Textbook in Mathematics For Class IV
Textbook in Mathematics For Class IV
Textbook in Mathematics For Class IV
as ics
4
IV
fo he ok i
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MATH - MAGIC
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1 Building with Bricks
Brick Patterns for Jagriti School
This is the true story of Jagriti School in Murshidabad (West
Bengal). When its building was being made, there was a plan to
make brick patterns on the floor and walls. Jamaal, Kaalu and
Piyaar were the masons for the brick work. They wanted to get
new ideas for the school building. So they took their other friends
to see the old tomb of Murshid Kuli Khan. (See photos.)
This building has a big floor with about two thousand beautiful
brick patterns. These were made by masons long back – about
three hundred years ago.
1 2
Look how the bricks are arranged in these five floor patterns.
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3 4 5
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A B C
D E F
G H I
J K
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How to Draw a Brick?
These are two photos of the same brick.
Photo
In one photo we can see only one face of the 3 faces
brick. In the other we can see three faces. Circle
the photo showing three faces.
✤
How many faces in all does a brick have? ____
Photo
✤
Is any face a square? one face
✤
Draw the smallest face of the brick.
✤
Which of these are the faces of a brick? Mark a (ü
).
✤
Which of these is a drawing of a brick? Mark a (ü
).
✤
Make a drawing of this box to show 3 of its faces.
✤
Can you make a drawing of a brick which shows 4 of its faces?
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A Wall that will not Fall
One day Muniya and Zainab are playing with bricks and making
their walls. Each makes a different wall.
Zainab Muniya
Zainab says her wall will not fall easily. Masons too do not put
bricks one on top of the other, as Muniya has done.
What do you think? Which wall will be stronger?
Look for walls where you can see different brick patterns.
Different Wall Patterns
D Here are photos of three kinds of brick walls. Can you see the
difference in the way the bricks are placed?
D Now match the photo of each wall with the correct drawing
below:
5
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Looking Through a Brick 'Jaali'
The masons who built Jagriti School had also made different
'jaali' patterns on the walls.
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This is a drawing of another
beautiful 'jaali'.
✤ Now colour some bricks red and
make your own 'jaali' patterns
in the wall drawn below.
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This 'jaali' is from a library
building in Kerala.
See how the edge of the bricks
is used to make a triangle in
the wall.
Find out
Look for other arches around you
and draw them.
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Have you seen arches in
a bridge?
✤ Where else have you
seen an arch?
___________________
A Special Arch
In this photo from Orchha, see how the arch is made. It has a
nice name – Ghoonghat Waali Mehraab ( the arch with a veil ).
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Jamaal and Kaalu, the masons of Jagriti School, said that their
grandfathers used many different kinds of bricks. Some of these
are shown in this photo.
✤ Which of these bricks have
curved edges?
✤ How many faces do you see of
the longest brick?
✤ Is there any brick which has
more than six faces?
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Ganesh and Sahiba love to look at
the pattern of bricks in the long,
long lines kept out to dry. They also
watch how bricks are made.
Here are four pictures from the brick kiln. These pictures are
jumbled up. Look at them carefully.
Write the correct order. ________________________
A B
'
J
How do you think a brick is made out of soil dug from the earth?
Look at the pictures and discuss in groups.
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Have you seen a brick kiln? Did you try to guess the number of
bricks kept there?
There are many, many brick kilns in India – thousands of them!
More than one hundred thousand! Can you imagine how big this
number is? This number is also called one lakh (1,00,000). Can
you try to write it? Ask your friends where they have heard of a lakh.
Find out
Look at these photos and guess how many bricks are carried by this
truck.
Also find out from a truck driver how many bricks they can carry in
one truck.
Do this without
writing!
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2 Long and Short
How Far Apart are the Dots?
D
I K
C
O
B
M
A F
J
L
N
G
E
H
★ Guess the distance between any two dots.
How many centimetres is it? Now measure it
with the help of a scale. Did you guess right?
★ Which two dots do you think are farthest
from each other? Check your answer.
★ Which two dots are nearest to each other?
Check your answer.
Children can play this game in pairs, making dots on a plain sheet and asking their partner to
guess the distance. This can also be extended to estimating bigger distances on the floor.
The border of this chapter should also be used as a scale.
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1zZ
£2
The Shorter Line
Akbar was a famous king. He had a smart minister called Birbal.
11
Once Akbar gave him a difficult question. He drew a line on
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the floor.
Birbal, here is a line.
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Make it shorter
without erasing.
6L
8L
Now your line
is shorter.
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9L
Akbar's line
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Birbal's line
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Look at the picture and explain how Birbal made Akbar's line
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shorter.
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Now can you be as smart as Birbal? Make his line shorter without
LL
erasing it. Just think — is there any longest line?
OL
Try This
6
★ Make her right arm 1 cm longer than the left arm.
8
L
★ Draw a cup 1 cm shorter than this cup.
9
9
14
0
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0
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name height (in cm) height (in cm) have they grown?
8
6
0L
LL
2L
Jhumpa once read a list of the tallest people in the
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world. One of them was 272 cm tall! That is just
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double of Jhumpa's height. How tall is Jhumpa?
__________ cm.
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Wow! His height
is exactly double
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my height.
Imagine
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★ Could that person pass through the door
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of your classroom without bending?
★ Will his head touch the roof of your
81
house if he stands straight?
6L
The Long and Short of Your Family!
02
★ Who is the tallest in your family? _____
L2
★ Who is the shortest in your family? _____
★ What is the difference between their
22
heights? _____
£2
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Inter-School Sports Meet
Race
This is a 100 metre race for girls. Arundhati is nearest the
finishing line. She is about 6 metres from it.
Behind her is Rehana. Konkana and Uma are running behind
Rehana. Look at the picture. To answer the questions below
choose from these distances:
– 3 metres
– 6 metres
– 10 metres
– 15 metres
6 metres
Rehana
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Have you heard about marathon races in which people have to
run about 40 kilometres? People run marathons on roads
because the track of a stadium is only 400 metres.
10 rounds of a stadium track = _______ km
So, if you run a marathon on a stadium track, you will have to
complete __________ rounds !
Long Jump
This is the long jump for boys.
Dhanu has the longest jump of 3 metres 40 cm. Gurjeet is
second. His jump is 20 cm less than Dhanu's. Gopi comes third.
His jump is only 5 cm less than Gurjeet's jump.
★ How long are Gurjeet's and Gopi's jumps?
________________________________________________________
★ Try and see how far you can jump.
★ How far can you throw a ball? ___________ metres.
