கவனிக்க: இந்த மின்னூலைத் தனிப்பட்ட வாசிப்பு, உசாத்துணைத் தேவைகளுக்கு மட்டுமே பயன்படுத்தலாம். வேறு பயன்பாடுகளுக்கு ஆசிரியரின்/பதிப்புரிமையாளரின் அனுமதி பெறப்பட வேண்டும்.
இது கூகிள் எழுத்துணரியால் தானியக்கமாக உருவாக்கப்பட்ட கோப்பு. இந்த மின்னூல் மெய்ப்புப் பார்க்கப்படவில்லை.
இந்தப் படைப்பின் நூலகப் பக்கத்தினை பார்வையிட பின்வரும் இணைப்புக்குச் செல்லவும்: Mathematics 2: Grade 6

Page 1
MATHEM GRADE PART
X X X =
750
700
N.
CO
Education

TATICS O
E-6
E
al Publications Department

Page 2


Page 3
MATHEI
Gra
PAR
EPD Educational Publicat

MATICS
de 6 T - II
ions Department

Page 4
First Published in 2006 Second Print
2007 Third Print
2009 Fourth Print
2010 Fifth Print
2011
The Government h this book which is prese
Published by : The Educational P
Printed by : Karunaratne & Sor
67, UDA Industrial

is spent Rs. 75.00 on nted to you free of charge.
iblications Department
s (Pvt) Ltd. Estate, Katuwana Road, Homagama.
II

Page 5
The National Anthe
Sri Lanka Matha Apa Sri Lanka Namo Namo Nai Sundara siri barinee, surendi athi Dhanya dhanaya neka mal palatu Apa hata sepa siri setha sadana je Piliganu mena apa bhakthi pooja Apa Sri Lanka Namo Namo Nar Oba we apa vidya Obamaya apa sathya Oba we apa shakthi Apa hada thula bhakthi Oba apa aloke Apage anuprane Oba apa jeevana we Apa mukthiya oba we
Nava jeevana demine, nithina api Gnana veerya vadawamina reger Eka mavakage daru kela bevina Yamu yamu vee nopama Prema vada sema bheda durerad Namo, Namo Matha Apa Sri Lanka Namo Namo Na
K&S 1260 EN-2

m of Sri Lanka
no Namo Matha sobamana Lanka ru piri jaya bhoomiya ramya tewanaye matha
Namo Namo Matha no Namo Matha
a pubudukaran matha na yanu mena jaya bhoomi kara
no Namo Matha

Page 6
අපි වෙමු එක මවකගෙ දරු එක නිවසෙහි වෙසෙනා එක පාටැති එක රුධිරය වේ අප කය තුළ දුවනා එබැවිනි අපි වෙමු සොයුරු එක ලෙස එහි වැඩෙනා ජීවත් වන අප මෙම නිවසේ
සොඳින සිටිය යුතු වේ
සැමට ම මෙත් කරුණා ගු
වෙළී සමගි දමිනී රන් මිණි මුතු නො ව එය ම කිසි කල නොම දිරනා
ஒரு தாய் மக்கள் நாமாeே ஒன்றே நாம் வாழும் இல் நன்றே உடலில் ஓடும் ஒன்றே நம் குருதி நிறம்
அதனால் சகோதரர் நாமா ஒன்றாய் வாழும் வளரும் நன்றாய் இவ் இல்லினிலே நலமே வாழ்தல் வேண்டும்
யாவரும் அன்பு கருணைய ஒற்றுமை சிறக்க வாழ்ந்தி பொன்னும் மணியும் முத்து யான்று மழியாச் செல்வம்
ஆன்
கவி

උවෝ
සොයුරියෝ
නී
ය සැපතා
ආනන්ද සමරකෝන්
வாம் งเh
வோம் நாம்
என்றோ
புடன்
டுதல் பமல்ல - அதுவே
ன்றோ.
ந்த சமரக்கோன் தையின் பெயர்ப்பு.
//

Page 7
The Message of His Ex
ANG OPERE peine
Beloved Sons and Da
Many countries that lag time we gained inder passed us and gone far not be prepared to c or work according to models of those nation no purpose in continu our lost heritage. Wha is to surpass them ar overall development th and show new paths the world. Dear Sons and Daug engaged in building y
Mahinda Rajapaksa President of the De Republic of Sri Lank
(An extract from the : President Mahinda Raj
Water Filling Ceremon Port on 15.08.2010) Segunda Dios

cellency the President
ughters,
;ged behind us at the sendence have now ahead. But, we must opy those countries ) the development s. Similarly, there is ing to lament about t we shall do instead ad reach a stage of ey have not reached, and possibilities to
hters, we are now Four future !
mocratic Socialist
speech delivered by apaksa at the historic y of the Magampura
Der Grenze

Page 8
Message from the Ho
Beloved Sons and Daughter
You are the most valuable tr value is enhanced through accomplish that task aim at o
This textbook produced by collected from the tax payin the sole intention of making y You will undoubtedly enhar the light of education you g you a helping hand to awak proud descendent of a great g enabled to carve statues d compassion out of hard hear of great literary value on the
I express my gratitude to Department and to all the ot in offering this textbook to y
Bandula Gunawardhana
Minister of Education

n. Minister of Education
easure of our motherland. Your
education. We, committed to offering you the best.
spending the national wealth g public is offered to you with ou a virtuous and skillful citizen. nce the national wealth through ain. This textbook will provide en your creativity, as you are a eneration whose creative power epicting loving kindness and tless rock and compose graffiti
Mirror Wall’.
the Educational Publications hers who dedicated themselves
Du.
VI

Page 9
Forev
The expectation of our nation is equipped with virtues and skills. TI of Sri Lanka offers you this te accomplishing that target.
Our aim is to make you accessible education by getting the optimum the gateway for you to become ar
motherland.
By making this textbook your trus able to enter the path of becoming the country and undoubtedly, Sri La Knowledge, attitudes and skills yo help you to win the world beyond t “Pearl of the Indian Ocean” will shi armed with competencies.
Iextend my gratitude to the writers and their knowledge in compiling others including the officers of Department, the editors and the m
W.M.N.J.Pushpakumara Commissioner General of Educat
Educational Publications Departm Isurupaya,
Battaramulla. 26. 05. 2011
VI]

ord
a glorious younger generation e Democratic Socialist Republic xtbook with the intention of
to the world of wisdom through use of this textbook and to open zal inheritor of the prosperity of
tworthy companion, you will be ja patriotic citizen beneficial to inka will prosper because of you. 1 gain by using this textbook will
he horizon. The brilliance of the ine brighter because of you when
s who dedicated time, endeavour this textbook along with all the the Educational Publications embers of the evaluation board.
ional Publications
ment

Page 10
Monitoring and Supervision - Repris Mr. W.M.N.J. Pushpakumara
Commiss Education
Direction
Mrs. K.V. Nandani Sriyalatha C
Co - Ordination Mr. K. D. Lal Chandrasiri
C
Co - Ordination - Reprint 2011 Mrs. T.D.C. Kalhari Gunasekara
Assistan Educatio
Panel of Writers
Mr.S.J. Palihawadanage
BSc., ( Mr. V.P.S. Weerasingha
K/Upad Mrs. Nalani Hettiarachchi K.Sri Su
Translated By
Mr.R.B.L. Weerakoon
Deputy | Oxford I
Edited by - Reprint 2010 Mr.A.D.W.S Manamperi Former Mr.W.Kirthisena
Retiredl

at 2011
ioner General of Educational Publications, nal Publications Department
ommissioner (Developement)
„ssistant Commissioner
ducational Publications Department
Commissioner
inal Publications Department
jeneral Degree) yaya Vidyalaya - Panadura
mangala Maha Vidyala - Panadura
Principal nternational School - Nawalapitiya
Project Officer (NIE)
Mathematics Teacher.
/III

Page 11
Conte
15
Length
16
Algebraic Symbols
17
Solids
18
Volume of Liquids
19
Algebraic Expressions
20
Algebraic Expressions - Sul
21
Mass
22
Ratio
23
Collecting Data
24
Representation of Data
25
Interpretation of Data
26
Indices
27
Area
28
Possibility
IX

ents
| 1-11
12-14
15-22
23-27
28-31
ostitution -
32-35
36-42
43-53
54-57
58-61
62-65
66-68
69-76
77-81

Page 12


Page 13
15 - LEI
Are the heights of your friends same? Who is the shortest? To decide this you and y sometimes difficult to decide. By measuring fair conclusion. We can use the length of the
A metre ruler can be used to measure t of the metre ruler is used to find the height
You will find the distances from the p the teacher's table and to the wall are diffe these distances. How can we use a metre ru You can use a ruler with centimetre divi
Mathematics book.
Consider that you have to plant a ma garden. Do you know that length and depth find whether a stick is sufficient to find the length a rope can be used to measure the de well is measured using the length of the rop
Find the thickness of your books in piece of thread can be used. Depending on 1 that the length of the thread differ. In all length, thickness a length of a tape, length o or length of rope were used.
Distance, width, depth, thic
What did you use in the lower clas written using the symbol "m".
In measuring a length, units should b measured.
Example 1 The millimetre is used to
able to measure small le
or thickness of an exerci Example 2 The unit suitable to measu
a book is the centimetre. length of arm, collar size measured in centimetres.
For free distribution

NGTH
Or are they different? Who is the tallest? Four friends can stand along a line but it is
with a measuring tape, you can come to a e measuring tape to find the height.
he height of the chair you sit. The length of the chair. lace where you sit, to the blackboard, to rent. You can decide this by measuring Ller or measuring tape to find distances? sions to find length and width of your
ango sapling or a coconut plant in your
of the pits required,differ? You want to e depth of the pit. Here according to the epth of your well. Here the depth of the
pe.
the school bag. To find the thickness a the thickness of each book, you will see these to measure height, width, depth, of ruler, length of stick, length of thread
kness are all lengths.
ses to denote the length? "metre" . It is
pe selected according to the length to be
measure a small length. The unit suitengths such as the length of an eraser
se book is the millimetre. are a lengh such as the length or width of
When stitching a dress the waist length, E and other dimensions of the dress are

Page 14
Mathematics - Grade 6
Example 3 The suitable unit to me
a class room, height o
metre. Example 4 The suitable unit to me
cities etc, is the kilome
Activity 15.1
Rewrite and fill in the blanks, usin
The distance between two to 2. The distance from your scho
The height of a mountain ca 4. The height of a building can 5. The suitable unit to measure
The width of the class room 7. The length of a pencil can b
The thickness of an exercise
To state the thickness of an 10. The unit suitable to measure
Activity 15.2.
Discuss with your friends about the of various objects using millimetre, cent
According to the above activities metre and kilometre are used to measure
The lengths millimetre, cen kilometre are known as uni
Activity 15.3
TTTTTT
|тттттттттттттттттттттттттттттттттттттттүтттттттүтіп
2 3 4
5 cm
M.

easure lengths such as the length, breadth of -f a school building, height of a tree is the
easure lengths such as distance between two
etre.
ng most appropriate units. owns can be given in ........ pol to home can be given in .
n be given in .. | be given in = width of the school garden is ...........
can be measured in . e given in ... = book can be given in ...
eraser the unit .........is suitable e the length of a finger is.
e situations in which you can measure length timetre, metre and kilometre.
you would see that millimetre, centimetre, e length.
timetre, metre and ts of measuring length.
MITTTTTTTTTTTTTTTTTTTTTTTTTTT
94
95 96 97 98 99 100
etre Ruler
For free distribution

Page 15
Obtain an ordinary measuring tape, or is one metre. What is the length of the mea graduated.
Metre ruler is divided into equal parts How many centimetres are marked in You will see that 100 centimetres are i Into how many parts is a space betwe
Observe that the space between two ce and are marked as millimetres. Likewise fir is difficult to use the metre ruler for measui centimetre, 15 centimetre rulers are used in length that can be measured using the centin
marked on it?
We know that 10 millimetre is 1 centi
It is convenient to write measuring uni
Unit
Millimetre Centimetre Metre Kilometre
Table
10 mm 100 cm 1000 m
IL || ||
Exercise 15.1
Measure the following objects using on the next page.
For free distribution

15 - Length
a metre ruler. The length of metre ruler suring tape? See how the metre ruler is
and centimetres are marked. the metre ruler? marked in the metre ruler.
en two centimetre marks divided?
ntimetre marks are divided into 10 parts ad how the measuring tape is marked. It sing because of its length. Therefore 30 day to day needs. What is the maximum netre ruler ? How many centimetres are
metre and 100 centimetre is 1 metre. it using symbols.
Symbol
mm
cm
m km
15.1
1 cm 1 m 1 km
suitable units and fill in the table given

Page 16
Mathematics - Grade 6
|Length Measured
Length of the blackboard
Width of the blackboard Length of the teacher's table Breadth of the teacher's table Height of the teacher's table Breadth of a student desk Length of Grade 6 Mathematics book Thickness of Grade 6 Mathematics book
Tab
Conversion of units
Activity 15.4 Copy the table into your exercisel
Metres
1x100
3 x 100
10
....X....
.... X ....
34
....X ....
Tab
Centimetres can be converted into
100 cm = 100 : 100 = 11 400 cm = 400 : 100 = 4
Activity 15.5 Rewrite and fill in the blanks. 1. 300 cm = 300 - 100 = 2. 1000 cm = 1000 +...... = 3. 1800 cm = ............. = 4. 7500 cm = ............. =
stra

cm
Instrument used for measuring
le 15.2
book and fill in the blanks.
Centimetres 100 cm 300 cm
.... X ....
....X ....
.... X ....
le 15.3
- metres.
m
..m
..m
...m
....m
For free distribution
Hoitsdizaib 99t

