matters given in the video with your partner (you are expected to ask your partner some questions, give your reasons in explaining various phenomena, support different points of views, etc).

http: //www.youtube.com/watch? v=i4fhMtDhAFQ

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Using Math in Mechanics. Present this information to the group.

Lesson 5

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Using Mathematics in Mechanics

Two Different Systems

Mechanics use mathematics all the time in their daily routine of repairing and modifying internal-combustion automobiles. Their use of numbers takes on many forms; from determining the size of the wrench they need to loosen a bolt to calculating torque, today's mechanics need to have a good head for numbers. They also have to deal with two different numeric systems: metric and American (sometimes called British). The metric system is based on a 10-digit numerical system, but the British system, which we also use here in the United States, is based on the English foot (which comes in units of 12, yet still uses the same 10-digit number system). As a result, most modern mechanics are constantly switching from one system to another – an activity that is not as difficult as it sounds.

The Nuts and Bolts of Mechanic's Math

The first and probably most obvious use of mechanic's math is in the area of fractions. Every bolt or nut in an engine or car body has a certain designated size. The head of a bolt is usually six-sided, but on occasion, you might find one that is square, with only four sides. (The battery terminal has square bolts.) If you are using the English system, the smallest unit of measurement is the inch. Anything less than 1 inch is referred to in fractions. In auto mechanics, this is a common occurrence, as most bolts that go into the making of a modern engine average around 1/2 inch to 5/8 inch. It is even possible to have bolts that are 3/4, 1/2 or 9/16 inch in size. As you can see, understanding fractions is fundamental in comprehending the English system.

On the other hand, the metric system is designed so that fractions are almost unheard of. Instead of using fractions, one simply drops down to the next level. For instance, there are approximately 2-1/2 centimeters in 1 inch. If you have a bolt with a head that is less than 1cm, which is a common occurrence, instead of using a fraction to designate the size, you merely go to the next level, which is measured in millimeters. There are 100 millimeters in one centimeter, so a 1/2-inch bolt ends up being equal to about 13mm.

It really is not that difficult to comprehend, especially once you get some hands-on experience. Just remember that a different set of tools is needed to work on each type of car. A good mechanic needs to have both.

Torque and Engine Displacement

Numbers also come into play in many other ways, such as calculating torque, engine size and displacement, horsepower and firing sequence. Torque is expressed in foot-pounds, and is a measurement of the force needed to tighten a bolt.

" Horsepower" is a common term, yet few people realize that is also a mathematical formula. You calculate horsepower by multiplying the diameter of a cylinder (in inches) by the number of cylinders and then dividing that figure by 2.5.

Engine size is the volume of the engine. It is the combination of the volume of all 4, 6 or 8 cylinders, whichever may be the case. This is also called engine displacement. The firing sequence refers to the order in which each cylinder is ignited, or fired; it is determined by the manufacturer. The sequence is not random, but occurs in a highly researched order, designed to give maximum power and efficiency to the engine.

It is easy to see how important numbers are in the manufacture and maintenance of automobiles, and it is also important that mechanics and machinists have a good understanding of these two numerical systems.

Henri Bauholz

http: //www.ehow.com/how-does_4570197_mechanics-use-math.html

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. Mechanics use mathematics all the time in their daily routine of _____________ and __________________.

2. The metric system is based on a _________________, but the British system, which we also use in the United States, is based on __________.

3. The first and probably most obvious use of mechanic's math is _______________________.

4. If you are using the English system, the smallest unit of measurement is _________.

5. You calculate horsepower by multiplying the __________________ (in inches) by _________________ and then dividing that figure by 2.5.

6. _____________________ is the volume of the engine.

2. Work in pairs to find out:

1. What purposes do mechanics use mathematics for?

2. How do mechanics use numbers? In what forms?

3. Most modern mechanics are constantly switching from one system to another, aren’t they?

4. What is the head of a bolt like?

5. What is called engine displacement?

6. How important are numbers in the manufacture and maintenance of automobiles?

7. Mechanics and machinists have a good understanding of the two numerical systems, don’t they?

Find in the text adjectives in their different degrees: positive, comparative, superlative. Define their function in the sentence; give possible variants for their translations.

