Unit 1 Describing Objects and Math Basics PDF

# Unit 1 Describing objects and math basics ## 1.1 Objectives After studying and working with this unit, you will be able to: 1. identify types of geometric objects 2. describe in English geometric objects writing about their physical features, shapes, properties and locations 3. describe geometr...

# Unit 1 Describing objects and math basics ## 1.1 Objectives After studying and working with this unit, you will be able to: 1. identify types of geometric objects 2. describe in English geometric objects writing about their physical features, shapes, properties and locations 3. describe geometric objects use descriptive phrases, structures of sentences in English and verb phrases appropriate for describing 4. describe numbers and equations ## 1.2 Introduction It is necessary for students to learn how to use English for describing places, people and objects, etc. They have to equip themselves with the knowledge and use of English structures and vocabulary to be able to meet the requirement of the job market after their graduation. Whatever field they choose, they will need English for their efficient functioning in that field. This unit comprised of four sub-topics: types of geometric objects, property of geometric objects, locations and math basics. ## 1.3 Vocabularies | shape | ellipse | square | sphere | |-------------|--------|--------|--------| | rectangle | triangle | pyramid | edge | | vertex | angle | radius | diameter | | circumference| locate | situate | subtraction | | division | addition | multiplication | power | ## 1.4 Geometric objects and types A geometric object or geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object. That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape. Objects that have the same shape as each other are said to be similar. If they also have the same scale as each other, they are said to be congruent. Many two-dimensional geometric shapes (2Ds) can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points. Such shapes are called polygons and include triangles, squares, and pentagons. Other shapes may be bounded by curves such as the circle or the ellipse. Many three-dimensional geometric shapes (3Ds) can be defined by a set of vertices, lines connecting the vertices, and two-dimensional faces enclosed by those lines, as well as the resulting interior points. Such shapes are called polyhedrons and include cubes as well as pyramids such as tetrahedrons. Other three-dimensional shapes may be bounded by curved surfaces, such as the ellipsoid and the sphere. ## Figure 1-1 Types of geometric objects by shapes: 2Ds, 3Ds | SHAPE (2 dimensional) | NOUN | ADJECTIVE | SHAPE (3 dimensional) | NOUN | ADJECTIVE | |-----------------------------|-------|-----------------|-------------------------------|--------------|--------------------| | **[circle]** | circle | circular | **[sphere]** | sphere | spherical | | **[ellipse]** | ellipse| elliptic(al) | **[cube]** | cube | cubical | | **[square]** | square | square | **[rectangular solid or prism]** | rectangular | rectangular | | **[rectangle]** | rectangle | rectangular | **[cylinder (circle as base)]**| cylinder | cylindrical | | **[triangle]** | triangle| triangular | **[cone (circle as base)]** | cone | conical | | **[inverted triangle]** | | triangular | **[pyramid (square as base)]** | pyramid | pyramidal | ## Language focus: Describing geometric shapes Geometric shapes can be used to describe objects in various ways. This section presents some examples for describing object shapes. - ....is shaped like + n. Example: A coin is shaped like a circle. - .........is + Adj. + in shape. Example: A coin is circular in shape. - .............is + Adj. Example: A coin is circular. ## Exercise 1.1 Describe shapes of the following laboratory objects using words in the box. | | Objects | | -------- | -------- | | 1. | Rotary evaporator flask | | 2. | Test tube | | 3. | Water bath | | 4. | Funnel | ## 1.5 Properties of geometric objects for measurement When we talk about 2D shapes, we talk about sides and angles. The angles of a 2D shape are also sometimes referred to as 'vertices' (singular: vertex). For example: this 2D shape has four sides and four angles: **[Image of a square with four sides labelled and four angles