SJO PW - Język angielski ogólnotechniczny, Poziom B2 Opracowanie: I. Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,

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1 GEOMETRY AND MEASUREMENT - Teacher s notes and key to tasks Introduction (5 minutes one week before the actual LESSON): 1. Elicit vocabulary connected with geometric figures ask the students (SS) to look around the class and name different shapes they can see (triangle, square, etc). These shapes will be found in the form of the board, desk, patterns on the floor, etc. 2. Ask SS what a geometric figure is. ( A geometric figure is any set of points on a plane or in space ) 3. Distribute the GLOSSARY and pages 1,2,3,4 of 4A, allowing SS a week to get acquainted with their contents. 4. Set tasks 1, 2, 3, 4, 5, 6, 7, 8, 9 as homework. NOTE: Tasks belong to the LESSON next week. VARIATION: with stronger groups, who would need less time for in class reading, you could do task 1 as part of the introduction. The LESSON (20 minutes): 1. SS work in pairs checking the homework tasks. Open class feedback with pronunciation check and help where necessary. Practice the pronunciation of the most problematic words. 2. SS do task 10 on p.3 (the crossword puzzle) as a revision exercise, then they check with the glossary. Monitor and offer help if necessary. Open class feedback 3. SS do task 11 on p. 4, testing each other in turns on the measurements and checking with the previous pages. 4. Without looking at the previous tasks, SS do task 12 as recap. 5. Set task 13 for homework During the following class (5 minutes): 1. Check tasks As a quick revision, ask SS to draw a circle and mark on it: the diameter, the radius and at least one chord. REFERENCES: 1. Słownik naukowo-techniczny, Wydawnictwa Naukowo Techniczne, Ibbotson Mark, Professional English in Use Engineering, Cambridge Krukiewicz-Gacek Anna, Trzaska Agnieszka, English for Mathematics, AGH University of Science and Technology Press Kraków Szkutnik Leon Leszek, An Introductory Course in Scientific English, PWN Szyke Grażyna, What, Why & How in the World of Science, WSiP, Discovery Puzzlemaker 7. The Internet 0

2 GEOMETRY AND MEASUREMENT Geometric Figures Two-Dimensional Geometry Task 1. Point and lines, angles, triangles, quadrilaterals, polygons and the circle i. Point and Lines: Read the following sentences and choose the appropriate word in each pair. A straight line is a particular set/combination of points. Two lines which lie in the same plane and which do not intersect, i.e. they do not share one common point are called perpendicular/parallel lines. They remain the same distance apart at all times. Two lines that intersect and form right angles are called perpendicular/parallel lines. ii. Angles: Look at the attached glossary and match the name to the angle. a) An obtuse angle 1._b b) A right angle 2._c c) An acute angle 3._a Triangles ABC is a triangle. It has three equal angles and three equal sides. A triangle that has three equal sides is called an equilateral triangle. ABC is an isosceles triangle. It has two equal sides (AC and CB). When a triangle has two equal sides then it also has two equal angles. All triangles can be classified into three categories: acute (-angled) triangles, obtuse (-angled) triangles, right (-angled) triangles. Two triangles may be called similar only if their corresponding angles are congruent and their corresponding sides are proportional in length. iii. Quadrilaterals and Polygons Polygons can be divided into regular polygons (when a polygon has all sides and all angles equal), and irregular polygons. We can also describe polygons as convex or concave. A convex polygon is a polygon that has all interior angles less than 180. A polygon that has one or more interior angles greater than 180 is concave. iv. The circle: Choose the correct word in each pair. All points on the circle are equidistant from the centre. The distance across a circle through the centre is called the diameter / radius. The diameter / radius of a circle is the distance from the centre of a circle to any point of the circle. The diameter / chord of a circle is twice as long as the radius so it is as long as two radii. The diameter / chord is a line segment that joins two points on a curve. A circle can have many different diameters / chords but if the diameter / chord passes through the centre it is called the diameter / chord / radius. The area of a circle equals πr 2 where r is the radius. The perimeter of a circle is called the circumference. The circumference is calculated by the formula C=2πr, where r is the radius. Task 2. Match the angle names a, b, c to their descriptions 1, 2, 3 a. A right angle (3) 1. It measure more than 0 O but less than 90 O. (90 degrees) b. An acute angle (1) 2. It measures more than 90 O and less than 180 O. c. An obtuse angle (2) 3. It measures 90 O. Task 3. Choose the word in italics that fits the following sentences describing pictures on the right. ABC here is a/an acute/obtuse/right triangle because all the angles are acute/obtuse. ABC is a/an acute/obtuse/right triangle because one of the angles is a right angle. 1