Page 17
We know that lcm is 10 mm. Let us convert centimetres into milli
1 cm = 1 x 10 = 10 n | 5 cm = 5x 10 = 50 n
Activity 15.6
Rewrite and fill in the blanks. 1. 2 cm = 2 x 10
8 cm
= 8x ..... = 3. 12 cm = .....x 10 = 4. 23 cm = .......... = 5. 30 cm = .......... = Now let us convert millimetres into o 1. 10 mm = 10 = 10 = 1 cm 2. 120 mm = 120 : 10 = 12 ci
S
Activity 15.7
Rewrite and fill in the blanks.
30 mm
= 30 : 10 = 80 mm
= 80 : ..... = 3. 140 mm = ....... 4. 560 mm = ........... 5. 1200 mm = ........... =
You know that 1 kilometre is 1000 met
1 km
= 1 x 1000
II
=
3 km
= 3x 1000 Activity 15.8 Rewrite and convert kilometres into I 1. 4 km
= 4 x 1000 2. 12 km = 12 x ...... 3. 20 km = ......X...... 4. 300 km = ......X...... 5. 340 km = ......X.
***...N
| || || || ||
....
..
..H
For free distribution

15 - Length
metres.
am
am
mm
mm
mm
mm
mm centimetres.
...cm
...cm
...cm ...cm
...cm
res. Let's convert kilometres into metres.
1000 m
3000 m
netres.
5

Page 18
Mathematics - Grade 6
Rewrite and convert metres into ki
1000 m = 1000 : 1000 = 3000 m = 3000 : 1000 =
.. =
| || ||
Activity 1.5.9 Rewrite and fill in the blanks. 2000 m = 2000 : 1000 = 8000 m = 8000 : ........ 15000 m = ....................
33000 m = Exercise 15.2
1. Rewrite and fill in the blank
(i) 1 km = ..........m = ... (ii) ..........km = 2000 m (iii) 25 cm = ..........mm (iv) 3 m = ..........cm = ...... (V) ..........m = 500 cm = .. (vi) ..........cm = 90 mm (vii) ..........m = ..........cm =
Manoharan took ten coins of measured the thickness of the What is the thickness of the
3.
Fathima needs 2-m of clot
she needs in centimetres. 4. Express (i) 2 m 10 cm
(ii) 5 cm 2 mm
(iii) 1 km 500 m Estimation
S
Activity 15.10
In chapter 6 you have learned at each of the following.

lometres.
1 km
3 km
..km .. km ..km ..km
....cm = .......
.mm
....mm
..mm
8000 mm FRupee 1 placed one over the other and he e heap. The thickness of one coin is 2 mm. heap ?
h to stitch a frock. Find the length of cloth
in centimetres in millimetres in metres
pout estimation. Give estimated values for
For free distribution

Page 19
i m + n
1. The length of a an eraser in m
Your height in centimetres. The height from floor of the o The distance from your home
What do you think should be t nut sapling?
The thickness of your Sinhala
Exercise 15.3
Write estimated values without mea 1. The distance from your school
The length of your school gard 3. The height of your Mathemati
The thickness of a Rupees 5 c The depth of the flower vase i
UN A W N
Measuring
s Activity 15.11
(1) Let's measure the length of lin
Figure 1
cm
Figure 2
Draw a line segment similar to the o
Draw short lines at the ends A and B Keep the 15 cm ruler so that 0 falls The edge of ruler should be along A
For free distribution
K&S 1260 EN-3

15 - Length
illimetres.
lassroom to the roof in metres.
to the school in kilometres or metres. he depth of a pit suitable to plant a coco
text book in millimetres.
suring.
to the closest hospital in kilometres.
len.
Cs teacher in centimetres.
pin in millimetres. on the classroom.(if any)
e segment AB.
TI||TTTTTTTTTTTTTTTTTTT
one is figure 1. - as seen in figure 2.
on A.
B. Read the value of the ruler at B.

Page 20
Mathematics - Grade 6
Write the length of the line segmen Let us measure the length of anothe
Figure Let us measure the length PQ.
Place the edge of the ruler on line PC read the value at Q on the ruler.
PQ = 4 cm 5 mm (2) Let us draw a line segment of
line segment of length 4 cm 2
Mark a point 'C'.
TTTTTTT
cm
Figu Place the edge of 15 cm ruler along short line on the line where the ruler read point D. Exercise 15.4
(1) Draw a straight line segment ar (2)
Draw the line segments (i) AB = 3 cm
(iii) F (ii) CD = 5 cm
(iv)
D
Figure 1

t in centimetres. er line segment.
TTTTTTTTTTTTTTTTT
cm
Q so that value 0 of the ruler lies on P. Now
given length. Suppose you have to draw a mm. Draw a straight line as shown below.
TTTTTTTTTTTTT,
are 4
the line so that 0 falls on C. Now mark a Is 4 cm 2 mm, remove the ruler. Mark the
nd name it as RS. Measure the length of RS.
PQ = 3 cm 5 mm. AN = 5 cm 4 mm
Figure 2
For free distribution
tot i.

Page 21
(i) Measure the length of AB (ii) Is BC or DC equal in leng (iii) Measure PQ, QR and RP
Is PQ = QR = PR ? Upul placed the edge of the rul
ruler and N at 7cm point on the Perimeter
It was decided to erect a barb wire feno of the length of barbed wire needed has to has to be known. If the fence was to be fiv wire needs five times the length around the known as the perimeter of the garden.
The length around a plane surface is length. Thus units for measuring perimeter
S
Activity 15.12 Find the perimeter of each of the follo
10 cm
5 cm
5 cm
10 cm
figure 1
2 cm
2 cm
2 cm
2 cm
2 cm
2 cm
figure 3
For free distribution K&S 1260 FN-4

15 - Length
, BC, CD and DA. gth to AB.
er in the line LN. L was at 2cm point on
ruler. What is the length of LN ?
ce around the school garden. The amount be found. The length around the garden e lines around the garden, the length of garden. The length around the garden is
known as the perimeter. Perimeter is a are same as units for measuring length.
-wing plane figures.
15 cm
8 cm
10 cm figure 2
12 cm
13 cm
5 cm
5 cm
12 cm figure 4

Page 22
Mathematics - Grade 6
Example 1
In figure 1, the perimeter = 10 + : Find the perimeter of each of the
Exercise 15.5
(1) Find the perimeter of the fig
3 cm
In th 3 cm
side
(2) Find the perimeter of each i
3 cm
3 cm (i)
5 cm 3 cm
|3 cm
5 cm
(iii)
8 cm
8 cm
8 cm
6 cm
10 cm
8 cm
(3)
(4)
Ramanathan prepared a rect
What is the perimeter of the Sheela cut out a square from Find the perimeter of the sq The length of a rectangular |
What is the minimum length 5 lines around the block of 1
(5)
10

5 + 10 + 5 = 30 cm
other figures.
gure given below. ne figure given all sides are equal, each
is 3 cm.
figure given below.
12 cm
(ii)
a 2 cm
2 cm
12 cm
6 cm
cm
cm
6 cm
angular flower bed 3 m long and lm wide. flower bed? a sheet of paper. Side of the square is 8 cm. nare. block of land is 30 m and its width is 15 m. of barbed wire needed to erect a fence with and.
For free distribution

Page 23
Additional Exercises
1. Rewrite and fill in the blanks.
Measurement
(i) (ii)
The distance to be covered
in a bicycle race (iii)
Length of a house (iv) (V)
Length of a carbon pen 2. Jagath won a 1500 metre race.
and metres. 3.
The rainfall of a certain place wa
millimetres.
4.
5.
Write 3 situations where estimat There are 8 combs in a bunch o fruits in one comb, estimate plantains.
Find tl
10 cm
5 cm
20 cm
7.
The perimeter of a rectangular bl Find the breadth.
Summary
Height, length, breadth, depth Millimetre, centimetre, metr length. The length around any planes
For free distribution

15 - Length
Suitable measuring unit
centimetre
millimetre
Write the distance he ran in kilometres
s 46 mm. Express this in centimetres and
cion is used.
f plantains. Assuming that there are 15 the number of fruits in the bunch of
he perimeter of this figure.
4 cm
ock of land is 110 m. The length is 30 m.
a and thickness are lengths. e, kilometre are units of measuring
surface is known as its perimeter.
11

Page 24
16 - ALGEBR
16.1 Symbols
When you walk along the road, so below. Can you mention what they mea
Figure 1
Figure 3 Figure 1 Indicates that a hospital i Figure 2 Indicates that a railway 1 Figure 3 Indicates that the road is Figure 4 Indicates that the road is Activity 16.1 1. Express the following messa
(i) Smoking is prohibited (ii) This can cause deat
insecticide) (iii) Easily broken or dama
(iv) School is ahead.
Exercise 16.1
1. Write the ideas expressed by th These signs were in baggage boxe
(i)
(iii)

AIC SYMBOLS
ome of the road signs that you see are given
n?
Nannan
Figure 2
Figure 4
s ahead. evel crossing is ahead. slippery. narrow.
ages in symbolic form.
h. (Hint : This is shown on a bottle of
aged.
e signs, given below.
CS.
For free distribution

Page 25
Express these ideas in symbolic (i) Signal lights ahead. (ii) An ambulance (iii) A telephone booth. (iv) A bend ahead.
(V) A bridge ahead. You would see that different idea In mathematics symbols are used to I
Simple letters are generally used to r symbols.
Eg:- a,b,c,d.......... x,y,z Any letter can be used as an Algebraic
16.1 Expressing unknown terms
There is a certain number of birds on a the number of birds on the tree can be writt written as 'y'. To show this number we can
Example 1.
Prema says that the amount of mone expressed using an algebraic symbol. Prem Soma has.
Activity 16.2 Rewrite and fill in the blanks using Al (i) The number of books in Kamal (ii) The amount of money in Shan's (iii) There are ............. coconuts in (iv) There are
buns in the sl
Exercise 16-1
Premalal plucked mangoes fror count them. Express the numb
ing an Algebraic symbol. (2)
Karuna could not count the num perahera. But she expressed the press the number of elephants u
For free distribution
19 TON

16 - Algebraic Symbols
form.
is can be expressed symbolically. epresent numbers. epresent numbers. Then we call them
: symbol.
using Algebraic Symbols tree. We do not know the number. Here en as 'x' or the number of birds can be ise any letter of the English alphabet.
ey in Soma's pocket is Rs. b. This is za does not know the amount of money
gebraic symbols. s bag is .
pocket is Rs. .. the bag. howcase.
n a tree and made a heap. He did not er of mangoes Premalal plucked us
ber of elephants that were parading in a = number by an Algebraic symbol. Exsing an Algebraic symbol.

Page 26
Mathematics - Grade 6
As the bus was completely not issue tickets to all. Exp
an Algebraic symbol. (4) State a situation where a
algebraic symbol.
| 16.2 Expressing a variab
Ramesh said "I have Rs. x with has ? It can be any number of Rupees 'x' does not have any particular value. V
Activity 16.3 (1) Show by an Algebraic sym
class, on a certain day.
Exercise 16.2
(1) Express the number of ch
Algebric symbols. (2) A number of pineapples we
the number of pineapples u
Additional Exercises
1. State 5 situations where exj 2. State advantages of making 3.
Wimal has a certain amour symbol. Fill in the blanks using alge There are.... crows in a tre
came back to the tree. 5.
When a dice numbered 1 t number turned up. If this is If n is the number of memb can be taken for n.
Summary
Simple letters in the Ei unknown value in an Alg

packed with passengers, the conductor could -ress the number of passengers in the bus by
n unknown term can be expressed by an
le by an Algebraic symbol
me". Do we know the amount of money he . It can be Rs.50, Rs.30, Rs.1 or any other. Ve refer to such value as a variable.
bol the number of students who came to the
Lairs brought from a class to the hall using
ere arranged in a heap at the market. Express
sing an Algebraic symbols.
pressions are made using symbols. ; expressions with symbols. it of money. Rewrite this using an algebraic
ebraic symbols. e. Out of them... crows flew away... crows
o 6 was thrown, a prime number or an odd
X, write the different values x can take. ers in a family. State five different value that
nglish alphabet are used to express an ebraic expression.
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Page 27
17 - SO
| 17.1 Properties of Solids
Figure 17
Consider the objects in the above pict any of these objects does not change with re
e Activity 17.1.
Write the names of the solids placed ir a cupboard in your classroom. Write the nam solids inside a cupboard in the school. You see that the cupboard is sometimes full with ids like books and bottles. When books in one of the cupboard are removed, you would n that a space is left.
This means that solids occupy space. is the space which was earlier occupied by
books.
Solids occupy space.
For free distribution

LIDS
e to
7.1
ure. You will notice that the shape of spect to the place where they kept.
iside es of
will solshelf ptice
That I the
15

Page 28
Mathematics - Grade 6
Surface
Activity 17.2
Draw pictures of, a book, box of dice, a coconut shell, a piece of chalk,
Any solid has a surface. This s sometimes curved surface parts. A pla
Plane surface
Fig
Activity 17.3 Copy the table given below and f
Name of Solid
Has only p
surface pa
Brick Tin Ball Dice Book
2.
Exercise 17.1
1. Name two solids that have
Name two solids that have 3.
Name two solids that have parts. How many plane surface When a lime is cut into two there? How many curved s
i m + n
16

matches, eraser, tennis ball, rubber ball, tin, a rectangular piece of wood, glass bottle, etc. surface consists of plane surface parts and
ne surface part is known as a face.
curved surface
uré 17.2
ill in the blanks.
-lane Has only curved Has both plane and arts
surface parts
curved surface parts
Fable. 17.1
only plane surface parts. only curved surface parts. = both plane surface parts and curved surface
parts are there in a box of matches?
equal parts how many plane surface parts are urface parts are there in one half of the lime ?
For free distribution

