MATHEMATICS

Standard III

Part - 2

Government of Kerala
JT 537-1/ MATHS-3 (E) (Vol-2)

DEPARTMENT OF EDUCATION

State Council of Educational Research and Training (SCERT), Kerala

2015
 THE NATIONAL ANTHEM
Jana-gana-mana adhinayaka, jaya he
Bharatha-bhagya-vidhata.
Punjab-Sindh-Gujarat-Maratha
Dravida-Utkala-Banga
Vindhya-Himachala-Yamuna-Ganga
Uchchala-Jaladhi-taranga
Tava subha name jage,
Tava subha asisa mage,
Gahe tava jaya gatha.
Jana-gana-mangala-dayaka jaya he
Bharatha-bhagya-vidhata.
Jaya he, jaya he, jaya he,
Jaya jaya jaya, jaya he!

PLEDGE
India is my country. All Indians are my brothers and
sisters.
I love my country, and I am proud of its rich and varied
heritage. I shall always strive to be worthy of it.
I shall give respect to my parents, teachers and all elders
and treat everyone with courtesy.
I pledge my devotion to my country and my people. In
their well-being and prosperity alone lies my happiness.

Prepared by :
State Council of Educational Research and Training (SCERT)
Poojappura, Thiruvananthapuram 695012, Kerala
Website : www.scertkerala.gov.in
e-mail : scertkerala@gmail.com
Phone : 0471 - 2341883, Fax : 0471 - 2341869
Typesetting and Layout : SCERT
First Edition : 2014, Reprint : 2015
Printed at : KBPS, Kakkanad, Kochi - 30
© Department of Education, Government of Kerala
Dear students,
Numbers, figures, patterns!
We are into a new world of math.
Let’s learn math to add, to subtract,
to multiply.
Let's go on, playing with our friends,
enjoying ourselves, finding out new
things, correcting mistakes.
Let’s move ahead with confidence and
get ready for more exciting math!
With best wishes,

Dr. S. Raveendran Nair

Director
SCERT Kerala
 TEXTBOOK DEVELOPMENT TEAM

PARTICIPANTS
Vasu K.G.
Ashraf C.V.
AEO (Rtd.) Tirur
Asst. Teacher, Vanimel UPS, Kozhikkode
Syam Kumar
Unnikrishnan M.V. HSA, JNHS Kadukulanhi
HSA, GHS Kumbla, Kasaragod
Sambasivan
Prasanth K.P.
Master Trainer, IT@School
UPSA, Devadar UP School, Nediyirupp,
Thiruvananthapuram
Malappuram
Suresh C.
Narayananunni M.P.
Trainer, BRC Thanur, Malappuram
Lecturer, DIET Palakkad
EXPERTS
Dr. Radhakrishnan Chettiyar
Prof. (Rtd) University College, Thiruvananthapuram
Baiju S.
Asst. Prof., Govt. College, Karyavattam, Thiruvananthapuram

ARTISTS
Harikumar K.B
Kunhiraman P.C
Kazhakoottam, Thiruvananthapuram
DIET Ernakulam Hari Charutha
Rakesh Nemam, Thiruvananthapuram
Neyyar Dam,Thiruvananthapuram Hassan K.M
Paulose M.K GHS Pezhakkappilli, Ernakulam
Govt. HSS, Perumbavoor, Ernakulam

Academic Co-ordinators
Sujith Kumar G
Research Officer, SCERT
Dr. Lidson Raj. J
Research Officer, SCERT

ENGLISH VERSION

Dr. C. Gokuladasan Pillai Dr. E. Krishnan Biju.G.S

Head (Rtd.), Prof.(Rtd) Asst. Professor,
Curriculum Department, University College, College of Engineering,
SCERT Thiruvananthapuram Thiruvananthapuram

Academic Co-ordinator
Sujith Kumar G, Research Officer, SCERT
Contents
7. In Rows and columns ........103

8. Measure and Tell ...............115

9. Divide and Make Equal ....131

10. Know the Weight................141

11. Pictorial Mathematics .......151

Certain icons are used in this
textbook for convenience

Additional activity/
Extended activity

How I found out

How my friends found out

Assessment

Computer Activity
 7
In Rows and columns
Farm Club
See the banana trees planted by the members of the Farm Club of
Minnaramkunnu School.

How many trees are there in one row?

How many rows ?

Let's colour
How many trees in all ? Colour the boxes, same
colour to same answer.
To make four more rows like this,
how many trees are needed? 3 2 2 6
6 2 4 3
How many rows in all?
4 5 2 3
How many trees in all?
6 3 5 4
3  6 = .........
3 4 3 6
4  6 = .........
Total 7  6 = .........

103
 Let's plant
See the okra seedlings planted by the Farm Club on the first day.
How many plants in one row?

How many rows?

How many plants in all? 7 + 7 + 7 + 7 + 7 = 35

That is 5  7 = 35
On the second day, they planted 3 rows with 7 seedlings in each row.
How many seedlings did they plant on the second day?
How many on both days together ?

First day .....  ..... = .....

Number of
Second day .....  ..... = ..... rows 5  3 = 8
Number of plants in one
Total row = 7
Total number of
plants 8  7

104
 Manuring plants
See the pictures of the yam manured on the first day:

How many plants in one row?

