Page 39
03 - Mathei
When one number is divided result obtained is called the is called the remainder".
In the example 1, the quotient is 114 an In the example 2, the quotient is 57 and
Activity 3.9 1. Find the quotient and the remaind
(i) 4557(ii) 584 = 8 2. If 155 marbles are distributed amo
each get? What is the remainder Now let us learn how to divide by multi Dividing by 10.
When dividing a number with 0 at the ur side of the divisor can be removed.
Examples: (1) 320 + 10 = 32
(ii) 500 = 10 = 50 (iii) 4050 - 10 = 405
(iv) 5600 + 10 = 560 Dividing a number with 00 at the ten 300 - 100 = 3; here, the 00 at the right removed. Examples: (i) 600 - 100 = 6
(ii) 6800 - 100 = 68
(iii) 7 200 + 100 = 72 Dividing a multiple of 10 by 10, may be the dividend. Dividing a multiple of 100 by 100 may digits (00) of the dividend. Activity 3.10 1. Rewrite and fill in the blank cages.
(i) 310 + 10 = 0 (iii) 500 - 100 = 0 (V) 8000 + 100 = 0
For free distribution
matical operations on whole numbers
by another number, the quotient". What is left
1 the remainder is 0. the remainder is 2.
er.
(iii) 874 - 5
(iv) 682 - 6 ng 6 children, how many marbles will
ples of 10 like 10, 50, 300, and 1000.
nits place by 10, the 0 at the right hand
s place and units place by 100:
hand side of the dividend can be
done by removing the last digit, (0) of
be done by removing the last two
(ii) 6700 + 10 = (iv) 8200 + 100 = 0
27
Page 40
Mathematics - Grade 6
2. Write the suitable number i
(1) 70+D=7. (ii) | Consider the divisions given belov 1. 416 + 13
32
13 416
39
26
The quotient 32, remainder o Exercise 3.4
1. Find the quotient and the remai
(i) 378 - 9 (ii) 518 - 8 (iii) 4580 - 12 (iv) 520 - 17 (v) 215 - 20 (vi) 589 - 16 (vii) 4682 - 23 (viii) 3148 - 15
2.
Wimala's class was chosen Wimala who was the class i The total number of studei distributed among them, 1
Will there be any remaind Rewrite filling the blank ca (i) 805 = 13 (ii)
(iv) (806) + 4 = 12 (v) Additional exercises 1. Add
(i) 35 648
(ii) + 19 432
+ || ||
28
the blank cages. 1+ 10 = 36
(iii) + 100 = 48
I.
2. 512 + 17.
30 |17|512
51
02
The quotient 30, remainder 2
nder if any.
n as the cleanliest classroom in the school.
monitor has received a parcel of 718 toffees. ats in the class is 25. If toffees are equally now many toffees will each of them get? er? ges with +, -, * or + signs. 13 D3 = 10 (iii) 32 O4 = 8 24 O3 + 4 = 12 (vi) 5 + (802) = 9
260 492 (iii) 1 250 632 359 208
+ 3 425 248
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Page 41
03 - Mathe
2.
Subtract. (i) 687 892
- 352 471
(ii) 3 245 (
- 1 352 -
3.
Multiply.
(i) 675 x 10 (ii) 2 0 4. Multiply.
(i) 378 x 27
(ii) 10 5. Find the quotient and the remaine
(i) 372 - 8 (ii) 6 9 Rewrite filling the blank cages. (1) 1 802 (ii) 060
+ 3 D5 8
| + 2 3 4 O 9 30
1 202 7. A train can accomodate 725 p.
passengers that can be accomoda 8.
A sum of Rs. 25 is collected from amount of money collected from The maximum number of students a school is 40. How many classes s
Grade 6 students? 10. The population in two towns are
(i) What is the total population
(ii) What is the difference betw Summary
In addition and subtraction of should be considered.
Multiplication is repeated addi Any number multiplied by 1 gi Any number multiplied by 0 gi Division is repeated subtraction The answer obtained when a nu is known as the quotient. The remainder.
9.
* * * * * *
For free distribution
natical operations on whole numbers
38 (iii) 4 620 032
– 2 398 754
19
48 x 100 (iii) 1972 x 1 000
48 x 54 (iii) 35 624 x 68 ler in each division. 54 - 12 (iii) 2 695 - 25
15 (iii) 5 0 0 8
+ 040 D 4 2 5
assengers. Find the total number of
ted in 12 such trains. each student for the sportsmeet. Find the 378 students for this sportsmeet? that can be admitted to a Grade 6 class in hould there be in that school to admit 280
12 765 and 10 986. i in the two towns? een the population of the two towns? .
numbers, the place value of number
tion. ves the same number. ves 0.
mber is divided by another number number that left is known as the
29
Page 42
“Time is gold" “Do not waste time?” “You cannot take back tim “Time taken for the journe “It will take some time to "Now its time for the mus “The time school closes is Observe that the word tim Hence let us study about ti What is the instrument use
Activity 4.1 1. What do you know al
in the past? 2. What are the instrum Now do the following activ
- i m t + n
Activity 4.2 Answer the following ques 1. How many hours do
What is the duration 3. What is the time tak
What is the time tak
What is the time allo 5. What was the time :
100 metres at the O
Activity 4.3 1. Identify the hour hand & 2. Have you noted that cei 3. (1) What is the time takı
(ii) What is the distance
30
4 - TIME
e?”
y is too long” recover from the illness?” cal show” 1.30 p.m.” e is highlighted in all the statements given above.
me. d to measure time today?
bout the instruments that were used to measure time
Lents used to measure time in the modern world? vities.
-tions.
you stay in school during a day? of time which your school is held? en by the Earth to rotate round its own axis? en by the Earth to revolute round the sun? -cated for each period in your school ? taken by the Sri Lankan athlete Susanthika to run lympic games?
nd the minute hand of a clock. tain clocks have a second hand also? en by the minute hand of a clock to go round once? the hour hand moves by then?
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Page 43
What is the time taken by
once? (ii) What is the distance the m 60 seconds = 1 minute 60 minutes = 1 hour How many hours are there in a day? A day begins after 12 midnight, the da A duration of a day is 24 hours.
60 seconds 60 Minutes 24 Hours 7 Days 4 Weeks 12 Months 365 Days 366 Days
Indicating time
You would have seen notices such as th “ School starts at 7.30 a.m.” “School closes at 1.30 p.m.” This shows that the school starts and cl This clarifies that time denotes a cert denotes a time duration.
R
Activity 4.4 1. Draw clock faces and indicate the
in the class leave home to come t Draw clock faces and indicate the school.
2.
For free distribution
04 - Time he second hand of a clock to go round
nute hand moves by then?
y ends after 24 hours.
Il ||| || || || || ||
1 Minute 1 Hour 1 Day 1 Week 1 Month 1 Year 1 Year 1 Leap Year
Le following.
pses at a fixed time. ain moment and a difference of time
time that you and three of your friends D school. time each of them reaches home after
31
Page 44
4.
Mathematics - Grade 6
3. Draw clock faces and indica
Write down the times indica morning or in the evening. I to denote time after noon. Example : (1) Time leaving
|(2) Time going to * Note that a.m is Ante Meridiem a
From 12 midnight to 12 noon is a. Time duration:
Nimal starts from home at 6.30 a the duration of time he has taken The time taken by Nimal to come
Time taken from 6.30 a.m. Time taken from 7.00 a.m.
The total time taken is 30 + An aeroplane leaves an airport at p.m. Find the flying time of the ae
Time from 1.10 a.m. to 2.00 Time from 2.00 a.m. 12.00 Time from 12.00 noon to 2 The total time taken
Activity 4.5
Kamal woke up at 5.00 a.1 7.20 a.m. What is the durat
time he left for school? 2.
A cricket match commenci
Find the time duration of tt Exercise 4.1
1. (1) At what time do you
At what time does thi
32
te the time they go to sleep. ted in question 3. Mention whether it is in the Tse a.m. to denote time before noon and p.m.
home to go to school 6.30 a.m. sleep 9.00 p.m. id p.m. is Post Meridiem.
m. and from 12 noon to 12 midnight is p.m.
.m. and reaches school at 7.25 a.m. What is to reach school?
to school. to 7.00 a.m. is 30 minutes. to 7.25 a.m. is 25 minutes.
·25 = 55 minutes.
1.10 a.m. and reaches another airport at 2.00 eroplane. Da.m. is 50 minutes.
noon is 10 hours. .00 p.m. is 2 hours
= 50 minutes + 10 hours + 2 hours = 12 hours 50 minutes
m. He started from home to go to school at ion of time from the time he woke up to the
ed at 10.15 a.m. and concluded at 5.50 p.m.
e cricket match.
wake up? e school begin?
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Page 45
(iii) At what time is the school
(iv) At what time do you go to 2.
Find the duration of the following (I) 4.30 p.m. to 6.50 p.m. (II) 8.00 a.m. to 2.00 p.m. (III) 10.00 a.m. to 6.30 p.m.. (IV) 9.10 a.m. to 1.20 p.m. (V) 9.40 a.m. to 8.25 p.m. In a certain television channel th
ends at 10.20 p.m. What is the du 4. The school interval begins at 10.
* 20 minutes. At what time does th 5. A film show begins at 6.30 p.m.
minutes. At what time does the fil Rewrite filling the blanks. (1) 1 hour 40 minutes = (II) 12 minutes 25 seconds = ... (III) 125 seconds =
(IV) 12 minutes 8 seconds = .. 24 Hour clock :
12
6.
11.
23 24
9 21
O O
20
8
| 19
19
18
You may have seen clock faces as stations, post offices etc. 24 hour clock helps standard.
For free distribution
04 - Time
nterval ? sleep?
time intervals.
e transmission starts at 6.55 a.m. and ration of time of the channel? 45 a.m. The duration of the interval is e interval end?
The duration of the show is 1 hour 40
m show end?
...minutes
.....seconds minutes
...seconds ..seconds
13
13 2
14
15 3
16 A
17
hown above in airports, railway o represent the time in international
33
Page 46
Mathematics - Grade 6
a Activity 4.6
Draw a clock face as shown in i from 13 to 24 in the inner circle.
Observe the following statemen clock and the relevant times in the 241
7.25 a.m. in a 24 hour clock is w 7.25 p.m. in a 24 hour clock is w 1.38 a.m. in a 24 hour clock is w
12 Hour clock 2.40 a.m. . 7.00 a.m. 12.00 Noon 1.35 p.m. 6.00 p.m. 12 Midnight
S
Activity 4.7
Copy the table given below
Time in a 12 hour clock
1.20 a.m. 3.50 a.m. 10.35 a.m. 11.58 a.m. 12.15 a.m. 1.00 a.m. 8.40 a.m. 11.52 a.m.
age 33. Mark 1 to 12 in the outer circle and
s which show different times in the 12 hour our clock. This is 24-hour clock face. ritten as 0725h. ritten as 1925h. ritten as 0138h.
24 Hour clock
0240h
0700h 1200h 1335h 1800h
0000h Table 4-1
i and fill in the blanks.
Time in a 24 hour clock
......
0025h 0240h 0600h 0935h 1107h 1259h 1408h 1755h 2020h 0600h
Cable 4.2
For free distribution
Page 47
i m =
Exercise 4.2
1. The following table shows the tii
his training. Write the duration o
Day
Starting
time Monday
1430h Tuesday
1510h Wednesday
1725h Thursday
1740h Friday
1635h Saturday
0845h Sunday
0925h
Table 4 An aeroplane starts from Katu Trichinopoli airport at 1235h. Fi A train starts from Colombo at 07 Find the duration of the time for t A bus carrying students of a scho scheduled to reach the school at 2 bus it reached the school 1 hour a
bus reach the school? 5.
The school cricket match was s day. But due to bad weather, the
At what time did the match start Hours, minutes and seconds are u
Examples Example 1:
30 minutes 15 seconds 15 minutes 20 seconds
Date in standa The standard form to state a year,month,date are written i Examples : 1. 23“ September in th
2004.09.23 2. 1st of April in the yea 3. 25" of December in
Monday is the first d
For free distribution
04 - Time
nes a sportsman commences and finishes f his training periods in the last column.
Finishing
Duration time
of time 1550h 1735h 1842h 1835h 1820h 1015h 1110h
nayake airport at 1150h and reaches nd the duration of time for the journey. 20h and reaches Anuradhapura at 1335h. che journey. -ol who were on an educational tour was 2030h. Due to a mechanical defect in the nd 15 minutes late. At what time did the
cheduled to start at 1000h on a certain
match started 2 hours 30 minutes late.
2
sed to measure time.
: past 8 a.m. -- 083015h
past 10 p.m. -- 221520h rd form late: 1 order.
e year two thousand four is written as
r 2006 is written as 2006.04.01 he year 2006 is written as 2006.12.25
1y of the week.
35
Page 48
Mathematics - Grade 6 Exercise 4.3
1. Fill in the blanks
State the times given below i (i) 30 minutes 10 seconds (ii) 8 minutes 5 seconds pa (iii) 40 minutes 12 seconds In a track event a runner completed the race at 1545. the race. Bandula took part in a 100 m s
He completed the event at 09 4.
Write the following in the st (1) Your birthday (ii) The day Sri Lanka gai (iii) The day your school v
2.
Additional exercises
1.
Rewrite filling the blanks. (1) 3 hours = ... (ii) 2 hours 20 minutes = (iii) ................
.hours ..
(iv)
hours ..
(v) 5 minutes = (vi) 2 minutes 10 seconds (vii) 1 hour 5 minutes 20 (viii) .............
hours.
(ix)
hours.
36
n 24 hour clock
past 11 a.m. ast 3 p.m.
· past 10 p.m. -- started a 1500 m race at 154025 h. He 40 h. Find the time he has taken to complete
wimming race. Swimming started at 085000 h. 20030h. Find the time taken for the event. andard form.
ned independence. vas inaugurated.