labelled]** When we talk about 3D shapes, we talk about faces, edges and vertices. **[Image of a square-based pyramid with a face labelled "Face", a vertex labelled "Vertex", and an edge labelled "Edge"]** The faces are the flat parts of the shape. The edges are the lines where two faces meet. The vertices are the points where two or more edges meet. For example, this 3Ds shape has 6 faces, 12 edges and 8 vertices: **[Image of a rectangular prism with six faces labelled]** ## Exercise 1.2 Read the text and label the shapes below with the underlined words. Two-dimensional, or 2D shapes have sides. So a square has four sides and a pentagon has five. Where two sides meet they make an angle. On a square each angle is 90°. A circle only has one side and the distance all the way round this is called the circumference. When we measure a circle the distance from one side to the other through the center is the diameter and the distance from the side to the center is called the radius. Three dimensional, or 3D, shapes are more complex because you can measure the height, width and depth. The surfaces on a 3D shape are called faces. The number of faces on a cube is six and on a cylinder only three. Where two faces meet are the edges. A cube has twelve edges. Where two edges meet there is a corner. A cube has eight corners. **[Image of a square with an arrow pointing to a side and an arrow pointing to a corner]** **[Image of a rectangular prism with arrows pointing to a face, an edge, and a corner]** **[Image of a circle with an arrow pointing to the circumference, an arrow pointing to the diameter, and an arrow pointing to the radius]** ## Language focus: Describing dimensions of geometric objects Stating dimensions using adjectives such as follow: - x is 3 cm long, high, wide, deep, thick. - x has a length, height, width, depth, thickness of 3 cm. - The length, height, width, depth, thickness of x is 3 cm. ## Circle: Words used to describe for circle measurement are radius, diameter, circumference and area. For example: - Area of a circle = A = πr² - Circumference of a circle = 2πγ ## Rectangle: Words used to describe for rectangle measurement are width and height. For example: - 2 dimensions: width, height - circumference = 2h + 2w - area = hw **[Image of a rectangle with a width labelled "w" and a height labelled "h". Another arrow points to the circumference, another points to the diameter, and another points to the radius]** This rectangle is 1 centimeter in width and 4 centimeter in height. 1 cm by 4 cm ## Rectangular prism: Words used to describe for rectangular prism measurement are height, length and width. For example: - 3 dimensions: height, length, wi - surface area = 2lw + 2lh + 2hw - cross-sectional area = wxh - volume = 1 xhxw **[Image of a rectangular prism with length labelled "l", width labelled "w", and height labelled "h"]** Example: 3 centimeters in length by 1.5 centimeters in height by 1.5 centimeters in width. 3 cm by 1.5 cm by 1.5 cm ## Exercise 1.3: Complete the following sentence using the picture below. **[Image of a brick with sides labelled 5 and 10, with a circle next to it. An arrow points to the circumference of the circle, another to the diameter, and another to the radius.]** 1. The brick is 10 cm ___________ 2. The brick is 5 cm ___________ 3. It has a ___________ of 5 cm. 4. The ___________ of brick is 5 cm. 5. It has a ___________ of 4 cm. 6. It is 4 cm ___________ 7. It has a ___________ of 20 cm² (square centimeter). 8. It has a ___________ of 220 cm². 9. It has a ___________ of 200 cm³ (cubic centimeter). 10. The r of the circle in the drawing stands for ___________ 11. You can calculate the ___________ of a circle using this multiplication: 2r. 12. You can calculate the ___________ of the circle using this multiplication: 2πr. 13. You can calculate the area ___________ of a circle using the multiplication: πr². 14. The well is 30 meters deep. It has a ___________ of 30 meters. 