How many rows?

How many plants in all?

On the second day 3 rows were manured and each had 8 plants. How
many in all?
On the third day, 8 rows were manured with 4 plants in each. How
many plants were manured in all three days together?
First day .....  ..... = .....
Second day .....  ..... = .....
Third day .....  ..... = .....
Total .....  ..... = .....

Let's multiply
JT 537-2/ MATHS-3 (E) (Vol-2)

The software to be used : G compris of IT @ School Gnu/linux

The way to use the software:
Open Gcompris  Operations  games in Mathematics 
Multiplication

105
 Crop
The farm club had the first crop of spinach. Some of it was used for
the noon-meal. 3 kilograms of spinach was left and this was sold to
the members at 9 rupees a kilogram. How much money did the club
get?

How many kilograms of spinach did they sell?

What is the price of one kilogram of spinach?
How much money did they get? .....  ..... = .....
On the second day, they sold 6 kilogram of spinach at the same rate.
How much money did they get on both days together?
First day .....  ..... = .....
Second day .....  ..... = .....
Total
On the third day, they sold 19 kilograms at 10 rupees a kilogram. How
much did they get that day? .....  ..... = .....

How much did they get on all three days together?

If they had sold at 9 rupees a kilogram on all three days. How much
money would they have got?
What if they had sold at 10 rupees a kilogram on all three days? What
is the difference in the amount they had got?

106
Fill in the empty cells
When a
 1 2 3 4 5 6 7 8 9 10 number is
multiplied
1 1 2 3 4 5 6 by 1, we get
2 2 4 6 8 10 12 the same
number
3 3 6 9 12 15 18
4 4 8 12 16 20 24
5 5 10 15 20 25 30
6 6 12 18 24 30 36
7
8
9
10

What is the speciality of the numbers in the blue cells?

I can do any
multiplication if
I have this table

 1 2 3 4 5 6 7 8 9 10
1
2 4
3 6 9
4 8 12 16
5 10 15 20 25
6 12 18 24 30 36
7 14 21 28 35 42 49
8 16 24 32 40 48 56 64
9 18 27 36 45 54 63 72 81
10

107
 Patterns and tables
7 17=7 8 18=8 9 19=9
7+7 2  7 = 14 8+8 2  8 = 16 9+9 2  9 = 18
7+7+7 3  7 = 21 8+8+8 3  8 = 24 9+9+9 3  9 = 27
7 + 7 + 7 + 7 4  7 = 28

I know
The price of one pen is 7 rupees. What is the price
8  7 = 56
of 8 pens?
7 balls in one packet. How many balls in 9
97=
packets?
What is the price of 7 notebooks at 7 rupees
....  .... =
each?
There are 6 buttons in a shirt. How many
buttons are there in 9 shirts? ....  .... =

9 unniappams in one packet. How many

....  .... =
unniappams in 9 packets?

6 seats in a row. How many seats in 8 rows?

88=

Times
When a number is multiplied by
What is the total? 2, the answer is 28. If the same
Find the total of 8 times 8 and 6 number is multiplied by 4, what
times 6 would be the answer? What if it
is multiplied by 8?

108
 Ramu's class has a tiled floor. There are 8 tiles in one
row. And there are 9 rows. How many tiles are used in
the classroom?
Ramu's father sells 6 litres of milk everyday. How many
litres of milk does he sell in one week?
There are 5 notebooks in one packet. How many note-
books are there in 9 packets?
Planting tapioca
Aneesh brought 16 tapioca plants. In how many different ways can
these be planted in rows? The Farm Club members thought about it.
Look at the pictures they have drawn:

28

82 44
If there are 24 tapioca plants, in how many different ways can we
plant this in rows and columns? Draw pictures.

109
 How many members?
The Farm Club members were divided into 8 groups. In each group
there are 3 students from Class IV and 4 students from Class V. How
many members are there in the club?
How many seeds?
The Farm Club got bitter-gourd seeds from the Krishi Bhavan. Sana
and Latha looked at the packets they got.
And I
I have have 16
12 packets

There are 4 seeds in each packet. How many seeds does each girl
have?
How do we find it out?
Sana has 12 packets. In each packet there are 4 seeds.
To find the total number of seeds, we have to multiply 4 by 12.
12 fours means 10 fours and 2 fours together.
That is, 12  4 = (10  4 ) + (2  4)

= 40 + 8 = 48

12  4 = 48

That is, 12  12 
4
4 48
2 4  8
10  4  40

That is 48
How many seeds does Latha have?
110
 How many packets?
How many seeds in one packet?
To find the total number of seeds, we need to multiply 4 by 16.
16  4 = (10  4) + (6  4)
= 40 + 24 = 64

That is, 16  16 
4 4 16 
6  4  24 24 4
10  4  40 40 64
64 64
• The price of one packet of seed is 15 
8 rupees. What is the price of 15 8
40 15 
packets? 8
80
Total price = 15  8 120
120
= 120
One packet of seed contains 7 seeds. How many seeds are there in
14 packets?
The Farm Club bought 6 notebooks at 13 rupees each. How much
money did they spent for this?
Planting seeds
There are 14 packets of pumpkin seeds, each containing 12 seeds.
What is the total number of seeds?
How do we find out? We have to calculate 14  12.