... minutes
... minutes
... minutes = 75 minutes
.. minutes = 250 minutes.
... seconds
. seconds
econds =..
.... Seconds
... minutes
. seconds = 80 seconds .. minutes ............. seconds = 3670 seconds
For free distribution
Page 49
2. Copy the table given below ano
Time in the
12 hour clock
(i)
(ii)
1.10 a.m. 7.30 a.m.
(iii) (iv) (v) (vi) (vii) (viii) (ix) (x)
3.15 a.m. 6.00 a.m. 8.30 a.m.
12.10 a.m.
Summary
In a 12 hour clock the time following day is considered as to 12 midnight is considered a The standard time is shown b The standard form for a date and date.
For free distribution
04 - Time
fill in the blanks.
Time according to 24 hour clock
0800 h 1110 h 1445 h
2330 h
e from 12 midnight to 12 noon the antemeridiem (a.m.) and from 12 noon as postmeridiem.(p.m.)
y a 24 hour clock.
: is written in the order year, month
Page 50
05 - NUI 5.1 Numbers on a straight|
Nimal and his friends wanted to money they had. Nimal had Rs. 8, Her Vishan had Rs. 5.
We can show these numbers on a s ascending order.
We will first examine how to draw
A line on which points can be repre be called a number line.
0 1 2 3 4 5 6 : In the above number line, only th
The above amounts of money whic number line.
Let A - be the amount of money N Let B - be the amount of money H Let C- be the amount of money K Let D - be the amount of money R Let E - be the amount of money V
Now observe the number line drar
0 1 2 3 4 5
S
Activity 5.1 1.
Chandra is 8 years old, Hen Leena is 4 years old. Mark 1 Let C be Chandra's age
H be Hema's age S be Shanthi's age L be Leena's age
38
IBER LINE
ne go to a shop and checked the amounts of nal Rs.10, Kamal Rs.7, Ranjan Rs.12 and
raight line in such a way that they are in the
a Number line. 'sented by numbers in an accepted order can
! 8 9 10 11 12 13 14
le whole numbers are marked.
:h the five friends had can be marked on this
imal has Temal has Camal has Lanjan has ishan has
vn.
C A
B
6 7 8 9 10 11 12
na is 10 years old, Shanthi is 5 years old and heir ages on a number line.
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Page 51
Sanath, Hemani and Samadara a ages are marked on the number 1.
A
0 1 2 3 4 5 Fill in the blanks. A - Samadara’s age is .............years. B - Hemani’s age is .............years. C - Sanath's age is .............years.
We know that the level of water in the re or decreases during dry seasons. We have hear “there is a little water in the well” etc. The i relation to marks in the walls of the well. But in the well cannot make a statement as abov
When we look at a reservoir, we will or not. But we cannot decide whether the wat person who is familiar with the reservoir co level based on marks familiar to him with w be compared.
A water gauge resembling a large v the diagram) may sometimes be seen at a
If the water level in the reservoir is ab sluice gate level the reservoir could overflow as “the water level has decreased by 10 met: zero, a number line could be drawn as follov
Sluice gate
-5-4-3-2-1 0
When the water level takes a positive v and when it takes a negative value, it is belo
e Activity 5.2
Now we would record in a table the ar had. If the cost of a bun is Rs. 8 we will fill on the next page in relation to the cost of al
For free distribution
05 - Number Line re members of the same family. Their ne given below.
6 7 8 9 10
servoires increases during rainy seasons d statements such as “the well is full” or vater level in a well is usually stated in a person who is not aware of such marks
N W
notice whether it is full ser level is high or low. A puld tell about the water rhich the water level can
Sluice Gate
vertical ruler (as seen in reservoir or a tank. Dout 10 metres above the
. You may have heard statements such res” etc. Taking the sluice gate level as
Is.
level
1 2 3 4 5 alue, then it is above the sluice gate level
w the sluice gate level.
mounts of money Nimal and his friends the amounts each has in the table given pun.
39
Page 52
Mathematics - Grade 6
Name
Cost of al
Amount of money each has (Rs.)
(Rs.)
10
Nimal Hemal Kamal Ranjan Vishan
00 00 00 00 00
. 12
Ta
The amount of money in excess c could be written as negative (-). Then th is -3.
Now let us compare the amounts of that Nimal has. According to the table, H Let us show this on a number line.
Nima S ON
-4-3-2-1 0 P - Hemal, Q - Kamal, R - Ranjan Example 1: Diagram given below
Taking the step in wh which others are stano
Kumari, Ama
Nimali
Ira
Soma
pun
Excess money
(Rs.)
Shortfall of money (Rs.)
ble 5.1 puld be written as positive (+) and a shortfall e excess Rs.2 is +2 and the shortfall of Rs.3
Emoney that the friends have with the amount emal +2, Kamal -1, Ranjan +4 and Vishan -3.
al's money
Р
R
1 2 3 4 , S- Vishan. i shows some girls standing on a staircase. ich Nimali is standing, as base the steps in ling can be stated.
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Page 53
Amali and Kumari are stai staniding on 1 step below N
Nimali. Let us compare the positio Let us consider those abov below Nimali are in the na
are at +2 position. Ira is at The above information can be sł
A- Nimali's position B - Kumari's and Amali's C- Ira's position D - Soma's position
D
с А -4-3-2-i O
Example 2 The following tabl
at a certain test. TI
Name
Marks obtained
Marks
. Obt:
15
18 14
Nimali Ranjala Hemali Malithi Kumudu Ranmali Sarojini Amani Lavanji Sujatha
10
16
20
Table With reference to Ranmali’s marks are positive and all marks below are negat:
For free distribution
05 - Number Line ding on two steps above Nimali. Ira is mali and Soma is standing 3 steps below
is of other friends with respect to Nimali. e Nimali as in positive (+) side and those gative () side. Then Amali and Kumari -1 position and Soma is at –3 position. own on a number line.
position
B
1 2 3 4
e shows marks obtained by 10 students he total marks is 20.
Ranmali ained
Marks obtained when
compared to Ranmali’s marks
+5
+8
+4
10 0
+6 +10
10
10
-5 +2
5.2
in this example, all marks above hers
ve.
41
Page 54
Mathematics - Grade 6 A Activity 5.3
Show the marks of table 5.2 on a n Consider the numbers -5, -4, -3, -
......-5, -4, -3, -2, -1 are negative 1, 2, 3, 4, 5, .........are positive wh
Numbers without fractions are zero, negative number
Consider the number line given b
+
-6-5-4-3-2-1
Numbers on the right hand side o the left hand side of 0 are negative integ
Exercise 5.1
(1)
0 1 2 3 (1) Write the numbers giv (ii) What are the numbers
What are the numbers
(2) Represent the following on :
(1) Numbers between 0 ano (ii) Whole numbers betwe
(3) The ages of some children
years, Nipuna 13 years, Sarat Compare the ages of other cl using + and - symbols. Repre
42
umber line with reference to Ranmali's marks. 2, -1, 1, 2, 3, 4, 5. e whole numbers.
ole numbers.
s are known as integers. They s and positive numbers.
elow.
0 1 2 3 4 5 6
f) are positive integers and the numbers on
ers.
4 5 6 7 8 9 10 ten on the number line.
marked between 1 and 4? marked between 3 and 8?
a number line. 120, which are divisible by 3. en 0 and 10 which are not divisible by 2.
ire given below. Nimal 8 years, Sukitha 10 111 years, Susil 14 years and Vishal 15 years, hildren with Sarath’s age and write their ages sent this information on a number line.
For free distribution
Page 55
5.2 Comparison of numbers
The number line given below shows out of 10 questions by 5 students. The corresponding numbers.
Dimathi Surangi Ravis
0 1 2 3 4 5 6
According to the number line;
Marks obtained by Malithi = M Marks obtained by Ravisha is le
The symbol < is used to sho
Marks obtained by Ravisha <
Marks obtained by Surangi is used to s
The above facts can also be shown as The symbols <, =, and > can be used “Marks obtained by Ravisha > Marks
Example I: 5
5 = 5
Гул
U N
8>6
6 < 8 15 > 109
(i) Five is less than seven can be wri (ii) Eight is greater than six can be w (iii) Ten equals ten can be written as
For free distribution
05 - Number Line
the number of correct answers written names of students are written at the
na Priya Malithi
7 8 9 10 11 12
larks obtained by Priya. !ss than marks obtained by Malithi.
ɔw "less than"
Marks obtained by Malithi. Tarks obtained by Ravisha. how “greater than"
follows.
- to compare numbers. - obtained by Suranji”
10 = 10 0 < 15 95 > 94 3 < 94
tten as 5 < 7.
Fritten as 8 >6. 10 = 10.
Page 56
Mathematics - Grade 6
Example II: 3 > 0
-1> -2
w N
V V
N O
Activity 5.4
The number line given below sho had with them.
Wasantha Pubudu, Kumara
0 1 2 3 4 5 6 Rewrite the following and fill in th (i) Number of coins Wasantha h (ii) Number of coins Kumara ha (iii) Number of coins Lahiru has (iv). Number of coins Priyal has .. (v) Number of coins Priyal has ..
number of coins Pubudu has.
Exercise 5.2
1. A B,C
0 1 2 3 4 5
The above number line shows the Names of the Children are marked as ‘A
Who is the eldest child? (ii) Who is the youngest child? (iii) Who are of equal ages? (iv) Name a child older than ‘A’ a (V) Who is older than ‘B’ and yo
44
1> 0 0 > -1 -7 > -12
ws the number of coins that five children
Lahiru
Somapala
Priyal
7 8 9 10 11 12 13 14 me blanks using the symbols.
as ..........
....number of coins Pubudu has.
..number of coins Pubudu has. ...number of coins Somapala has. ..number of coins Somapala has. ..number of coins Lahiru has..
E,F
6 7 8 9 10 11 12 ages of 6 children who attended a party. , 'B', 'C', 'D', 'E', 'F'.
ind younger than ‘D’.
unger than ‘E’?
For free distribution
Page 57
(2)
0 1 2 3 4 5 6 7 (1) What is the largest number show (ii) What is the smallest number sho (iii) What are the numbers on the nu (iv) What are the numbers on the nui (V) Write numbers less than 6. (vi) Write numbers greater than 8. (vii) Are values of numbers increasin,
from the number denoting 3? I
increasing or decreasing. (3)
(4)
-6 -5 -4 -3 -2 -1 0
(i) What is the largest nu
(ii) What is the smallest n Fill in the blank spaces using the (i) 10 ......–10 (ii) -7 (iv) 0 ....... -3 (V) -2 (vii) 2 ....... -1 (viii) –1 (x) 2 ....... - 4 Rewrite the following numbers arı (i) –1, 4, -3, 0, 5 (ii) 3, -7, 5, -1, 7 (iii) 0, -4, -2, +4, +2
(5)
Additional Exercises
1.
Draw a number line and mark th -2, +2, +5, -3, 1, 4, 0, -7, -6
For free distribution
05 - Number Line
8 9 10 11 12 13 14 n on the above number line? wn on the above number line? nber line, between 6 and 11? nber line, between 3 and 8?
; or decreasing when moving to the right Vhen moving to the left, are numbers
1 2 3 4 5 6 7 mber on the above number line? number on the above number line?
symbols <, > or=. ....... -5 (iii) -3 ....... -8 ....... 5 (vi) -4 ....... -4
(ix) -3 ...... 3
)
ranging in the ascending order.
e following numbers.
45
Page 58
Mathematics - Grade 6
-4-3-2-1 0 1
4.
What are the numbers mark 3. Rewrite using the symbols -
(i) 3.......7. (iv) -7.......7 (vii) –4.......-4 (ix) -150.......–200 Arrange each set of number (i) 3, –5, 0, 2, -1, 8 (ii) -7, -4, 4, -1, 6 (iii) 5, 6, -3, -1, 8, -5
(iv) 10, -8, -7, 0, 1, 5, -6 5. Arrange each set of number
(i) 1, 2, -2, 15, 6, -5, -8. (ii) -3, -2, -5, -8, -15, 1, (iii) 12, -9, -12, 5, 2, -11,
Summary
*
Whole numbers positive o Whole numbers with + sigi numbers with – sign are k A straight line on which an accepted order is called The symbols >, = and < a less than for comparison o
46
2 3 4 5 6 7 8 ed on the above number line? <, > or = to fill in the blanks. ii) –3.......–5
(iii) 0.......–2 v) 12.......12
(vi) 1.......0 viii) –25...–10 x) 1000.......1005 s in the ascending order.
s in the descending order.
- 10
2
-7, 3
ir negative and 0 are known as integers. 1 are known as positive integers and whole nown as negative integers. points can be represented by numbers in 1 a number line. re used to show greater than, equal to or
f numbers.
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Page 59
06 - ESTIMATION AND 6.1 Estimation of quantities
Activity 6.1 1. At what time did you come to so
What is your height? 3. What is your age?
What is the height of the school What is the length of the classro
What is the length and breadth o 7. What is the length of your middle
When answering the above questions d
You have decided on a value here using form is known as “estimation”.
Let us consider some more examples.
i m = n o
Example 1.
When buying a cluster of bananas, th counted. A value is arrived considering the value is assumed as an estimated value. Here counted and from the number of combs, t
Example 2.
The value of a jak fruit or a breadfruit Here fruits equal in size are given a certain val fruits are valued low.
The fruits are graded by assuming that is estimated. You have heard that fruit traders {
Without measuring or weighing and guessir multiplication or division and arriving at si
Without measuring or weigh multiplication, division, adı decide on the number and q known as estimation.
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O APPROXIMATION
hool today?
building where your class is? pm?
f your Mathematics text book? e finger? id you do any measuring?
common sense. Deciding a value in this
e number of bananas is not normally number of combs in the cluster. This e, the number of fruits in a comb are
he total number of fruits is decided.
is normally fixed according to its size. lue. Big fruits are valued high and small
some fruits are big. The size of the fruit get fruit trees on lease during fructiscence. ng correctly using addition, subtraction, zes and numbers is called estimation.
ning but surmising using dition or subtraction to quantity approximately is
Page 60
Mathematics - Grade 6
S
Activity 6.2 Discuss with your parents, the situ E.g. * Buying provisions for
Supplying material foi Exercise 6.1
1.