Page 29
Edges
An edge is formed when two surface p curved edges.
Straight edges
Figure
An edge formed when two plane surfa in a straight edge.
A straight edge can be formed when surface and a curved surface meet too. Se 17.4.
A straight edge can be formed when tw
· surfaces meet too.
By examining a jam tin or a salmon ti curved surface meet to form a curved edge.
Are there any other situations where
S
Activity 17.4
Copy the table given below and fill in Name of Solid
Solids with
Solids only straight edges only curve
1. Box of matches 2. Ball 3. Brick 4. Salmon tin 5. Tumbler 6. Bottle of drinks
10.
Table
For free distribution

17- Solids
arts meet. These can be straight edges or
curved edges
No
edges e 17.3
Straight edges
ces meet
- a plane ce figure
o curved
Log of wood
Figure 17.4 n you will see that a plane surface and a
curved edges are formed?
i the blank spaces by marking 'V' or 'x'.
with
Solids with
Solids d edges
straight edges and
without edges curved edges.
IL SI
17.2
17

Page 30
Mathematics - Grade 6
Exercise 17.2
Fill in the blanks using suitable w 1. A box of matches has 2.
A log of wood, the shape of length wise has ...
.... has only curv .... does not have a
i m =
Vertices
ver
Box of matches
Figu
A point where three or i 17.5 is known as a vertex
Activity 17.5 Fill in the blanks with suitable nu 1. A box of matches has.. 2. In a box of matches .... 3. In the piece of jack fruit sho
...... curved edges me The point where three or
meet is a vertex. Exercise 17.3
Write names of two solids tex. Name a situation where two
form a vertex. 3.
Name of a situation where t to form a vertex.
How many vertices are thei
2.
5.
figure (a)
18

ords.
... edges. which is a cylinder when cut into two pieces . edges and ...
....... edges. ed edges. curved or straight edge.
tices
vertex
00 0 0 0 0 0 0 0 0W
piece of jack
fruit
ure 17.5
nore edges meet as shown in diagram
mbers.
..........faces. ..... straight edges meet to form a vertex. own in fig 17.5 ................. straight edge and eet to form a vertex.
- more edges of a solid
where only straight edges meet to form a ver
- curved edges and one straight edge meet to
wo straight edges and one curved edge meet
te in a cubical dice?
figure (b)
For free distribution

Page 31
Fill in the blanks with reference to the In figure (a), the number vertices is In figure (b), the number of vertices i
17.2 Cube
Activity 17.6
Figure 1 Draw a net similar to the one given he or a piece of thick paper. Cut it along the bo Paste it using the shaded strips.
What is the result ?
Do you get a model of a solid which vertices.
B
Activity 17.7 Fill in the blanks. In the solid you made (activity 17.6
......, number of faces are .. number of vertices are..
. We call tt example for a cube.
A cube has 12 edges of equ in shape and 8 vertices.
For free distribution

17 - Solids
e vertices of the above figures.
7.6
ere (figure 17.6) on a piece of cardboard order edges. Fold along the dotted lines.
A you used to identify faces, edges and
5) all faces are .............., all edges are -.., number of edges are............The nis solid a cube. A 6 sided dice is an
al length. 6 faces equal

Page 32
Mathematics - Grade 6
| 17.3 Cuboid
Activity 17.8
Figu
Draw a net similar to the one shov thick paper. Cut it along the border ed
paste this using coloured strips.
The solid you get here is known examples for cuboids.
Exercise 17.3
Fill in the blanks. 1. (i) Number of vertices in
are
) A cuboid has (iii) A cuboid has .
and all together has ...
(iv) Write similarities and
A cuboid has 12 edges c edges and 8 vertices.
20

ure 17.7 vn in figure 17.7 on a piece of cardboard or ges. Fold along the dotted lines, fold and
as a cuboid. Box of matches and brick are
i a cuboid are
. . Number of edges
-...... set of edges equal in length. ...... pairs of faces of equal size and shape
.......... faces. differences in a cube and in a cuboid. onsists of 3 sets of 4 equal
For free distribution
Loitudine

Page 33
Regular Tetrahedron
Activity 17-9
Draw a net similar to the one giv figure 17.8 on a piece of cardboard or paper. Cut along the border edges. Fold : dotted lines. Fold and paste the shadded st
Answer the questions below with re to the model of the solid you obtained.
How many faces are there? Wh: you say about the shape and si
The number of straight edges 3. Are the straight edges equal in The model solid you have made is a
A tetrahedron has 6 equal shape and size and 4 verti
Exercise 17.4
1. Write the names of two solids you
in shape. 2. Write the names of three solids yo
in shape. 3. Copy the table given below, and f
Numb
Solid
Number of faces
Vert
Cube Cuboid
| Tetrahedron
Table
Additional Exercises
1. Name a solid which has a curs
For free distribution

17 - Solids
en in thick along crips. spect
Figure 17.8 at can ize of these faces ? it has is .. a length?
"Tetrahedron".
edges, 4 faces equal in ces.
have seen in your school which are cubic
ou have found at home which are cuboids
ver of
ill in the blanks.
Number of Straight edges
Ices
Are there curved edges.
17.3
red surface and a plane surface.
21

Page 34
Mathematics - Grade 6
2. Rewrite and selecting the correc
(1) All solid objects have ( (II) A dice has a (plane / cu
(straight / curved) (III) An unsharpened pencil
There are (vertices / no 3.
Name a solid with only one y 4.
How many triangular faces a 5.
Draw a solid in which there two plane surfaces.
**
*
Summary
Solids occupy space. An edge is formed when tw The point where three or m A cube has 12 equal edges vertices. A cuboid has 12 edges, 3 pa size and 8 vertices. A tetrahedron has 6 equal e 4 vertices.
*
22

et word from those given within brackets.
edges/ vertices / surfaces) rved) surface. All edges of a dice are
does not have (curved edge / straight edge).
vertices)
vertex. re there in a regular tetrahedron? are 2 curved edges, 1 curved surface and
O surfaces meet. more edges meet is known as a vertex.
, 6 faces of equal shape and size and 8
nirs of plane surfaces of equal shape and
dges, 4 faces of equal shape and size and
For free distribution

Page 35
18 - VOLUME
Diagran All objects like a cup, saucepan, bott lake, tea spoon, spoon occupy space. These s quantity of liquid. The quantity of liquid e capacity.
Thus the maximum amount of liquid known as the capacity of that container.
Example. The capacity of a domesti
spoon is 5 ml.
Activities 18.1
Pour water to a tumbler carefully. Y tumbler rises as you continue adding water. come to its brim, the water poured, overflo into a saucepan. You will notice that sever into the saucepan till it overflows. Note do into the saucepan.
You can decide how many tumbleri Tea spoons, table spoons and other type quantities of liquids.
S
Activities 18.2
Fill a tea spoon with water and pour t many tea spoonsfull of water are required to
For free distribution K&S 1260 FN-5

OF LIQUIDS
n1 cle of milk, domestic water tank, pond, solid objects can accommodate a certain cach can accommodate is known as its
- that can be poured into a container is
c water tank is 500 1. Capacity of a tea
ou will see that the water level in the
When the level of water in the tumbler ws. Now pour the water in the tumbler al tumblerfulls of water can be poured wn the number of tumblerfulls poured
full of water would fill the saucepan. of spoons are used to measure small
his water into a table spoon. Find how » fill the table spoon.
23

Page 36
Mathematics - Grade 6
The maximum amount of hold is the capacity of th
It seems that capacity can be me how to measure capacity.
Standard unit for meast
Millilitre (ml) is one thousandt 2 l means 2 litres and 3 l means 3 li
1000ml = 1
Activity 18.3
Equip yourself with bottles of dif can find empty glass bottles or plastic b
Look at units shown on these bot
In big bottles you would, see 1. medium size bottles you would see 7501 375 ml, 50 ml and so on.
Fill a 500 ml bottle with water ai times does the small bottle use to fill tł
1.51 bottle can be filled using th : 3 x 500 ml = 1.51
Try this with the 750 ml bottle. bottle twice.
2 x 750 ml = 1.51 The litre bottle can be filled usin 2 x 500ml = 1000 millilitres = 1
11 = 1000 m 0.51 = 500 ml 0.11 = 100 ml 1.31 = 1300 m

liquid that a container can at container.
sured in different ways. Now let us consider
iring capacity is the litre. h part of a litre. One litre is wrtitten as 11.
ires.
ferent sizes where the capacity is stated. You vottles.
tles.
5 l or 1.5 litres or 11 or 1 litre stated. In ml or 750 millilitres, 500 ml or 500 millilitres,
nd pour this into the 1.5 l bottle. How many ne large bottle ? ne small bottle three times.
Then 1.5 I bottle can be filled using 750 ml
g 500 millilitre bottle, twice.
litre
For free distribution

Page 37
Exercise 18.1
(1) For how many days can a pi
5 ml of medicine every 6 hours' (2) How many 500 millilitre bottles (3) The capacity of the petrol tank o
when 10 litres of petrol were fil
of petrol were there in the tank (4)
Express each of the following is (i) 21 (ii) 31 (ii
(vi) 0.51 (vii) 2.351 (v (5) Express each quantity of liquids
(i) 2500 ml (ii) 5000 ml (ii
(vi) 100 ml (vii) 50 ml (v. |(6) (i) Express each of the followi
(i) 11 30 ml (ii) 3 1 400 m (ii) Express each of the above i
Addition
There is 20 i 200 ml of water in a tan What is the total volume of water now ?
1 ml 20 200 200 ml + 900 10 900
31
100
This can be done by converting to li swer can be given in litres or millilitres or li
20 1 200 ml = 20.2 1 101 900 ml = 10.91
31.11 = 3111 20 I 200 ml = 20 200 ml 101 900 ml = 10 900 ml
31100 ml = 31 1 1
For free distribution K&S 1260 FN-6

18 - Volume of Liquids
utient use 100 ml of medicine using
can be filled with 1000 litres of water? fa vehicle is 50 litres. The tank was full led at a filling station. How many litres before filling? a millilitres. 1)51 (iv) 0.11
(V) 0.25 1 iii) 0.05 1 (ix) 0.005 1 - in litres. G) 10000 ml (iv) 750 ml (v) 375 ml iii) 20 ml (ix) 10 ml (x) 2 ml
ng in millilitres. El (iii) 15 1 40 ml
n litres.
k. 101 900 ml of water is added to this.
= 1100 ml Il 100 ml
tres or millilitres and adding. The anitres and millilitres.
00 ml
50 ml
25

Page 38
Mathematics - Grade 6
Subtraction
Volume of liquid in a vessel 51 3 the quantity of liquid left.
1 ml 5 300
51 - 1] = 41 - 2 500
11= 1000 ml
800
1000 ml + 300
This subtraction can be done in o (i) 5 1 300 ml = 5.3 1
2 1 500 ml =-2.5 1
2.8 1
5.3 1 - 2.5 I
2.8 1
2 1 800 ml
or
51 300 ml = 5300 ml 2 1 500 ml = 2500 ml
then
5300 ml – 2500 ml
2800 ml
2 1 800 ml
Exercise 18.2
1. Add. (i) 51 200 ml and 2 1 900 ml (ii) 0.25 l and 0.65 I (iii) 2 1 100 ml and 11 900 ml 2. Simplify. (i) 2 1 200 ml - 11 100 ml (ii) 31 100 ml - 2 1 900 ml (iii) 0.25 1 - 0.025 1
26

00 ml. 21 500 ml of this was removed. Find
nl - 500 ml = 800 ml
ther ways too.
For free distribution

Page 39
Additional Exercises
1.
The capacity of a table spoon is capacity of water in the table sp
of the tea spoon ? 2.
Convert each of the following in
(i) 2000 ml (ii) 750 m 3. Convert each of the following in
(i) 2.71 (ii) 0.8 1 3 1 400 ml of water was added
water already. Find the present i A milkman sold 1 litre 350 milli the volume of milk left. The capacity of the fuel tank o when 26.7 litres of fuel was pun tank was full. How many litres
was filled, at the filling station?
4.
5.
6.
Summary
The maximum volume of liqui as the capacity of that contain Standard unit for measuring 1000ml = 11
For free distribution

18 - Volume of Liquids
twice the capacity of a tea spoon. If the Don is 10 millilitres, What is the capacity
ato litres.
(iii) 500 ml (iv) 1250 ml to millilitres.
(iii) 1.75 1 to a container which had 5 1 750 ml of volume. Elitres of milk from 2 litres of milk. Find
f a certain vehicle is 40 1. It was found nped into the tank at a filling station the of petrol was there in the tank before it
id that a container can hold is known ier. capacity is the litre.
27

Page 40
19 - ALGEBRAI
19.1 Numerical expressio
Look at the statements given belo (i). Add three to two (ii). Subtract two from seven (iii). Multiply six by three (iv). Divide ten by two. (V). Add three to five and then s (vi). Add two to eight and then n The above operations can be writt (i) 2 + 3 (ii) 7-2 (V) (5+3) - 2 (vi) (8+2) As numbers are used for these ope
s Activity 19.1
1. Rewrite the following stater
(i) Add three to fifteen. (ii) Subtract eight from tv (iii) Divide twenty four by (iv) Add four to five and n Express the following mathe (i) 2 +5 (ii) (iv) (8 + 7) x 4 (v)
Exercise 19.1
(1) Nimalani brought 12 cocon
the relevant mathematical e

C EXPRESSIONS
ns
W.
ubtract two. multiply by three. en in numerical form as given below.
(iii) 6 x 3 (iv) 10 - 2
<3
erations they are mathematical expressions.
nents as mathematical expressions.
venty five and add five.
a three.
nultiply the result by three ematical expressions in words.
36 : 12
(iii) 8 - 3+5 (9 + 3) = 3
cuts to home and used 2 for cooking. Write
xpression.
For free distribution