I did it like this

In 10 packets, 10  12 = (10  10) + (10  2 ) = 100 + 20 = 120
In 4 packets, 4  12 = (4  10) + ( 4  2 ) = 40 + 8 = 48
In 14 packets, 14  12 = (14  10) + (14  2 ) = 140 + 28 = 168

Difference Three and Nine

What is the difference between When one number is
the products 16  12 multiplied by 3, we get 36.
and 13  14? Find also the What would we get if the same
difference between the products number is multiplied by 9?
16  14 and 18  13.

111
 I did it like this : Zero of ten
12 each in 14 packets 3  10 = 30
5  10 = 50
10 + 4  10 + 2 =10  10 = 100
7  10 =
10  2 = 20
9  10 =
4  10 = 40
11  10 = 110
4  2 = 8
15  10 =
= 168 
20 10 =
That is 14   = 168 Do you see an easy
See how I did it : way to multiply by 10?

10 4
10 100 40 14 12 = 100 + 40 + 20 + 8 = 168
2 20 8 14  12 = 168

Thirty six
14  14 
12 12 Fill in the cross below so that the
2  14  28 28 product of numbers in each line
10 14  140 140 is 36.
168 168
What are the possibilities if the
Difference in prices:
middle number is 3.
Part of the okra crop of the farm club
was used for noon-meal and the
remaining 14 kilograms was sold to
the members at 16 rupees a kilogram,
which is 4 rupees less than the market 3
rate. How much money did the club
get?
How do we calculate this?
How many kilograms were sold?
Price of 1 kilogram
Total price
10 4
10 14  16 = 100 + 40 + 60 + 24 = 224
100 40
6
60 24

112
 14 
14 = 10 + 4 16
16 = 10 + 6 6  14  84
14  16 = (10 + 4)  (10 + 6) 10  14 140
10  10 = 100 224
10  6 = 60
4  10 = 40
4  6 = 24
224

If the 14 kilograms of okra was sold in public market, how much more
money would the club have got?
How I found out

How my friends found out

I understood what to find out

I could find this out without computing the total at market
rate
The calculation was correct.
I could explain the method of calculation

Babu needs 12 bars of soap. He checked the prices in two shops.

In the first shop, if 3 soaps are bought, one is free. But the price of
JT 537-3/ MATHS-3 (E) (Vol-2)

one soap is 14 rupees. In the second shop, the price of one soap is
12 rupees. From which shop should Babu buy? Why?
Radha sells 15 litres of milk every day to the society. How many
litres of milk did she sell in the month of November?

113
 In the Mathematics Talent Number steps
Examination, there are 25
questions. Each correct answer is
given 4 marks. For every wrong
answer, 1 mark is subtracted from
12
the total marks. Abu got 19 answers
correct and 6 wrong. How many 2 6 3
marks does he get?
In Sabir's school, 13 kilograms of
rice is needed each day for noon-
16
meal. How many kilograms of rice 4 2 8
is needed for 22 days?
The price of one notebook is 16 rupees. How much money is
needed to buy 17 such notebooks?
The price of pipe is 20 rupees a metre. Unni bought 15 metres of
pipe. How much money did he spend?
In the school assembly, students are standing in 18 rows. Boys
make 8 rows and girls, the remaining. In each row, there are 15
students. How many boys are in the assembly? How many
students are in the assembly? Compare your method with your
friends.
Write a problem, which can be solved by calculating the product
12 7.

Calculate without
Pretty Multiplying
Products
7  8 = 56
37  3 = 111 8 9 = 72
37  6 = 222 9  10 = 90
37  9 = 333 ... ... = 110
...  ... = 444 ... ... = .....
...  ... = ..... ... ... = .....
...  ... = ..... 13 14 = .....
...  ... = ..... How did you find
the answer?

114
 8
Measure and Tell
Buying flowers

The flowerman
measured out 10 cubits
of jasmine. When I mea-
sured, it was 12 cubits.
When teacher measured,
it was 9 cubits.

Got different measures of same thing. Why?

Measure the length of your bench like this:

Does everyone on your bench

get the same length?

115
 Try measuring with a stick or a piece of string.

What do we do to get the same measure for everyone?

Measuring length using a ruler

How about measuring with the ruler in your pencil box?
How do you measure using a ruler?
What all things are marked on it?

There are small Distance between The length of

lines and large two large lines is 1 Let's start this ruler is 15
lines centimetre measuring from centimetres
the zero mark

Length of Pencil

What is the length of the pencil in the picture? .......

116
Measure the length of this pencil and write it down...
My pencil
The length of my pencil is …. centimetres.

What is the length of the pencil of each

one on your bench?
Length of longest pencil

Length of shortest pencil

What is the length?

Toy cart
See the toy cart Abu made using 5 boxes, each of
length 20 centimetres.
• What is the length of Abu's toy cart?

100 centimetre = 1 metre 100 centimetre is

100 cm = 1m called 1 metre.

117
 Let's buy ribbon
Ramya bought 3 ribbons, each of
length 50 centimetres. Arya bought 2
ribbons each of length 1 metre. Placed
side by side, whose ribbon will be
longer?
How to check?