Select a page from your Sinh in that page. Count the num
value with the estimated vali 2.
How many normal size cup
bring to school if any? 3. Estimate the values of the ot
Objects
1. Length of the blackboard in the 2. Breadth of the blackboard 3. Length of the teacher's table 4. Breadth of the teacher's table 5. Height of your best friend 6. Weight of your best friend 7. Capacity of a normal cup of tea 8. The length and breadth of your
Mathematics text book
Tab
4.
Estimate the length of you exercise book. Write the esti with written, what you have
Find the length of the classroom exercise book, Compare this value with
48
ations where estimation is used.
one week
a function
iala text book. Estimate the number of words ber of words in the page and compare this
ue.
s can be filled with the bottle of water you
pjects in the table given below.
Estimated value
- class
ble 6.1 r classroom in metres. Write this in your
mated values your friends have and compare
written.
i by your steps. Write this number in the 1 the estimated value.
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Page 61
B How many boxe
How many time column ‘Y' ?
7.
How many complete squares
6.2 Approximation
Sometimes it is sufficient to express r 100 etc. Normally, these are not exact value
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06 - Estimation and Approximation
s of size ‘B’ can be packed in box ‘A’?
es the height of the column ‘X’ is in the
are there in the uneven picture?
numbers to the nearest 10, to the nearest
s. But for certain purposes it is sufficient.
49
Page 62
Mathematics - Grade 6 This process is known as "rounding off 1 (A) If we are expressing a number to
multiples of 10 on either side of t! When the units place is less than 5 taken. eg. 54 is rounded off to 50. When
multiple of 10 above the number is eg. 57 to the nearest 1
65 to the nearest 1 Activity 6.3 Fill in the blanks in the table given
Number
When rounded of
12
25
44
46
67
83
99
Table 6.2 Writing a number rounded “Approximation”. Here, the number
Exercise 6.2
1. The cost of a mango is Rs. 12.
the amount of money nee approximation.
Mother gave Rs. 16 to the s total amount of money give There are 12 kg of potatoes f of a shop. How many 'kg' of the total to the nearest 10.
A certain number when appre Can this number be 65?
3.
4.
50
o the nearest 10, nearest 100" etc. the nearest 10, we have to consider the ne number and decide on the closer ten. the multiple of 10 lower than the number is
the units place is 5 or more than 5 then the - taken.
0 is 60. 0 is 70.
below. f to the nearest 10
off to a given number is known as s were approximated to the nearest 10.
You approximate this to the nearest 10. Find ded to buy 18 mangoes based on the
on and Rs. 25 to the daughter. Express the i to both of them to the nearest 10. or sale and another 33 kg in the store room. potatoes are there in the shop? Approximate
Iximated to the nearest 10, the answer is 60.
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Page 63
Additional Exercises
1.
Floor
A
Estimate the number of ‘B’ tiles the diagram. The picture below shows two se small set. Estimate the number of
2.
3.
Estimate the number of triangles
‘C’ and ‘D’ are two flower beds. greater than or less than the lengi
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06 - Estimation and Approximation
ile
needed to cover floor ‘A’ shown in
ts of coins. There are 10 coins in the 'coins in the large set.
- of size ‘B’ needed to cover triangle ‘A’.
D
Is the length around flower bed ‘C’ Eh around flower bed 'D' ?
Page 64
Mathematics - Grade 6
5. In the figures partially shac
each figure is greater than case.
Amal got 65 marks, Ramar Kavindra got 61 marks in al the nearest 10.
Ages of 8 persons are given
Age in years
48
33
35
< 0 O A L D E
45 38
27
18
Ta
8.
Mother bought 9 metres of 12 metres of table cloth. Api the nearest 10 metres. Fine approximate this to the near
Summary
Deciding by taking appro multiplication, divisio measuring or weighing
52
led , indicate whether the shaded portion of half, less than half or equal to half, in each
(iii)
(iv) ni got 62 marks, Kumudu got 68 marks and Mathematics test. Approximate each mark to
in the table. Fill in the blanks.
When rounded off to the nearest 10
ble 6.3
coloured poplin, 8 metres of white cloth and proximate the lengths of cloth she bought to I the total length of cloth she bought and 'est 10 metres.
ximate quantities or amounts related to n, addition or subtraction without 5, is known as Estimation.
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Page 65
07 - ANG
Consider the positions of the hour hand 1.00 p.m. to 8.00 p.m.
12
12
11
9
o o
8
3
o
9
5
5
We see that the positions of the hour har
S
Activity 7.1
Take two pieces of ekel, place two end ways. Different positions are shown below exercise book.
Figure 7.1 An angle is formed when two straight lir
Angle
Angle
Figure 7.
For free distribution
GLES
and the minute hand of a clock from
12
11
0
2
>
8
>
LO
6 5
ad and the minute hand are different.
s together and other ends in different in diagram 7.1. Draw them in your
nes meet as shown below.
Angle
Angle
53
Page 66
Mathematics - Grade 6 Assignment 1 Name the situations you
E.g.: Angle formed by rods s Activity 7.2
Look carefully at the four corner these pictures in your exercise book.
Draw the positions of the hour h time is 3 o’clock and 9 o’clock. Mark
Observe the picture below.
The marked angles you see abov
This shape is named as a right
The angles that we come across ir This is clear when we look at the angle at 2 o’clock or 4 o’clock. Let us see h angle.
R
Activity 7.3
Take 2 ekels and place two ends positions. Observe and draw them in y
54
I see in the environment where angles are formed.
in an antenna.
s of the ruler, four corners of the door. Draw
and and the minute hand of a clock when the the angles in the pictures.
11 12
4
5
e take the shape drawn below.
angle. 1 the environment are not right angles always. s made by the hour hand and the minute hand ow we can name angles other than the right
together and move the other ends in different our exercise book.
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Page 67
You would notice that each of the abov Angles smaller than a right angle
Activity 7.4
Take 2 ekels and place them as shown b your exercise book.
You will note that each of the angles o right angle.
Angles greater than a right an angles are obtuse angles.
E
Activity 7.5
Now take 4 pieces of ekel and make tw
Now plac The ekels Remove
|2 3
Then you will get an angle like the one
here.
This angle is equal to two right angles. Draw several angles like this in your exercise
For free distribution
K&S 1219 FN-5
07 - Angles
e angles is smaller than a right angle. are acute angles.
elow. Observe them and draw them in
Im In
btained in this manner is greater than a
gle but less than two right
-o right angles as shown below e ekels 2 and 3 together as shown below. 51 and 4 lie on the same straight line.
ekels 2 and 3.
seen
e book.
55
Page 68
Mathematics - Grade 6
If the two arms of an ang the angle is called a stra
SActivity 7.6
Observe the directions shown by clock shown below. Draw this diagram
Now place two ekels as shown bel your exercise book.
11 12
N
3
You will note that each angles sho
Angles greater than a stra
Activity 7.7 Complete the table given below.
Angle
Whether
56
gle form one straight line ight angle.
the hour hand and the minute hand of the in your exercise book. Low. Observe the positions and draw them in
awn here are greater than a straight angle.
aight angle are reflex angles.
the angle is acute/obtuse/right/straight/reflex
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Page 69
Angle
Whether the an
Table no. Exercise 7.1
01. Copy the table given below and fi
Time
Positions of the hands i
10
3.00 p.m
12
10
6.00 p.m
9
10
7.00 p.m
12
11
10
9.00 p.m.
12
10.00 p.m
Table No
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K&S 1219 FN-6
07 - Angles
le is acute/obtuse/right/straight/reflex
7.1
11 in the last column. n the clock Type of the angle formed
7.2
57
Page 70
Mathematics - Grade 6
02. Draw two figures for each.
i. Acute angle ii. Right
iv. Straight angle v. Reflex 03. Rewrite and fill in the bland
i. An acute angle is an ii. An obtuse angle is
thar
iii.
A reflex angle is an ar angle.
Assignment 2
Draw diagrams to show how the and complete a full turn (rotation). Drav formed by the hour hand and the minut
Additional exercises
1. State the type of angle in th
S. < z B: : -
LA
58
angle
iii. Obtuse angle - angle Es with less than/ greater than. angle ..
...............a right angle. an angle greater than a right angle but i a straight angle.
gle ...
... a straight
hour hand of a clock moves from 12.00 noon v angles for each hour. Note the type of angle se hand.
ve blank space given in front of each angle.
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Page 71
2.
The diagram shows six straight li State the type of angle formed at
i. By E and F ii. By A and E
By A and D iv. By A and C v. By E and B vi. By E and C. vii. By C and F...
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07 - Angles nes converging at the point ‘O’. Fo’ by diffrent lines.
B
59
Page 72
08 - DIF
Let us go to the school garden and start
s Activity 8.1
The lesson for today is about dire
Stretch your right hand to the dire direction of sun setting. Here you will i sets from the West.
Activity 8.2
Now stand facing the East and str towards the South and your left points
1.
Activity 8.3 Now you have identified the four
Place a student facing Nortl 2.
Ask another student to stan
student to stand behind the 3. Ask another student to stano
left side of the first student.
You would see that the students v
Bimal Bimal O.
x]
- i m = 0
Fill in the blanks of each of the fo
The arrow shown above is
Nimal stands.
...stands Sout ...stands Nort ..stands West
RECTIONS
the lesson with an activity.
ctions. ection of sun rising and your left hand to the dentify that the sun rises in the East and sun
etch your hands. Now your right hand points towards the North.
E
main directions.
d in front and another first student. 1 on the right side and another to stand on the
vould be standing as shown below.
Upul
|
Amal
Nimal
Dinal
lowing statements. pointed to the
...of Amal. 1 of Amal. h of Amal. of Amal.
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Page 73
Observe the directions Upul, Bimal, Di to Nimal.
e Activity 8.4
x Upul
Amal
Nimal
x Dina
Let Nimal face North. Ask Upul to sta right, and Amal on the left of Nimal.
Now write the names of students who ; the West of Nimal.
Draw a diagram to show the positions an arrow. When you examine a map or a plan by an arrow.
Sub Directions: In addition to four main directions, there ar
North-west North N
West -
LS
South-west South Sol Activity 8.5 Let O', A', 'B', 'C', 'D', 'E', 'F', 'G', stand as shown in the diagram.
(•
M . .
For free distribution
08 - Directions nal and Amal are standing with respect
Bimal
nd in front. Dinal behind, Bimal on the
are in the North, the South, the East and
of the students and indicate North with , you will notice that the North is shown
e four sub directions.
orth-east
East
ath-east
‘H’ represent nine students who
Z
Page 74
Mathematics - Grade 6
Let us find in what direction are the sti Identify that ‘B’ is standing North'D’ is standing South-east of ‘O’, ‘H’ is standing North-west of ‘O’.
The main directions and : called the "Eight Directio
Write in your exercise book, 4 mai school office. Also write 4 places in the i indicates all these places based on the so
Assignment 8.1
1. Obtain a map of Sri Lanka. W all main directions and sub directions as
Example: Balangoda town is situat
Exercise 8.1
Marke
Post office 0
Police station
Hospital I
TO
62
adents ‘D', 'B', 'H', 'F' in relation to student ‘O’. -east of ‘O’. FF’ is standing South-west of ‘O’.
sub directions are together ns".
n places in the 4 main directions from your four sub directions. Draw a diagram which chool office.
rite the names of the towns situated in suming Kandy as centre. ed South of Kandy.
ZE
Bus stand
School
Railway station
Library)
wn hall
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Page 75
(i) In which direction is the t (ii) What is situated to the W (iii) In which direction is the p (iv) in which direction is the s (V) In which direction is the b (vi). What are the places situat (vii) What is situated in the So
Write the letter "X" in the
exercise book. (ii) Write the digit 1 in the fo
Write digit 2 in the fourth 3 in the fourth cage to th
fourth cage to the South f Now, in which direction is 4 siti
X 1
Vertical and Horizontal Con
Activity 8.6
The trees you see here are a kind of f trees grow in coniferous forests in the climate. They grow straight upwards.
Also you must have seen masons usi when they build walls of houses. They, as i walls are not built straight upwards there ar the walls collapsing. We use the plum
whether something is vertical.
An improvised plumb-line can be ma piece of string to a weight. This weight i stone with a regular shape. The picture sho an improvised plumb-line with his hand. I picture is planted vertical.
There are volleyball courts, netball courts in schools. The grounds of these cc
For free distribution
08 - Directions own hall situated from school? !st of the school? ost office situated from the school? :hool situated from the library? us stand situated from the hospital? ed to the West of the railway station? uth-east of the market?
middle cage of a page in a square ruled
vurth cage to the East of the letter "X". cage to the North from 1. Write the digit e East from 2. Write the digit 4 in the rom 3. lated from ‘X’ ?
cepts.
pine trees. These cool temperate
Ing a plumb-line
vell as we know if se possibilities of b-line to check
de by tying a hard may be a piece of ws a pupil holding "he flag staff in the
PERO
courts, and tennis purts are flat. Also
63
Page 76
Mathematics - Grade 6 the playground of the school too is flat this flatness is termed as horizontal. buildings are horizontal.
We can draw horizontal lines vertical lines as well. See the diagram. At a point where a vertical straight line m straight line, an angle of 90° is formed. In your box of instruments you will fine called set squares. See the diagram.T. find out information about them, magnitudes of angles. Carpenters and masons too need an instr their construction work. You can se
instrument is called a vertical and between then check wheth floor. That is the vertical a
A Try Square
The first step to be taken in buildin the following diagram.