★ Look for a big ball, like a football or volleyball. How far can you
kick it? ___________
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Here are the Indian Records and World Records for some jumps.
Sports World Record Indian Record
High Jump (Men) Javier S. (2m 45 cm) Chandra Pal (2m 17 cm)
Long Jump (Men) Mike P. (8m 95 cm) Amrit Pal (8m 8 cm)
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0
1
500 m
The field was very far from his
500 m
complete 2 km?
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10
★ One day the weather was very good and a cool breeze was
11
metres !
13
14
your classroom?
18
19
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From Kozhikode to Thalassery
Subodh is going to Kozhikode which is 24 kilometres (km) away.
Manjani is going to Thalassery which is 46 km away in the
opposite direction.
How far is Kozhikode from Thalassery? ________________
How much does Momun walk every day to reach school? _______
Is it more than 1 km? _______
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0
★ Find out how far your friends live from school and fill the table.
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from school
iz
S
9
Z
8
6
Who among you lives nearest to the school? ___________
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Who lives farthest from the school? ___________
LL
How many children live less than 1 kilometre away from your
2L
school? ____________
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll^
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Is there anyone who lives more than 5 km away from the school?
How do they come to school? __________________________________
iz L
_____________________________________________________________
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Guess and Find Out
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1. How long is the thread in a reel?
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2. How long is the string of a kite reel? Can it be more than a
81
kilometre long?
6L
3. If a handkerchief is made out of a single thread, how long
02
would that thread be?
L2
22
Children will get a good idea of 1 kilometre distance if it is possible to take them for a 1 km
walk, preferably along a straight path.
£2
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I Wish I Were !
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3 A Trip to Bhopal
Today Sugandha is very excited. All the children of her school are
going on a trip to Bhopal with their teachers.
Ms. Meenakshi and Mr. Rakesh are talking
about the number of buses needed.
We can
For just a few share seats.
children, we can't
get another bus!
Children should be encouraged to estimate first and then find out the answer using any
method they want. It is important to discuss the methods children use to solve a problem.
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Waiting for the Buses
Sahiba jumps out of the line to see
if the buses are coming. She
shouts loudly — Hey! I can see
them. Run! Grab the window seats.
Many children start jumping in
excitement. But ..........
p! se
Sto ? The l!
s l
i s thi s ma
at s o
Wh es are
bus
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t
n n o w, ge The Journey Begins
o
Come t. It'
s
i n f a s k.
o'cloc As the buses start moving from
d y 9
alrea Hoshangabad, children sing at the top of
their voices. Some look outside to enjoy
the view of the green fields and the hills.
Indra — When will we reach Bhopal?
Ms. Asha — If we don't stop anywhere, we
should reach there in 2 hours, that is
around ______ o' clock.
Manjeet — Is it very far?
Mr. Bhimsen — It is about 70 km.
Ruby — Are we going to stop anywhere?
Mr. Rakesh — May be at Bhimbetka, about 50 km from here.
D If they go to Bhimbetka, they will reach there
— Before 10 o'clock
— Between 10 o'clock and 11 o' clock
— After 11 o' clock
As they are talking, Bahadur shouts — Hey! look at the Narmada.
Everyone looks out of the windows.
Ruby — Wow! it is soooo long and so wide!
Let us guess how wide it is.
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Gopi — Uhm---m, 100 metres? No, it is much more.
Can't say.
Ms. Asha — See, our bus is about 5 metres long. Imagine how
many buses can stand in a line on this bridge.
✤ Have you ever crossed a long bridge? About how many metres
long was it? ____________
Everyone looks down at the river.
Mr. Rakesh — The water level now is quite low. It must be about
40 metres below the bridge.
Ms. Asha — But in the rainy season, the water had risen. Then
it was just about 15 metres below the bridge.
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Suddenly, the bus stops with a jerk.
Oh! The petrol pump. Two buses need to be refilled.
The buses stand in a line. Children are sticking their necks out to
see how diesel is filled in the bus. Some children have got down to
look more closely.
✤ Each bus takes about 15 minutes to refill and there are two
buses to be refilled. So they stop there for about _________
minutes, which means they are late by about _______ minutes.
.00
Ltrs 100
Rupees: 175.00
Litres: 5 RS
Rate per Litre: 35.00
Diesel
✤ Look in the picture and find the price of 1 litre of diesel. ______
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To Bhimbetka
After the buses are refilled, the journey starts again. Now the
children are told that they are stopping at Bhimbetka.
Anjan — What is Bhimbetka?
Ms. Raina — It's a place with lots of caves and cave-paintings
made by people ten thousand years ago.
Sumonto — Ten tho....uu....saa....nd years! I cannot even
think of one thousand years back!
Gopi — Oh! one thousand years is a big thing, I can't
even think of one hundred years.
Gauri — I can think of 100 years because my father's
grandmother is 100 years old.
Manjeet — That means those caves are almost hundred
great grandmothers old!!
Everybody bursts into laughter – Ha! Ha! Ha!
Now the children are really excited to see the cave-paintings. It is
about 11 o' clock when they reach Bhimbetka.
Oh!
The
0 00 de are se r
oc
a thou
10 e m s, sand ks
n l g year s
E ve eop tin ! s old of
! p in ks !
ow go, y pa roc
W a el n
a rs lov o o
ye uch t to
s ha
t
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Shankar — This painting also has very big bisons. Hey, I got
an idea. I will count the bisons and you count the
deer in the paintings.
Bonomala — I will count people. Let us see which are the most
— bisons, deer or people.
so ...
bi 37
.
ns
37 36,
go 35,
,
34
t
I
ot
. 1 1 2 , 1 1 3 , 114 ... I g
..
Yeh!
117 deer!
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Lunch Time
The children are hungry by this time so they take out their lunch-
packs. Biscuits, oranges and bananas are also distributed in all
the buses.
Each child is to be given 1 orange, 1 banana
and 5 biscuits.
All the children take oranges and biscuits but
38 children do not take bananas.
Children can be asked to solve many more similar questions or puzzles, both orally and in
writing. They should also be encouraged to explain the strategies they use.
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D
Think of a number
which can be divided by
2, 3 and 5 and comes E A small ant climbs
between 25 and 50. 3 cm in 1 minute but
slips down 2 cm. How
much time will it take
Can you solve these? Try them out.
to climb to 2 cm?
They are so lost in puzzles that they do not notice they have
reached the lake in Bhopal. It is a very big lake with a small
island in it.
The lake looks very beautiful at this time. There are a lot of ducks
making a loud noise. Some children give them popcorn.
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There are different kinds of boats. Each has a different ticket
price, and also different trip times.