Can you say the length of each ribbon in centimetres?

Ramya .............. cm Arya .............. cm

And in metres?
50 centimetre
Ramya ….. metre… cm is called half
metre
Arya ….. metre… cm

My height
The maximum height of
children on my bench

Minimum height
The maximum height of
children in my class

Minimum height

118
• Make a chart showing the heights of all children in your class in
order and put it on the wall.
• Make some questions on it, to ask your friends.
• Who all are of the same height?
•
•

Make a guess!
Guessed Measured
length length
Table .............. .............
Eraser .............. .............
Chalk .............. .............
Blackboard .............. .............
Mathematics textbook .............. .............
Bench .............. .............
Umbrella .............. .............
Chart paper .............. .............
Classroom .............. .............

Flag post
Look at the shadow of the flag post of your school. Measure its length at
each hour of a day.
Make some questions to ask your friends.

Construct
• At what time is the shadow
longest? Take three eerkkil bits of length
5 centimetres. Can you make
•
a triangle using these? To
• make a square, how many
more pieces do you need?

119
 Guess the height!
Guessed Measured
height height
Door
Bench
Desk
Chair
Window
Wall

Canteen
See the vessels of different sizes in your canteen. Measure the girth of
each vessel and write in the note book.
Put a string
around and then
measure the string
with a ruler? We can also use
a tape to
measure

Find the depth of each vessel and write down.

Triangle
With two sticks of length
4 centimetres and another
stick of 5 centimetres,
can you make a triangle?

120
 Measure the thickness of the door Shapes
frame of your school
Make the figure below using
eerkkil bits. How many of these
And of your home are of the same length?

My guess
Actual measurement

Can you guess?

Guess Actual measure
Thickness of a pencil
Thickness of your wrist
Thickness of your thumb
Thickness of a tree in the
school ground
Thickness of the school flagpost
Height of a chalk box
Depth of a bucket
Depth of a drinking glass
Length of a desk
Thickness of a pillar
Height of a step in a
staircase
Thickness of a dictionary.
Distance between two pillars
in the school
JT 537-4/ MATHS-3 (E) (Vol-2)

Distance between the two

bars of a window.

121
 Fill in the table
230 centimetres 2 metres 30 centimetres
173 centimetres
3 metres 60 centimetres
One and a half metre
5 metres 50 centimetres
4 metres 5 centimetres

How many metres?

Suma had a piece of cloth 3 metres and 30 centimetres long. She bought
2 metres and 90 centimetres more and made two skirts for her daughter.
How much cloth did she use in all? m cm
How do we calculate it? 3 30 +
2 90
What Suma had : 3 metres 30 centimetres
6 20
What she bought : 2 metres 90 centimetres
First let's add the centimetres
30 centimetres +
90 centimetres
120 centimetres = 1 metre 20 centimetres
Adding the metres: 3 metres + 2 metres = 5 metres
Adding together 1 metre 20 centimetres +
5 metres
We get 6 metres 20 centimetres as the total.

To make curtains, first 16 metres and 50 centimetres

cloth was purchased. This was not enough and so 3 metres
and 75 centimetres of cloth was also bought. How much
cloth was bought in all?
12 metres and 60 centimetres of blue ribbon, and 8 metres
and 40 centimetres of white ribbon were bought for chil-
dren doing group dance. The price of ribbon is 12 rupees
a metre. What is the total price?

122
What is left
In the shop, there is a piece of blue cloth of length 12 metres and 60
centimetres. Of this, 8 metres and 80 centimetres was sold today. How
much of the cloth is left?
How do we find out?
Stock : 12 metres 60 centimetres
Sold : 8 metres 80 centimetres
First let's find the difference of centimetres.

Take 1 metre from the

We cannot subtract 12 metres and add to
80 centimetres from 60 centimetres
60 centimetres. What 11 160
do we do?
12 metres 60 centimetres
8 metres 80 centimetres
we get 3 metres 80 centimetres as the
difference

The shop has a rope 16 metres and 25 centimetres long.

From this, a piece 5 metres and 75 centimetres long is cut
off. What is the length of the remaining piece?
Janu bought a saree six and a half metres long and cut out
80 centimetres for a blouse. What is the length of the saree
now?
An 8 metre long iron rod is cut into pieces of 50
centimetres. How many pieces can be got?
The School Sports is going on. One lap around the ground
is 200 metres. How many laps should be done for 800
metres?

123
 Uniform
Arya's class has 22 boys and 18 girls. Each boy needs 1 metre and
20 centimetres for shirt, and 90 centimetres for shorts; each girl needs
1 metre and 10 centimetres for shirt, and 1 metre and 90 centimetres for
skirt. How much of each kind of cloth should be bought?

How I found out

How my friends found out.

I understood what to do to find the answer

Used the relation beteen centimetres and
metre correctly
Did the calculations correctly
I could explain to others how I got
the answer
How to say?
Centimetre Metre
Height of a one-year old child 
Width of a bench
Depth of a well
Length of a finger
Length of a bus

124
Measuring jars
Look at these pictures:

500 200 100 50 1l.

ml. ml. ml. ml.
Have you seen such jars?
What do we use them for?
What all can we measure using them?
• Milk
•
•
Have you ever measured anything using them?
Let's measure water
How much water is there in your water bottle?
How about measuring it?
What all things are needed?