15. The coin is 1 mm thick. It has a ___________ of 1 mm. 16. The river is 2 km wide. Its ___________ is 2 km. ## 1.6 Location Location can be indicated with an absolute reference: the objects are then located relative to the whole (for example the page). The description remains valid when you move the other objects around. Example: Look at the picture. At the top of this picture there is a circle. In the middle of the page you see a triangle. There may also be relative reference: the objects are positioned in relation to (an) other object(s). Hence the description no longer holds when you relocate the objects. Example: Next to the triangle there is a line. Above the line there is another circle. ## Language focus: Useful expressions and vocabulary for describing location. | Absolute reference | Relative reference | |--------------------|--------------------| | In the middle | Above/over | | At the top | Between | | At the bottom | Below/under | | On the right/left (of)| Beside | | At the back | On either side of/on this side of| | In the front | Behind/beyond | | Below | Inside | | | Outside/outside of/out of | | | At the end of/at the top of/at the bottom of| | Over | directly above | | Above | higher in general | | Under | directly below – touching or not | | Below | lower in general | | Underneath/on top of| often means that it is touching the object | | Between | relates one object to two others | | On | higher and touching | | Beyond | further away in the distance (than something) | | Behind | directly behind | ## Figures 1-2 Useful preposition of place **[Image of a grid with different prepositions of place] ** Examples: The triangle is to the left of the box (= outside the box). The circle is on the left of the box (= in the box, on the left). ## Exercise 1.4: Listening to the dialogue and make the drawing. Look at the drawing and fill in the words that indicate location. **[Image of a square with a blank inside]** ## 1.7 Math basics ## 1.7.1 Reading numbers Examples: - 100,000 = a/ one hundred thousand - 1,953 = one thousand nine hundred and fifty-three - 11.539 = eleven point five three nine - 78.01 = seventy-eight point naught one Note: - 0 = zero or naught (also pronounced ‘oh' in Great Britain) - nil = sports results : Milan 3 – Barcelona 0 - null = nothing (not a figure but a concept) ## Exercise 1.5: How do you pronounce the following numbers and expressions? - 10.455 - 2,899 - 10,000,000 - 0.631 - 45.07% ## 1.7.2 Equations | Example | Noun | Verb | Reading | |---------|---------------|-------------|------------------------------------| | 2+5=7 | addition | to add up | 2 plus 5 equals 7 | | 5-2=3 | subtraction | to subtract | 5 minus 2 equals 3 | | 5 x 2 = 10 | multiplication | to multiply | 5 times 2 equals 10 | | | | | 5 multiplied by 2 equals 10 | | 10/5 = 2 | division | to divide | 10 over 5 equals 2 | | | | | 10 divided by 5 equals 2 | | 10² | power | raise a | 10 squared | | 10³ | | number to | 10 cubed | | 10⁹ | | the nth power| 10 to the ninth/ 10 to the power 9| | | | | | |--------|----------|---------------------------------------------------|--------------------------------------| | √10 | root | extract the root of | the square root of 10 | | ³√10 | | | the cube root of 10 | | ⁹√10 | | | the ninth root of 10 | Note: - Do not get confused: m³ : cubic meters - 3³: three cubed (do not forget to pronounce the [d]) - ³√: the cube root ## Exercise 1.6: Match the equations with their corresponding pronunciations. 1. ___________ k³ + k³ 2. ___________ r = R/n 3. ___________ 7.6x10-3 4. ___________ e-x/2 5. ___________ 1/x 6. ___________ 3a4 a. one over x b. k cubed plus k squared c. three times a to the fourth d. little r equals big R over n e. seven point six times ten to the minus three f. e to the minus x over two ## Homework 1 ## Homework 1.1: Fill in the correct word. Use either a preposition or a geometric figure. **[Image of a cube, a sphere, a cylinder, a cone, a square, a rectangle, an ellipse, and a triangle]** 1. There is a cube ___________ the left of the sphere. 2. The pyramid is situated under the ___________ 3. The cylinder is located ___________ the cone. 4. The cylinder is located ___________ the sphere. 5. The cube is situated ___________ the cone. 6. The ___________ is behind the rectangle. 7. The square ___________ the ___________ and the triangle. 8. The triangle is ___________ the square. 9. The rectangle is situated ___________ the ellipse. 10. You find a geometric figure ___________ the square. ## Homework 1.2 Write down how to read these numbers and formulae. - x (2y – 4) = y² + 1 - a² – b² = (a + b)(a - b) - (a x b)² = a² + 2ab + b²