Page 41
(2) Madhava plucked 15 mangoe
another tree in his garden. Wri
number of mangoes plucked. (3) The teacher distributed fiftee
students. Write the mathematic
one of them received. (4) Write the mathematical express
(i) 5+7 (ii) 8 - 3 (iv) (7+6) x 2 (V) (7-3)
19.2 Building up of Algebra
Imagine that you have 20, one rupee take the number of coins remaining if you ! is 20 – 4.
You have ‘a’ number of coins in your your pocket when you give 4 coins to you coins remaining with you as (a – 4). We kn is an algebraic expression.
Let us write another algebraic expres
In a class there are 'x' number of chi class joined that class, the total number of ch
S
Activity 19.2
Write algebraic expressions for the f (1) Vishal's mother brought home
remaining if Vishal ate one of (2)
The number of members in An and grandfather joined them. I
home? (3) 40 students planned to go on ar
and could not join the tour. He Exercise 19.2
Write Algebraic expression for the si (1) There were ‘a’ number of stude
How many students are there is
For free distribution

19. Algebraic Expressions- Building Up
s from one tree and 10 mangoes from se a mathematical expression for the total
n exercise books equally among three al expression to find the number of books
sion given below in sentence form.
(iii) 12 + 5 - 3 : 2
ic Expressions. e coins with you. Write an expression to had given four coins to your friend. That
r pocket. How many coins will remain in r friend? We can express the number of ew that ‘a’ is an algebraic symbol. (a – 4)
ision. ldren. When three students from another ildren in the class can be written as (x+3).
ollowing statements. 'y' number of buns. How many buns are them? uradha’s family is ‘p’. Her grandmother How many are there now at Anuradha's
I educational tour. Two students fell sick ow many students took part in the tour?
atements given below. ents in a class. Two of them left the class. i the class now?
29

Page 42
Mathematics - Grade 6
(4)
(5)
(2) The total number of students
in the class if the number of The cost of a pencil is Rupee than that of a pencil. What is The number of passengers i passengers in the bus, if ‘p' halting place. Rajitha was 125cm tall in 3 y
What is the increase in Rajit (6)
Mohan is 12 years old. His Mohan. What is the age of h There were 10 birds sitting o
How many birds are there o (8)
The cost of a pair of trousers
Write an algebraic expressio
cost of the shirt is ‘x’ rupees (9)
Rewrite and fill in the blank (i) Add 5 to 'b' (ii) Subtract 'p' from 12 (iii) Subtract 3 from 'a' (iv)
(7)
(vi)
(vii) (10) The distance from Vasanthi
and she travels the rest by b
bus? Additional Exercise
1.
Write these numerical expre (i) 2 +7 (ii) (2 x 3) + 10 (iii) 10 – (2 x 3)

in a class is 45. How many boys are there girls are ‘x’? s y. The cost of a pen is three rupees more s the cost of a pen? n a bus is 50. What is the total number of number of passengers got into the bus at a
rears ago. His height now is 'c' centimetres. ha’s height during these three years? younger brother is ‘t’ years younger than is younger brother? na branch. ‘m’ number of birds flew away. a the branch now? is 150 Rupees more than the cost of a shirt. ons for the cost of the pair of trousers if the
s using symbols, letters or statements.
= b05. = 0-0 = O-O = m+15 = C - 3 = 2 + d = 15 - a s house to school is 5km. She walks 'n' km us. What is the distance Vasanthi travel by
ssion in word form.
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Page 43
Write the following as numeric (i) Multiply twenty by three (ii) Add six to fifteen and dit (iii) Divide fifteen by three ar Build up algebraic expressions (i) The total number of stud
were absent. How many (ii) My age is 't' years. What v
my age after three years? (iii) The amount of money m
Rs. 25, Find the amount (iv) The number of marks obt
Saroja needs 12 more ma
marks did Saroja obtain f (V) How many days are there
Summary
Symbols are used to express expression. Simple letters of the English al
For free distribution

9. Algebraic Expressions- Building Up
al expressions. and subtract eight. vide the answer by three. ad add six. for the situations given below. ents in a class is 'n'. One day 5 students
vere present on that day? vas my age three years ago. What will be
nother gave Kasun was Rs p. He spent
of money left with Kasun ? cained by Gayan for mathematics is 'x'. rks to equal Gayan's marks. How many or Mathematics? e in 'p' weeks?
; unkown quantities in an algebraic
phabet are used as algebraic symbols.
31

Page 44
Moitarias
20 - ALGEBRAIC
- SUBSTI
Number of pigeons in a cage are 'y cage the total number is y+3. If the initi:
We can write 12 for 'y' in the express 12+3=15. 12 is substituted for 'y'.
S
| Activity 20.1
Hemali had ‘a’ number of rupees Ishani had ‘c’ number of rupees. All thr algebraic expressions for the remaining :
Initially if Hemali had 50 Rupees, Rupees, find the amount of money each
Example 1 The amount Hemali has is Rupees if a = 50 then, : a - 5 = 50 – 5 = 45
The amount of money Hemali was amounts of money remaining with Premar
b = 25 and c = 34
|s
| Activity 20.2
Let us assume the amount of mone an algebraic expression for the remaining 10.
If p= 100, then p - 10 = 100 - 10 The amount of money remaining i Find the amount remaining by sub (i) p = 50 (ii) p = 75 (iii) p = 44
|s
Activity 20.3 (1) Find the value of.
(i) 8 + x when x = 9 (iii) b + 15 when b = 10

: EXPRESSIONS ITUTION -
. When three more pigeons are put into the al number of pigeons were 12. Then y=12. ion y+3. Now the number of pigeons is
, Premani had 'b’ number of rupees, and ee spent 5 Rupees each as bus fare. Write amounts of money with each of them. Premani had 25 Rupees and Ishani had 34 person has after spending for bus fare.
a-5
left with is Rupees 45. Similarly find the ai and Ishani substituting,
=y in Hameed's pocket is Rupees ‘p’. Write - amount in his pocket, if he spends Rupees
= 90. n his pocket is Rs.90. estituting different values where
(ii) 12 - a when a = 5 (iv) d– 6 when d = 13
For free distribution

Page 45
20
(3)
The number of students in Bim students by substituting each va (i) m = 24 (ii) m = 32 The sum of two numbers is 65 number using symbols. Find th below. (i) x = 12 (ii) x = 30
Exercise 20.1
(1) Find values of algebraic express
given below.
(i) n= 15 (ii) n= 18 (2) Find the value of each algebraic ex
(i) 20 – a (ii) 8 + a (3) Find value of 16-t for each valu
(i) t=5 (ii) t= 0 (4)
The number of brooms in a sho sold. How many brooms are left
how many brooms are left ? (5)
The number of mangoes my yo was 5 more than what I bought. What is the number of mangoes
mangoes, how many mangoe (6)
From a rope 12 metres long a ler of the remaining piece of rope f (i) p = 2 (ii) p= 2.5
(iii) p= 3.8 (7)
Krishantha took 'c' coconuts coconuts, find an expression fo If (i) x = 30
(ii) x = 36 (iii) x = 45
find the number of coconu
For free distribution

- Algebraic Expressions - Substitution
al's class is m + 5. Find the number of lue of 'm' given below.
(iii) m = 41 (iv) m = 35 One number is 'x'. Express the other e other number for values of 'x' given
(iii) x = 55
-ion n – 3, substituting each value of 'n'
(iii) n= 24 pression given below substituting 5 for 'a'
(iii) a - 3 (iv) a +5 e of 't' given below.
(iii) t= 8 (iv) t = 16 -p was 16. 'y' number of brooms were ? If the number of brooms sold was 5,
unger brother bought from the market The number of mangoes I bought is 'y'. s my brother bought? If I bought 15 ; did my brother buy?
gth 'p' metres is cut off. Find the length or each value of 'p' given below.
to the market for sale. If he sold 25 or the number of coconuts left.
ts left.
33

Page 46
Mathematics - Grade 6
A cement block is sold after the cement block. Write an a cement block. (i) If the cost of producti
selling price of a ceme (ii) If the selling price of a
production? There are 20 oil cakes in bo 40 pieces of Aluwa in box E 30 pieces of cake in box C
35 gingelly balls in box D A mother distributed them among
(i) Find how many sweets (ii) If there are
poil cakes in box A q pieces of Aluwa in t r pieces of Cake in bo s gingelly balls in box find the number of sv
distributed sweets froi (10) Fill in the blanks with suitabl
(1y + 5 = 15 +0= (ii) p- 5 = 30 -0 = (iii) c- 3 = 0-0= (iv) 12 - b = 0-3 = (V) 10 + m = 10 +0= (vi) n+11 = 0+11 = (vii) z - 8 = D-8 = (viii) 10 - k = 10-0 =
34

adding Rs. 10 to the cost of production of gebraic expression for the selling price of a
on of a cement block is Rs.20. What is the
at block? cement block is Rs. 25. What is the cost of
K A
; her 5 children taking one from each box.
are remaining in each box.
ох В
x C
D
veets remaining in each box when mother m each box to her 5 children. Le numbers.
1
S
26
12
7
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Page 47
20
Additional Exercises
1. Find the value of (a + 12) for ei
(i) x = 5 (ii) x = 16 (ii 2. Find the value of (25 - a) for ea
(i) a = 10 (ii) a = 25 (ii 3. Amal is 5 years older than Thara
Amal's age when Tharanga is 't' (i) Tharanga is 20 years old (ii) Tharanga is 22 years old. (iii) Tharanga is 30 years old (iv). Tharanga is 50 years old.
There are two consecutive odd n the first odd number is 'a'? Find is. (i) a = 5 (ii) a = 9 (iii) a = 25 (iv) a = 37 (v) a = 75
Summary
The numerical value of an Alg substituting a given value for symbol)
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- Algebraic Expressions - Substitution
ach the values of 'x' given below. 1) x = 40 (iv) x = 12 (v) x = 0 ch of the values of 'a' given below. a) a = 8 (iv) a = 1 (v) a = 13 nga. Write an algebraical expression for years old. Find the ages of Amal, when
umbers. What is the next odd number if the next odd numbers if the value of 'a'
gebraical expression can be found by the unknown expression (Algebraic
35

Page 48
DIS
21 -
21.1 Measuring Mass
s Activity 21.1
Get three plastic buckets of the sa with pebbles and the other with cotton
Lift a bucket at a time and see wł You will find that the bucket containing when compared to the buckets containi
You would have noticed that a lor with greater effort than a lorry loaded v equal in size.
Then why was there a difference wool when compared to the bucket wi difference in mass.
In other words we can move easil
Now consider the mass of an elep a horse.
When you go to a shop to buy foc
Now you would realize that a sta mass.
The standard unit of me
kilogramme.
It can be written as kilogramme o
s Activity 21.2
If you go to a shop you would no are marked in kilogrammes or kg. Exai cement 50 kg etc.
Most of these are weighed in adv
You can get a rough idea about tt Some weights of weighing are shown i
36

MASS
ime size. Fill one bucket with sand, another
wool or coir dust. nich bucket could be lifted with least effort. ; cotton wool or coir dust will be easy to lift ng sand or pebbles. ry loaded with cement will move on the road vith sand. Assume that these two lorries are
: in effort in lifting the bucket with cotton ith pebbles? The difference is due to the
-y a quantity with less mass.
hant and the mass of a small animal such as
od items, how do you ask for the items ? andard unit should be necessary to measure
easurement of mass is
or kg.
ptice that information about food items etc. mples: sugar 1 kg , rice 5 kg , flour 10 kg ,
ance and are marked for information. me mass of different weights by lifting them.
n the next page.
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Page 49
2kg
1 kg
500g
Figure 21.1
Gramme is needed to weigh small qui dard unit is the kilogramme which is eqi
That is,
1 kg = 1000 g
There are units smaller than the gran mass of medicinal tablets etc.
Note that in most of the medicinal tab or shown on the carton or the bottle where i
You could note 500 mg, 250 mg, 1251 This unit is called milligramme.
1 kg
= 1000 g 1000 mg = 1 g
The use of kg, g, mg in measuring mass
How do we measure mass? For measu scales are used which are usually found in sa
Figure 21.2
There are two pans and an arm with a You have seen that the required measu
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21 - Mass
(201010 M DE
antities. Internationally accepeted stan
al to 1000 grammes.
mme which are used for expressing the
lets the mass is marked on its face itself chey are packed. ng, 100 mg marked in medicinal tablets.
ring mass, devices known as measuring les outlets.
Pointer
vointer to show equilibrium of the pans. ring weight is placed on one pan and

Page 50
Mathematics - Grade 6
the material to be weighed is pla that both sides of the scale are balanced. measuring weight and mass of material
The accuracy of the tools and the there could be problems involved.
It should be noted that there are dif comparing mass.
TTTTTTTTTTTTTTT
Platform balance
Spring bala
Figu These balances though different measure different masses. These balanc
Example:
When an item or material is requ spring balance. If the pointer stop the object hung is 5 kg. Let us find out how to convert k 4 kg = 4 x 1000 g = 4000 g 4 kg 15 g = 4 x 1000 + 15 g = 40 45 kg = 45 x 1000 g = 45000 0.45 kg = 0.45 x 1000 g = 450 £
Exercise 21.1
(1) Convert to grammes.
(i) 2 kg
(ii) 5 kg (iv) 7.5 kg
(v) 6.2)

ced on the other pan till the pointer shows Vhen the scale is at equilibrium the mass of weight are equal. instruments used should be maintained as
ferent kinds of scales for measuring mass or
ką. L
SEMI
Laululumilaulustatului
Alumitid al mlauf
nce
Electronic balance
re 21.3 t from an ordinary scale can be used to ces are calibrated.
aired to be weighed it is suspended on the s at 5, and the scale is in kg then the mass of
ilogrammes to grammes.
-00 + 15 g = 4015 g
ԵՐ
10 g (iii) 1 kg 200 g
(vi) 0.06 kg
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Page 51
Converting grammes to kilogramm
Convert 3750 g to kilogrammes.
3750 g = 3750 kg = 3 in
1000 Exercise 21.2
Convert to kilogrammes. (i) 575 g (ii) 860 (V) 6227 g (vi) 565
21.2 Addition of mass
Example:
In a certain bag there is 5 kg 200g added to this. What is the mass of sugar n
200 g + 900 g = 1100 g 1100 g = 1 kg + 100 g ' total mass of sugar = 5 kg + 2
= 8 kg 100 This can be done by another metho 5 kg 200 g = 5000 g + 200 g = 2 kg 900 g = 2000 g + 900 g
5200 +2900
8100 =
8 kg 100 g
Or
5 kg 200 g = 5 kg + 0.2 kg 2 kg 900 g = 2 kg + 0.9 kg
|| ||
kg
5.2 2.9
8.1
8 kg 100 g
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21 - Mass
!S
kg = 3.75 kg
g (iii) 25 g (iv) 1250 g
of sugar. Another 2kg 900g of sugar is ow?
kg +1 kg + 100 g
5200 g
2900 g
5.2 kg 2.9 kg
39