` 30
` 15
` 25
` 15
t a ke a
il l e
o f us w nd rac p. We w
il
r a ou moto l take the
Fou le boat her gr r-boa
d d
pad uri an costl t.
y but It is
G a
with Zooo
fun —
...m!
Based on the table showing ticket rates, trip time etc. some questions are given in the book.
Children should be motivated to make many more questions themselves.
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-
e oar Hey!
h y We a
k e t costl doub re
us
t a
not tim
e le-de going on
Let . It is more ide. has m cker t
t usic. . It a he
t r l so
boa we ge eful but w It
e get costs a l
c
and a pea more
time.
ot
fo r
D Indra and Bhanu first went in the motor-boat, and then took
the oar-boat.
How much did they pay for both the boats? ` __________
How much time did they get for both rides? __________
D One group of children went for the double-decker trip.
They paid ` 450 in total. How many children went for the
double-decker trip? ______________
D Which boat makes two trips in 1 hour?
D Which boat takes less than half an hour to complete a trip?
D Which boat gives them the most time taking the least money?
D Javed went twice for boating. He paid a total of ` 40. and
boated for 50 minutes. Which two boats did he take? ________
Time to Return
Children enjoy different boat rides till
4 o'clock. It is time to return. Now they
will not stop anywhere and reach back
in two hours.
So, they should reach Hoshangabad by
__________ o'clock.
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Find out
Have you ever been on a school trip? How many
children were there in all? How did you go and
how far? How much time did it take? Try to find
out the cost of travel for each child.
Practice Time
2. One bus can carry 48 children. How many children can three
buses carry? About —
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4 Tick-Tick-Tick
Pamposh and Shazia were discussing whose home is 0425CH04
But
ur I ch I start for school
s i b l e! Yo my w ecked at 7 o' clock.
os r atch
Imp is farthe .
e l.
hom s choo
fro m
11 12 1
10 2
9 3
8 4
7 6 5
When I reach
e
school, the minute i tb 7
t
hand points at 2.
d n' ast
l p
h ou es 2?
s ut :0
12 1 So min r 7
10
11 2 2 o
3
9
4
8
7 6 5
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ou
a re w rong! Y . How?
You :10
c h o ol at 7
reach
s ese
o u s ee th
Can y s between Yes. So what?
ine
thin l mber
s?
e n u
th
11 12 1 11 12 1
10 2 10 2
9 3 9 3
8 4 8 4
7 6 5 7 6 5
Practice Time
1) Three friends read time from a clock. Who is right?
11 12 1
10 2
9 3
8 4 12:03 12:15 3:00
7 6 5
11 12 1
10 2
9
8
3 7:25 5:07 5:35
4
7 6 5
11 12 1
10 2
9 3 3:35 7:03 7:15
8 4
7 6 5
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2) Show the following times in the clock:
11 1
10 2
8 4
7 5
7 6 5
11 12 1
10 2
b) When does the sun set? ——— 9
8
3
4
7 6 5
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Look at the photo and guess the time at this place.
This photo was taken in Paris, France. In Paris the sun sets
after 9 pm at night during summer. This photo was taken at
night! But in winter it becomes dark here by 4 pm in the
evening.
3) Find out
❋ How long will it take the minute hand to move from
11 12 1 11 12 1
10 2 10 2 11 12 1 11 12 1
a)
9
8 4
3 to 9
8 4
3
——— c)
10
9
2
3 to
10
9
2
3 ———
7 6 5 7 6 5 8 4 8 4
7 6 5 7 6 5
11 12 1 11 12 1 11 12 1 11 12 1
b) 10
9
2
3 to
10
9
2
3
——— d) 10
9
2
3 to
10
9
2
3
———
8 4 8 4 8 4 8 4
7 6 5 7 6 5 7 6 5 7 6 5
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❋ Draw where the hands will be:
a) 20 minutes after c) 10 minutes after
6 o' clock 7 o' clock 11 12 1
11 12 1
10 2 10 2
9 3 9 3
8 4 8 4
7 6 5 7 6 5
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❋ How many minutes can these activities take? Make a guess
and then check at home.
Activity Time
❋ In one minute, how many times can you —
a) Snap your finger _______________
b) Skip a rope _______________
c) Jump up and down _______________
d) _______________ _______________
Write more such fun activities in this column.
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❋ Let's look at a clock again! Solve this one —
a) The minute hand started from '2'. How many minutes will
it take to come back to '2' again? _______________
c) Look around you and list the activities that take about one
hour to complete.
1. _________________
2. _________________
3. _________________
4. _________________
5. _________________
Children will enjoy doing activities to see all the things they can do in one minute. Observing
activities at home will give them a sense of time and also help them value the effort of others.
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Rani's Diary
Come let's go
to see my new
baby sister.
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
I will note down in
Here are some pages
my diary when she
first starts talking,
from Rani's Diary —
eating, walking....
5 March
2005 15 September 10 November mber
20 Nove
2005 2005 2005
Muniya is
Muniya got up Muniya started
born today! Muniya sat
her first tooth! crawling.
2 February
5 January 5 September
2006
2006 2006
Muniya started
Muniya ate
Muniya walking
a banana
stood up
Was born
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Rani had a pet puppy. After 2 weeks it opened its eyes. She
watched it grow like this:
Started walking
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Find out
Do all animals grow at the same speed?
Discuss about the growth of —
1. A hen
2. A cow
3. A bird
Draw pictures of the baby animal and the big animal.
This is a good opportunity for children and teachers to find out about the life spans and
growth patterns of different animals. The idea is to compare and discuss without having to
memorise any such information.
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Holidays are Fun!
Atif's holidays had begun. He was very excited. He had made some
wonderful plans and wanted to tell his cousin Shabana. So he wrote
her a letter —
Ajmer
1/5/06
Dear Shabana aapa,
Hello!
How are you? I am fine here. Aapa, my holidays have
started from today! I am going to my Nani's place on
5/5/06. I will be back on 20/5/06. My school will reopen on
30/6/06. When does your school close? Why don't you
come here? We will have great fun!
Bye for now
Atif
Nagpur
7/5/06
Dear Atif,
Hello!
I am doing well here. I got your letter yesterday. Happy
holidays! My school will close on 1st June 2006. It will
reopen on 10th August. I will go on a school trip to Goa and
will return on 7/6/06. I will try to come to Ajmer after
that. Bye
Shabana
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Now write which dates these stand for –
5/5/06 5 May 2006
___________________________
20/5/06 ___________________________
7/6/06 ___________________________
1/1/07 ___________________________
Write these dates in numbers.