2nd room
Toilet
1“ room
Sitting room
The foundation, which is on the gi Now let us observe how walls are
64
The property of The floors of
.. We can draw,
Vertical
eets a horizontal
Horizontal
d two instruments alk to your teacher and length of sides and
ument of this nature for e a diagram of that here. The instrument
Try square. One blade of a Try square is the other is horizontal. Therefore the angle n is a right angle. This instrument helps us to er a wall is built vertical to a horizontal 5 checking whether the angle in between ind the horizontal is a right angle.
ga house is to construct the foundation as in
The foundation is horizontal.
"ound, is said to be horizontal. constructed on the foundation.
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Page 77
The walls are vertical.
wall
The floor is horizontal
Draw a diagram of a house and show t the breadth and the height.
x Activity 8.7
In an earlier lesson you have ide board or a piece of wooden pla corner with the right angle betw room and verify whether the wall Find out more vertical and horizo when two vertical walls meet, a v in between the cement floor and :
For free distribution
08 - Directions
floor
wall
The walls are vertical.
he floor and walls showing the length,
ntified a rectangle. Get a piece of card ank having right angles and place its ween the wall and the floor of the class 1 and the floor are at right angles. Dntal places like this. In the classroom, ertical edge is formed. The edge formed a vertical wall is a horizontal edge.
65
Page 78
Mathematics - Grade 6
Have you seen instances when ma an instrument like the one shown in the to check whether two walls placed fair are in the same level.
Activity 8.8
Fill water into a transparent bottle that an air bubble is made inside. Close i
Now place the bottle on the classroc Mark the position of the air bubbl
Now lift the bottle from the lid side slightly.
What happens to the air bubble?
Raise the bottom side of the bottle slightly.
Examine the position of the bubbl
Discuss with other students the p zontally and otherwise.
Activity 8.9
Make an improvised plumb-line in Use it and examine whether the w table legs, surfaces of the classroo cupboard etc. are vertical.
Exercise 8.1
1. Write 4 objects at home or i
Write 4 things that are horiz Keep a box on the table and (i) How many vertical pla (ii) How many horizontal
i m
66
Water level
bons use diagram ly apart
Transparent plastic
tube
e in full and remove a little water from it so t tightly. om floor horizontally as shown in the diagram.
Ground Stopper
Air bubble
Water
osition of the air bubble when placed hori
1 the classroom. alls,
Using a simple plumb-line to see whether
walls are vertical .
m
n the classroom that are vertical. ontal.
observe it. ines of the box are seen?
planes of the box are seen?
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Page 79
4. 5.
(iii) How many vertical edges a (iv) How many horizontal edge Stand in the classroom. Can you ra Can you change the position of t
Are there planes that are not vertica 7. Are there planes that are not ho
examples.
Is the surface of a water in a reser Additional Exercises Draw diagrams to illustrate the information g 1. The gate is situated to the North
house there is a tree full of flower North-west of the house there i
to the West of Shantha’s house.
2.
Hemantha cycles 5km to the Nort 2km. He then cycles 3km to the cycles 1km to reach his uncle's h Find what is horizontal / vertical
The surface of the door in a Planted electricity wire pos The floor of the classroom. The top surface of the teach The seating part of the teac The surfaces of the walls of
3.
Summary
The main directions are North, The sub directions are NorthNorth-west. The eight directions are the i sub directions. A right angle is formed at af and a horizontal straight line
For free distribution
08 - Directions -e seen? s are seen? ise your hands so that they are vertical? he hands so that they are horizontal? l in the environment? Write 2 examples. rizontal in the environment? Write 2
voir horizontal, when the water is still?
iven in questions 1 and 2.
of Shantha's house. To the East of the es and to the South there is a well. In the is a firewood shed. Mallika’s house is
Eh and then turns to the East and cycles
North-east and turns to the South and puse. out of the following.
a house.
ts.
ner’s table. cher's chair.
the school building.
East, South and West. -east, South-east, South-west and
four main directions and the four
point where a vertical straight line e meet.
67
Page 80
09 - FR. 9.1 Unit fraction and Proj
"Dear salesperson, please give n one quarter of a loaf of bread. "You w do these activities to identify a half, a
S
| Activity 9.1
Each student can find a square st Fold this into two so that there will be well and unfold it.
You will get one of these pictures have got.
Out of the two equal parts of the
Half is written as .
Draw pictures of a - of a loaf, a
S
Activity 9.2
Each student can find a square that there will be two equal parts. Wi that there will be two more equal part paper.
You would see that the paper is it is like one of the pictures shown belo
68
ACTIONS
per fraction ne a half of a loaf of bread. Please give me puld hear these requests in boutiques. Let us quarter, threeforths.
rip of paper with the help of the teacher. two equal parts. Sharpen the folded edge
.. Look at the pictures your friends in the row
strip of paper, colour one part.
- of a bun.
sheet of paper. Fold the paper into two so thout unfolding the paper, fold it again so is. Sharpen the folded edges and unfold the
; divided into 4 equal parts. Find whether
w.
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Page 81
Draw them in your exercise book. Sha
The shaded part is shown as . The teacher will show that you can contir shown below using three square sheets of pa
This paper is divided into eight equal parts.
shown as
Exercise 9.1
In association with the above activities
1. How many -s are there in 1?
3. How many -s are there in 1?
5. How many 's are there in a =
|-
S
Activity 9.3
Draw pictures to represent the fraction Get the assistance of your teacher for t In a fraction the number above the ! number below the line is known as t Examples:
(1) In - the numerator is 1, the den
For free distribution
09 - Fractions
de one part out of the four parts.
nue this activity and obtain pictures as -per.
Only one part is shaded. The shaded part is
s answer the following questions.
2. How many -s are there in 1?
4. How many - 's are there in a =?
How many
8
's are there in a
1 1 1 1 is 3' 5 3 10 in your exercise book. This activity.
line is known as the numerator and the the denominator.
ominator is 2.
69
Page 82
Mathematics - Grade 6
(ii) In the numerator is 1, the
Fractions with numerator
Activity 9.4
Write 10 unit fractions.
Proper fractions
Activity 9.5 Draw any formal figure you like,
What fraction is the unshaded par Seek the assistance of your teache
S
Activity 9.6 (1) Draw any formal figure you
parts. If the shaded fraction
(ii) Draw squares or circles and
(ii (iii) Is there any difference betw
ied earlier? What can you sa (iv) Write ten proper fractions.
Fractions with numeratc denominators are know
Exercise 9.2
1. Separate the following fract
3 1 2 7 1 9 1 8° 2' 5° 10' 3° 20' 25
70
e denominator is 4.
1 are known as unit fractions.
divide it into 4 equal parts and shade one part. t out of the whole figure? er for the answer.
| like, divide it into 8 equal parts and shade 5 is , what is the unshaded fraction? shade the fractions shown below. i) = (iv)
een fractions and the unit fraction you studay about the numerators in these fractions?
ors less than the n as proper fractions.
ions into proper fractions and unit fractions.
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Page 83
9.2 Equivalent fractions
S.
Activity 9.7
From a sheet of square ruled paper Divide one strip into two equal parts and four equal parts and shade two parts. Pas
write the relevant fractions.
Shaded fraction =
2
Shaded fraction = -
You would see that the shaded parts a
:. =
From a sheet of square ruled paper parts and shade one part. Divide the other Paste the strips in the exercise book and wri
Coloured fraction =
=|N
Coloured fraction = 2
Eur
You will see that The shaded parts are equal.
For free distribution
09 - Fractions
ut two strips with four squares in each. hade one part. Divide the other strip into te these strips in your exercise book and
ire equal.
ut two strips. Divide one strip into two equal strip into 10 equal parts and shade 5 parts. ite the relevant fractions.
71
Page 84
Mathematics - Grade 6 e Activity 9.8
Fill in the blank spaces in the tabl Number of squares
Number of sq in a strip
shaded when di
P
10 12
20
50
Tal
Fill in the blank squares.
1 2
() -2 )
NI
Fractions of this type are known a
Activity 9.9 1. Assign the previous activitie
Divide one strip into 3 equa other strip into 6 equal par exercise book.
Coloured fraction =
W|N
Coloured fraction = Write the relation between
2.
Draw two figures with 10 e shade them as shown belov
Coloure
e given below.
uares to be vided into two
The fraction that indicates
the shaded part
ble 9.1
(i(iv) ;-&
Ls equivalent fractions.
es, cut strips of paper with 6 squares. 1 parts and shade 2 parts. Divide the rts and shade 4 parts. Paste them in your
]
AM 1
qual squares in your exercise book and
ed fraction = 0
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Page 85
Coloured
Write the relation between
Such fractions are known as 3. Fill in the blank squares in acco
Draw the figures given below i fraction shaded in each.
w|-
4
For free distribution
09 - Fractions
fraction = 3
F and 6.
10
equivalent fractions. rdance with the figures given below.
Fraction coloured ==
Fraction coloured =
O D
359 ı your exercise book and write the
Page 86
Mathematics - Grade 6 Exercise 9.3
Fill in the blank squares in the tabl
Fraction
Equivale
N|No|unw|- 0 |w n| A
Table No. 9.2 To obtain equivalent fractions the be multiplied by the same number.
Examples:
2 2x2
(ii).
(1) 3 3x2 6
||
ܬܗ
(iii)
4 4x5 20
4x5 7x5 35
(iv)
Likewise equivalent fractions can and the denominator by the same num
219
|| |
5|a ola
|| ||
w|N Un | WIN
(iii)
50
Exercise 9.4
1. Write three equivalent fractio
(1) * (ii)
(i)
e given below. nt fraction
e numerator and the denominator should
2x4 3 3x4 12
3x4
| 00
N|A w|N
4 4x3 12
| 7x3 2
ı be obtained by dividing the numerator Iber.
|| ||
O| 00 |9
|| ||
| AA | w
(iv) 24 = 8 = 4
ns for each of the fractions given below.
(iv) + (v) 25
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Page 87
2. Simplify.
@ : (i) ; (ii) 25
9.3 Comparison of Fractions
Let us consider fractions in which den
Fraction coloured
00|w
You would see that
V
00|
Comparison of Fractions (continued)
Activity 9.10 Cut two strips of paper with six equal equal parts and shade two parts. Divid and shade five parts. Paste them in yo
Fraction coloured =
Fraction coloured = 2
Let us find the greater fraction.
2 = 4
(Look at the squares i
Therefor
a| un
4
| un
w|
For free distribution
09 - Fractions
(iv)
AE
L
al:
ominators are equal.
Fraction coloured
* C0 | un
squares. Divide one strip into three le the other strip into six equal parts pur exercise book as shown below.
n the strips of paper.)
75
Page 88
Mathematics - Grade 6
|Give your answer using the correct
Example 1 Find the greater fraction
3x2 4 = 4X28
4x2
:: 0 | P | w
00|Un og
<
Here both denominatio
same magnitude to f Example 2 Use the correct symbol
2 2x3 6
- 3x3 9
Now
1 2
... ->
STO
9. 3 Instances where denominators are e
Example 3
2.
7. 6
979
Instances where numerators are equ
Fraction coloured =
Fraction c
- w|-
Here we see that
| M
Example 4. >=
N|w WIN ATH
00 w AYN
v v
|w un
Example 5. >>>
76
symbol out of < and >.
put of
prs are converted to a number with the ind the greater fraction. but of <, > to show the magnitudes of , and
qual
4
al
oloured ==
Fraction coloured
|-
Here the numerators remain unchanged but he denominators increase in magnitude.
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Page 89
(1)
(ii)
Activity 9,11
Write in ascending order.
1 1 1 1 1 () 10° 8' 3 5 2
13 7 8 4 18 (3)
25' 25' 25° 2525
|(4)
3 3 3 3
8° 4' 5' 7 Exercise 9.5
(1) Write in ascending order of the fr:
3 1 5 17 4° 2' 8' 16 5 3 11 2
(iv) 6 4 12' 3 Write in descending order of the i 5 3 7 11
(ii) 6° 4' 8' 24 5 3 1 7 8' 4' 2' 10 Mother brought home two botti She gave of one bottle to the o
son. Who got more drink? (4) Two buns of equal size were give
of the bun she got and Prema ate
3 @ e 3
9.4 Addition of fractions
Activity 9.12 Draw the figures as shown below and i
(1)
00| w
+
| 00
For free distribution
09 - Fractions
5 7 3 1 12° 12' 12' 12 4 2 3 5 1 7' 7 77 7 7 7 7 7 10’ 12° 9' 15
actions given below.
7 2 5 11 9' 3' 6' 18 13 9 4 1
20° 10' 5 2 ractions given below.
8 2 21 3
es of soft drink with the same volume. laughter and of the other bottle to the
en to Kamala and Prema. Kamala ate = e 2 of the bun she got. Who ate less?
Fill in the blank boxes.
Page 90
Mathematics - Grade 6
NO"
In addition of fractions V result can be obtained b Examples 1. 25 7
Exercise 9.6
Fill in the blank boxes.
38 -
(1)
20* 20 - 20 9 O 12
(3) 25 *25 25 (5) - i
Addition of fractions with related de
e Activity 9.13
Cut three strips of paper with 8 strip into 4 equal parts and shade thr equal parts and shade one part. Com total of 7 squares are shaded. Divid and shade 7 parts. Paste these strips i
C0 | -
78
O| W
with the same denominator, the y directly adding the numerators.
-- 1515 - 15
13
(4) 1818 - 18
12
enominators
squares of equal size in each. Divide one ee parts. Divide a second strip into eight pare the two strips. You will see that a e the remaining strip into 8 equal parts n your exercise book and write the fractions.
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Page 91
| w
m| t
||
co |
*
Let us add the fractions given below. 31
The denominators in 4' 8
equal by writing equiv
+
| 00
|| ||
00| 9 00|a Pw
X X + NN | 00
||
Examples 32
W +
2x2
5x2 - 344 10 * 10
|| ||
|w aw
10
Exercise 9.7
(1) Add.
|- O|-
6 12
+ +
w | N N un
8 ata -ta
(iv) ?