Page 52
Mathematics - Grade 6
21.3 Subtraction of mass
Subtract 8kg 800g from 14kg 400g
kg
g
14 400
800
600
i'. Answer 5 kg 600 g Let us consider this again.
kg
800 cannot be de 400. So, let us w 1 400g.
14
400 800
Exercise 21.3
(1) Fill in the blanks using <, = or
Example - 100 g > 29 g (i) 100 g ....... 98 g (iii) 1 kg ....... 800 g (v) 1 kg .......1300 g (vii) 1.5 kg ....... 1500 g (ix) 1.3 kg ....... 1400 g Add. kg g
(ii) kg 2 50
4 50 +3
75
+5 300
(v)
kg
(vi)
512
kg
3 391 +1 916
+5 817
• 3..
Subtract. kg g
5 200 - 2 125
(ii) kg g
3 415 – 2 510
40

> 400 g < 800 g. Let us convert 1 kg
from 14 kg to grammes. 14 kg - 1 kg = 13 kg 1 kg = 1000 g 1000 g + 400 g = 1400 g 1400 g - 800 g = 600 g
KE
educted from
rite it as 13kg
13 14
8
1400 800 600
(ii) 20 g ....... 1 kg (iv) 1 kg 600 g ....... 1 kg 900 g (vi) 2 kg .......200 g (viii) 1.25 kg ....... 1250 g (x) 2.2 kg ....... 2201 g
(iii) kg g
8 500 + 3 750
(iv) kg g
600 + 925
(iii) kg g
4 817
915
(iv) kg g
3 25 -1 138
14
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Page 53
Additional Exercise
1. Copy the table given below. W
of the material.
Material A bag of cement A loaf of bread
Orange Pumpkin
Potato
A bunch of plantains A cake of soap
Copy the table given below. F
gramme (g)
kilog
2000
3500
750
400
35
3. Express in kilogrammes and
(i) 1050 g
(ii) 4. Express in grammes.
(i) 3 kg 450 g
(ii)
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21 - Mass
rite the unit needed to measure the weight
Unit
gramme (g)
kilogramme (kg)
ill in the blanks. rammes (kg)
0.8 0.25
3.6
0.05
grammes.
3 250 g
(iii) 2 075 g
2 kg 45 g
(iii) 12 kg 08 g
41

Page 54
Mathematics - Grade 6
5. The mass of a parcel of mang
of mangoes is 4 kg 275 g.
kilogrammes and grammes. 6.
The mass of a pumpkin fruit i
off from it. What is the mass 7.
The mass of a bag of rice was it. 6 kg 350 g of the same qu What is the mass of the bag of
Summary
Different kinds of scales are
**
*
The international unit of me
42

pes is 2 kg 750 g. Mass of another parcel
Find the total mass of both parcels in
s 3 kg 75 g. A portion of 1 kg 250 g is cut of the remaining portion? 30 kg 425 g. A trader sold 10 kg 750 g of ality of rice was added to this bag again.
rice now?
used to measure mass.
easuring mass is kilogrammes.
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Page 55
22 - F
22.1 Ratio between two qu
There are so many situations in da mixing different material.
Example 1. Mixture of cemen
2. Mixture of fertiliz 3. Mixture of medici 4. Mixture of fruit dr 5. Mixtures made wł
S
Activity 22.1 1. Write 5 situations, in additi
made.
State the quantities of materi You would have seen how mason mixture in building houses. Also you wo of cement and sand for flooring a hous brick walls when constructing a house. sand and cement they take for the mixtu
Masons normarlly prepare the mix with 7 masonry pans of sand.
1 pan of cement
1 bucket of cement
7 bu
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ΙΑΤΙΟ
antities y to day life where mixtures are made by
ers
nes inks like cordials en preparing sweets like cakes
on to above examples where mixtures are
al used for these mixtures. s mix cement and sand to make masonry puld have seen how they prepare a mixture e. You would have seen masons building You would have seen in what quantities of ire. ture by mixing one masonry pan of cement
7 pans of sand
ckets of sand
43

Page 56
Mathematics - Grade 6
For the masonry mixture
For 1 pan of cement 7 pans o For 1 bucket of cement 7 buci
For 1 shovel of cement 7 shov In cementing a floor normally for li sand are mixed.
1 masonry pan of cement
For 1 masonry pan of cement,
For 1 bucket of cement, 5 buc When a mixture of paint is prepared, 4 parts of water.
10 l of water and 10 ml of insecti insecticide to be sprayed on a cultivation In making masonry mixture it was s
1 pan of cement to 7 pans of s 1 bucket of cement to 7 bucke 1 shovel of cement to 7 shovel If cement is measured in mas
masonry pans. If cement is measured in bucke
the same size. If cement is measured in a certain u unit. The numerical relation can be stated
When mixtures are made, by mixing of the same unit.
The numerical relation bet quantities in the same unit
The relation between cement and sai This is written as 1:7. This is read as ‘one is to seven’.
44

E sand sets of sand els of sand nasonry pan of cement 5 masonry pans of
5 masonry pans of sand
5 masonry pans of sand kets of sand
generally one part of paint is mixed with
cide are mixed to prepare a mixture of
tated earlier that, and ts of sand s of sand onry pans, sand should be measured in
ts, sand should be measured in bucket of
nit, sand should be measured in the same as ‘one is to seven’. ; different material, quantities should be
ween two or more is known as "Ratio".
d in the above example is 1 is to 7.
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Page 57
A ratio does not have units Example 1: Family members
2 females In a certian family shown above are males to males in this family is written as 2
The ratio of males is to females is 3
Example 2: Ro
1st sprig
The ratio of flowers in the 1st sprig te (4 is to 5) Ratio of flowers in the 2nd sprig and
My younger sister was given twice th The ratio of toffees given to me to m
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21 - Mass
3 males
2 females and 3 males, the ratio of fe2 is to 3 or 2:3.
: 2.
3 and 2 are terms of the ratio.
2nd sprig
o the flowers in the 2nd sprig is 4:5.
flowers in the 1st sprig is 5:4 (5 is to 4) te number of toffees I was given. ay sister is 1 is to 2. That is 1:2.
45

Page 58
Mathematics - Grade 6
Exercise 22.1
(1) Select the phrases that denot
An elephant is heavier than : The coconut tree A is twice :
My age is equal to your age. iv.
The mass of a pencil is 15g. v. The number of students in G1
Grade 7. vi. The marks obtained by Nim
that he obtained for Mathem vii. I have three times the amoun viii. A bird has two legs and a do ix. A father's age is twice as his X. The speed of the bus is high.
2
3.
| 22.2 Writing the ratio betwe
Examples : 1. The number of birds in the m
The number of birds in the 'j The ratio of birds in the ‘mai The number of girls in a clas class is 15. The ratio of girls to boys is 1 The ratio of boys to girls is 1 The cost of an apple is Rs.15 The cost of an orange is Rs. The ratio of the cost of an or The height of a coconut tree The height of a king coconut The ratio of the height of the king coconut tree is 8:7. The mass of a pumpkin fruit The mass of a sweet melon f The ratio of the mass of a pu
mass of a sweet melon fruit i Look at some more examples. (1) The mass of parcel A is 4kg.
The ratio of the mass of the t
5.
46

e a ratio. ı bull. as tall as the king coconut tree B.
The mass of a book is 25g. rade 6 is less than the number of students in
_al for Sinhala language is 60. The marks
atics is 90. at of money my younger sister has. g has four legs.
son's age.
en two quantities (continued)
nango tree is 15. Tamboo’ tree is 23.
ngo’ tree to the ‘jamboo’ tree = 15 : 23 s is 18, the number of boys in the same
8: 15. 5: 18.
20.
ange to the cost of an apple is 20 : 15. is 8 m.
tree is 7 m. coconut tree to the height of the
is 3kg.
uit is 2kg. mpkin fruit to the s 3 : 2.
The mass of parcel B is 5kg. wo parcels A to B is 4:5.
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Page 59
(2) The quantity of soft drinks con
of soft drinks in a small bottl drinks in the big bottle and th pressed in the same units. The quantity of soft drinks in t
:. The ratio is 1000 : 400. When the ratio of two quan shoud be expressed in the
Exercise 22.2
1. Find the ratio of the first quant (i) The mass of the first bag
The mass of the second 1 (ii) The amount of money M
The amount of money R (iii) The length of a rubber sti
1 m 500 cm. (iv) The time taken for a ce
time taken for the same jo (v) The cost of a pen is Rs.
2.
3.
There are 400 boys and 50 girls of boys to the number girls.' The mass of the packet of rice The mass of the packet of dhal Find the ratio of the mass of the dhal.
4.
The length of a building is 101 the ratio of the length to the br
5. To make a mixture of fruit dri
juice are needed. Find the ratio
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21 - Mass
tained in a big bottle is 11. The quantity 2 is 400 ml. If we find the ratio of soft e small bottle, the values should be ex
he big bottle is 1000 ml.
tities is to be found, they same units.
ity to the second quantity.
is 75 g. pag is 150 g. Lohamed has is Rs. 250. anjith has is Rs. 300. rip is 2 m. The length of a wooden strip is
rtain journey by Wimal is 2 hours. The ourney by Kamal is 1 hour and 30 minutes. 10. The cost of a pencil is Rs. 4.
s in a school. Find the ratio of the number
is 5 kg. I is 200 g.
packet of rice to the mass of the packet of
m 50 cm. The breadth is 8 m 75 cm. Find eadth of the building.
nks, 800 ml of water and 200 ml of fruit - of water to fruit juice in the mixture.
47

Page 60
Mathematics - Grade 6
22.3 Equivalent Ratios
Consider the mixture of cement ai
Masonry pans of
Masonry of cement
of sai
10 15
20
O 00 y a un A W N -
25 30
35 40 45
50 Tab
According to the table above, for 1 of sand are needed.
When the mixture is large in quant increases according to the number of ma cement remains as 1:5.
The ratios in the above table can 1:5 = 2 : 10 = 3 : 15 = 4:2
Since all these ratios are equal to t ratios.
Example 1: Write three ratios e
1:8 = 2: 16 1:8 = 3:24
1:8 = 4:32 Example 2:
Write three ratios e 3:4 = 6:8 3:4 = 9: 12
3 : 4 = 12 : 16 Equivalent ratios can be obtained the same number.
48

ad sand.
pans
Ratio of cement and sand
id
1:5 2: 10 3 : 15 4 : 20 5: 25 6: 30 7: 35 8: 40 9:45
10 : 50 le 22.1
O masonry pans of cement 50 masonry pans
tity the number of masonry pans of cement Lsonry pans of sand. But the ratio of sand to
be written as, 0 = 5: 25 he ratio 1:5, they are known as equivalent
quivalent to 1:8.
quivalent to 3:4.
by multiplying both terms of the ratio by
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Page 61
1. Writ
Exercise 22.3
Write two equivalent ratios fo (i) 1:4 (ii) 3:5 (iii) 2:7 (iv) 3:2 (V) 8:5
Fill in the blanks. (i) 3:4 = 6 : ...... (iii) 7:8 = 35 : (v) 5:4 = 35 : ..
2.
22.3 Equivalent Ratios (Co
2:16 = 1:8 both term of the ra 3:24 = 1:8. both terms of the ra 4:32 = 1:8 both terms of the ra
The terms of the above ratios are equivalent ratios.
40 : 50 = 4:5 both terms in the Number of biscuits Soma's sister re Number of biscuits her brother rece The ratio of biscuits given to the sis By dividing the terms of the ratio bi
S
Activity 22.2 (1) Find the ratio of the number
number of wild olives Mahes
wild olives each. (2)
A rubber paint and water we mixture . How many litres of water?
Equivalent ratios can be each term of a ratio by t|
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ali 21 - Mass
*** 12.
r each of the following ratios.
(ii) 2:5 = ...... : 15 (iv) 2:1 = 6: ......
ntinued) tio are divided by 2 atio are divided by 3 atio are divided by 4
divided by the same number to obtain
e ratio are divided by 10. -ceived is 6. ived is 6. ster and the brother is 6:6. y 66.6 = 1:1
. 6 6
- of wild olives, Ranjani received to the swari received, when both were given 50
ere mixed in the ratio 1:1 to prepare a f paint is needed to mix with 10 litres of
obtained by dividing he same number too.
49