1 June 2006 _____________________________
30 May 2006 _____________________________
10 Aug 2007 _____________________________
❋ How long did it take the letter to reach from Ajmer to
Nagpur?________
❋ How many days will Atif spend at his Nani's place? ________
❋ Fill in the table:
Dates Number
From To of days
Shabana's holidays
Atif's holidays
Dates Number of
Occassion From days
To
Summer holidays
Autumn Break
Winter Break
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On 15 May 2006 Chandran went to a shop to buy butter. He
checked the packet to see if this butter was safe to eat.
It was written on the packet — Best before 180 days from the date of packing.
Then he checked the date of packing. It was 15/01/06.
Help him find out if he should buy this butter or not.
— In which month was the butter packed? ________
— Which month will it be 180 days after 15/01/06? ______
— Can Chandran eat it on 15th May 2006? ________
Do you ever check the date of packing of things you buy?
Have you seen medicines which have the expiry date written on
them? It tells you after which date it is unsafe to take
the medicine.
Find Out
❋ Which are the other things that come with an expiry date?
On a cough syrup it was written:
Mfg. date 07/03
This shows it was made in July 2003.
Exp. date 07/05
This shows the month and year till
when it is safe to take.
❋ What month and year is written as
07/05 ? _______________
Would it be safe to take the cough
syrup in September 2005? __________
Children are not expected to know the words 'manufacturing' or 'expiry' dates, but only
to recognise these as symbols that show when the medicine is made and till when it is safe
to take. Teachers could encourage children to read and observe more such dates on
different products.
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Tutun Missed the Train
Tutun's school had closed for the summer holidays. He went to
his grandma's place. He met a lot of his cousins there. He was
enjoying himself and didn't want to go back home.
Platform 4
Hurray! That
means I am not
going back today.
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Actually the train had left at 5:30 in the morning! Tutun's
parents were upset. They asked the station master —
?
Why? se
e y u k.
e th loc
u s c
e ca hour
B 4-
a2
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Now can you tell why a 24-hour clock is called so?
Time of Sunrise
Time of Sunset
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5 The Way The World Looks
That stupid
Chinky is looking
for cheese. Can't
even see it is kept
on top of the jug.
The story demands a high level of imagination and children need adequate discussion about
how things look differently in shape and size when you see them from different views and
distances. However, the story should not lose its fun element.
52
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D Can you think why Gappu could see the cheese on the jug but
Chinky could not?
When I ran around in my
Just then a strong wind pushed the house, it looked so big! But
balloon out of the room. from here, it looks small.
How is that?
The balloon flew up and Gappu
started going up in the sky. As he looked down, he
could see his house.
As he went higher he could see things around his house —
the park, the Gurudwara, the railway-line, a sweet-shop
and Suhasini's house with the big water-tank on its roof ...
53
Rationalised 2023-24
D Imagine how your classroom looks from above. Try to draw it
and mark the benches, blackboard, doors, windows etc.
The balloon went up, up and up. Gappu kept wondering how big
the world is! Now he could see lots of houses, streets, roads
and buses.
54
Rationalised 2023-24
But when he fell on the
track, the railway line
looked like this.
D Look at these pictures and discuss why things look wide and
big at this end but narrow and small at the other end.
55
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These are two different views of the same bowls.
1 2
✤ Draw lines to match the side view with the top view of
— A pipe
— A funnel
✤ Try to draw pictures of a shoe from the side, top, front etc.
It would be exciting for children to imagine and find out how different things can look from
different angles. It also helps to improve their spatial understanding.
56
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The Park behind Gappu's House
Do you remember the park behind Gappu's house?
Here is a bigger picture of that park. Look at it carefully and
answer the questions. Gappu’s House
Young children tend to think of directions like left, front etc. in absolute terms. It is important
for the development of spatial understanding to make them aware that directions are relative
to one's position. Something that is towards the left from one position can be towards the
right from another position. More activities can be done in the class based on this concept.
57
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Ismail's Home
On the phone Ismail told Srijata the route to his house from her
house. The route map is shown here.
Ismail's House
Park
Bridge
Milk-booth
Srijata's House
58
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Gibli and the Big Box
Do you remember Gibli the ant in the Math-Magic
Book 3? 4
Well, one day Gibli saw a big box on her way.
It looked like this.
1
Gibli was confused. What was this box? She
climbed on a cup and tried to see from there. The
box looked like this. 5
4
Can you guess what that box-like thing was?
The numbers on the opposite faces of this box add up to 7.
✤ Which number was on the opposite side of 5?
✤ In the picture, which number will be at the bottom?
✤ Which number will Gibli see if she again turns left from 5?
✤ What will this box look like if you opened it up? Mark the
correct picture.
3
3 4
3
2 1 6 1
1
2
5
5
2
4 4 5 6
A 6 B C 3 D 4
2
Try it out
Draw a shape like this on a thick paper. Cut it out and colour the
different faces in different colours.
Can you use this box to play a game?
59
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6 The Junk Seller
Have you ever met a Kabariwali – a woman who buys and sells junk?
This is a true story told by Kiran, who has a junk shop in Patna.
I studied in a Hindi medium school in my village. My father
wanted girls to study like boys. I loved Hindi and Science, but I
hated Maths! Today Maths is most useful for my work. I could
never imagine this in school.
What about you? Do you also find Maths difficult?
What is the most difficult thing in your Maths book?_______
What do you think is the easiest lesson? ________
When I was young, my father died in an accident. So my mother
worked as a servant in some houses. We had a difficult time.
I had to leave school after Class VIII. I wanted to study more but my
mother got me married.
My husband's family lived in a mud house. His two brothers and his
sister did not go to school. He had a tea stall.
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Find out: how much for a cup of tea?
Ask people and find out the cost of a cup of tea
H at a tea stall ____________
H at a hotel ________________
Hariya Babu
Who has to pay back more — Hariya or Babu? ___________
61
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People laughed and teased us about our work. They called it
ganda kaam or 'dirty business'. But I did not think so. I knew
this idea would work.
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] In a week how much does Kiran earn from one rickshaw?
] Do it mentally and write the answers. 4 × 81 is 4 more
than 4 × 80.
2×6 = __________ 4 × 80 = __________ Am I right?
20 × 6 = __________ 4 × 81 = __________
2 × 60 = __________ 9 × 25 = __________
3 × 42 = __________ 31 × 9 = __________
I have my own small junk shop. I buy junk from junk collectors.
They go from house to house and bring junk on handcarts. I then
sell it at the big shop.
This exercise encourages children to use different strategies (other than the standard
algorithm) for doing multiplication.