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09 - Fractions
both fractions can be made
3 6 zalent fraction 2
o | O
|- w|-
79
Page 92
Mathematics - Grade 6
2 2 1
(vii) 3* 153
(vii (vii
(2)
There are two bottles of equ the other bottle has - of se
bottle to the other. Find the (3) Hemapala gave of his we
fraction of his wealth has h 9.5 Subtraction of fractio Subtraction of fractions with the sa
Activity 9.14 Draw the diagram given below in y coloured. Out of that 7,4 are in dar
What fraction of the diagram is c 7 4 3 10 10 10. Examples
Subtract : 1 5 1 4
1. 99
Exercise 9.8
Write the correct answer in the blank t
| (1) > 1 - 0
7 77
7 O 3 (3)
10 10 10 Subtracting fractions with related d
Activity 9.15
Prepare 3 strips with 8 squares i Divide one strip into 4 equal parts and equal parts and colour 3 parts. Compare
80
A 7 3 1
-+-+- 25
1) 40' 10* 5
al size with soft drink. One bottle has - and oft drink. Kamala poured the drinks from one e quantity of soft drink in that bottle.
ealth to his daughter and to his son. What
e given to both his daughter and son? ns
me denominator
Four exercise book. Out of the 10 squares, 7 are
k blue.
coloured in light blue ?
Subtract :
2. 116 5
12 12
Run
boxes.
(2)
|
3
à un|no|un
|| ||
un|n Din
(4) 5 5
enominators.
n each from a square ruled sheet of paper. shade 3 parts. Divide a second strip to 8 the two strips. You would notice that 3 more
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Page 93
squares are coloured in one strip. Divide the 3 parts. Paste these strips as shown in your
Let us subtract these fractions formally
3×2 4x2
3-8
3-4 ==
-- (183-8
318 6-8 3-8
4 318
The denominat writing an equ
Examples
Subtract.
|2
10.5
1 ===
7|7|
-- - 3|이
프있te
프 40
이 | | ||
90"이나 이와 || || 504 217 프것4
Exercise 9.9 (1) Subtract.
1 2
(1) 39
For free distribution
09 - Fractions e third strip into 8 equal parts and colour exercise book and write the fractions.
| w
||
O| 00
00 |w 0o | w
| w
-
||
co | w
- as shown below.
Lors in both fractions are made equal by ivalent fraction for
lant froation for 3 6
m|t
as
O| 00
3. 3
al la
NIN
o || || ||
alm X X olo
on | | |
o e o A o|A
G = 5
= ?
9 3
20 40
(iii)
81
Page 94
Mathematics - Grade 6
(iv)
5 1 7 8 2 (2) Simplify.
3 5 3 (48 16
2 3 5 34 12
(ii)
a e = 0
-+--
(iv)
A man sells a
irt and the part of his land that ren (4) - What fraction of plate Gun
it to his dog and to the
Additional exercises
1. Write two equivalent fractio
| w
00 | WIN
(v)
(vi)
2.
Write the following fraction
1 1 1 1
(1) 3'2'8' 7
2 5 3 7
(ii) 3'6'4' 12
3 7 13 7 (iii)
5'10'15' 30 Write the fractions given be
2 2 2 2
3.
(1) 5’3’7' 9
(ii)
3 1 7 5 8'4'12' 6 5 8 1 11
(iii) 6'9' 3' 18
82
7 5
V/
*12
(vi) 8 24
2 4 7 3 918 4 3 4 5 1015
+ +
/A
a i part of his land. Find as a fraction nains unsold. napala's of rice remains if he gives - of
cat?
ons for each of the following fractions.
|
(vii)
در |
(viii) ;
s in ascending order.
low in descending order,
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Page 95
4. Simplify the following fractions
0o | w | W
16 8 (v) 3.
1 3 3 (iv) 4 16 *3 5. A cake was cut into 12 equal p
Write the remaining portion of 6.
A chocolate was cut into 16 equ and Kamal. Kamal ate 5 pieces. 2 pieces. Find, (i) who ate the biggest share o (ii) who ate the smallest share What fractions of a journey has part, went by bus a 1 part and
8.
Srimathi and Saraswathi have ti with equal quantities. Srimathi ; of her bottle. Soma drank what of the drink that Soma had.
*
Summary
In a fraction the number above the number below the line is knı Fractions in which the numerat Fractions in which the numerati
known as proper fractions. * Equivalent fractions can be obt
nominator of a fraction is (i)
*
(ii)
When comparing, adding or sub denominators, equivalent fract
For free distribution
09 - Fractions
3
(iii) =
10
14 3
5 15 10 5 3 12 24 ieces. Manel ate 3 pieces out of them. the cake as a fraction of the whole cake. al pieces and given to Hemal, Priyal
Priyal ate 7 pieces and Hemal ate
of the chocolate?
of the chocolate? a person to complete, if he cycled a by another vehicle a part?
12
No bottles of soft drink of the same kind
drank of her bottle. Saraswathi drank t was left in the two bottles. Find the fraction
the line is known as the numerator and own as the denominator.
ors are one are known as unit fractions. ors are less than the denominators are
ained when the numerator and de
multiplied by the same number.
divided by the same number. otracting fractions with different cions should be used.
83
Page 96
10 -
Tiger
Dee
Duck
S
Crow
Cat
Dog
Do the following activity to learn ab
4.
S
s Activity 10.1
1. How do you identify the ani 2. What are the common featur | 3. Separate the animals into gi
them.
Name each group. Activity 10.2 Let the students in the class, group i of transport they use to come to scl 1. Students who walk to schod
Students who come to schon Students who come to schoc
Students who come to schoc Activity 10.3 1. Prepare a list of containers i
following manner. 1. Containers made of cl 2. Containers made of me 3. Containers made of gla
4. Containers that do not In doing these activities, you wil objects according to a common property
2. Group the students in your class
- i m =
84
SETS
Cock
Cobra
Python
a Parrot
Viper
Mynah
out sets.
mals shown in the above picture ? res that you see in these animals. ? roups, according to the features you see in
hemselves according to the following modes 1ool.
ol in public vehicles. »l in private vehicles.
l cycling.
ised in your kitchen, and group them in the
ay.
;tal.
ISS.
belong to any of the above groups. 1 acquire the ability to separate and group
i according to the criteria given on the next page.
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Page 97
- i m
Students with a brother or a sister, Students who have two brothers
Students who have three brothers 4. Students who do not have brother
When you do the above activities you common property.
Grouping is possible in this manner bec could be definitely ascertained as belonging to
Therefore, when it is possible that a particular thing belongs a group is known as a "Set".
Things belonging to such groups are call are also known as “elements” of the set.
Let us consider the names given to those
Group 1.The group of animals including Cobra, Pyth 2. The group including Mynah, Parrot and Cro 3. The group of animals including Tiger, Deer
Compare how you have grouped the ar given to the groups.
Check whether there are any objects th belonging to any specific group.
S
Activity 10.4
See whether it is possible to group stu manner.
1. Students who are good in Mathem
Students who can sing well. Students who are short haired. Students who are good in long jur
Students who are tall. You will realize that it is not possible t belong to each of the above groups.
i m =
For free distribution
10 - Sets
or two sisters.
or three sisters. S or sisters.
will notice that each group has a
ause objects, children or animals etc.. - such particular groups. e to ascertain definitely to a certain group, such
led as the members of the group. They
e groups in activity 10.1.
Name of the Set. on and Viper
Set of snakes
Set of birds. and Dog.
Set of quadrupeds. nimals in activity 10.1 and the names
sw.
at cannot be definitely ascertained as
idents in your class in the following
natics.
np.
o definitely ascertain which students
85
Page 98
Mathematics - Grade 6
As an example, write the names o all the other students in your row to students who have cut their hair short, you have written and each of their lists. that these lists are not similar. The name in the lists of the others, and also there each of them. This means that members definitely ascertained.
Then, it is clear that such group ascertained are not sets.
S
Activity 10.5
Consider whether you could grou statements given below.
(i) Students who have scored
paper at the last monthly te (ii) Students who can jump mo (iii) Students whose height is o
You will realize that the meml ascertained, and therefore they are set Exercise 10.1 1)
Select from the following, those that cannot be ascerta
i.
Members of your fam ii. Days of the week. iii.
Good orators in your iv. Tall students in your v. Multiples of 3 betwee vi. Odd numbers betwee vii. The types of angles ti viii. Students who are we:
The poor people who X. Beautiful flowers.
1X.
86
of students who have cut their hair short. Ask write down different lists of names of such
without discussing with them of the names Compare such different lists. You will realize es that you have written in your list may not be will be differences among the lists written by belonging to a group of this nature cannot be
ps where the members cannot be definitely
ap the students in your class according to the
I more than 50 marks for the Mathematics est.
re than 2 metres distance. ver 130 cm. bers of the above groups can be definitely
those that can be ascertained as sets, and ained as sets. nily.
class.
class: en 0 and 10. en 0 and 25. hat you have learned. ak in Mathematics in your class.
live in your village.
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Page 99
(3). Write
xi. Major rivers in Sri Lanka.
xii. Colours of the rainbow. (2) Write 5 groups that can be terme
Write 5 groups that cannot be tei Additional Exercises
1. Separate the trees jak, arecanut, E
palmyrah, jamboo and margosa ir
suitable names for the two group 2.
Divide the directions, North Sou South-west, North-west and Wes rections. Separate the sports, soccer long i
metre race, chess, hockey, volle
into two sets you prefer. Suggest 4. Write the elements of the set of
Fill in the blank spaces in the elements of the sets.
3.
A set of flowers
Rose
. : :E
V.
vi.
vii.
viii.
ix.
X.
Summary
If a thing can be decided collection, that collection ca
For free distribution
K&S 1219 F.N-7
10 - Sets
.as sets. ned as sets.
teadfruit, coconut, jaggery palm, lime, o two groups as you prefer. Suggest two
S.
th-west, South-east, East, North-east, t to sets of main directions and sub di
ump, cricket, netball, high jump, 100
ball, putt shot, elle, 1500 metre race two suitable names for the two sets. lays of the week. table given below with appropriate
A.set of fruits
Oranges
efinitely as belonging to a certain a be termed as a set.
87.
Page 100
11 - FACTORS 11.1 Factors
1 1 2 3 4 2 2 4 6 8 1 3 3 6 9 1121
12
12)
18
NO)
28
10
Fig
1.
Let us learn about factors and multiples SActivity 11.1
Draw a 10 x 10 table as
complete it. 2.
Study the multiplication tabl of two numbers. 18 = 2 x 9 18 = 3 x 6 18 = 6 x 3
18 = 9 x 2 Observe how 8 is written as a pro
8 = 2 x 4 8 = 4 x 2
8 = 8x 1 2 and 9 are multiplied above to obta Likewise 3 and 6 are also factors
Also : 8 = 4 x 2 The factors of 8 are 1, 2, 4, 8.
88
AND MULTIPLES
7 8
9
10
6
(12
35
45
72
100
mure 11.1
shown above in your exercise book and
e and observe how 18 is written as a product
luct of two numbers in three different ways.
n 18. Hence 2 and 9 are called “factors” of 18. of 18.
8 = 1 x 8
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Page 101
Therefore, the same number and 1 are:
18 = 9
18 = 2
The number 18 is divisible by 2,3,6,9 clear that a factor of a number divides that ni
If a number is divisible by another second number is a factor of the first nun
z Activity 11.2
Using the 10 x 10 multiplication table, below, in as many ways as possible.
36,15,48,72,5 Exercise 1.1
Write all the factors of each of the num
(1) 10 (2) 16 (3) 18 (4) 36 (5) 72 11.2 Multiples
You have learned how to find the f multiplication table. Now let us learn about
In a 10 x 10 multiplication table 6,12,18,24,36,42,48, 54,60. We call these nu
In the same way 20, 30, 40, 50, 60, 70 Activity 11.3
With reference to the 10 x 10 multiplin 1. Write multiples of 3. 2. Write multiples of 5. 3. Write multiples of 9.
When a whole number is m whole number, the number is known as a multiple of th
For free distribution
11 - Factors and Multiples .ctors of any number.
18 = 3
18 = 6
ind without a remainder (see above). It is
nber without a remainder.
number without a remainder that ber.
write the factors of each number given
bers given below. |(6) 7 (7) 40 (8) 3 (9) 8
Pactors of a number using a 10 x 10
multiples of a number. e, numbers along the 6th line are
mbers multiples of 6. , 80, 90, 100 are multiples of 10.
cation table
ultiplied by another obtained as the product e first number.
89
Page 102
Mathematics - Grade 6 Exercise 11.2
1. Write the first ten multiples
Write the first five multiple Write the first ten multiples
Which number has the mult 5.
Write the first five multiple
Are multiples of 2 and 3 fo 7.
Write three other multiples 11.3 Divisibility
Let us find out whether there is divisible by 2, 5 and 10 without a remai
6.
:
Let us find out whether a number is
Refer to the 10 x 10 multipl Multiples of 2 are 2,4,6,8,1
Look at the digits in the uni Accordingly, when the la place of a number is 0,2,
is divisible by two withou Exercise 11.3
Write five numbers with tw 2. Write five numbers with thr 3. Is 1954 divisible by 2 ? Giv 4. Using the digits 3,2,5 write i 5.
Write all the numbers betwe remainder.
Write the dates of a mont
mainder. 7.
Write five multiples of 3 div
6.
Let us find whether a number is divisib
Activity 11.4
*
Refer again to the 10 x 10 n along the fifth line.
pf 4.
of 8. of 2. ples 7,14,21,28 ? - of 10. und in multiples of 8?
hat contain in the multiples of 5.
a method to find out whether a number is nder, without actually dividing.
divisible by 2. ication table. 5,12,14,16,18,20. its place. They are one of the digits 0,2,4,6,8. ist digit or digit in the units 4,6,8 then such a number ut a remainder.