Page 62
Mathematics - Grade 6
(2)
Exercise 22.4
(1) Write equivalent ratios to ea
terms by the same number. (i) 20:15 (ii) 14 (V) 42 : 30 (vi) 35
Fill in the blanks. (i) 15:12 = 5: ...... (ii) 32:16 = 4:......
(iii) 18:6 = ...... :1 (iv) 64 : 40 = (V) 81:45 = 9:
(vi) 12: 12 = 1:
22.5 Writing a ratio in the
2:16 as 1:8 Terms of the ratio 40 : 50 as 4:5 Terms of the ratio The ratio 1:8 and ratio 4:5 canno Example : 64 : 32 = 32 : 16 = 8: 4 Here the terms are divided by 2 repe 40 : 50 = 20 : 25 (divided by 2) 20 : 25 = 4:5 (divided by 5) :. 4:5 is the simplest form of the
A ratio that cannot be sim to be in the simplest form
22.6 Writing a ratio as a fra
A ratio 1:5 can be written as =

ch of the ratios given below, dividing both
: 16 (iii) 72:9 (iv) 16: 48 : 35
(vii) 8:8
simplest form o divided by 2 when it is 2: 16. o when divided by 10 it is 4 : 5. ot be simplified any further. 4 = 2:1
eatedly.
ratio 40 : 50.
plified any further is said
iction
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Page 63
Example 1: The number of girls are 15 and the i Ratio of girls to boys is 15 : 20
15
As a fraction it is
20
V. Z
153 20 4
(both numerator and 15:20 = 3:4 The ratio 15 : 20 is simplified and Example 2: Express the ratio 300 : 400 as a frac
300 3 300 : 400 = 3:4, -
400 4 300 : 400 can be simplified as 3:4. Exercise 22.5
(1) Express each of the following
i. 16: 28
ii. iv. 56 : 64 (2) Fill in the blanks.
(i) 28 : 21 = 4 : (ii) ........ : 40 = 3:5 (iii) 18:27 = 2 : (iv) 110: 440 = 1:
(v) 90 : ........ = 10 : 3 (3)
Find ratio of each of the follo simplest form. (i) 750g and 2 kg. (ii) 2 m 50 cm and 75 cm. (iii) 11 50 ml and 250 ml (iv) 3 ml and 5 ml
(v) 1 kg 750 g and 2 kg 250 (4)
Write the ratios given below a
(i) 2:3. (ii) 4:5 (5) Write the fractions given belo
(ii)
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21 - Mass
number of boys are 20 in a class.
denominator are divided by 5)
written as 3:4 as well.
tion.
ratios in the simplest form. 72: 36
iii. 250 : 150 49: 63
vi. 108 : 84
owing quantities and express them in the
is fractions.
(iii) 8:3 (iv) 1:2 (V) 3:7 w as ratios.
(ii) ? (iv) 12 (V) 33
51
100

Page 64
Mathematics - Grade 6
*
* *
22.7 Rate
Observe the clauses given below.
5 mandarins for Rs. 20 500 g of fish for Rs. 150
The bus travelled at a speed o * The buying price of an Amer: The clauses above show relations be The relation that exists b of different units is known
Activity 22.3 Application of rate. Example 1: If the cost of 5 mang
The cost of 1 mango
The cost of 3 mango Example 2: If the cost of 41 of p
of petrol. Cost of 41 of petrol
Cost of 1l of petrol Cost of 71 of petrol
Example 3: If 1 American dollar
equal to 20 America 1 American dollar 20 American dollars
Exercise 22.6
(1) Write 5 examples for ratios o (2) Write 5 examples for rates.
If the wages of a worker per days.
If the cost of 3 pineapples is I (5)
If 1 American dollar is Rs 108 in Rupees.
52

of 40 kilometres per hour. ican dollar is Rs. 108. etween two quantities of different units.
etween the two quantities a as a rate.
Foes is Rs.60, find the cost of 3 mangoes.
= Rs. 60 = Rs. 12 es = Rs. 12 x 3 = Rs. 36 petrol is Rs. 452, find the cost of 7 liters
= Rs. 452
D. 452 = Rs. = Rs.113
4.
= Rs. 113 x 7
= Rs. 791 is Rs. 108, find the number of Rupees n dollars.
= Rs. 108 = Rs. 108 X 20 = Rs. 2160
f two quantities.
day is Rs. 350, calculate the wages for 5
Rs. 150, find the cost of 8 pineapples.
, express the value of 70 American dollars
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Page 65
1.
Additional Exercises
Write ratio of each pair of qu simplest form. (i) 35 and 25 (ii) 16 and 8 (iii) 8 and 16 (iv) 6 kg and 15 kg
Find the ratio of the number o of a cube. In a cricket match, Peter score (i) Find the ratio of runs sc (ii) Find the ratio of runs sc The length of a room is 3 m 7
ratio of the length to the breac 5. The monthly income of a pers
this amount. Find the ratio of 6. Write each fraction given belo
(1) 2 (ii) (iii)
Write each of ratio given belo
(i) 2:5 (ii) 9:10 (iii) 8. If the cost of 5 cakes of soap i
soap. Summary
The numerical relation that same units is known as a rat A ratio does not have units. Ratios that are equal an equivalent ratios. An equivalent ratio can be ol terms of a ratio by the same Ratios that cannot be simp simplest form. A relation between quantiti
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i 21 - Mass
aantities given below and express in the
(v) 75 cm and 100 cm (vi) 250 g and 2 kg (vii) 45 minutes and 1 hour
(viii) 2 1 250 ml and 31 500 ml f faces of a cuboid to the number of faces
ed 140 runs. Mahesh scored 60 runs. Pored by Peter to runs scored by Mahesh. -ored by Mahesh to runs scored by Peter. 75 cm and its breadth is 3 m 25 cm. Find
th.
on is Rs. 12 500. He saved Rs. 250 out of his income to his savings.
Dw as a ratio.
11. 17. 11 + (iv) 100 20 ow as a fraction.
3:2 (iv) 7:10 s Rs. 100, find the cost of 7 such cakes of
- exists between two quantities given in tio.
ad given in different numbers are
btained by multiplying or dividing both e number. plified any more are said to be in the
es of different units is known as rate.
53

Page 66
23 - COLLEC
Deepika won the prize for be Four centuries were scored ir 14 students in my class play The majority of the students
"Head" turned up 3 times wh You would have heard statemen statements we arrive at certain conclus data has to be collected.
Let us obtain some information by life.
You would realize that data has (correct) information for various needs.
| Activity 23.1
Suggest a method by which data ca to school.
s Activity 23.2
Ask the students in your class, the : given below to collect this data.
When a student expresses his pref marked. This is called a tally mark.
Suppose that you have marked //. if another student prefers the same sport
Thus 5 is shown as H.
Using such tally marks decide the class.
54

CTING DATA
Est attendance during last month. a 10 innings.
'Elle' and 20 play Basket ball. sin a school come to school walking.
en a coin was tossed 5 times. nts like the above, earlier. From these ions. To arrive at conclusions the relevant
collecting data continuously in day to day
to be clearly recorded in order to obtain
in be collected to show how students come
sport they like most. Follow the procedure
erence to a certain sport the symbol '/' is »
// (four) preferences for a certain sport, , it is marked as HH .
most popular sport of the pupils of your
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Page 67
The table given below shows the respo school regarding the sport they like mos questions given below.
Sport
Tally marks
HH
Volley ball Soccer
Net ball Elle Cricket
////
HH HH III/ HH | HH |
Table 23 (1) According to the tally marks in tl
How many students like to play (3) What is the sport most students
What is the sport that an equal n (5) What is the total number of stud
Activity 23.3
Toss a coin 20 times, complete the tabl questions.
Tally marks
Side Head Tail
Table 23.2 1. How many times did the "head" tur 2. How many times did the "tail" turn Exercise 23.1 1., Find from the students of your
his / her birthday falls and com Day
Tally ma Monday Tuesday
Wednesday Thursday Friday Saturday Sunday
Table 23
For free distribution

23 - Collecting Data
nses of students of Grade 6 in a certain . Observe this table and answer the
The number of students
1.1
he table complete the column left blank. Volley ball? like? Write the number of students. umber of the students like ? ents in the class?
e given below and answer the following
Total
n up? up?
class on which day of the week does plete the table given below.
rks
Number of students

Page 68
Mathematics - Grade 6
Answer the following questions i
On what day of the w ii. On what day is the hi iii. How many student
Wednesday? iv. Are there any students v. What is the total num 1kg of lime fruits were weig contained each time are give
18 17 18 2 19 18 20 21
20 17 18 1 Fill in the table given below
Number of Limes in 1kg.
2.
17
< Z E: E:
18 19 20.
21
Tak Now answer the questions ! (i) How many kilogramı
number of lime fruits (ii)
What is the highesi
kilogramme? (iii) How many kilogramn
number of lime fruits
Additional Exercise
1. What is the number shown
The table given in the next ! of 5 students to the questi table.
56

using the information of the above table.
eek is the lowest number of students born? ghest number of students born? s are there whose birthday falls on a
= whose birthday is not included in this table?
ber of students included in this table? shed 20 times. The number of lime fruits that en below. 1 18 21 20 D19 17 19
20 18 - using the above data. Tally marks
Number of weighings
>le 23.4
given below.
nes of lime fruits were there with the least
: number of lime fruits contained in a
les of lime fruits were there with the highest
by the tally mark H H III ? vage shows the number of correct responses ons given to them. Fill in the blanks of the
For free distribution

Page 69
Name
Tally marks
J NJ INJIL
Amali Kamal Sarojini
Mohamed
IN IS IN
Sanjeewa
Table 2 3. The points scored by a Volley b
12, 14, 14, 16, 13, 12, 13, 13, 1 14, 10, 10, 14, 13, 13, 10, 13 Fill in the blank columns of the
Points scored
Tally m
10 11
12
13
14
16
Table 2 (i) What is the score obtained in m (ii) What is the lowest score? (iii) What is the score obtained in le
Summary
* It is easy to tabulate data usin
For free distribution

23 - Collecting Data
Number of correct responses
23
15
20
23.5
all team in 25 matches are given below. 2, 14, 13, 10, 12, 12, 12, 13, 13,
cable given below.
arks
No. of matches
23.6
ost number of matches?
ast number of matches?
ng tally marks.
57

Page 70
24 - REPRESEN
We have learnt in previous lesson and preparation of tables.
Let us now study representing data
*
We can use a picture graph ar the table given below, which
were absent from school dur
Day
No. of students
Monday Tuesday
Wednesday Thursday Friday
Tabl
Look how this data is illustrated
Day
Monday
Tuesday
Wednesday
|
Thursday
K
R
Friday
Tabl
* Represents one student
58

TATION OF DATA
s about collecting of data, using tally marks
a.
mong many others, for this purpose. Look at shows the number of students in a class who ring a certain week.
who were absent
N00
e 24.1
in the picture graph given below.
Number of students
R
R
R
8
e 24.2
For free distribution

Page 71
| Activity 24.1
1. The table given below shows th
in a cricket match.
Name
Number of rı
Mangala
35
Vinodhan
25
Anil
Mohamed
60
Kamal
40
Table 2 Illustrate the above data by a picture runs scored.
40 balls should be drawn to show the denotes one run. This is difficult. Therefo To show 5 runs half a ball ( has to be dr
Name
Mangala Vinodhan
Anil
Mohamed
Kamal
Table :
O Represents 10 runs
Exercise 24.1
1. The table given below shows
factory for the first 5 months i Draw a suitable picture graph t
For free distribution

24 - Representation of Data
e number of runs scored by 5 players
ins scored
24.3
graph. Use the symbol o (ball) for the
40 runs scored by Kamal if one • (ball) ire let us denote 10 runs by one • (ball)
awn.
uns scored
24.4
the number of dolls manufactured in a of a certain year.
illustrate this information.
59

Page 72
Mathematics - Grade 6
Month
Number of
January February
March April May
T O n +
Table 24.5
2.
The table given below show produced by 5 farmers durir
Name
Weight of
Herath Banda
Swaminathan
Wijerathna
Joseph Daniel
Table 24.6 Draw a picture graph, usin potatoes.
W NN
2
The following table shows the
Name
Incor
Anil
Kamal
Wimal Sunil
Nimal
Table 24.7 Draw a picture graph to re symbol for Rs.1000.
60

dolls
500 000 500
750
500
s the number of kilogrammes of potatoes ng a certain season.
potatoes (kg)
500.
250 750 125 000
g the symbol to represent 250 kg of
income of 5 persons during a certain month. ne (Rs)
6750 8000
4500
9250
5500
present this information using a suitable
For free distribution
Koincideihe

Page 73
Additional Exercises
1.
The table given below shows t who scored in the given range during a certain year.
Marks - Range Less than 50 Above 50 and less than 100 Above 100 and less than 150
Above 150 less than 200
Table Using the symbol to represe represent the above informatio The table given below shows t 6 of a certain school about the volley ball or cricket.
Sport
NI
Football Elle Volley ball Cricket
Table
(i) Find a suitable picture to (ii) Draw a picture graph to
Summary
* Data could be illustrated usi
For free distribution

24 - Representation of Data
he number of students in a certain school s at the Grade 5 scholarship examination
Number of students
20
36
18
06
24.8
ent 4 students draw a picture graph to
he data collected from students of Grade sport they prefered, out of football, elle,
umber of students
12
16.
24.9
o represent 4 students.
represent the above information.
ng picture graphs.

Page 74
25 - INTERPRET
In previous chapters we have learn Let us now interpret the presented data.
S
Activity 25.1
The table below shows the number who came late to school on a Monday.
Grade
Grade 6 Grade 7 Grade 8 Grade 9 Grade 10
Tally marks HH HH || HH III HH HH III HH
Tabli
- m + n
Fill in the blank column in th Which Grade shows the high Which Grade shows the least What is the total number of 1 How many times is the numbe with the number of late com
4. Wh.
Activity 25-2
Draw a picture graph to illustrate t SActivity 25-3
The picture graph given below illu brick maker during 5 weeks.
5th week 4th week 3rd week 2nd week
1st week
Represents 2 000 brick 1. How many bricks were prod
62

TATION OF DATA
ed how to collect data and represent them.
of students in a school from Grade 6 to 10
Number of students
e 25.1 ne above table est number of late comers to school? * number of late comers to school?
ate comers? ir of late comers in Grade 6, when compared ers in Grade 10?
he information in the above table.
strates the number of bricks produced by a
iced during the third week?
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Page 75
2. How many more bricks were
compared to the output during
In which week was the least nu 4. What is the total production of
Exercise 25.1
The table given below shows the nu dairy farm during the first 5 months of a cei
Month
Number of pa
January
February
March April May
Table a Answer the following question 1. In which month was the le 2.
Find the difference bety in March and the numbe
Find the total number of
five months. 4. Taking to present 10
data in a picture graph.
With reference to the nur two months where the
For free distribution

25 - Interpretation of Data
produced during the fifth week when g the second week? umber of bricks produced?
bricks for the whole week?
mber of packets of milk produced by a rtain year. ckets of milk produced
60 000
65 000
57 500 55 000
62 500
25.2 s on the information given below. east number of packets of milk produced? veen the number of packets produced r of packets produced in May.
packets of milk produced during these
000 packets of milk, illustrate the above
mber of packets of milk produced, name ere is a difference of 5000 packets.

