Pre-listening match the words from the left column with their Ukrainian equivalents in the right column.

1. addition	a. ділення
2. subtraction	b. математика
3. multiplication	c. рахувати в умі
4. division	d. віднімання
5. stuff	e. додавання
6. mental arithmetic	f. матеріал
7. maths	g. множення

10. Listen to the text and complete the sentences.

2. When I was a kid I was _______________ in maths.

3. Things were _______________, It was all addition and subtraction, multiplication and division.

4. I knew my times tables _______________ my hand.

5. We had to _______________ algebra and geometry and lots of other stuff I can’t remember the names of. Suddenly.

6. I _______________ maths any more. I think there were a few reasons for this.

7. One was my maths teacher, another was because _______________ back of the class, and another was _______________.

8. _______________ when I was at university and loved that.

SPEAKING

Discuss the following questions in small groups.

- What counting systems do you know?

- Analyse the advantages and disadvantages of each system.

12. Make a short presentation on one of the following topics: "Maya numerals", "Babylonian numerals" or find another to your liking.

WRITING

Choose one of the following quotations and explain what it means. Write a short paragraph (60 - 80 words) to express your opinion.

1. “Genius is one percent inspiration and ninety-nine percent perspiration.”

Thomas Edison

2. “To do two things at once is to do neither.”

Publius Syrus (Latin author).

3. “One friend in a lifetime is much; two are many; three are hardly possible.”

Henry Adams (American journalist, historian and novelist).

4. “A man who dares waste one hour of time has not discovered the value of life.”

Charles Darwin

GRAMMAR IN USE

These tasks can help you to practise Conditionals: Type 0 - Type 1 (See Appendix 1 p. 241 – 243) and do the following exercises.

14.Match two parts to form conditional sentences.

1) If iron is left in contact with air and water,	a) it rusts.
2) In the event of collision,	b) unless there are better safety measures.
3) If heat is applied,	c) download them onto your computer.
4) If you want to study the files from the Internet,	d) we are successful.
5) The tests won’t be continued	e) we will estimate the experimental error.
6) If we run an additional test,	f) the substance decomposes.
7) If we work hard,	g) the airbag will inflate.

Match the items in two columns in order to make correct Type 0 conditional sentences, as in the example.

Example. If you wash woolen clothes in hot water, they shrink.

 

0.Wash woolen clothes in hot water.	They shrink.
1. Mix blue and yellow.	a. They die.
2. Don’t water plants.	b. It becomes ice.
3. Put water in the freezer.	c. It falls to the ground.
4. Leave metal out in the rain.	d. It sinks.
5. Drop something.	e. You get green.
6. Throw a pebble into the sea.	f. You have to ring the bank.
7. Lose your credit card.	g. It gets rusty.

Underline the correct tense form in the following sentences.

1. If his car breaks / will break down, he calls the auto club.

2. You will be able to see / are able to see better if you turn on the lamp.

3. You'll pay higher insurance if you will buy / buy a sports car.

4. You won't pass the course if you won't study / don't study.

5. When I get / will get a letter, I usually write back immediately.

6. If I will be / am in Venice, I will rent a boat.

7. If we surf / will surf the Internet, we will find a lot of information.

Put the verbs in brackets in the correct tense. Add a comma where necessary.

1. Please call me if you ….. (to need) any help.

2. If he ….. (to arrive) on time we’ll discuss our plans before we go out.

3. She won’t go to Australia unless I ….. (to pay) for her tickets.

4. ….. she ….. (to be) angry if we don’t go to the meeting?

5. If you ….. (to work) hard you may be promoted.

6. If you help me I ….. (to repair) it.

7. If you leave now you ….. (to get) there before it closes.

UNIT 15

GEOMETRIC FIGURES

LEAD-IN

 

Match the geometric figures to their names.

A Square	B Rectangle	C Arc	D Triangle	E Hexagon	F Cylinder	G Circle	H Cube

 

What other geometric figures do you know? Name the objects in the classroom that have the shape of a circle, triangle, square, rectangle, oval, arc, cube, cylinder, hexagon, etc.

READING

Read the text and correct the statements that follow.

Geometric Figures

Geometry is the mathematical study of shapes, figures, and solids. Circles, triangles, and squares, rectangles, parallelogram are some of the geometric figures or geometric shapes.

Circles, triangles, squares, rectangles, trapezoids, and parallelograms are some of the most memorable geometric figures. The area and perimeter of these solids are calculated using the following formulas,

· Square: Squares are four sides polygon and all the four sides are equal in length. All the four angles in the squares are equal to 90°. If the length of the side of a square is a, then,

· Area = a² square units,

· Perimeter = 4a units.

· Rectangle: Rectangle is also a four-sided polygon and the opposite sides are equal in length. Each angle in the rectangle is equal to 90°. If the length of the side of a rectangle is l, and the breadth of the rectangle is b, then,

· Area = l×b square units,

· Perimeter = 2 (l + b) units.

· Circle: Circle is a two-dimensional object drawn by a curve with same distance from the center. If the circle has a radius of r, then,

· Area = πr² square units,

· Perimeter = 2πr units.

· Triangle: Triangle is a three-sided polygon. If the height of the triangle is h, and the breadth of the rectangle is b,

· Areaof triangle = (1/2) b×h square units,

· Perimeterof triangle = a + b + c units,

· where, a, b, c are side length of the triangle.

Among other geometric figures are:

· Acute Angle

An acute angle is less than a right angle, or less than 90 degrees.

· Arc

Any part of the circumference of a circle or other curve; a segment of a circle. The conic sections are the ellipse, parabola, and hyperbola.

· Cube

A regular, solid body with six equal square sides.

· Cylinder

A solid body supposed to be generated by the rotation of a parallelogram round one of its sides; or a long, circular body, of uniform diameter, and its extremities forming equal parallel circles.

· Diameter

A right line passing through the center of a circle, or other curvilinear figure, terminated by the curve, and dividing the figure symmetrically into two equal parts.

· Ellipse

In conic sections, a figure formed by the intersection of a plane and cone when the plane passes obliquely through the opposite sides of the cone.

· Hexagon

A plane figure of six sides and six angles. If the sides and angles are equal, it is a regular hexagon. The cells of honey-comb are hexagons, and it is remarkable that bees instinctively form their cells of this figure, which fills any given space without any interstice or loss of room.

 

1. Any part of the circumference of a circle or other curve is called diameter.

2. All the four angles in the squares are different.

3. Square is a two-dimensional object drawn by a curve with same distance from the center.

4. Hexagons are four sides polygon and all the four sides are equal in length.

5. Rectangle is a four-sided polygon and the opposite angles are equal in length.

6. A plane figure of six sides and six angles is called triangle.

7. Geometry is the mathematical study of shapes, figures, and liquids.

 

LANGUAGE DEVELOPMENT

4. Match up the words in column A with the words in column B to form meaningful phrases, translate them into Ukrainian:

Column A Column B

1. geometric a) section

2. regular b) body

3. conic c) angle

4. solid d) object

5. right e) figure

6. acute f) line

7. two-dimensional g) hexagon

5. Match the English words with their Ukrainian equivalents:

1. polygon a) коло

2. curve b) прямокутник

3. arc c) обертання

4. circumference d) трикутник

5. triangle e) дуга

6. rotation f) багатокутник

7. rectangle g) крива