63
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Rate–List
] How much will Kiran pay for
Kind of Junk Price of 1 Kg 42 kg newspaper?
] Also find the cost of:
1. Waste Paper ...... ` 4/-
a) 22 kg of plastic
2. Newspaper ......... ` 5/- b) 23 kg of waste paper
3. Iron ..................... ` 12/- c) 12 kg of iron
4. Brass .................. ` 170/-
Today she has gone to sell plastic, newspaper, iron and brass at
Dinu's big shop.
Dinu weighs 32 kg iron, 4 kg brass, 152 kg newspaper, 63 kg
plastic.
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A. How much will Dinu pay for 63 kg plastic?
The rate of 1 kg plastic is ` 12.
So the cost of 63 kg plastic will be Dinu's Rate–List
` 12 × 63.
Kind of Junk Price of 1 Kg
Remember, you used boxes to multiply
two numbers in Class III. 1. Newspaper ........ ` 6/-
65
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B. Kiran sells 32 kg iron
] How much money will Dinu pay for 32 kg iron?
] Kiran buys 1 kg iron for ` 12, but sells it for `14.
How much does she earn when she sells 32 kg iron? ` _________
C. What will Dinu pay for 152 kg newspaper?
The rate of 1 kg newspaper is ` 6. So the cost of 152 kg newspaper
is ` 6 × 152.
Dinu writes: 6 × 100 = 600. So, the
answer is more than
100 50 2
600. Is the answer
100 × 6 50 × 6 2×6 less than 1000?
6 How did you guess?
600 300 12
Guess the
answer first.
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First guess the answer and then calculate:
a) 37 × 18 = e) 142 × 5 =
b) 45 × 24 = f) 382 × 3 =
c) 69 × 52 = g) 2 × 175 =
d) 77 × 55 = h) 4 × 206 =
Fill My Diary
Kiran bought some junk from the junk collectors. She paid them
` 841. She sold the junk at Dinu's big shop and Dinu gave her
these notes and coins.
3 note
s of
6 notes of
f
8 notes o
7 no
tes o
f
4 coins of te s of
6 no
11 March 2007
Money I paid — ` 841
Money I got — ` 600
— ` 150
— ` 140
— ` 60
— ` 40
—` 4
Total ` 994
` 994
– ` 841
Money I earned : ` 153
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Later she paid ` 919 to the junk collectors. When she sold the
junk she got these notes and coins from Dinu.
of
ns
coi
28 of
es
not
18
5 notes of
9
no
1n tes
ote of
of
18 March 2007
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7 Jugs and Mugs
ppy Anniversary
Ha
69
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Long Live! Bunny and Banno
70
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The frog hopped along with nine other friends. He said — Oh, we
only want 100 millilitres each!
100
mL
71
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*
'
x % w >
Don't worry, they won't drink much. Each of them will take only
one millilitre. That is all. I will share my kheer with them — the
elephant said and wiped the cat's tears with his ear.
How many are you all together? — the elephant asked.
We are only one thousand — said the ants.
The cat said — Oh no, one thousand! We have to give kheer to
1000 ants!
After thinking the elephant said — No problem, I can manage.
Each ant drinks 1 millilitre of kheer.
So, 1000 ants drink: 1000 × 1 mL = _________ mL.
Ah! they will need the same as the ten frogs — said the donkey.
All the ants drank the kheer. Everyone was happy. They sang and
danced to celebrate the wedding anniversary.
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Who can have 1 Litre Kheer
Do you like kheer? What do you call it at home?
How much kheer can you have?
Can you drink 1 L water at one time?
mL 100 mL
+ +
mL ____ mL
+ +
mL
____ mL
+
____ mL
73
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Look Around
Look at these pictures. Now look for some other things we get in
packets or bottles like these. Make your own list.
Milk 500 mL
My Litre Bottle
Have you seen a one-litre water bottle?
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Bottles My guess My measure
Check if your guess is
correct and fill the table. Bottle 1
Bottle 2
Bottle 3
Adithyan
500 mL ____
250 mL ____
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My Measuring Bottle
Find your own way to make a bottle which can measure 200 mL,
400 mL, 600 mL, 800 mL and 1 litre. Discuss with your friends
and teacher how you made this.
My Guess My Measure
Mug
Glass
Pot
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Neetu in Hospital One injection gives
Neetu has to take 3 injections 5 mL of the medicine
to your body.
in a day for 5 days.
How much medicine will she
need for one day? I am not
afraid of
How much medicine in all for injections!
5 days?
How much
medicine will
I need for
one injection?
✤ _____________ _____________________________________________
✤ _____________ _____________________________________________
✤ _________________________________________________________
✤ _________________________________________________________
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Practice Time
1. Amina's water bottle holds one litre of water. She drank
250 mL of water and her friend Govind drank 150 mL. How
much water is left in her bottle?
2. Yusuf runs a tea shop. For making a glass of tea he uses 20 mL
of milk. Yesterday he made 100 glasses of tea. How much milk
did he use?
Tea Shop
3. Radha's grandma was ill. The doctor gave her a bottle with
200 mL of medicine. She has to take the medicine every
morning for 10 days.
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Water- Water
The table shows the water used in one day by a family of 5 people.
They live in Goodallur village.
Water in
Activity
litres (L)
Cooking and drinking 30 L
Washing clothes 40 L
Bathing 75 L
How many litres of water does your family use in a day? Guess
and fill in this table.
Water used Water used
Activity
(in buckets) (in litres)
Cooking and drinking
Washing clothes
Cleaning pots, pans
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Find out how much water is wasted in a day. _________
In a week? ___________
In a month? _________
In a year? ___________
Milk Soc
the ie
At
ty
>
<
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8 Carts & Wheels
You must have seen many such round things around you.
List some more in your notebook.
81
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Round Bangle
Have you ever gone to a bangle shop?
❊ Take a wire and make a bangle for yourself. Can your madam
or mother wear this bangle? ___________
❊ A bangle can be used to trace a circle. What are the other
things around you that you can use to trace a circle?
__________ __________ ____________________
__________ __________ ____________________
❊ Trace a circle with the help of some of these things in your
notebook or on the ground.
Which thing makes the smallest circle?
Which thing makes the biggest circle?
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Games with Circles
Children are playing some
games ...............
Game 1
Game 2
83
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Making a Circle
Naina, Chippu and Ariba want to play a game. They want to make
a big circle on the ground. But they cannot make it by tracing. So,
Ariba tries to draw a circle with a stick.