Page 76
Mathematics - Grade 6
Exercise 25.2
The picture graph given below ill for Mathematics in a monthly test.
Name of student
Anil
Sarojini
• • • •
Nihal
Rihana
Malani
O Represents 20 marks Now answer the questions given b 1.
What is the difference beti Rihana?
What is the highest mark? W How many marks does Niha obtained by Anil? If a student who gets 75 mark according to the above grapl
i m =
4.
Additional Exercise
1. The picture graph given belo
factory in 5 years.
Year
Production
2005
2004
2003
OOO OOO OOO OOO OOO.
2002
2001
represents 5 000 tyres

ustrates the marks obtained by 5 students
Marks obtained
elow. veen the marks obtained by Sarojini and
Jho obtained the highest marks? al need to be equal to the number of marks
Es, gets an “A” pass. Who gets an “A” pass
w shows the production of tyres in a tyre
DOC C
For free distribution
HOS FC

Page 77
(1) Which year records the highest (ii) What is the total production of (iii) In which year was the least pro (iv) Find the ratio of production of
year 2005.
2. The picture graph given below
an Educational Zone during ac
Grade
No. of b
10
Represents 10 000 t
(i) Which Grade is given the highe (ii) What is the difference between t
9 and the number of books disti (iii) What is the total number of bo
10?
Summary
Information can be represented in
For free distribution

25 - Interpretation of Data
production ? tyres during the 5 years?
duction?
the year 2001 to the production of the
shows the distribution of text books by ertain year. ooks distributed
III IIII IIIII IT II IIIT
books
est number of textbooks ? che number of books distributed to Grade ributed to Grade 7? ooks distributed from Grade 6 to Grade
picture graphs.
65

Page 78
30AN
26 - IN
|| ||
T
Let us review square numbers 1,4
1 = 1 x 1
= 2 x 2
9 = 3 x 3 See how these numbers are obtain same number. These numbers are squar numbers.
|4 = 2 x 2 = 22 25 = 5 x 5 = 52
9 = 3;
9 = 3 x 3 = 32
Writing as a power
9 is a number that can be shown t
Multiply 9 by 3. Then 9 x 3 = 27 = 3 x 3 x 3 = 33 The index of this number is 3, base Example: 81 = 3 x 3 x 3 x 3 = 34
When 3 is multiplied four times by
Then the index is 4. Here 81 is expressed as 3 to the p
Activity 26.1 (1) Write the numbers given bel
(i) 49 (ii) 64 (ii
66

NDICES
4,9,16...............
ned by multiplying numbers 1, 2, 3, ... by the es of the numbers or the second power of the
x3 = 324— Index
- Index
Power
base
py 3° in index form.
e is 3. The number is three to the power 3.
y itself, the result is 81.
Power 4. Here the index is 4, the base is 3.
low as squares. ci) 81 (iv). 100
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Page 79
Consider 16 It can be written as 16 = 4 x 4 = 42 Also 16 = 2 x 2 x 2 x 2 = 24
Now when 16 = 42 the base is 4. Fou the base is 2. Two is a prime number. 16 can be written as a product of prin Example :
Write 48 as the product of prime num 48 = 2 x 2 x 2 x 2 x 3 The above in terms of indices = 31 x The above result can be obtained as f 2|48 2 24
2|12. 26
3 3
: 48 = 2 x2 x 2 x 2 x 3 That is 48 = 24 x 3
When a number is expressed in index by expanding it. Example 1 : 25 = 2 x 2 x 2 x 2 x Example 2 : 23 x 32 = 2 x 2 x 2 x
Example 3 : 34 = 3 x 3 x 3 x 3
Example 4 : 22 x 33 = 2 x 2 x 3 Exercise 26.1
(1) Write the following in words. (i) 52 (i) 42 (iii) 33 (2) Fill in the cages.
(1) 4 = 20 (ii) 8 = 2
For free distribution

26 - Indices
r is not a prime number. When 16 = 24
ne numbers as 16 = 24 = 2 x 2 x 2 x 2
bers and express it in index form.
bllows.
form, the value can be obtained easily
2 = 32
3 x 3 = 72
= 81 x 3 x 3 = 108
(iv) 84 (V) 74
- (ii) 81 = 30
67

Page 80
Mathematics - Grade 6
(iv) 49 = 70 (V) 100 = 10(3) Fill in the cages. (i) 4 = 20 (ii) - 9 (4) Write the values in the blan
(1) = 23 (ii) ] |(5) Express 64 (i) as a power o
(ii) as a p
(iii) as af (6). Express 16 in index form w (7) Express the following num
write in index form.
(1) 100 (ii) 24 (ii Additional Exercises
1.
Show 32 as a power of 2. (i) What is its base?
(ii) What is its index? 2.
Write the following number them in index form. (i) 128 (ii) 144 Fill in the blanks using the (i) 32 ..... 23 (ii) 52 .. Evaluate. (i) 44 (ii) 53 (iv) 32 x 52 . (V) 102
3.
68

= 30 (iii) 25 = 50
k cages. = 34 (iii) = 43
f 8 ower of 4 power of 2
with two different bases.
bers as the product of prime numbers and
G) 72 (iv) 54
Es as products of prime numbers and express
(iii) 243 (iv) 150 symbol > or <. .... 25 (iii) 43 ...... 34 (iv) 71 ..... 17
(iii) 23 x 3
x 22
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Page 81
27 - AF
27.1 Introduction
Figure 27 Shown above are 4 windows with a sqı A,B,C and D. The number of squares in wii squares in each of the other three windows. and D is the same. The number of squares in squares in each of the other three.
What is the largest window? What is the smallest window?
What are the windows of equal s This can be decided by the number of Imagine you are painting the walls of t
You would be aware that the quantity length and breadth of the walls increase. Ass surfaces of the walls. The quantity of paint surface of the wall.
Extent of a surface is known
The extent of a wall is known its area. window is greater than the area of a small w
For free distribution
e da

REA
В
. 1
uare mesh in each. They are named as ndow A is greater than the number of The number of squares in windows B a window C is less than the number of
ize?
squares.
his house.
of paint required increases when the sume that paint is applied on the outer E required is decided by the extent of
as its Area You would notice that area of a large window.
69

Page 82
Mathematics - Grade 6
S
Activity 27.1
Take a stamp of square shape. such stamps. If you do not have sta square pieces of paper equal in size to Get an ordinary envelope and a leaf cise book. Paste the stamps on the f the envelope as shown in the diag the face of the envelope is full w count and note down the numbe Paste the stamps or square pieces of page of the exercise book, as done with Count the number of stamps or squar
more stamps? On the envelope or the larger? The exercise book page or the
27.2 Finding the area of a pla
fig (i)
Area of the shaded p Area of the shaded p
Exercise 27.1
(1)
Figure 1 Figure 2 Count the number of (shade thereby find the area of each

Collect more mps, prepare o the stamp. from an exerace of one of gram. When with stamps, er of stamps. paper on the
Figure 27.2 the envelope. e pieces of paper in each. Where do you get e page of the exercise book ? Which area is
envelope?
ane figure by counting squares.
fig (ii)
part of fig (i) = 17 squares part of fig (ii) = 20 squares
Figure 3 1) squares in each of the above figures and
For free distribution

Page 83
(2) Count the number of shaded squ
(3) Draw three figures on a sheet o
counting the number of squares.
Activity 27.2
figure A
Find the area of the two figures abovel Area of figure A = ..
......... squ Area of figure B = ....
... squi Is the number of squares equal in both Is the space occupied by A equal to th Is the area of A greater than the area of
Here you will see that you cannot comp the squares are not equal in size. You will h you want to compare.
This shows the need of a standard unit te and breadh lem is used as a standard unit to
This measure is known as square cen thus the square centimetre.
For free distribution

27 - Area
ares and thereby find the area shaded. ***
f square ruled paper. Find the area by
figure B
by counting squares. ares. ares.
cases? ne space occupied by B? F B? pare the area of figure A and figure B as a
ave to use squares of the same size, if
o measure area. A square of length lcm
measure area. timetre. The unit of measuring area iš

Page 84
Mathematics - Grade 6
A standard unit is used to measu
1cm
2cm
1cm
1em 1em 201
1cm
2cr
(i)
(ii)
Fig (i) is a square of side lcm. ... The area of fig (i) is 1 squar Area of fig (ii) is 2 cm?. Area of fig (ii) is 3 cm?. Area of fig (iv) is 4 cm.
Area of a square
4 cm
1 cm
1 cm
4 cm
Consider a square with side 4 cm. 1 centimetre squares are marked. The area of the square = Total number
72

re area.
1cm
2cm
2cm
(iii)
(iv)
re centimetre or 1 cm2.
6 cm
cm
1 cm
6 cm -
of centimetre squares, that is 16 cm2.
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Page 85
Consider a square with side 6 cm long 1 cm2 squares are marked. The area of the square = Total number The length and breadth of a square are The area of the first square can be wri Similarly 36 cm? = 6 x 6 cm? The area of any square can be found as Multiply the magnitude of the length a
Wri
Example (i) Find the area of a square of side The area of the square = 10 >
= 100
Activity 27.3 Find the area of each square when len (i) 2 cm (ii) 9 cm
Activity 27.4 Find the length of one side of each sq If the area is (i) 25 cm?
(ii) 36 cm? (iii) 64 cm?
27.4 Area of a Rectangle
Activity 27.5 Draw a rectangle 4 cm long and 3 cm
Mark 1 cm? squares. Find the area of t
CA
AI
3 cm
=t
4 cm
For free distribution
Eudiseih 991 10

27 - Area
- of centimetre squares = 36 cm? - the same. tten as 16 cm? = 4x4 cm? = 42 cm?
s follows.
nd the magnitude of the breadth.
10 cm. < 10 cm?
cm2
gth of a side is, (iii) 11 cm
iare.
broad. he rectangle.
rea of the rectangle total number of centimetre squares 12 cm?

Page 86
Mathematics - Grade 6
The rectangle has 3 rows. Let us Line A has 4 squares. Area of rov Line B has 4 squares. Area of rov Likewise, area of row C There are 3 rows with area 4 cm : The area of the rectangle
Example: Let us find the area o The area of the rectangle
Exercise 27.2
(1) Find the area of each figure
10 cm

name them as A,B and C.
VA
= 4 cm2 v B
= 4 cm2
= 4 cm2 - in each.
= Area of one row x 3 = 4 cm x 3 = 4 x 3 cm2 = 12 cm2 fa rectangle 5 cm long and 2 cm broad. = 5x 2 cm? = 10 cm?
-given below.
5 cm
2 cm
8 cm (ii)
4 cm
4 cm
(iii)
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Page 87
(2) Copy the table given below and | Length of rectangle Breadth o
8 cm
4 cm
(i)
9 cm
(ii)
(iii)
5 cm
3 cm 20 cm
(iv)
(v)
..cm
40 cm
3. The length of a rectangle is 40 cn
a square is 20 cm. What can you The area of a square is 49 cm?. F
27.5 Use of Area
Arranging household goods in suitable some order makes the place beautiful. We us
s Activity 27.6
Look how the teacher's table, teacher's cupboard are arranged in the classroom. Th You may notice that the arrangement seen as
Exercise 27.3
A certain floor has the shape of breadth is 5 m. How many squar the length of a side of a square ti A flower bed is 2 m long and 1 a space of 20 cm?. Find the ma planted in this flower bed.
2.
For free distribution

27 - Area
fill in the blanks. f rectangle
Area of rectangle
.....cm2
...cm
72 cm2
..........cm2
...cm
600 cm? 800 cm?
N
1 and its breadth is 10 cm. The length of say about the areas of the two figures? ind its perimeter.
- places, planting trees in the garden in e area in situations as above.
chair, blackboard, desks, chairs and the ey may be arranged in other ways too. s the best.
F a rectangle. Its length is 6 m and the ce tiles are needed to cover the floor, if ile is 20 cm?
m wide. If one plant has to be allowed iximum number of plants that can be
75

Page 88
Mathematics - Grade 6
Additional Exercise
1. Copy the table given belov
Length of a side of th
(i)
6 cm (ii)
9 cm
(iii)
(iv)
(v)
15 cm
The length of a rectangular
Find its area. 3.
How many rectangles of len a rectangular board of leng (i) Find the area of a wir
(ii) Find the length of a s 5. Copy the table given below
Area of rectangle
30 cm?
e 8 =
120 cm2
600 cm2
(iv)
(V)
Summary
Space occupied by a surfa Square centimetre is a un cm2.
*
Area of a rectangle = p breadth.
78

v and fill in the blanks.
Le square Area of the square
144 cm? 25 cm2
wooden tray is 60 cm. It's breadth is 40 cm.
ngth 15 cm and breadth 10 cm can be cut from
th 60 cm and breadth 40 cm? e mesh 80 cm long and 50 cm wide. quare mesh equal in area to above mesh.
and fill in the blanks.
length
breadth
6 cm
10 cm
30 cm 15 cm 25 cm
12 cm
. 17 cm
ace is known as its area.
it used to measure area. This is written as
roduct of the magnitudes of length and
For free distribution
Baitudizteib 39 S

Page 89
28 - POSS
28.1 Possibility of an event
Consider throwing a dice, numbers from are aware that any number out of the numbe Suppose you need to get a four. When you i that number. This means we cannot definitel number when a dice is thrown.
SActivity 28.1
A class was divided into 10 groups a selected as the leader. We will name them A asked to throw a six sided dice 6 times and th the 6 throws.
Number A B C D E Number obtained
//
Table 28
Study the above table and answer the i (i) Was there any group who got nu (ii) How many groups have got the s (iii) How many groups did not get ni (iv)
How many groups are there wh
throws? (V) Are there any groups who got th (vi) How many groups are there who
For free distribution

SIBILITY
m 1 to 6 are written on the six faces. You rs 1, 2, 3, 4, 5, 6 can turn up as results. Chrow the dice you may or may not get y say whether we could get the required
and one student from each group was ,B,C,D,E,F,G,H,J,K. The groups were ne table given below shows the result of
F G
| H | J
| K
3.1
following questions.
mber 6 in all 6 throws? same number in all 6 throws? umber 2 in any of the 6 throws?
o did not get the same number in all 6
e same numbers three times or more? - got the same number twice?