3 ABC is a/ an acute/obtuse/right triangle because one of the angles is an obtuse/acute angle. In a right triangle, the side opposite the right angle is called the hypotenuse and the other two sides are called the legs. If c represents the length of the hypotenuse and if a and b represent the length of the legs, then c 2 =a 2 + b 2 (which reads: c squared equals a squared plus b squared). This is Pythagorean Theorem, which states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Task 4. Match the name to the figure: square, hexagon, pentagon a) hexagon b) square c) pentagon These are examples of some regular polygons. A polygon which has four sides only is called a quadrilateral. The rectangle, the trapezium and the rhombus are examples of quadrilaterals. Task 5. Decide if the following sentences are true or false: 1. A rectangle is a quadrilateral that has four equal angles. T 2. A square can be described as a rectangle that has two adjacent sides of equal length. T 3. All quadrilaterals are polygons. T 4. All polygons are quadrilaterals. F 5. If each angle of a rhombus is 90 degrees, it is a square. T Geometric Figures Three-Dimensional Geometry 3-D geometry is the geometry of three-dimensional space. It is called three dimensional, or 3-D, because there are three dimensions: width, depth and height. There are two main types of solids (3-D shapes): polyhedra and nonpolyhedra, (singular polyhedron, plural polyhedra/polyhedrons). Polyhedra have flat faces. Task 6. Match the name to the solid: cube, cuboid, pyramid, prism, cone, cylinder, sphere, torus (pl. tori) 1. cube 2._cylinder_ 3._cone_ 4._sphere_ 5._prism_ 6. cuboid 7._pyramid_ 8._torus_ Task 7. Weight Weights and Measures 1 gram (g) = kilogram (kg) The weights in the table have been mixed. Match the metric values to their GB&US equivalents: UK&US Metric 1 ounce (oz) grams 1 pound (lb) = 16 ounces (oz) kilograms (kg) 1 stone = 14 pounds (lb) kilograms 1 US Short ton = 2,000 pounds (lb) kg 1 UK Long ton = 2,240 pounds (lb) 1, kilograms 2,204.6 pounds (lb) 1 tonne (t) = 1,000 kg Task 8. Length, area, volume, liquid: capacity/volume long length deep depth wide width heavy weight tall / high - height 2

4 i. Length: Complete the lengths table below by writing the missing values. 1 milimetre (mm) = metre (m) 1 centimetre (cm) = 0.01 m 1 kilometre (km) = 1,000 m UK&US Metric 1 inch (in) milimetres (mm) 1 foot (ft) 1 = _12_ inches (_12_ ) centimetres (cm) 1 yard (yd) = 3_ feet metres (m) 1 mile (mi) = _1.760_ yards kilometres (km) 1 sea (or nautical) mile kilometres ii. Area 1 square metre (m²) = 1m x 1m (1 metre by 1 metre) 1 square millimeter (mm²) iii. Volume 1 cubic metre (m³) = 1m x 1m x 1m 1 cubic centemetre (cc) = 1cm x 1cm x 1cm iv. Liquid capacity/volume 1 litre (l) = m³ UK US Metric 1 pint (pt) pints litres (l) 1 gallon (UK - gal) = 8 pt US gal litres 1 liquid galon/1 dry gallon litres / l Task 9. Temperature: What do the following values represent? Complete the table below with the phrases from the list: freezing point, boiling point, absolute zero, room temperature, blood heat: Fahrenheit (ºF) Centigrade (ºC ) degree Celsius Boiling point Blood heat Room temperaturę Freezing point Absolute zero Task 10. Do the crossword below. Across Down 3. cięciwa chord 1. przeciwprostokątna- hypotenuse 6. wielokąt - polygon 7. czworokąt- quadrilateral 2. kąt - angle 8. promień - radius 9. trójkąt triangle 4. średnica - diameter 10. przyprostokątna - leg 11. równoboczny - equilateral 5. okrąg circle 3

5 Task 11. Which is greater? a) 7 pt or 3 l f) 212F or 212C b) 3 gal or 15 l g) 1 oz or 30 g c) 1 mi or 1 km h) 2 lb or 1 kg d) 1 yd or 4 ft i) 1 ton or 1 tonne e) 10 m or 10 yd Task 12. Complete the following sentences using appropriate words from the list below (one word may be used more than once): diameter, deep, depth, long, length, wide, width, weigh, heavy, weight, tall, high, height 1. The highway from Warsaw to Cracow is about 500 kilometres in length. 2. What is the height of the highest mountain in Poland? 3. They couldn t get the piano through the door because of its width. 4. Draw a circle which is 10 centimetres in diameter. 5. The _depth of the Śniardwy Lake at its deepest point is 23.4 m. 6. They hung a picture at a height of 6 feet above the ground. 7. This parcel is very heavy. What is its weight? Task 13. Answer the following questions. a) In the UK I was told my friend weighed 10 stone 10 pounds. What is her weight in kg? 68.10kg b) If the speed limit in Warsaw is 50 kms/h, what speed is the speed in mp/h? mph c) The bath has hot and cold-water taps which admit 30 litres and 40 litres per minute. The bath holds 500 litres. If both taps are turned on, how many litres would flow in per minute? How long will the bath take to fill? 70 litres / 7 minutes and 7.2 seconds d) If you want to convert Centigrade temperature into Fahrenheit, multiply by 9/5 (nine/fifths) and add 32. What is the outside temperature now? What was it at the weekend? Give the answers in Celsius and Fahrenheit. Read the result aloud. Answers depend on the outside temperature. REFERENCES: 1. Słownik naukowo-techniczny, Wydawnictwa Naukowo Techniczne, Ibbotson Mark, Professional English in Use Engineering, Cambridge Krukiewicz-Gacek Anna, Trzaska Agnieszka, English for Mathematics, AGH University of Science and Technology Press Kraków Szkutnik Leon Leszek, An Introductory Course in Scientific English, PWN Szyke Grażyna, What, Why & How in the World of Science, WSiP, Discovery Puzzlemaker 7. The Internet 4