400 in my In my water bottle

bottle
In my friend's water bottle
We say 400
In the bottles of my friends on my bench. millilitres
• •
• •

125
 Fill it up!
Joby's water bottle contains 400 millilitres
and Rafeek's water bottle contains 500
millilitres. If the water in both is poured into
a big bottle, how much water would it have?

1000 millilitres = 1 litre

1000 ml = 1l

Measuring milk

At my home we buy We buy

1 litre of milk from 3 packets of 500
the society millilitres from the 500 millilitre
booth means half
a litre

Are the milk used in both houses

same?

Water in the bottle

Vinu's water bottle contains 550 millilitres of water. Shan's bottle
contains 250 millilitres more. How much water is there in both the
bottles together?

126
One litre
How many times each measuring jar is to be used to fill a one litre
vessel?
Measuring Jar Times
1 litre 1
500 millilitres
200 millilitres
100 millilitres
50 millilitres

How many times?

Using 500, 200 and 100 millilitre measuring jars, what are the possible
ways of filling a one litre can?

One 500 millilitres

Two 200 millilitres
One 100 millilitres
1
litre

Like this, can you fill a 2 litre can in different ways?

How many litres?
There was 2 litres and 500 millilitres of coconut oil in the shop. Today, 6
litres and 750 millilitres of coconut oil was added. How much coconut
oil does the shop have now?
In shop : 2 litres 500 millilitres
1000 millilitre
Added today : 6 litres 750 millilitres.
means one litre
First, add the milliliters.

127
 What did you get? 1250 millilitre = 1 litre 250 millilitre
Now add the litres
1 litre 250 millilitres +
Litre Millilitre
8 litres 2 500 +
Total 9 litres 250 millilitres 6 750
9 250

For a marriage party, 4 litres and 500 millilitres of milk was bought
for tea, and 15 litres and 500 millilitres for making payasam. How
much milk was bought in all? If the price of milk is Rs. 36 a litre,
how much money was spent for milk?
At Achu's home, cows are milked in the morning and evening.
8 litres of milk is got in the morning, of which 6 litres and
700 millilitres is sold; 5 litres is got in the evening of which 3 litres
and 800 millilitres is sold. How much milk is sold each day? The
wages for milking is 6 rupees a litre. How much is spent each day
on wages? How much milk is sold in one day?
Selling problem
There was 6 litres and 750 millilitres of coconut oil in the shop. Today,
3 litres and 350 millilitres was sold. How much oil is left?
How do we find out?
In the shop : 6 litres 750 millilitres
Sold : 3 litres 350 millilitres
First find the difference of millilitres.
How much did you get?
The difference in litres?
How much is left in all?

128
 A can contained 4 litres and 500 millitres of kerosene. 2 litres and
150 millilitres was used to fill the stove. How much oil is left in the
can?
13 litres and 500 millilitres of paint was bought to paint the house.
6 litres was used on the first day and 5 litres 500 millilitres on the
second day. How much paint is left?
Honey

Appu Vaidyar had three and a half litres of honey in his shop. He first
filled 10 bottles of 50 millilitres. The rest he used to fill 100 millilitre and
200 mililitre bottles. How many bottles of each type did he use?
What is the total amount of honey in each type of bottle?
If the number of bottles are to be equal, how much honey should be
filled in each type of bottle?

How I found out

129
 How my friends found out

I understood what to do to find the answer

Used the relation between litres and milliliters

correctly

Did the calculations correctly

I could explain the steps for getting the answer

Measure puzzle
Ammu came with a can to buy milk. She needs 4 litres. The
milk man had only 5 litre and 3 litre cans. He had another
can with no mesaure marked. Yet he managed to measure
out 4 litres for Ammu. Can you say how he did it?

130
 9
Equal Shares

Smart club
Puthumala
Dear Friends,
We have decided to give free note-
books, pens, pencils, crayons, slates
and rulers to all children of
Puthumala LP School.
Please join us and help us!

Read the notice?

Which all things are given out? Have you got any free school materials
like this?

There are 18
notebooks of 100
pages in a bundle

If each child is given two notebooks, how many

children get books?
How do we find out?
Can you draw a picture?
Suppose we start giving two notebooks to each.

How many will get notebooks?

131
 That is, 18 - 2 = 16
Let us Multiply
16 - 2 = 14
Look at the number in the boxes.
14 - 2 = 12 Which all pairs have their product
12 - 2 = 10 also in same box here?
10 - 2 = 8
8 - 2 = 6
3 4
6 - 2 = 4
4 - 2 = 2 12 2 16
2 - 2 = 0
6 8

We subtracted 2 repeatedly from 18.

How many times was 2 subtracted?
18 notebooks of 100 pages are to be divided equally among 9 children.
Then how many notebooks would each get ?