ɔ digits, divisible by 2. ee digits, divisible by 2. e reasons. umbers divisible by 2 without a remainder. en 35 and 50, divisible by 2 without a
1 that can be divided by 2 without a re
sible by 2 without a remainder.
e by 5.
ultiplication table and write multiples of 5
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Page 103
* They are 5,10,15,20,25,30,35,40,4. * In the above multiples of 5, the last
Accordingly, if in any numb place is either 0 or 5, that n without a remainder.
Exercise 11.4
1. Write five numbers divisible by 2. Write five numbers between 50 3. Write four numbers with three 4. Write ten page numbers in your 5. Using digits 2,3,5,7 write numb
Let us find whether a number is divisibi
Activity 11.5
Write the multiples of 10 refe prepared. Check whether you have writte These numbers are divisible by
If the last digit or the digit i numbers is 0, then that nur
Exercise 11.5
1. Write multiples of 10 between
Write five numbers with three Write multiples of 10 between Write five numbers with four (
i m
For free distribution
11 - Factors and Multiples
50,......
ligits are either 0 or 5.
er the digit in the units umber is divisible by 5,
5.
and 100, divisible by 5. digits divisible by 5.
Mathematics textbook divisible by 5. sers with two digits divisible by 5. le by 10.
rring to the multiplication table that you
en10,20,30,40,50,60,...... 10 without a remainder.
n the units place, of a nber is divisible by 10.
50 and 100. Higits which are multiples of 10. 100 and 200. igits which are divisible by 10.
91
Page 104
Mathematics - Grade 6
5. Write two other numbers by
Additional Exercises
1. Write all factors of the numb
(i) 28 (ii) 42 (v) 60
(vi) 66 (1) Of what numbers are & (ii) Write the first five mul (iii) Write three multiples o (iv). Write all multiples of 1 From the numbers given bele without a remainder.
12, 15, 21, 26, 34, 37, 40, 55 4.
From the numbers given bele
without a remainder. 20, 25, 31, 40, 55, 62, 70, 84 From the numbers given belo
without a remainder.
20, 24, 30, 35, 48, 50, 70, 73. Summary
If a number is divisible by the second number is a fact
When a whole number is number obtained is a multi If the last digit of a num divisible by 2 without a ren If the units digit of any num 5 without a remainder. If the last digit or the digit that number is divisible by
*
*
92
which any multiple of 10 can be divided.
ers given below.
(iii) 54
(iv) 36 (vii) 80
(viii) 81 | 16, 24, 32 multiples? ciples of 9. ommon to 4 as well as 3. 1 less than 100. Dw find the numbers that are divisible by 2
, 68 and 98 Dw find the numbers that are divisible by 5
, 95 and 98
w, find the numbers that are divisible by 10
77 and 80
another number without a remainder, or of the first number. ultiplied by another whole number the ole of the first number. per is 0, 2, 4, 6 or 8, that number is
ainder. per is 0 or 5, that number is divisible by
1 the units place of a number is 0, then
0 without a remainder.
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Page 105
12 - RECTILINEAR
When we observe our environment, various shapes. The objects that you com sometimes those shapes are man made.
Activity 12.1
Select some objects that are easily a of matches on your exercise book and draw the different sides of these objects one by o as shown below.
Pencil
The ler
lid of a box of matches
(flat side)
Observe how a box of matches is positions. Draw along the edges around thi
Find some other objects and continue
Examples; A ruler, a small diary. containing various items, nails, nuts and bol bolts, nuts and bolts with heads, different sl The plane figures that are enclosed by stra plane figures”
B
Activity 12.2
When you go to a hardware shop y kinds of small objects. Draw the shapes of
For free distribution
PLANE FIGURES
ve see that it is filled with objects of across have shapes of their own, and
railable. Place one of them, say a box along its boundaries with a pencil. Draw ne in your exercise book using a pencil
igth of a box of matches.
The height of a box of matches.
placed on the exercise book in three e faces as shown in the diagram. this activity.
a small box of a cake of soap, boxes ts, tools used for tightening such nuts and nape of electrical plugs and switches. ght line segments are called “rectilinear
ou would notice that there are various some of these in your exercise book.
Page 106
Mathematics - Grade 6
You would have seen milk rice or pieces in your kitchen. Or else, imaginel
Draw in your exercise book the sh; Activity 12.3 Examine the shapes of planes in ot
Nuts and bolts
Арі milk
A stool
a piece of milk rice
A nail head. Af
Draw these shapes on a sheet of squ given. Draw separately the shape of the Eg: Picture frame wire attached to hang, Square net :- The diagrams shown below a
squares. z Activity 12.4
4
Diagra
a sweet meat like “ Aluwa” being cut into ow cakes are cut. pes of those sweets or pieces of milk rice.
jects given below.
ece of toffee
A window frame A window
curtain
picture frame
How a picture frame is
hung on the wall are ruled paper or graph paper in the order faces of different parts of these objects. glass of the picture frame etc. ire drawn on a background which is a net of
| 12.1
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Page 107
Consider number 1 of diagram 12.1. Th sides. It has 4 angles and 4 sides. What can you say about the length of sides? (Count the square opposite sides are equal and all the angles are called a rectangle.
In a Rectangle, the opposite s angle is a right angle. Now refer number 2 of diagram 12.1
Does it have the same properties as It seems that all angles are equal and equal.
Therefore, it is a square. Here, not only the opposite sides are e equal. Therefore, all sides are equal to one ai rectangle. That is why such a figure is called a
*
In a square, all sides are equa right angle.
Now refer number 3 of diagram 12.1. We triangle is a closed plane figure with 3 sides an
S
| Activity 12.5
Draw a few triangles on a square net, am equal, three sides equal and one angle is a right
A triangle is a closed plane figure with
S
* * * * *
Activity 12.6
Now refer to number 4 of diagram 12.1
Are the opposite sides equal in this Count the number of squares. Is at least one of the angles a right Is it a rectangle? You will realise th Let us find the distance between th
For free distribution
K&S 1219 EN-8
12 - Straight Lined Plane Figures s is a rectilinear closed figure with 4. say about the angles ? What can you s) In this shape, it can be seen that the right angles. This type of a figure is
ides are equal. Each
s number 1?
they are right angles and all sides are
qual, but the adjacent sides are also nother. This is a special situation of a square.
al. Each angle is a
call this type of diagram a triangle. A d3 angles.
Long which triangles with a two sides : angle.
ithree sides and three angles
figure?
angle? hat it is not a rectangle. e opposite sides.
Page 108
*
Mathematics - Grade 6
Look for the distance betv through 5 squares. Similarly, the distance bet Therefore, the distance bet Hence we call AB and DC Likewise, since the dis throughout, we say that If in a quadrilateral the parallelogram. Therefore
*
In a parallelogram, the equal. The pairs of opi
Use the above properties and dr:
Draw two straight lines w the relevant end points of formed. Draw two straight lines PC Draw another straight line parallel to MN. What can intersection of lines?
*
Find whether parallelogra
Activity 12.7 Consider number 5 of diagram 1 In the diagram (i) Are AB and
(ii) Are AD and (iii) What can yo (iv) What can yo
(v) Are all angle By using answers to the above parallel and all four sides are not equal a trapezium. The special feature here i
96
veen AB and DC. The two sides always pass
ween AD and BC is always 4 squares. tween AB and CD is the same throughout.
are parallel to each other. tance between AD and BC is the same
AD and BC are parallel. opposite sides are parallel it is called a ABCD is a parallelogram.
pairs of opposite sides are posite sides are parallel.
aw a parallelogram on a net of squares. ith equal lengths, parallel to each other. Join "the lines and see whether a parallelogram is
and RS with any length parallel to each other. - MN to intersect PQ and RS. Draw a line XY you say about the closed figure formed by the
ms could be drawn by any other method.
2.1
CD equal? BC equal? u say about the distance between AB and CD? u say about the distance between AD and BC? es in the quadrilateral equal? questions it can be noted that AB and CD are in length. A quadrilateral of this type is called is, that one pair of opposite sides are parallel.
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Page 109
Figure (i)
Figure Three trapeziums are shown in the three In Figure (i), two angles are equal. In Figure (ii), two sides are equal. In Figure (iii), sides are not equal, two
equal.
In all three figures above, only one pair You will see that it is sufficient for a qui opposite sides for it to be a trapezium.
A quadrilateral in which one are parallel is known as a tra Activity 12.8
Observe the quadrilaterals shown here a next page.
For free distribution
K&S 1219 F.N-9
12 - Straight Lined Plane Figures
Figure (iii)
= (ii) e figures above.
- sides are parallel and angles are not
of opposite sides are parallel. adrilateral to have two parallel
pair of opposite sides pezium.
nd fill in the table 12.1 given on
97
Page 110
Mathematics - Grade 6
Type of
quadrilateral
1. Square
2. Rectangle
3. Parallelogram
4. Trapezium
5
Exercise 12.1
1. Write 3 rectangular shape
see in your day-to-day life 2. Write 3 objects with triang 3.
Give an example for a par 4.
Draw in your exercise boo the roads.
Mother prepared milk ric Dinal saw that pieces of m “These pieces of milk rice Then Amal said, "I can di by cutting them in triangi I.
Show separately 1 triangular shapes o Dinal's father who is give me a small piec the shape of the tra
cut. In bridges, roofs of buildin towers you see a special d Draw a diagram to illustra
98
Figure number
Table 12.1
d objects and 5 square shaped objects that you
gular plane shapes. allelogram and for a trapezium. k, the shapes found in highway sign posts along
e and cut it into pieces. Amal and his brother ilk rice were cut in the shape of parallelograms. e are too big. We will eat half each” Dinal said. vide the piece of milk rice into two equal pieces alar shapes or parallelogram shapes”. how the pieces of milk rice were cut into
r parallelogram shapes. a teacher said “I needed only a small piece. You ce triangular in shape. You take the piece with pezium”. Show the piece of milk rice Dinal
gs, iron purlin, electric pylons and transmission Listinct plane figure. What is that plane figure? te one. You see that these structures are strong.
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Page 111
7. Fill in the blanks.
(1) The four sided figures in a ch
shape of
A vesak lantern with six squa
shapes and... (iii) A volleyball ground is of the (iv)
. takes the shape
В.
***.... sha
8.
Copy the parallelogram on to a sh and separate triangle DEC. Examine the shape of ADEB. Place the triangle DEC so that DC Examine the shape of ADEF. Fill in the blanks below with suitab (i) ADEB has the shape of ......
ADEF has the shape of .......
Additional Exercises
Find true statements from the follo (1). A triangle is a closed plane fi (ii) In a square, all angles are rig (iii) In a rectangle, all angles are (iv) In a square, all sides are equa (V) In a rectangle, all sides are e (vi) In a parrallelogram, the oppo
For free distribution
12 - Straight Lined Plane Figures
ness board or a draught board take the
re faces (Ata pattam) has ... apes. e shape of a .. e of a parallelogram.
neet of paper. Cut along the line DE
falls along AB.
le words.
swing statements. igure.
ht angles. right angles.
al.
qual.
osite sides are parallel.
99
Page 112
Mathematics - Grade 6
(vii) In a trapezium, oppo (viii) In a rectangle, oppos (ix)In a parallelogram, (x) In a trapezium, oppo Observe the diagram given
In the above diagram,
(i) there are (ii) there are (iii) there are (iv) there are . (v) there are
Summary
In a rectangle, the oppo angle. In a square all sides are In a parallelogram the o
A quadrilateral in which trapezium.
100
psite sides are equal. site sides are parallel. opposite sides are equal. psite sides are parallel.
below and fill in the blanks with suitable words.
*
squares.
rectangles. .. parallelograms. .. triangles.
... trapeziums.
osite sides are equal. Each angle is a right
equal. Each angle is a right angle. -pposite sides are equal and parallel. a one pair of opposite sides are parallel is a
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Page 113
13 - DEC
13.1 Decimals Let us do the following activity to learn abo
a Activity 13.1.
Figure 1 Prepare a strip of paper from a square Figure 13.1. Colour one part in the s 10 equal parts. Paste this in your boo The cage you have coloured is one ter
Figure 1 In Figure 13.2, the fraction coloured
When a unit is divided into 10 parts a 10 or as a decimal 0.1.
Figure 1 When 2 parts of the unit is considerd i decimal 0.2.
is expressed as zero point on
10
is expressed as zero point tw
For free distribution
CIMALS
put decimals.
3.1 e ruled sheet of paper as shown in -trip of paper which is divided into -k. You may colour any cage. ath or of the whole figure.
3.2
is 1
| 10
nd 1 part is taken, that is expressed as
3.3
that is expressed as
1.
or as a
2 (0.1)
ro (0.2)
101
Page 114
Mathematics - Grade 6
10 is expressed as zero point thre In the diagrams 13.1, 13.2 and 13
coloured, the fraction would be
Figur
The coloured parts in Figure 13.4 a expresed as 1.3.
Activity 13.2 Representing a decimal on an Abacus
100
10 Draw the above abacus in your exe
In the abacus on the left of units pla
Now consider the abacus shown be
100
10
The number shown in the above al
100
10
Can you write the number shown in the 23.4. It is read as twenty three point fou
102
ee (0.3) .3 if all the cages were 2. That is a complete unit or 1.
e 13.4 are, a unit and three decimals which is
| 1 ercise book.
ce are 10, 100 and on the right is = or 0.1.
elow. Draw them in your exercise book.
pacus is 3.2. It is read as three point two.
10
above abacus? You can see the number is
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Page 115
Observe a metre ruler
mmmmmmET
TTTTTTTTTTTTTTT
2 3
4
cm
A section of a
1 cm is divided into 10 equal pa when you look in the ruler not between any two consecutive
One part of the division of 1 cr expresed as 0.1 cm or “zero po
Exercise 13.1
1. Show each of the following dec
(i) 0.3 (ii) 0.7 (iii)
Write each of the following nu them on abacus. (i) 0.7 (ii) 0.9 (iii)
Write each of these numbers us (i) Three point six. (ii) Two point two. (iii) Twelve point one. (iv) Three hundred eight and i (V) Eight hundred ninety and
Write each of these lengths by n (i) The length of a pencil. (ii) The thickness of Grade 61 (iii) The length and width of th (iv) The length of a carbon per
4.