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Making a Circle with a Rope
Ariba decided to use nails and a thread to make a circle on the
ground. She took a thin rope and tied nails on both ends of the
rope. Then she made a circle with the help of her friend. Look at
the picture and see how they are making the circle.
85
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❊ Draw the radius of this bangle using a ruler.
Measure the length of the radius.
Now see what your friends have drawn. Discuss the length of the
radius they measured. Is it the same as yours?
Find out
❊ Measure the radius of the wheels of a bicycle or a bullock-cart.
You can use a thread or a measuring tape.
Are all the wheels of a bicycle or a bullock cart of the same
radius? ___________
❊ Have you seen a tractor or a road roller?
❊ Which is the biggest wheel you have ever seen?
❊ Are all wheels of a tractor or road roller of the same radius?
Children need a lot of interesting exercises of making and measuring the radius of circles of
different sizes. They can also make wheels and carts.
86
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❊ Lali and Kali are tied to a
pole with ropes. Kali has a
longer rope. Who can look
for more grass to eat?
________ Kali
Lali
Daljeet's Design
Daljeet has made these designs using a compass.
His sister came and started making more designs with him.
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Using a Compass
❊ Have you seen a compass before? How
will you use this to make a circle?
— Open your compass.
— Press the tip of the compass on the
paper. Hold the compass from the top.
— Without moving the tip, try to move
the pencil around.
— Do you get a circle?
Look for a mark where you had kept the tip of the compass.
❊ Is this circle better than the one you made earlier without a
compass? Draw the radius of this circle and measure it.
❊ Now you can make your own designs like Daljeet had made.
How many did you make?
Guess how this design has been made. Use a compass to make a
similar one in the box.
Encourage children to explore their own designs with a compass. This will also give them
more practice in drawing circles with a compass.
88
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Is It a Circle?
Guess
89
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Find the Centre
Sadiq and Sameena want to make circles for themselves.
90
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Then she folded it again like this.
❊ Now you trace a circle on a paper using a bangle. Cut it. Then
find its centre like Sameena did.
We can also make the design on page 88 like this. How did you
do it?
91
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Balancing Act
Can you balance a plate on your finger?
I will balance
it ...
Oops!...
I will try again.
I think I have
found the centre
of the plate.
Zakir, Appu, Naina and Guddo were getting bored. It was raining.
So they could not go out to play.
Suddenly Appu said — Let's each make a top.
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They took a piece of cardboard traced a circle on it. Then they
made a hole and put a matchstick in it.
Guess
❊ Whose top will not spin at all? _________
❊ Whose top will spin a little? _________
❊ Whose top will spin the best? _________
❊ In whose top is the stick nearest to the centre? _________
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9 Halves and Quarters
Mintu cat and Mottu cat were friends. Once they stole a chapati
from Malini’s kitchen. I will take it — said Mintu. No, I will take it
— said Mottu. While they were quarrelling, there came Tittu
Monkey. Hi! What is the problem? why are you quarrelling? — he
asked. “We don’t know how to divide this chapati between us —
the cats said. OK! don’t worry. I will divide the chapati equally for
both of you — he said. Clever Tittu divided the chapati like this:
These are not equal, the left part is bigger — Mintu and Mottu
said. Oh, no problem, I will make it equal — Tittu said. He then
cut a part of the left piece and ate it.
equal?
Now is it
Oh! Now the right part is bigger — the cats cried. I am sorry —
said Tittu. He cut a part from the bigger piece and ate it. When
there was only a small piece remaining, he said — This is my
share for the work. Tittu then quickly ate the last piece and
climbed the tree.
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Half-Half
✤ If the cats ask you to divide the chapati equally,
how will you divide it?
If you do not cheat like Tittu, the cats will have these parts.
Half of Half
✤ If two more cats come for food, how will you divide one chapati
equally for four cats?
Each of us got a
quarter of the
chapati. You are a
good 'divider'. Ha!
95
Rationalised 2023-24
How many pieces of chocolate are there? _________
How many pieces were left with Rani? _________
96
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In how many different ways can you cut a rectangle into half ?
✤ Draw 5 different ways .
✤ In how many different ways can you cut a rectangle into four
equal parts? Draw 5 different ways.
97
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Cutting the Cake
Rajni’s father brought a cake. She divided the cake into 4 equal
parts — for herself, her brother Raju, her father and her mother.
98
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Greedy Kundu
Kundu is a greedy man. Whenever he goes to the market, he
wants to get more and more but doesn't want to spend much
money.
One day he wants to eat pumpkin halwa (sweet dish). He tries
to buy a big pumpkin with only `10. He asks the first pumpkin
seller the price of a big pumpkin.
First pumpkin-seller — ¼ of this pumpkin is for `10.
Kundu walks to the next seller and looks for a pumpkin of the
same size.
Kundu — How much of this pumpkin will I get for `10?
Second pumpkin-seller — Half.
D This full pumpkin will cost ` ___________.
.
99
Rationalised 2023-24
Kundu— Eh! Why not give me ¾?
Second pumpkin -seller — Run away! Go, get your pumpkin
from that man. He sells such bad vegetables that he will even
give you a full pumpkin of this size for ` 10.
The greedy Kundu walks to the next pumpkin seller. He looks
at a pumpkin of the same size
and asks him —will you give
me this big one for ` 10?
- ¼ kg
10
2. kg
100
Rationalised 2023-24
Practice Time
a) What part of the whole is coloured? Write below each shape.
¾
½ ¼
¾
½ ¾
c) Cut in half
Draw a line which divides these shapes into half.
101
Rationalised 2023-24
d) Colour half the number e) Colour ¼ of these shapes.
of shapes as shown here.
f ) Match the coloured part as shown.
Quarter
fb
¾
Half
z)
Three Quarters ½
&
Whole
©
¼
9
102
a
Rationalised 2023-24
g) Make the other half
½ of the picture is drawn here. Can you complete the picture
by drawing the other half?
Remember,
1 metre = 100 cm
103
Rationalised 2023-24
So
½ metre= ……… cm
¼ metre= ……… cm
¾ metre= ……… cm
Can you see that when we add ½ and ¼ we get ¾?
Sharing Milk
This bottle is full of milk and it holds one litre. The milk is put
into 4 other bottles so that each bottle has ¼ litre of milk.
✤ Shade the bottles to show the level of milk in each.
104
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Balance the Weight
0
50g 25g
1kg
0
50g 20
g0 200
g
0
10g
0 250 25
50g g g0
2) ........................
kg
3) ........................
¾ kg kg
105
Rationalised 2023-24
Why is It Wrong?
Kannan shaded some parts as shown. But his friend Mini says
that it is wrong. Explain why it is wrong.