1+1

If one each is given to 9, then the

total number given out is and the remaining is
Again give one to each. How many
notebooks are given? And the remaining is

Total number of notebooks given

18 -
9 Each got
9-
When 18 notebooks are divided equally among 9 children,
9
0 each gets
When 9 children are given 2 each, the total is 18

132
 Book distribution
One bundle has 15 notebooks of 200 pages. If 3 books are given
to each child, how many children will get notebooks?
For the first 15 -
3
The second 12 -
3
The third 9 -
3
The fourth 6 -
3
The fifth 3 -
3
0
15 notebooks can be given to 5 children, each getting 3. This we write
using signs as 15  3 = 5.
Read as 15 divided by 3 equals 5.
One bundle has 15 notebooks of 200 pages. If these are equally divided
among 5 children, how many would each get?

Children Notebooks Total

15 -
One each to 5 students 5
10 -
Again one each to 5 5
5-
Again one each to 5 5
0
133
 All the 15 notebooks are given to 5 students, each getting 3.
We say 15 divided by 5 is 3.
Using signs we can write it as 15  5 = 3.
The first one
15  3 = 5
3+3+3+3+3 = 15
5 3 = 15
When 15 is split into groups of 3, we get 5 groups. We say that when 15
is divided by 3, we get 5. This can be written using symbols as 15  3 = 5.
The second one is
15  5 = 3
5+5+5 = 15
3 5 = 15
When 15 is split into groups of 5, We get 3 groups. We say that when 15
divided by 5, we get 3. This can be written using signs as 15  3 = 5.

That is, to divide 15 by 5,

we should see by what
number 5 should be
multiplied to get 15
Class Library
56 books were given to the Class 3 A library. The bookshelf in the class-
room has 7 rows. The number of books in the rows must be the same.
How many books can we put in each row?
To find how many books can be
put in each row, we need only
divide 56 by 7.
For this, we should find, by
what number 7 should be
multiplied to get 56.
56  7 = ......

134
Banana grove
There are 72 banana trees in a grove. Each row has 8 banana trees.
How many rows are there?
......  ...... = ......
Pencils
3 packets of pencils, each containing 10, was brought for distribution.
How many can be given pencils, if each is given 2 ?
How many, if each is given 5 pencils?
How many packets?
6 candles can be put in a packet. How many such packets are needed to
pack 60 candles?
Making Shapes
4 triangles are used to make this. Using the triangles
given below how many such shapes can be made?

Using these triangles, how many shapes can be made

with 8 triangles in each?

How many shapes can be made with 6 triangles in

each?

How many with 3 triangles in each?

How many tables?

See the picture of chairs put around a table.
Like this, the chairs below can be put around how many
tables?

135
 Making Connections
Find the connections between the parts of the same color.

14
= 
4 15  3 =
 2
=
24

32  4 =
32  8 =

14 =
6
 15  5 = 
7
= 24

To get four

....  ....
20  ....

16  4 ....  8

4
4  .... 40  ....

....  6 8  ....

136
 What do you
Can you say? get when 7 is
Which number divided by 1?
divided by 5 gives
4?

What is got
when 120 is
divided by 10?

Any number divided

by 1 gives the number A Mistake
itself
Vipin was asked to
double a number, but
How many can be given?
he halved the number
instead. He got 14.
• I have 100 rupees. Among
how many people can I What is the first
distribute this, if each is to number?
get 20 rupees?

• How many if each is to get

10 rupees? Another One
When Regitha was
asked to divide a
• How many if each is to
get 5 rupees? number by 3, she
multiplied the
number by 3 instead.
She got 3. What is the
first number?

137
 Pencils and friends
There are some pencils in a packet.
When 2 each was given to 6 friends,
there were no pencils left. How many
can be given, if each is to get 4 pencils?

How many sweets?

I have some sweets, less than 10 in number. When

I made them into packets of 2, I had 1 left. I tried
packets of 3 and then also 1 was left. How many
sweets do I have?

Gooseberries
I have some gooseberries, less than 20. If I split them
into 2's none is left. I can also split them into 3's or 4's
with none left. How many berries do I have?
Can you find out all such numbers less than 100?

Division
Software to be used : : G compris in IT @ School Gnu/
Linux.
To open software : Open Gcompris and then
Mathematics  Using mental arithmetic  Division.

138
 35 rupees was divided equally among 5 persons. How much did
each get?
When 28 mangoes were equally divided among some persons,
each got 4. How many persons were there?
24 bangles are to be split into groups containing the same num-
ber. Do this in different ways. Write the number of groups and
the number of bangles in each group. Give this as a table.
8 times a number is 56. What is the number?
Write 48 as the product of two numbers in different ways.
What is the number?
• When one number is divided by 3, we get 8. What would
be obtained, if the same number is divided by 6?
• When one number is divided by 2, we get 8. What would
we get, if the same number is divided by 4? What if we
divide by 8?

Multiple and Part

• 7  8 = 56 • 56  7 = 8
• 5  6 = ...... • 30  5 = ......
• 8  4 = 32 • ......  ...... = 4
• 9  7 = ...... • ......  9 = ......
• 3 ...... = 27 • 27  ...... = ......
• 9  9 = ....... • ......  9 = ......
• 6  10 = ....... • ......  10 = 6
Fill in the blanks
• 16  4 = ...... • 36  6 = ......
• 45  9 = ...... • 54  9 = ......
• 64  8 = ...... • 48  8 = ......
• 36  9 = ...... • 28  7 = ......
• 49  7 = ...... • 100  10 = ......
• 50  10 = ...... • 110  10 = ......
139
 Draw two more figures of each pattern

(1)

................ , ................

