SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: I.Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyłą, E. Fronc
Lekcja 4 B
______________________________________________________________________________________________
GEOMETRY AND MEASUREMENT – Teacher’s notes and key
NOTE: As lesson B is a continuation and development of lesson 4A, before distributing materials for lesson
4B, make sure that all the students in the group have access to the glossary and lesson 4A materials.
INTRODUCTION:
I. A week before the class (5 minutes):
 write on the board a few expressions e.g. ‘a piece of cheese’, ‘a football’, ‘a box of chocolates’,
‘an Egyptian Pyramid’ etc and ask SS to say what shape these are, e.g. ‘a wedge’, ‘wedgeshaped’, ‘spherical’.
 distribute page 1 of lesson 4B to the SS and ask them to revise material from the glossary and
lesson 4A at home and set task 1 and 2 from 4B as homework.
Task 1.
Adjectives describing the shapes. Complete the table below.
2D shapes
NOUN
square
rectangle
triangle
hexagon
octagon
pentagon
circle
semicircle
spiral
3D shapes
ADJECTIVE
square
rectangular
triangular
hexagonal
octagonal
pentagonal
circular
semicircular
spiral
NOUN
cube
cylinder
tube
sphere
hemisphere
dome
cone
pyramid
helix
wedge
Task 2.
Decide if the following sentences are true or false. T/F
1. If a triangle is equilateral, it has three equal sides.
2. Space is a particular set of points.
3. Not all lines which lie in the same plane are parallel lines.
4. An obtuse triangle has two obtuse angles.
5. An acute angle measures more than 180O.
6. A rectangle is a polygon which has all sides of equal length.
7. Only some polygons are quadrilaterals.
8. A hypotenuse is the side of a triangle opposite the obtuse angle.
9. Any chord of a circle can be called the diameter.
10. A point has no thickness and breadth but it has length.
11. Two perpendicular lines share a common point.
12. Non - polyhedra have flat faces.
13. A cuboid is a prism.
14. A cone has two curved sides.
15. The base of a cylinder is the same as its top.
16. All points on the surface of a sphere are the same distance from the centre.
ADJECTIVE
cubic
cylindrical
tubular
spherical
hemispherical
dome-shaped
conical/cone-shaped
pyramidal/pyramid-shaped
helical
wedge-shaped
T
F
T
F
F
F
T
F
F
F
T
F
T
F
T
T
II. The lesson (20 minutes):
 While SS compare the answers from task 1 and task 2, monitor their answers and help if necessary.
Open class feedback.
 Referring to the table from task 2, SS play a short game in pairs, asking each other questions like:
‘If a box is the shape of a cube, it is …. (cubic)’
 Distribute p.2 of the student’s task sheet and ask SS to do tasks 3, 4 individually, then to compare
in pairs referring to lesson 4A
 Check their answers.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: I.Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyłą, E. Fronc
Lekcja 4 B
______________________________________________________________________________________________
Task 3.
Complete the sentences with an appropriate word from the list below:
meet, said, vertex, vertices, equally, length, diameter, sides, square, greater, less, times, interior, obtuse, ratio, by
Angles that share a common vertex and edge but do not share any interior points are called adjacent angles.
The area of a rectangle is the length of the side times the width.
Lines that meet in a right angle are said to be perpendicular.
An angle less than a right angle is called acute, an angle greater than a right angle but less than 180O is called
obtuse.
5. For any circle, the ratio of the circumference to the diameter is the same fixed number represented by the
letter pi.
6. A centre of a regular polygon is a point equally removed from all its vertices.
7. In a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two
sides.
1.
2.
3.
4.
Task 4.
Match two halves of the following sentences:
An isosceles triangle (e)
A hypotenuse (h)
A circle divides a plane (c)
The intersection of a straight line (g)
Lines and planes are proper subsets of (b)
When a regular hexagon is inscribed in a circle
(f)
7. The centre of a regular polygon (d)
8. If two distinct lines which are not in the same
plane do not intersect, (a)
1.
2.
3.
4.
5.
6.
a.
b.
c.
d.
e.
f.
they are said to be skew.
the universal set of points called space.
into three sets of points.
is a point equally removed from all its vertices.
has two equal sides.
the circle passes through all the angular points
or vertices of the hexagon.
g. and a plane is a point.
h. is the side of a triangle opposite to the right
angle.
 SS do tasks 5, 6 individually, compare in pairs and check with T.
Task 5.
1.
2.
3.
4.
5.
Underline the correct answer
Polyhedra figures include a cone / do not include a cone.
The cross-section of a triangular prism is a circle / a triangle.
The faces of a rectangular prism are rectangular / square.
If the base of a pyramid is a regular polygon, it is a regular / an irregular pyramid.
The Great Pyramids of Egypt are square pyramids / triangular pyramids.
Task 6.
Fill the gaps with the following verbs: join, bisect, intersect, label, cut
1. If you bisect something, especially an angle, you draw a line that divides it into two equal parts.
2. When you label something, you use a word or short expression in order to briefly describe them.
3. If something such as a line, a path, or a bridge join two other things, it connects or links them together.
4. To cut something means to be in the middle of it, dividing it into two parts.
5. If you intersect a place, area, or surface, you divide it by crossing it.
 Homework: Task 8 for everybody.
Task 7 (optional - to be done with stronger groups, or as a filler eg before Christmas) – ask SS to
draw at home a fairly clear but complex figure that consists of various shapes connected together.
Ask them to avoid drawing too obvious shapes like the sun or a Christmas tree. Tell them they are
going to instruct the others how to draw it during the next class.
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
DLA LEKTORA
Opracowanie: I.Zamecznik, M. Witczak, H. Maniecka, A. Hilgier,
B.Przybyłą, E. Fronc
Lekcja 4 B
______________________________________________________________________________________________
III. During the following class:
 Ask SS to test each other on task 8 questions, monitor their work and then check with the whole
class.
 (optional) SS work in pairs on the dictation game from task 7 (you must make sure that ALL the SS
have already done the preparation stage ). Monitor and help if necessary.
Task 7.
Figure Dictation Game
At home draw a fairly clear but complex figure that consists of various shapes connected together. Avoid drawing
too obvious shapes like the sun, a Christmas tree, a simple representation of a house.
In class work with another student and explain to him/her how to draw your figure so that it will be the closest
representation of what you have created.
DO NOT show the figure to your partner until he/she gets it right.
Task 8.
1.
2.
3.
4.
5.
6.
Answer the questions
the base of a cube is square and of a
cuboid is rectangular
What is the cross-section of a cone?
a circle / an isosceles triangle
What kind of a triangle needs to be rotated in order to create a cone? a right angled triangle
How many edges and vertices does a torus have?
none
Which 3-D figures are not polyhedrons? a torus, a prism, a cone, a cylinder.
What shape is a football ?
a truncated icosahedron
How is the base of a cube different from the base of a cuboid?
REFERENCES:
1. Słownik naukowo-techniczny, Wydawnictwa Naukowo – Techniczne, 1998
2. Ibbotson Mark, Professional English in Use – Engineering, Cambridge 2009
3. Krukiewicz-Gacek Anna, Trzaska Agnieszka, English for Mathematics, AGH University of Science and
Technology Press Kraków 2010
4. Szkutnik Leon Leszek, An Introductory Course in Scientific English, PWN 1979
5. Szyke Grażyna, What, Why & How in the World of Science, WSiP, 1986
6. Discovery Puzzlemaker
7. The Internet
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