¼ ½
Practice Time
D There are 60 mangoes. ½ of them are ripe. How many mangoes
are ripe?
D There are 20 stars. A quarter of them are red. How many stars
are red?
How many are not red?
106
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10 Play with Patterns
Tinu used this block to make a sari.
107
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He also made this dupatta with the same block.
Can you see how Tinu has made different patterns using the
same block? Now you too make 3 different patterns using .
Pattern 1
Pattern 2
Pattern 3
108
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Yamini has used her blocks to make a few patterns. Help her to
take these patterns forward.
We can also make patterns with numbers and letters. Below are a
few examples. Can you take them forward?
864 664
764
9 109 209
109
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Make a pattern without numbers.
No number comes
1 2 3 twice in any line!
3 1 2
2 3 1
We have not used the terms row or column here, but using the word 'line' teachers may discuss
the idea of rows and columns.
110
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Magic Patterns
2 3 7
Look at the pattern of numbers
1 to 7 . See how each line adds
up to 12!
4
1 5 6
Magic Triangles
3
Look at this number pattern .
Rule: Numbers on each side of the
triangle add up to 9.
4 5
3 + 4 + 2 = 9
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Now use numbers 1 – 6 to make your
own magic triangle.
Rule: Numbers on each side must
add up to 10.
Number Towers
Numbers can be arranged as a tower. We start from below and get
this number pattern.
80
30 50 Can you see the rule for this pattern?
10 20 30
Rule: We add 2 numbers below to get the number in the box
above them.
80
80
30 50
30 50 30 + 50 = 80
10 20 30
10 20 30
20 + 30 = 50
112
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Using the same rule, complete these number towers.
25
5 10 15 20
1 2 3 4 5
113
24-01-07
Rationalised 2023-24
Patterns with Addition
1 + 2 + 3 = 6
2 + 3 + 4 = 9
1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14
+ + + + =
+ + + + =
+ + + + =
+ + + + =
114
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Secret Messages What are I am trying to read
you doing? the note my friend
gave me ...... but I
cannot understand it.
7 15
15 4
14 9
78
20
Yamini explained the rule — Numbers have been used for letters.
For example, 'J' is 10, 'P' is 16. So JUMP is 10 21 13 16 .
❈ Complete this list of letters and numbers to help you.
A B C DE
1 2 3 4 5
Coding and decoding secret messages is also a part of recognising patterns. Recognising
rules is important for the development of mathematical thinking.
115
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More Secret Messages
IFMMP! ??!!
IPX BSF
GJOF
ZPV?
UIBOL
ZPV.
XJMM
ZPV QMBZ
XJUI NF? ZFT!
Shablu and Jaggu are playing a game. They are writing some
secret messages. But Kahuli is not able to understand them.
So Jaggu explained the rule —
Jaggu – You see, we have changed each letter by its next letter.
That is, we write 'G' in place of 'F', 'O' in place of 'N'. So
YES becomes ZFT .
Kahuli – Oh! Now I understand.
Kahuli – See what I have written XF BSF GSJFOE T
❈ What was Kahuli's secret message? ________________________
❈ What did Shablu and Jaggu write?
_________________________________________________________
❈ Use the same rule to write — 'Meet me on the moon'.
_________________________________________________________
❈ Make different rules and ask your friends to crack the secret
message.
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Upside Down
Anisha is playing. She is showing her friends that she can stand
on her head.
Now, Anisha is playing with this card. Draw what it will look like
when upside down.
Floor Patterns
Have you ever seen a floor with tiles of these shapes?
117
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a) Now, you cover this floor with this tile.
Can you make such a floor design with a tile like a circle?
b) Try with this green tile without leaving a gap. Could you do it?
Discuss with your friends.
118
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d) Ramaiya has made a wall with his blocks. Can you complete
this for him?
e) Renu began to paint this wall. Now you help her to complete it.
119
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11 Tables and Shares
Shyama's Garden
The concept of multiplication can be related to the arrangement of things in an array. Some
other problems, based on contexts like the arrangement of chairs, children in the school
assembly, etc., can also be discussed.
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Jars in the Shelf
Bheema made a shelf for 30 jars. This is a long shelf with two
rows. Each row has the same number of jars.
Easy Tricks
Guddu
Children will enjoy building new multiplication tables for themselves instead of only
memorising them.
121
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Table of 2 4×2 10×2
3×2 5×2 6×2 9×2
2×2 8 8×2 20
1×2 6 10 7×2 18
4 12 16
2 14
Table of 5 4×5 10×5
3×5 5×5 9×5
2×5 20 6×5 8×5 50
1×5
10 15 25 7×5 45
30 40
5 35
Table of 7 28 70
14 21 35 63
42 56
7 49
Table of 7
7
Which two tables will you use for writing the table of 12?
122
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How Many Cats?
Some of Gayatri's cats were playing in a box. When she tried to
count, all she could see were legs. She counted 28 legs. How
many cats are there in the box?
Encourage children to fill in the table and also proceed towards making generalisations. For
example, they should be able to see that 48 legs would mean there are 12 cats, or
vice versa. In fact, this forms the foundation for algebraic thinking in later years.
123
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Jumping Animals
Do you remember the jumping animals of Class III?
A frog jumps 3 steps at a time starting from 0.
✽ Count the jumps he takes to reach 27.
So, he has taken 27 ÷ 3 = _______ jumps.
43 42
44
41
45
40 1
46 39 25 10 9 2 0
26 24
47 11 8 3
38 37 27
48 36 23 1 20 19
60 59 58 49 28 22 2 12 7 4
18 6 5
57 50 35 13
29
51 17
56 34 30 14
52 16 15
55 31
54 53 33 32
66 67
Practice Time
1) 28 ÷ 2 = 2) 56 ÷ 7 =
3) 48 ÷ 4 = 4) 66 ÷ 6 =
5) 96 ÷ 8 = 6) 110 ÷ 10 =
Children have done similar kinds of exercises for multiplication and division in Class III.
Refer to pages 173-176, Math-Magic Class III, NCERT.
124
Rationalised 2023-24
Sea Shells
Dhruv lives near the sea. He thought of making necklaces for his
three friends. He looked for sea-shells the whole day. He collected
112 sea-shells by evening. Now he had many different colourful
and shiny shells.
I will make a necklace of
28 shells. Will these shells
be enough to make necklaces
for all my friends?
125
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B) One carton can hold 85 soap bars. Shally wants to pack
338 soap bars. How many cartons does she need for packing
all of them?
Gangu's Sweets
Gangu is making sweets for Eid. He has made a tray of 80
laddoos.
