BAHAGIAN PEMBANGUNAN KURIKULUM
JABATAN PENDIDIKAN NEGERI PAHANGSOLUTION OUTLINE FOR QUESTION 2
: ADDITIONAL MATHEMATICS PROJECT WORK 2015
(a)Estimation Method 1: (Area)
Area of pavement =
Area of a tile = 25 x 10
Number of tiles =
(a)Estimation method 2: ( Using concept of Arithmetic
Progression)
Starting from the interior, the number of tiles for the first
layer
The number of tiles for the second layer
The number of tiles for the third layer
This is an arithmetic progression with
Number of tiles
= 980*Alternative Method 3:
From the diagram on the right,
and
Hence, for the innermost layer, the number of tiles
For the second layer,
and
Number of tiles
For the third layer,
and
Number of tiles
For the fourth layer,
and
Number of tiles
This is an arithmetic progression: 25.3, 27.8, 30.3, 32.8,
a = 25.3, d = 2.5,hence, the total number of tiles
= 981Method 2 is a more accurate estimation compare with method
1. Method 2 takes into consideration the spaces between tiles
whereas Method 1 does not. Method 1 is quick and simple and
therefore easy to understand. This is a major reason why it is
being practiced by most masons with some modification. Due to their
experience, they deduct a certain number of tiles from the total
number required by the area calculation to compensate for the
spaces between tiles, and they are quite accurate.(b) Octagonal
pavement
Method 1 : (Area)Area of one trapezium =
Area of octogonal pavement =
Number of tiles =
= 905
Method 2 : (Arithmetic Progression)Referring to the diagramon
the right,
and this is an arithmetic progression.How many layers are
required?
Number of layers
and
Number of tiles required
Total number of tiles for the octagon pavement = 8 x 106
= 848
*Alternative Method 3: (Scale Drawing)
Using a scale of 1 : 20 and draw one eighth of the octagon.
Estimation from the scale drawing:There are 18 complete
layers.
Number of complete whole tiles needed = 18 x 3 + 15 + 12 + 9 + 6
+ 3
= 99To fill up the empty spaces, tiles will be cut into smaller
parts and the estimatednumber of tiles = 3 x 3
= 9
Total number of tiles = 8 x (99 + 9)
= 864There is quite a difference between Method 1 and Method 2.
This is probably due to the number of layers of tiles. Method 2
only considers 18 complete layers which does not cover the whole
area of the octagon pavement, whereas Method 1 considers the whole
area.(b) Comparing the circular design and the octagonal design,
the octagonal design will be easier to construct because of its
straight line layers and management of the few empty spaces between
the tiles. To lay the tiles in circles will be quite a task and
there empty spaces to fill in between every tile.FURTHER
EXPLORATION(a)Two circular plots pavement.Refer to the diagram
beside.
Method 1: (Using Area)
=1.172 radian
Area of segment KLMN
cm2
Number of tiles required
Number of tiles required for the pavement
= 1920
Method 2:
To calculate the number of tiles required for the arcs passing
through points K1, K2, K3 and K4.
(i) Arc passing through point K1 Arc length
Number of tiles required
(ii) Arc passing through point K2 Arc length
Number of tiles required
(iii) Arc passing through point K3 Arc length
Number of tiles required
(iv) Arc passing through point K4 Arc length
Number of tiles required
(v) Total number of tiles required for the pavement
(b)Refer to the diagram beside.Area of triangle EFG
Total area of pavement
cm2Number of tiles required
(c)Valid reasons must be given for which ever design chosen.
Alternative design suggested must also be accompanied with logical
reasons.(d)Reasons must be given as to whether it is practical to
use aluminium tins and sand to lay the pavement. Illustrations with
diagrams or pictures will be an advantage.
REFLECTIONStudents are free to express their feelings and
opinions while they are conducting the project. They should be able
to explain the related moral values during the process. They may
present these through usage of symbols, illustrations, drawings and
even through a poem or song.2 m
1 m
Circular pavement
Plants
MM1 = M1M2 = 10 cm
3 tiles
2.5 m
3 m