For free distribution
13 - Decimals
TTTTTTTTTTTTTTTTTTTTTTT",
metre ruler
rts. You can observe divisions like this
only between lcm and 2 cm but also, e centimetre divisions along the ruler.
n to ten equals cm. This could be
int one cm”.
imals by diagrams. 1.2 (iv) 2.5
mbers in words and show each of
12.7. (iv) 3.8 (V) 24.6. . ing digits.
point eight.
point nine.
measuring them.
Mathematics text book. e teacher's table.
103
Page 116
Mathematics - Grade 6
13.2 Comparison of D Do the following activity about compar
s Activity 13.3
0 = 0.3
Draw the above figures in your ex When we compare the fractions, v That is 0.5 > 0.3. | Similarly, as n > 1 then 0.7 >
Hundredths
SActivity 13.4
Answer the following questions i (You can draw a grid as shown below.)
1 2 3 4
10
1. How many columns are ther 2.
How many rows are there in 3.
Into how many squares is a Into how many squares is ar Accordingly how many squi Write the coloured area as a
104
ecimals cing decimals.
= 0.5
Lercise book.
ve see that
|un
aw
D.4.
n accordance with the 10x10 grid.
5 6 7 8 9 10
ce in the grid? a the grid?
column divided? Fow divided? ares are there in all ?
fraction if 1 square is coloured.
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Page 117
Write the fraction if 5 squares are o 8. Write the fraction if 25 squares are 9. Write the fraction if 38 squares are 10. Write the fraction if 40 squares are Activity 13.5
Using the answers obtained for the questi fill in the following table.
| No. of squares coloured
Fract
40
is written as 0.01. It is read as "zer
100
is written as 0.05. It is read as “zer
100
38
is written as 0.38. It is read as “zer 100 40
is written as 0.40. It is read as “zer 100 Example 1
Observe that 0.38 appears to be different Illustrate 0.38 on an abacus.
Hundreds place Tens place Units place
100 100 10
For free distribution
13 - Decimals. AgrioS.E.
coloured.
coloured. coloured. coloured.
ons in the above activity 13.4,
ion coloured n the grid
o point zero one”.
o point zero five”.
o point three eight”.
o point four”.
from the other numbers.
· Tenths place Hundredths place
10
100
105
Page 118
Mathematics - Grade 6
=
SIR
38 3 0.38
100 10 = 0.3 + 0.08 Example 2
Compare 0.75 and 0.48
75.
48
100 and ad
75 42
100 > 48
Illustrate these on the abacus.
0.1 0.01
10 110 100
2.
0.75 In 0.75, the tenths place value is
Therefore, 0.75 > 0.48. Exercise 13.2
1. Illustrate each of these de
(i) 0.45 (ii) 0.81.(
Insert the correct symbol > . (i) 0,7.... 0.8 (ii)
(iv). 1.6 ....1.7(v)
(vii) 12.6 .... 10.8 3. Insert the correct symbols
(i) 0.78 .... 0.48 (
(iv) 0.38 .... 0.09 ( 4. Compare these decimals u
(i) 0.5 and 0.72 (ii (iv) 0.8 and 0.94 (v)
Illustrate the above pairs o
106
0
0.1 0.01
10
10 1 1 1
10 100
0.48 greater than the tenths place value of 0.48.
cimals on the abacus. iii) 1.87 (iv) 2.25. > or < in the blank spaces. - 0.3 ....0.2 (iii) 0.6 .... 0.4 - 2.3 .... 1.9 (vi) 1.8 .... 2.6
> or < in each of the followings. ii) 0.45 .... 0.48 (iii) 0.79 .... 0.72 (v) 0.08 .... 0.01
sing symbols > or <. - 0.35 and 0.4 (iii) 0.38 and 0.30
0.79 and 0.8 (vi) 20.34 and 20.29 -f numbers on abacus and compare each pair.
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13.3 Addition of Decimals
Consider adding 12.8 and 2.45
Method 01:
12.8 = 12+
12.8
245 = 246 160
|2 + 2 <
, 8, 4 5 12.8 + 2.45 = 12 + 2 +
10
+
| + O
10
= 14 + 2 100
= 14410, 2, 5
|| || ||
**10* 10 * 100
= 15+ 2 5
= 15+ 0* 100
= 15.25
Method 02:
Let us add illustrating on the abacus.
Tens Unit Tenths. Hundredth
10 1 0 100
10 1.
10
100
= 15.25
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13 - Decimals
Ten
Units
Tenths Hundredths
Lo 1 10 100
107
Page 120
Mathematics - Grade 6
Add using place values.
Tens place
Units place 1
1
| 2
12.80
2.45
Un N
Method 03:
First write one number under th number is under the decimal point of places relevant to the place values of
12.8
Now add 2.45
should b 15.25 Add 4.32 and 256.9
4.32 256.9
261.22 Exercise 13.3
1. Add the following number
(i) 0.49 and 0.69 (ii) Using the abacus or place
(i) 25.25 and 21.22 (ii) 3.
Solve the following proble under the other correctly. (i) Amal drewa line 35.2
What is the length o: (ii) The height of a stude
height, and marks a
Find the distance fro (iii) 125 ml of water is ad
volume of the mixtu
108
Tenths Hundredths place
place
N A 00
transfer to units place
10
84. 12
10' 10101 e other number. So that the decimal point of one the other number. Numbers should be written in numbers.
as addition of whole numbers. Decimal points e kept one under the other as shown here.
S.
1.43 and 20.58 (ii) 1102.9 and 3.65 value, add the following numbers.
28.49 and 35.67 (iii) 408.34 and 294.99 ms. Add the numbers given writing one
2 cm long. It was extended by 1.53 cm. f the line now? nt is 129.3 cm. He gets on to a chair 45.4 cm in
point on the wall at the same level as his head is. m the floor to the point marked. ded to 5.5 ml of fruit juice. What is the total re?
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Page 121
(iv) 300 g of flour, 125 g of su
together to prepare a cake.
13.4 Subtracting Decimals
Subtracting by expansion: Subtract 10.48 from 25.42.
25.42
= 25 + 10* 100
| || || ||
+ +
10.48
= 10+-+-
o 10' 100
4 4
25.42 – 10.48
25- 10+10 10
|| ||
| 28 = 15+0+-
"100 100
100 28 = 14 +-+
100 100 10
94 = 14 +-
100 = 14.94
|| ||
Subtracting using placé values.
Tens
Units place
place
Tei
25.42
5 - (1)
10.48
| 10 3 | 10' 10
Answer } 14.94
For free distribution
13 - Decimals gar and 5.5 g of salt are mixed
What is the total mass of the mixture?
100 100
| "
aths place
Hundredths
place
> 10
10
4 - (1)
4
00
4
16
10
| 10. 2 8 4
100 100 100
100
109
Page 122
CATE
Mathematics - Grade 6
Subtracting using place value: Example 1: Now let us consider subtrac
162.81
Let us – 27.82
Write th | 134.99
The de Now, s decima
Example 2: Consider subtracting 7.82
162.3
7.82
162.30
– 7.82
As there ar
154.48
write a zer
whole nun Exercise 13.4
1.
Expand these numbers and s (I) From 62.3 subtract 22. (II) From 15.43 subtract 10 (III) From 120.25 subtract 1 Simplify using any method.
2.
(i)
(ii)
12.75 1.69
238.3 – 120.45
3. A bottle contains 750 ml (r
removed from this, find the
Thousandth Parts
10 can be expressed as 0.1, 100 Similarly good can be expressed as o
110
sing 27.82 from 162.81.
write as we did for addition. ne two numbers as shown on the left. cimal point should be one underneath the other. ubtract as for whole numbers and place the 1 points correctly .
- from 162.3.
re two decimals in the subtrahend (7.82) -o to get 162.30 and subtract as for
abers.
ubtract.
1.94 0.3
(iv)
(iii)
120.34 - 22.22
107.45 – 100.01
millilitres) of water. If 25.05 ml is volume of water remaining.
can be expressed as 0.01.
.001.
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This can be shown using a square gric parts. This division will give 1000 squa
- = 0.001. It can be expressed as 0.00 1000
1 2 3 4
= 0.001
1000
It is read as zero point zero zero one.
can be shown on an abacus as fi 1000
100
| 10
10
1.025 can be shown as.
100 101
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13 - Decimals Divide one small square into 10 equal es. One strip in the small square is
5 6 7 8 9 10
bllows.
100
1000
10 100 1000 100
1000
Page 124
Mathematics - Grade 6
Write the number shown on the a
Hundreds
Tens
0000
100
10
It is 145.342 Exercise 13.5
1. Add.
(i) 78.321 + 10.001
3 +| || SM ||
(iv)
12.753 + 4.639
Subtract.
(i)
7.254 3.141
* 2 || - E.
(iv) 325.823
· 123.457
13.5 Conversion of decima
You have expressed fractions as deci now convert decimals into fractions.
112
pacus.
Units
Tenths
Hundredths Thousandths
soood
ooo -19
1
100
1000
0.001 0.002
(iii)
20.341 + 30.002
5.608 2.792
(vi)
104.732 + 324.543
1.001 1.101
(iii)
100.345 - 99.453
(vi)
3.405
30.3
2.345
5.352
Is into fractions
nal. Let us
0.01 is 100
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Page 125
0.02 is 100 = 100 + 2 = 50
op i 2. 2+ 2 - 1
2:2
37.103 = 37 103
1000
4:4
0.04
04 100
100 = 4
08
1.08
1+
844 100 : 4
= 1
100
Exercise 13.6
Convert the following decimals into fr (i) 0.002
(ii) 0.062 (v) 1.832
- (vi)7.24
Additional exercises
Show each of the following on a
(i) 715.8 (ii) 1.75 2.
Rewrite the following in the ascend (i) 0.7, 0.69, 0.93, 0.78 (ii) 12.95, 20.07, 12.59, 20.75 (iii) 1.75, 25.325 Add. (i) 4.307
6.07 + 1.729
+ 3.4!
4. Add.
(i) 12.078 + 1.6 + 2.34 (ii) 3.24 + 2.785 + 6.7
For free distribution
13 - Decimals
23
actions.
(iii)0.3
(iv)0.34
(vii) 6.22
(viii) 121.12
ubacus.
(iii) 25.325 ling order.
O un
(iii) - 1.8
+ 14.52
3.078
113
Page 126
Mathematics - Grade 6
5. Subtract,
6.078 - 2.439
(ii) 1:
- 11
7.
Convert each of the followi (1) 5.21 (ii) 3.8 The height of a box is 20.5cr on the first box. A third box o
Find the total height of all tl 8.
A tank contains 15.30 litres (
is added to it, find the total q 9.
A ribbon is 12.25 metres lo
remaining part if 8.38 metre 10. Three pieces weighing 0.171
from a piece of cake weighir part remaining.
Summary
One tenths of a unit is knov One tenths, one hundredth as decimals.
**
When writing a number in important.
Decimals can be written as
114
708 1987
(iii 1.402
- 0.394
ng into fractions. 51 (ii) 12.75
(iv)7.005 1. A second box of height 15.8cm is placed
5.3 cm in height is placed on the second box. aree boxes. of water. 5.75 litres and 8.32 litres of water
uantity of water in the tank now. ng. Find the length of the s are cut off. kg, 0.185 kg and 0.22 kg were cut off ng 1.285 kg. Find the mass of the
vn as a decimal of the unit. 5, one thousandths of one can be shown
decimal form the decimal point is very
fractions.
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Page 127
14 - TYPES O
14.1 Odd numbers and Even
You would have noticed persons cour etc. count in twos. The person who counts .calls 'two' and puts another two; He calls th
Number called
u P w N -
25
50
When one counts like this up to 50, the it is counted in twos the heap of nuts, becon
|2 = 2x1
4 = 2 x 2
Even numbers
2,4,6,8.... are multiples of 2, and are di
We get these numbers by multiplying These numbers are called, “Even numbers
Numbers which are divisible even numbers.
S
Activity 14.1
Write all numbers from 1 to 25 ar remaining numbers as 1,3,5,7,9 .....25.
Now divide each of these numbers t What is the remainder ?
For free distribution
E NUMBERS
numbers
ting coconuts, fruits, arecanuts, cashew calls 'one' and puts aside two nuts, he ree and puts another two and so on.
Number of nuts.
10
50 100
number of nuts in the heap is 100. Since nes 2,4,6,8,....100
6 = 3 x 2 50 = 25 x 2
visible by 2. each counting number (1,2,3,4....) by 2.
e by 2 without a remainder are
d cross the even numbers. Write the
y 2. Are those numbers divisible by 2?
115
Page 128
Mathematics - Grade 6 Odd numbers
All the numbers 1,3,5,7,9.......25... divisible by 2 are odd numbers. All evei form counting numbers.
Numbers when divided b one are odd numbers.
B
Activity 14.2 Write all counting numbers from 1 1, 2, 3, 4
T- - T
------
1 2 1 4 6 8
| 3
| 5 Write the even numbers along a li
line.
You would notice that beginning fr
An even number+ 1 → A An odd number +1 + A
Activity 14.3
Add any two even numbers as shov of two even numbers?
2 + 6 4 + 6 2 +8
2 + 2
10 + 22 =......
The resulting number is an even nu
When two even numbers are ac
116
. are called "odd numbers”. Numbers not
numbers and odd numbers taken together,
y 2 leave a remainder of
to 25.
- - - - -
25
ne. Then write odd numbers along another
om 1, every other number is an odd number. nodd number n even number
vn below. What can you say about the sum
nber.
ded the sum is an even number.