Page 90
Mathematics - Grade 6
You would see that the numbers each other.
It cannot be definitely stated, wh thrown once. There is a possibility of
Compare the answers obtained fo answers same or not?
When comparing with other gro the same. We cannot definitely say the
up.
Events can be divided into 3 type
(i) Events that definitely wi (ii) Events that definitely wil
(iii) Events that may or may n 1. Sun rising in the East - Is a 2. A tortoise having wings - A 3. The principal coming to the
A possible event.
Activity -2
Separate the following incidents a place and may or may not takes place.
(i) A square number being a p (ii) A whole number being eitt (iii) An even number being a so (iv) "Head" turning up when a (V) "Head" or "tail" turning up (vi) Getting an odd number wh (vii) "Tail" turning up when a c (viii) Three sides of a triangle be (ix) Five students in the class o
test in Mathematics. (x)
The student who scored hi
first in the class. 28.2 Giving a value to the
10 marks are given to events th
78

s obtained by each group are different from
nat number will be obtained when the dice is obtaining any number out of the 6 numbers. or the above questions by the groups. Are the
ups, you would see that the answers are not e number of times a certain number will turn
es as;
Il occur. I not occur.
Lot occur.
definite event.
n event that will never occur. e class during the Mathematics period -
as definitely taking place, definitely not taking
prime number. ner an even number or an odd number. quare number too. coin is tossed.
when a coin is tossed. en two even numbers are added. oin is tossed. eing equal.
btaining over 60 marks each for the monthly
ghest marks for Mathematics becoming the
e possibility of an event nat definitely take place.
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Page 91
O mark is given to events that definit Events that take place can be award on the degree of possibility. Possibility will take a higher value if th Possibility takes a lower value if the ch Let us consider events that will definit
Occurance
1. Earth rotating on it's own axis. 2. Sun setting from the West. | 3. A bird having a beak.
4. A bird having four legs. 5. Getting a "head" or "tail" when a co 6. Getting a "head" when a coin with
both sides is tossed.
Table 28
Let us give a value to an event that ma 1.
If a coin is tossed two outcomes a Therefore the possibility of ‘hea half. Then the value that can be g is tossed is 5. (That is 10 = 5) Consider 10 cards of equal size n (i) Let us give a value to the p
the cards are shuffled and o In these cards there are five numbers 1, 3, 5, 7, 9. There
marks can be given for the i (ii)
Let us find the possibility
When considering the card 6, 9. That is three cards. The possibility of picking
between 0 and 5. (iii) The prime numbers betwee
The numbers that are not pi 6 cards out of all 10 cards a
For free distribution

28 - Possibility
tely do not happen. ed 1, 2, 3, 4, 5, 6, 7, 8 or 9 depending
e chances are more.
ances are less. ely happen or never happen.
Value
10 10
10
pin is tossed.
"tail" on
y take place. are possible. They are ‘tail’ or ‘head'. d’ turning up when a coin is tossed is iven to "head" turning up when a coin
Lumbered from 1 to 10.
ossibility of an even number when all one is picked.
even numbers 2, 4, 6, 8, 10 and 5 odd fore out of 10 cards 5 cards are even. 5 possibility of picking an even number. of taking a card with a multiple of 3. s the possible, multiple of three are 3,
a multiple of 3 from the ten cards is
n 1 and 10 are 2, 3, 5, 7. rime from 1 to 10 are 1, 4, 6, 8, 9, 10. ire not prime numbers.
79.

Page 92
Mathematics - Grade 6
When all the cards possibility of gettin be given a value beti
Activity 28.3 1. Get 10 balls of equal size a
i. How many balls are ii. How many balls are iii. How many balls are
five?
How many balls are v. How many balls are
How many balls are If the balls are put into a c give a suitable value for the
iy
vi. Hoy m
Event
1 Taking a ball with an odd i 2 Taking a ball with an even
Taking a ball with an a mu 4 Taking a ball with a prime 5 Taking a ball with a triangu 6 Taking a ball with a square 7 Taking a ball with number 8 Taking a ball with any numbe
Exercise 28.1
1. Write 5 events that will ha 2. Write 5 events that will ne 3. Write 5 events that may or 4. (a) If a dice numbered from 1
(i) a multiple of two. (ii) an odd or an even nu (iii) a prime number. (iv), a triangular number. (v) a multiple of 5.
ad

are shuffled and one card is picked, the g a number which is not a prime number can veen 5 and 10.
ind number them for 1 to 10. there with odd numbers? there with even numbers? there with numbers which are multiples of
there with prime numbers? there with triangular numbers? there with square numbers? ontainer, mixed well and a ball is taken out, e possibility and fill in the table given below.
Marks
number marked on it.
number marked on it. ultiple of 5 marked on it.
number marked on it. lar number marked on it. e number marked on it.
12 marked on it. r from 1 to 10 marked on it. able 28.3
ppen definitely. ver happpen.
may not happen. to 6 is tossed find the possibility of getting,
amber.
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(b) Asign a value for the possibility
2.
Additional Exercises
1. Write 2 events for each of the fo
(i) Events that will happen o (ii) Events that will never ha
(iii) Events that may or may r There are 5 blue bulbs, 3 red bult and shape in a box. Give a suital following occurances when a ball (i) The ball being red (ii) The ball being blue (iii) The ball being of any three (iv) The ball being black (V) The ball being red or yellow (vi) The ball being red or blue
Give a mark from the scale 0 - 10 (i) Getting an even number fro (ii) Getting multiples of 2 in the (iii) Obtaining "head" when a c (iv) Getting a crop of sweet pot (V) A piece of iron floating in
3.
Summary
Events can be separated into definitely occur, events that w occur or may not occur.
When evaluating an event on a an event that is defenite gets 10 an event that is impossible gets an event that occur or may not
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28 - Possibility
of getting number 7.
llowing. lefinitely. ppen. not happen. Os and, 2 yellow bulbs of the same size ble value from the scale 0 - 10 for the lis selected at random from the box.
colurs blue, red or yellow
- for the events given below.
m among the first ten prime numbers. e set of odd numbers. Din is tossed. atoes when potatoes are cultivated.
water.
three groups as events that are rill never happen, events that may
0 - 10 scale, | marks.
O marks. occur gets a mark between 1 to 9.
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Grade 6
Content
Learning
1.0 NUMBERS
1.1.
Natural Numbers, Integers 1.1.1. Large Numbers 1.1.2. Place Value 1.1.3.
Number Line
1.1.4.
Comparison
1.1.5.
Estimation 1.1.6. Approximation 1.1.7. Odd and Even Numbers
Reads ar Identifies Recogniz on a num Uses the Gives ar Gives an Approxin Classifie products Identifies Identifies Identifie numbers Adds an
Multiplies numbers Finds fac Recogniz
1.1.8.
Prime Numbers 1.1.9. Composite Numbers 1.1.10. Number Patterns
1.1.11. Addition and Subtraction 1.1.12. Multiplication and Division
1.1.13. Factors and Multiples 1.1.14. Divisibility 1.2
Fractions 1.2.1.
Unit Fractions and
proper Fractions 1.2.2.
Equivalent Fractions 1.2.3.
Comparison
Identifies Finds eq Compare related d Adds and nators (a
1.2.4.
Addition and Subtraction
1.3
Decimals 1.3.1. Concept
Recogni: represen Compare Adds an
1.3.2. Comparison 1.3.3.
Addition and Subtraction 1.4.
Indices 1.4.1. Notation 1.4.2.
Powers
Recogni: Expands (number prime fa
Understa
Writes a Applies i
2.1
1.5 :
Ratios 1.5.1. Concept 1.5.2. Simple form
1.5.3 Rates 2.0 MEASUREMENT
Length 2.1.1.
Concept 2.1.2.
Units 2.1.3.
Conversion 2.1.4. Estimation 2.1.5.
Measurement 2.1.6.
Perimeter 2.2
Area 2.2.1.
concept
Underste Uses mn Convert Estimate Measure Finds the
Underste of the su Uses cm Finds the
2.2.2. Units 2.2.3.
Rectilinear Plane Figures 2.3.
Mass 2.3.1.
Units 2.3.2.
Conversion 2.3.3.
Addition and subtraction
Uses g, Converts Add and
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- Mathematics yllabus
|Outcomes
id writes natural numbers up to a billion in words and in figures
what each digit in a number represents tes negative numbers and represents natural numbers and integers iber line
vocabulary and symbols (>.<. =) to compare and order integers number that lies between two numbers
estimate of a countable number of items rates a number less than 100 to the nearest 10
odd and even numbers. Identifies prosperous of the sums and of odd and even numbers
prime numbers composite numbers s number patterns including triangular numbers and square
1 subtracts natural numbers ; and divides natural numbers by 10, 100, 1000 and by two digit
stors and multiples of numbers using a 10 x 10 number grid Les divisibility by 2, 5 and 10
| unit fractions and proper fractions
uivalent fractions !s unit fractions, fractions with equal denominators. Fractions with enominators
subtracts unit fractions with equal denominators. With related domianswer limited to proper fractions)
zes decimal numbers (knows what each digit in a decimal number ats) es and orders decimal numbers
d subtracts decimal numbers
zes and uses index notation
a power. Expresses a number as a power and a power as a number s less than 100). Writes a number as a product of powers using ctors
ands the concept of a ratio between two quantities
ratio in simple form rates in transactions
ands distance, height, depth and width as lengths n, cm, m, km appropriately to measure length mm ,m cm m, m km s distance, height, depth and width s lengths e perimeter of given rectilinear plane figures
ands area as the measure (extent) of a bounded region on a plane or
rface of a solid 2 to measure area e areas of squares and rectangles
kg appropriately to measure mass sg kg
subtracts measurements with both kg and g
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Content
| Learning Outcom
2.4.
Liquid Measures 2.4.1.
Units 2.4.2.
Conversion 2.4.3.
Addition and Subtraction 2.5
Time 2.5.1. Units
Uses ml, 1 to meas Converts ml | Adds and subtracts
2.5.2. Twenty Four Hour Clock
Understands time a Uses seconds, min tionships
Reads time on a 2. clock time and vice Uses the date in sti
2.5.3.
Date in Standard Form 2.6
Directions 2.6.1. Eight Directions
2.6.2. Horizontal. Vertical 3.0 GEOMETRY
3.1 Angles 3.1.1.
Types
Recognizes and us Recognizes the hor
Classifies angles as angles or reflex ang
3.2. 3.2.1.
Solids Cube, Cuboids, Regular Tetrahedrons
Creates cubes, cub as the number of ve Cuboids and regula
3.3. 3.3.1. 3.3.2. 3.4. 3.4.1.
Circles Shape Patterns Rectilinear Plane figures Shapes and their characteristic properties
Identifies circular sh Constructs circular
Recognizes and dra trapeziums in a grid
4.0 ALGEBRA
4.1.
Symbols 4.1.1. Unknowns 4.1.2. Variables 4.2.
Algebraic Expressions 4.2.1. Construction
Represents unknow Identifies variables
Constructs algebrai using addition and variable into a nume
5.0 STATISTICS 5.1.
Data handling 5.1.1. Collection
5.1.2. Representation
Interpretation
Collects data of not tabulates it using tal
Represents data by Interprets data repre
discussion
5.1.3
6.0 SETS AND PROBABILITY
6.1
Sets 6.1.1. Sorting objects 6.1.2 Naming groups 6.2
Chance 6.2.1. Likelihood of occurrence
Sorts a group of obj Names groups of ot
Identifies the likeliho
Working Mathematically
Revises and develops the vocabulary related to numbers Develops and refines written methods for addition and sul ods, how to layout composition Understands the operation of multiplication and its relatio Knows to apply the associative and commutative laws Recalls multiplication facts and derives the correspondin Knows and derives rapidly doubles and halves Checks answers by doing the inverse operation Uses tests of divisibility to check answers Develops and uses mental strategies
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ure capacity
measurements with both land ml
ind duration utes, hours and days appropriately and knows their rela
--hour clock and converts 12 hour clock time to 24 hour
versa andard form
es the eight directions izontal and the vertical
= right angles or acute angles or obtuse angles or straight
les by comparing with right angles
oids and regular tetrahedrons identifies properties such ertices. Number of edges and number of faces of cubes.
r tetrahedrons
napes in physical objects patterns using physical objects such as bangles, coins etc.
aws triangles. Squares. Rectangles. Parallelograms and
ins by algebraic symbols and represents them by algebraic symbols
c expressions with one variable (coefficient equal to 1) subtraction Converts and algebraic expression with one erical value by substituting natural numbers
more than five kinds and less than hundred values and ly marks tables and pictograms sented by tables and pictograms Interprets results through
ects by similar attributes jects using common attributes »d of an event occurring as certain. Impossible or probable
measures, geometry, algebra, statistics and probability. straction - correct layout of sums, standard written meth
nship to addition and division
y division facts quickly
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ගණිතය (ඉ) 6 ශ්‍රේණිය - II කොටස

2012/E/06/096-P-II/74,500