(2)

................ , ..............

(3)

................ , .................

(4)

................ , ...............

140
 10
Measuring Weights
My Weight
Find the things in the class you can
lift up.
•
•
•

What all things in your home can you lift

up? Make a guess.
•
•
•

See the pictures. Which of these have you seen?

What is the use of all

these?
Which of these can be used
to find your weight?

141
 • My weight
• The greatest weight of
Twenty two
children on my bench kilograms.
• The least weight
• The greatest weight of
the children in my class

• The least weight

• Make a table showing inorder, the weights of children in your class.

• Make some questions based on this table to ask your friends.

˛ How many have the same weight?
˛
• Find the weight of your school bag.
Onam

Rice for Onam

to be given tomorrow.
5 kilograms for each.

142
 Our class has
40 children. How
many kilograms of
rice is needed?

• How much rice is needed for your class?

• If there is 50 kilograms of rice in a sack,
how many sacks are needed for your class?

• What if there is 100 kilograms in a sack?

Noon meal

For noon meal

programme, hundred
grams of rice a day is
allotted to each child.

Did you note what the teacher told in the PTA meeting?
How many grams of rice is needed for 10 students?
10 hundred grams is 1000 grams
1000 grams is equal to 1 kilogram
1000 grams = 1 kilogram

How many kilograms of rice is needed for the noon meal of children in
your class today?

143
 Fill the bag
Fill up each bag below with things in the list in different ways.

We say half
Item Packets kilogram for 500 grams
(in grams) and quarter kilograms
for 250 grams
Chilly powder 100
Coriander powder 250
Coffee 200
Dhal 500
Mustard 100
Cashew nut 50
Cardamam 50
Sugar 750
Items Number Grams

1
kilo
gram

Careful! Too much

weight will burst the
Items Number Grams
bag
2
kilo
grams

Items Number Grams

5
kilo
grams

Make another bag and list like this

144
Buying soap

Soap Sale!

75grams - 12 rupees
100 grams -15rupees
125 grams - 17rupees

Indu : Lissy : Shamna :

I bought one of I bought two of 125 I bought two of
each. grams and one of 100 grams and
100 grams. two of 25 grams

• What is the total weight of soap each bought?

Indu Lissy Shamna

• Which two bought the same weight of soap?

• How much did each pay?
Indu Lissy Shamna

rupees rupees rupees

145
 How many packets?

See what all things Ramu brought to the mill

for grinding.

Chilly 4 Rice Wheat

kilogram 20 kilogram 30 kilogram

Chickpea Coriander Turmeric

3 kilogram 5 kilogram 5 kilogram

Ramu packed the powders like this:

$ Turmeric-100 gram packets, Chilly-200 gram It would be easier,
packets, Chickpea-250 gram packets, Corian- if we make a table
der-500 gram packets, Wheat-2 kilogram pack-
ets, Rice- 1 kilogram packets. How many pack-
ets of each are there?

Found out what to tabulate

Made the table according to the details
Used the relation between kilogram and gram to complete the
table
Let's Weigh

The software to be used: The software to be used:

Gcompris in IT@school Gcompris in IT@school
Gnu/Linux Gnu/Linux
To open software : open To open software : open
Gcompris and then Maths  Gcompris and then Maths 
Calculation  Let's Weigh-1 Calculation  Let's Weigh-2

146
50 gram packs
The weights of various
things kept in jars in
Hamsa's shop are given
below:

Cashew nut Raisin

1 kilogram 500 gram

Cardamum Cumin seed

400 gram 200 gram
Have you noted the weights?
Each of these is to be packed in 50 gram packets. How many packets of
each would be there?
Two weights
Cashewnut
Ramu has two 1 kilogram
Raisin weights and two 5 kilo-
gram weights in his shop.
Cardamam
Abu wanted 4 kilograms
Cumin seed of sugar and 3 kilograms
of pulses.
Can you guess?
Joby wanted 6 kilograms
To weigh each of the things given below, of rice and 8 kilograms of
guess whether gram or kilogram is more wheat.
suitable.
Ramu measured out each
Item Grams Kilograms of these with a single
weighing.
Aracanut 
Can you say how he man-
Coconut
aged it?
Orange
Watermelon
Soap
Tooth paste

147
 What is the weight?
Suma bought 2 kilograms of pulses, 1 kilogram and 250 grams of
jaggery, and 300 grams of ghee. What is the total weight?
How do we find it?
First we add the grams. 1000 gram = 1

What do we get? grams kilogram

Now how about the kilograms?

2 kilograms + 1 kilograms = 3 kilograms
Kilograms Grams
2 500
Both together 1 kilogram 50 grams +
1 250
3 kilograms 0 300
We get 4 kilograms and 50 grams as total 4 050

Ravi runs a restaurant. He wants 4 kilograms and 650 grams of rice

for puttu and 2 kilograms and 850 grams of rice for appam. What is
the total weight of rice needed? The cost of grinding 1 kilogram of
rice is 10 rupees. What is the total cost of grinding?
Mumthas bought 4 kilograms and 350 grams of big bananas and
2 kilograms and 850 grams of small bananas. What is the total
weight?
Thomman the glutton
'Ha... Ha…' Thomman, who weighs 96 kilograms, is happy.
His favorite food is in front:
850 grams of avil
450 grams of banana
200 grams of sugar
Quickly tucked in
What is the total weight of the food he ate?