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Page 129
Activity 14.4 Add any two odd numbers and see whet
1+3
9 + 1 3 + 5
11 + 1
You would notice sum is an even numbe
When two odd numbers are ad number.
Now let us see what happens, when an e added.
Activity 14.5 Observe the resulting numbers of the foll 1 + 2 3 + 6 5 + 4 =.
The result is an odd number. When an even number and an the result is an odd number. Activity 14.6 Now let us multiply an even number by a 2 x 4 = ........
4 x 8 = 4 x 6 =
6 X 4 = When two even numbers are the result is an even number
Activity 14.7
Now let us multiply an even number by : 2 x 3 = .
4 x 5 = 6x1
2x7 =
=
For free distribution
14 - Types of Numbers
er the sum is odd or even.
3
ded the sum is an even
ven number and an odd number are
owing.
odd number are added,
n even number.
multiplied together,
in odd number.
117
Page 130
Mathematics - Grade 6
When an even numbe number the result is al
Activity 14.8 Now let us multiply an odd nun 1x 3 |3 x 5 7x1 7 x 3
When an odd number number the result is ar The first even number The second even number 4 The third even number Now find whether there is any The 20heven number, 2 x First odd number 1 + (2 Second odd number 3 » (2 Third odd number 5 + (2
Tenth odd number19 » (2 Exercise 14.1
1. When even numbers are v 2. What is the eighth even ni 3. Is the sum of the two num 4. Is the product of those tw 5.
Using your knowledge of number,
When the even numbers a
What is the 5th odd numbe 8.
What is the 7th odd numbe 9. Is the sum of 5th odd numi
7.
118
ris multiplied by an odd n even number.
aber by an odd number.
is mulitiplied by an odd a odd number.
→ 2 x 1 = 2 -> 2 x 2 = 4
→ 2 x 3 = pattern.
20 = 40. "x 1) - 1 = 1 X 2) - 1 = 3 x 3) - 1 = 5 x 10) - 1 = 19
yritten in order what is the position of 10? Imber ?
bers 10 and 16 odd or even ? ɔ numbers odd or even ? :ven numbers, find 10th odd number and 8th odd
re written in order, what is the position of 50? r?
r?
ver and 7th odd number odd or even?
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Page 131
10. Is the product of 5th odd number an 11. The product of two numbers is 130.
find the position of the other numb
Number patterns
S
Activity 149
Find some objects of the same size such place them according to the patterns given belo
A number can be shown by dots, balls, cr
1 square
2 squares door = 0
squares
OD
OD
3 squares Doo or for
3 squares
ODD
4 squares DOOD or
DOOD
A Activity 14.10
Refer to activity 14.9 above. Connect pairs of squares in each formation.
A BABE
A O
For free distribution
14 - Tjipes of Numbers 17th odd number odd or even?
If one number is the Steven number, er in the order of odd numbers?
as madder or gram seeds etc. and
Osses, Squares, triangles etc.
口
- 。 or
口 or 口 or 口
口口
口 口
口 口 口。口口 or 口 Or o口 To ab口口
or
日g 口 口 口 日向可口白
119
Page 132
Mathematics - Grade 6
E
出口出出出
E
E
GE
Draw figures to represent some pairs of squares.
Note the following. Numbers 2,4 do not leave a sing Numbers 3,7 leave one square i
14.2 Square numbers.
The numbers can be arranged a
4 is a square.
Number of ro Number of co :. Number of
Number 9 is square.
Number of rows = 3, Numbe
... Number of of rows = Nun
Numbers 16,25,36 are squar
These numbers are known as “ obtained by multiplying a number byt Number 1 is a square number to
1x1 = 1 |2 x 2 = 4 3 x 3 = 9
120
“” 。
E HE口HE | ロ
ロロロロロロ曰
other numbers as shown above and connect
gle square left unconnected. inconnected.
s above method to show different patterns.
ws is 2
2×2 口 口
lumns is 2
口口 'rows = Number of columns
口 口 口 口 口 口 口 口 口
r of columns = 3 1ber of columns.
es also. square numbers”. These square numbers are
he same number.
00.
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Page 133
4 x 4 = 16 5 x 5 = 25 9x9
10 x 10 = 14.3 Triangular numbers
BActivity 14.11
Have you noticed how objects like so: packets of biscuits etc. are arranged on the sl in your book.
3 can be arranged as
6 can be arranged as The numbers that can be represented i triangular numbers.
Such numbers are called triangular First triangular number is 1. Second triangular number is 3. Third triangular number is 6. (1) 1 = 1 First triangular nu (2) 1 + 2 = 3 When 2 is added
triangular number (3) 3 + 3 = 6 When 3 is added
triangular number (4) 6 +... = 10 To obtain fourth tr.
to the third triangu (5) .... + 5 = 15 5 added to whicl
triangular numbe Exercise 14.2
1. Write the first eight square numl 2. Square of what number is 100?
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14 - Types of Numbers
up, canned fish, cartons of milk powder, helves of a grocery ? Draw such patterns
This takes a triangular shape.
This takes a triangular shape. na triangular pattern are called
numbers.
mber to the first triangular number, second - is obtained.
to the second triangular number, third is obtained. Tangular number, what should be added
lar number ? a triangular number gives the fifth er?
pers.
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Mathematics - Grade 6
3. Show the first 6 triangular i
----
4. Write the seventh triangula. 14.4 Prime numbers
Consider the factors of 2, 5, 7, 11 2 = 2 x 1, 1 x 2 5 = 5 X 1, 1 X 5 7 = 7 x 1, 1 X 7 11 = 11 x 1, 1 x 11
The above numbers cannot be exp other than as a product of 1 and the sam of 7 aré 1 and 7 and factors of 11 are 1
Numbers which have only one pa numbers”.
Activity 14.11
Write numbers from 1 to 30. Follo
( 1 2 3 4 5
11 12 13 14 15 21 22 23 24 25
Circle number 1 above. Leave 2 and encircle all mul Leave 3 and encircle all mul Leave 5 and encircle all mul Leave 7 and encircle all mul
The numbers remaining unc 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
* * * * * *
122
numbers using dots.
III
| 1
r number and the eighth triangular number.
ressed as a product of two factors in any way ne number. Factors of 2 are 1 and 2. Factors and 11. ir of distinct factors are known as “prime
Dw the order shown below.
6 7 8 9 10 16 17 18 19 20 26 27 28 29 30
tiples of 2. This step is done as shown above. tiples of 3. tiples of 5. tiples of 7. ircled at the end are prime numbers. ............... are prime numbers.
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Page 135
Numbers with only two d prime numbers.
14.5 Composite numbers
Composite numbers are numbers that har Factors of 6 are 1, 2, 3 and 6. Factors of 18 are 1, 2, 3,6,9 and 18. Factors of 150 are 1, 2, 3, 5, 6, 10, 15
S
| 12
Activity 14.12 4 = 4 x 1
= 1 x 4
= 2 X 2 The factors of 4 are 1,2 and 4. Th
In the same way write the factors of e distinct factors are known as “Composite” ni
Exercise 14.3
1. Write all prime numbers from 30 2. Consider the following set of nuw
3, 4, 5, 6, 7, 8, 9, 10, 25, 35, 50, (I) What are the prime numbe (II) What are the composite nu
Write down the first and seco1 numbers.
Write down the composite numb numbers.
Write down the composite nu numbers too.
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14 - Types of Numbers
stinct factors are
e more than two factors such as 6, 18, 150.
25, 30, 75, 50 and 150.
12 x 1
= 6 X 2
= 3x4 e factors of 12 are 1, 2, 3, 4, 6 and 12.
5,9,8,10. Numbers with more than two umbers.
O to 50.
mbers. 51, 54, 55 rs among the above numbers? umbers among the above numbers.? nd odd numbers which are composite
ers less than 20 which are also triangular
mbers less than 36 which are square
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Page 136
i m
Mathematics - Grade 6 Additional Exercises
1. Write the even numbers be
Write the odd numbers beti Fill in the blanks. (i) Sum of two even nun (ii) Even number added i (iii) ..................... added t (iv) Sum of any two consı Write the 30th even number
Which number squared is 6 6.
Write the 8th triangular num 7. How many even prime nun
Write 36 as a product of tw
Write 90 as a product of pri 10. Find examples for a square i
a composite number. Summary
Numbers divisible by two Numbers with a remaino numbers.
When all even numbers al of counting numbers.
When one is added to an odd number.
When one is added to an even number. The sum of any two even
When an even number resulting number is eve When an even number resulting number is eve If a number is divisible by number. Numbers that would be a as triangular numbers. Numbers which have moi composite numbers.
* Nu
124
ween 25 and 35. veen 10 and 50 which are also multiples of 5.
abers is an ............. number.
o an ..................... gives an odd number. o an odd number gives an odd number. ecutive whole numbers is an...........number.
and 30"odd number. 4?
ber.
abers are there ?
o factors in different ways.
me numbers. number, triangular number, even number and
are even numbers. ler of one when divided by two are odd
nd all odd numbers together form the set
even number, the resulting number is an
odd number, the resulting number is an
number is an even number. is multiplied by an even number, the n. is multiplied by an odd number, the
n.
1 and the number itself only, it is a prime
rranged in a triangular shape are known
e than two distinct factors are known as
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Grade 6 - Math
Syllabu
Content
Learning Outcome
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 and writes na Identifies what each Recognizes negative on a number line Uses the vocabulary Gives a number that Gives an estimate o Approximates a num Classifies odd and products of odd and Identifies prime num Identifies composite Identifies number numbers. Adds and subtracts i Multiplies and divide numbers. Finds factors and my Recognizes divisibili
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
1.2
1.1.13. Factors and Multiples 1.1.14. Divisibility
Fractions 1.2.1. Unit Fractions and
proper Fractions 1.2.2.
Equivalent Fractions 1.2.3.
Comparison
Identifies unit fractio Finds equivalent fra Compares unit fracti related denominator Adds and subtracts u nators (answer limite
1.2.4.
Addition and Subtraction
1.3 1.3.1.
Decimals Concept
Recognizes decimal represents) Compares and orde Adds and subtracts
1.3.2. 1.3.3. 1.4.
Comparison Addition and Subtraction Indices
Notation Powers
1.4.1. 1.4.2.
Recognizes and use Expands a power. E> (numbers less than prime factors
Understands the cor
Writes a ratio in sim Applies rates in tran
1.5
Ratios 1.5.1. Concept 1.5.2. Simple form
1.5.3 Rates 2.0 MEASUREMENT
2.1
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
Understands distanc Uses mm, cm, m, kn Convert mm ,m cm i Estimates distance,
Measures lengths Finds the perimeter
Understands area as of the surface of a si Uses cm2 to measu Finds the areas of se
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, kg appropria Converts g kg Add and subtracts m
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ematics
tural numbers up to a billion in words and in figures
digit in a number represents e numbers and represents natural numbers and integers
and symbols (>.<. =) to compare and order integers lies between two numbers Fa countable number of items aber less than 100 to the nearest 10 even numbers. Identifies prosperous of the sums and even numbers bers numbers patterns including triangular numbers and square
natural numbers es natural numbers by 10, 100, 1000 and by two digit
ultiples of numbers using a 10 x 10 number grid ty by 2,5 and 10
ns and proper fractions ctions
ons, fractions with equal denominators. Fractions with
unit fractions with equal denominators. With related domied to proper fractions)
numbers (knows what each digit in a decimal number
rs decimal numbers decimal numbers
s index notation
Page 138
Mathematics - Grade 6
Learning
Content
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, Converts Adds and
2.5.2. Twenty Four Hour Clock
Understar Uses sece tionships Reads tin clock time Uses the
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
Recogniz Recogniz
Classifies angles or
3.2.
Solids 3.2.1. Cube, Cuboids,
Regular Tetrahedrons
Creates o as the nur Cuboids a
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 Construct
Recogniz trapezium
4.0 ALGEBRA
4.1.
Symbols 4.1.1.
Unknowns 4.1.2.
Variables 4.2.
Algebraic Expressions 4.2.1. Construction
Represen Identifies
Construct using add variable ir
5.0 STATISTICS 5.1.
Data handling 5.1.1. Collection
5.1.2. Representation 5.1.3.
Interpretation
Collects d tabulates Represen Interprets
discussion
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 gr Names gr
Identifies t
Working Mathematically
Revises and develops the vocabulary related to Develops and refines written methods for additi ods, how to layout composition Understands the operation of multiplication and Knows to apply the associative and commutati Recalls multiplication facts and derives the cor Knows and derives rapidly doubles and halves Checks answers by doing the inverse operatior Uses tests of divisibility to check answers Develops and uses mental strategies
126
Outcomes
1 to measure capacity
ml | subtracts measurements with both I and ml
nds time and duration onds, minutes, hours and days appropriately and knows their rela
ne on a 24-hour clock and converts 12 hour clock time to 24 hour e and vice versa
date in standard form
es and uses the eight directions es the horizontal and the vertical
angles as right angles or acute angles or obtuse angles or straight reflex angles by comparing with right angles
ubes, cuboids and regular tetrahedrons identifies properties such mber of vertices. Number of edges and number of faces of cubes. and regular tetrahedrons
circular shapes in physical objects s circular patterns using physical objects such as bangles, coins etc.
es and draws triangles. Squares. Rectangles. Parallelograms and is in a grid.
ts unknowns by algebraic symbols variables and represents them by algebraic symbols
s algebraic expressions with one variable (coefficient equal to 1) ition and subtraction Converts and algebraic expression with one ito a numerical value by substituting natural numbers
ata of not more than five kinds and less than hundred values and it using tally marks ts data by tables and pictograms data represented by tables and pictograms Interprets results through
oup of objects by similar attributes oups of objects using common attributes
he likelihood of an event occurring as certain. Impossible or probable
i numbers, measures, geometry, algebra, statistics and probability. on and subtraction - correct layout of sums, standard written meth
1 its relationship to addition and division ve laws responding division facts quickly
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