4. Define the following word combinations. Use them in the sentences or situations of your own:

· internal-combustion automobiles metric system

· the British numeric system a common occurrence

· difficult to comprehend horsepower

· engine displacement have a good understanding

Scan the text again, find the part which is of special interest and great importance to you, and explain why.

Write the plan of the text and make a report, based on it. It is desirable that you should apply new terms, concepts and phrases from above.

8. Listen to the text Sequences and retell it:

http: //englishon-line.ru/chtenie-nauchnii-tekst28.html

9. Watch the video Math History: Mechanics and Curves to define its main theses. Name at least 5 of them. Discuss the matters given in the video with your partner (you are expected to ask your partner some questions, give your reasons in explaining various phenomena, support different points of views, etc).

http: //www.youtube.com/watch? v=QG6zpNL-vek

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Application of Mathematical Modelling in Different Spheres of Life. Present this information to the group.

Lesson 6

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

How Do Mechanics Use Math in Their Job?

The Mechanic's World

A mechanic is, by definition, any person who works with machinery. Since machinery requires building, and building requires putting parts together, machinery is thus comprised of parts that must be designed and arranged in an organized way. The mechanic is the person who can see how these parts fit together and how they work within a machine. Just like the number " 9" can be seen as a single number, it can also be seen as many numbers such as " 3+3+3" or " 1+1+1+1+1+1+1+1+1." These are the ways that " 9" can be built, just like a car can be built with engines and wheels and gears and wires and seats and lights and....... you get the idea. Even the " +" symbol can be seen as a part in the " machine of 9, " like a hinge for the other numbers to attach to. A mechanic will use these parts not with numbers, but with machines, and decide if the parts are working correctly. If they are not, he will fix the parts or replace them. As you can see, doing math is very similar to building machines.

The Mechanic's Tools

Given that math is simply a way to look at the world, a mechanic will see his world in metal, screws, gears, heat or lubricant. A mechanic will use tools like wrenches and hammers instead of pencil and paper. These tools are designed to perform the jobs a mechanic requires. Wrenches can come in different sizes, like 1/2 inch or 5/16 inch, and their uses depend on the job. The mechanic needs to be able to figure out these numbers correctly by measuring the parts of his machine.

Math and the World

Whether a mechanic knows it or not, he's always using the mathematical part of his brain to calculate various things. For example: How much force to put into pushing a wrench and in what direction; or knowing the strength of materials and whether they can withstand the forces they'll be put through. Mechanics typically have less addition and subtraction to deal with, and more physics, which is math of the moving world. Since mechanics are most often dealing with moving parts, they must apply these mathematical principles to their work.

Jin Sunszine

http: //www.ehow.com/how-does_5008919_mechanics-use-math-their-job.html

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. A mechanic is, by definition, any person who ________________.

2. Since machinery requires building, and building requires putting parts together, machinery is thus comprised of parts that must be _________ and __________ in an organized way.

3. A mechanic will use tools like ___________ and __________ instead of pencil and paper.

4. Wrenches can come in different sizes, like _______ inch or _______ inch, and their uses depend on the job.

5. A mechanic is always using the mathematical part of his brain to ____________________________.

6. Mechanics typically have less ________ and __________ to deal with, and more _________, which is math of the moving world.

2. Work in pairs to find out:

1. What parts is machinery comprised of?

2. How will a mechanic use the parts?

3. In what way will a mechanic use tools?

4. What is the mechanic able to do?

5. A mechanic is always using the mathematical part of his brain to calculate various things, isn’t he?

6. What is typically the part of mechanics’ addition and subtraction to deal with? What about physics?

7. Since mechanics are most often dealing with moving parts, what principles must they apply to their work?

3. Find in the text ing-forms, define whether they are Participle I, Gerund or ing-Nouns. What is their function in the sentence? What is the role of Participle II: find them in the sentences and give their translations.

4. Define the following word combinations. Use them in the sentences or situations of your own:

· by definition

· be comprised of

· must be designed

· in an organized way

· fit together

· be very similar

· given that

· be designed to

· needs to be able to

· by measuring

· must apply

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