148
12 kilograms and 500 grams of jaggery was bought and from this,
9 kilograms and 250 grams was used to make payasam. How much is
left?
How do we find it?
Weight of jaggery
Kilograms Grams
bought : 12 kilograms, 500 grams
12 500
Used for payasam : 9 kilograms, 250 grams
9 250
Difference between grams
: 500 gram - 250 gram = gram
Difference between
kilograms : 12 kilogram - 9 kilogram = kilogram
Weight of remaining
jaggery : 3 kilograms, 250 gram

The shop had 10 kilograms and 500 grams of sugar in stock

and 8 kilograms and 450 grams was sold today. How much
remaining?
When 15 kilograms and 500 grams of wheat was washed
and dried the weight was reduced by 1 kilogram 350 grams.
Find the weight of the wheat now.

Total Weight
When Sainaba's water bottle is full, it
weighs 650 grams. When empty, it weighs
200 grams. What is the weight of the water
in the bottle? How much would it weigh
when it is half full?

From One to Thirteen

A stone of 13 kilograms fell down and broke into three
pieces. Using these pieces we can find all the weights from
1 kilograms to 13 kilograms. Can you find the weights of
these pieces?

149
 One day
There are 109 students in Nitha's Today is
school. 4 students were absent on Wednesday. We
Wednesday. For each student 100 have 35 kilograms
grams of rice is needed for the noon of rice
meal. How much rice is to be taken for
the noon meal?
On Thursday and Friday, all the
students were present. How much
rice is needed on these days?

After Friday, how many kilograms of

rice will be left ?

Story time
A king had severe stomach pain. All the doctors in the country
examined him and gave medicines. But he was still in pain. So there
was a royal proclamation. "I will give my elephant's weight in gold
to anyone who cures my illness".
A doctor from another country came and cured the king.
But an elephant's weight in gold...
"Find the elephant's weight first and come
back", ordered the king.
The doctor went home and told all this to
his son.
The son managed to get a boat. The doctor
went back to the palace and took the
elephant to the river. First they marked
the water level on the boat.
Then they got the elephant into the boat.
Again they marked the water level.
The king kept his promise and gave the elephant's weight in gold.
How?

150
 11
Picture Math
The picture shows various fruits got from Asha's yard.

Mango

Jackfruit

Banana

Pineapple

Guava

How many guavas?

Which fruit is the most?

How many more bananas than jack fruits?

151
 Garden
See the picture of the garden Asha and her friends went to.

There are various types of flowers. How many of each type? Write in
the table:

Flower Number

152
Domestic animals
Look at the picture of animals and birds of Asha's family keeps?

Animal/Bird Number

153
 How many ducks are there?

Which animal is the most?

And the least?

How many birds?

How many animals?

What you have

All students have the things shown in the table. Find the total
number of each in your class and write in the table.
Item Number

Math Fair
See the diagram of the pookkalam made for the Math Fair in the school

154
How many of each shape is used? Draw in the table.

Shape Number

Square

Triangle

Circle

Which shape is the most? Put a  mark against it.

Let's Count
The software to be used: Gcompris in IT@
School Gnu/Linux
To open the software : Open Gcompris and
then Maths counting  How Many

155
 Many kinds of houses
See the houses around Babu's school. In table below, write the door
numbers of houses of each kind. Also write the total number of each
kind.

167 169 168

138 139 150
152
134
133

132
131

130

129

128
125

Type of house House number Number of

houses

156
Make some questions on this to ask your friends.
• How many houses are there ?
•
•
Hobbies
Find the hobbies of all children in your class. In the table, draw
pictures to show the number of children who have each hobby.

Draw one child like this

Hobby Number of Children

Reading

Music

Travel

157
 Looking Back

What I can On my With Must

own teacher's help Improve

7. Rows and columns

• Formulating multiplication facts
through practical situations.
• Using multiplication facts in
problems solving.
• Using multiplication for problem
solving.
• Explaining number concepts
related with multiplication.
• Making up practical problems
using multiplication facts.
8. Measure and Tell
• Explaining the relation between
the units of length (centimetre/
metre)
• Measuring lengths accurately
using tape measure/ruler.
• Solving practical problems
related to measures of length.
• Explaining the relation between
the units of volume (Millilitre/litre)
• Measuring volumes accurately
using measuring jars.
• Solving practical problems
related to measures of volume.
9. Equal shares
• Explaining different methods of
division (Repeated subtraction,
making groups, sharing equally)
• Explaining different methods of
doing the division operation.

158
 What I can On my With Must
own teacher's help Improve
• Using division for doing practical
problems.
• Explaining the number concepts
related to division.
10. Measuring weights
• Explaining the relationship
between the units of weight
(gram/kilogram)
• Measuring weight accurately using
balance
• Solving problems related to
weight
11. Picture Math
• Explaining information given in
pictures
• Analyzing information given in
pictures
• Tabulating information given in
pictures
• Making conclusions by analyzing
given information.

159