Please pack 4
laddoos in a
box. I need 23
small boxes.
Rabiya
] Are the sweets in the tray enough to pack 23 small boxes?
____________
] How many more sweets are needed? ______________
For solving this problem, encourage children to use their own strategies — of making groups
in the tray, using multiplication to do division or repeated subtraction, etc.
126
Rationalised 2023-24
] Gangu also has a bigger box in which he packs 12 laddoos.
How many boxes does he need for packing 60 laddoos?
Practice Time
1) Neelu brought 15 storybooks to her class. Today 45 students
are present. How many children will need to share one book?
2) A family of 8 people needs 60 kg wheat for a month. How
much wheat does this family need for a week?
3) Razia wants change for ` 500.
127
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Children and their Grandfather
Rashi, Seema, Mridul, Rohit and Lokesh asked their grandfather
to give them money for the Fair.
One method
Rashi and Seema thought for a while and said — We know how to
do 70 ÷ 5.
Seema starts writing and says —
10 First I give ` 10 to each one of us.
5 70
– 50 So, I have distributed 5 × 10 = 50 rupees.
128
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Another Method
Mridul and Lokesh are trying 70 ÷ 5 in a different way.
Lokesh writes —
First, I give ` 5 to each. 5+6
5 70
I have distributed 5 × 5 = 25 rupees. – 25
Next, I give ` 6 more to every one. 45
I have distributed 30 rupees more. – 30
Now I am left with ________ rupees. ?
How will Lokesh distribute the rest of the money? Complete it.
So, each child gets 5 + 6 + ________ = ________ rupees.
Your Method
] Now use your own method to divide ` 70 equally among
5 people. If you want you can start by giving ` 2 to each.
Or you can even start with ` 11 to each.
a) 5 65 b) 84 ÷ 2 c) 3 69 d) 90 ÷ 6
129
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i) Meera made 204 candles to sell in the market. She
makes packets of 6. How many packets will she make?
If she packs them in packets of 12, then how many
packets will she make?
j) On Sports Day, 161 children are in the school playground.
They are standing in 7 equal rows. How many children are
there in each row?
Story Problems
Srishti's grandma is asking her to make problems.
Now you look at the other pictures and make questions like
Srishti.
130 *
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There are 8 packets
of rakhis.
Each packet has 6
rakhts in it.
Your question:
3.
Your question:
131'^
Rationalised 2023-24
4. Hari, Seema, Chinku and Lakshmi are going to Guwahati.
The cost of one rail ticket is ` 62.
Your question:
5. One metre of cloth costs ` 20. Lalbiak bought some cloth and
paid ` 140.
Your question:
Your question:
132
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200
g
1kg
Jaiju and Mannu were shifting house. They loaded all their things
on a horse-cart. There were many things like — a water tank, five
sacks of wheat, three tables, an almirah, four chairs, two
mattresses, three sacks of rice, a bamboo ladder, pots and pans.
When they were ready to move, the horse refused to start. They
wondered why. Their father said that this horse was not well and
would not pull a load heavier than 700 kg. Oh! But how heavy is
this load? — they asked.
200
g
1kg
1kg
200
g
133
200
g
1kg
Rationalised 2023-24
200
g
1kg
___________________________________________________________
___________________________________________________________
134
200
g
1kg
Rationalised 2023-24
200
g
1kg
Activity
Mannu and Jaiju put a pencil and a geometry
box in the two pans of the balance. Which pan
will go down? Why? Draw a picture to show it.
What is heavier?
❊ Make pairs of different things and use
the balance to decide which is heavier.
First guess which thing will take the
pan down and then check with your
balance.
1kg
❊ Make groups of three things. For example — eraser, ball and
paper. Use the balance to arrange them in order of weight – the
200
g
lightest, the one with in-between weight, the heaviest.
Complete the table with at least five examples.
The balance children make will not be very accurate but will be good enough to compare
weights which are different from each other.
135
200
g
1kg
Rationalised 2023-24
200
g
1kg
Making Weights
Do this activity in pairs. You need a balance, weights, a cake of
soap, plastic packets, sand and rubber bands. You can also take
help of an older person.
Get a new cake of soap. The packet will have the weight written
on it. You can use this soap to make your own different weights.
The soap weighs ____________ grams (g).
Take a small plastic packet.
Put it in one pan of the balance. Put the
soap in the other pan.
Slowly add sand to the packet till the pans
are balanced.
200
g
on it.
If you put the soap and the weight you just made
together in a pan, how many grams will both these
weigh? ________
136
200
g
1kg
Rationalised 2023-24
200
g
1kg
Practice Time
❊ Which pan of the balance will go down? Show by drawing
an arrow.
1kg
55g
200
g
105g 150g 245g 254g
200g 250g 700g 600g
137
200
g
1kg
Rationalised 2023-24
200
g
1kg
Which is Heavier?
Which is heavier —
one kilogram cotton or
200
138
200
g
1kg
Rationalised 2023-24
200
g
1kg
Items Weight
Rice 5
Sugar 1
Mustard seeds 10
Wheat 3
Dal 500
1kg
Tea 250
Pepper 25
200
g
Car and Tractor
Ritu is weighing her toys. She If I put 2 cars,
will the tractor
wants to know if her tractor is
still be heavier?
heavier than her car. How would
you help her to find out quickly?
Guess which is the heaviest —
a real car, a bus or a tractor?
Which is the heaviest thing you
have seen?
139
200
g
1kg
Rationalised 2023-24
200
g
1kg
On hearing this, doctors from all over the country came. But only
Dr. Vaidika could cure him.
Oh great! My pain
has gone. Thank So, can I have my
you, Dr. Vaidika. reward now, sir?
140
200
g
1kg
Rationalised 2023-24
200
g
1kg
Vaidika was unhappy when she reached home. She told her
daughter the whole story.
Don't worry Ma. I have
an idea ..... tell the king
to arrange an elephant
How can I weigh
and a big boat.
an elephant?
Where will I get
1kg
such a big balance?
200
g
Next morning, Dr. Vaidika invited the king near a river. The king
came with an elephant and a big boat.
141
200
g
1kg
Rationalised 2023-24
200
g
1kg
142
200
g
1kg
Rationalised 2023-24
200
g
1kg
Broken Stones
Abdu sells firewood. There was a
stone in his shop which weighed
13 kg. He used it to weigh firewood.
1kg
One day the stone fell down and
broke into three pieces which
200
g
weighed – 2 kg, 5 kg and 6 kg.
5 kg 2 kg
6 kg
But Abdu was very smart. He used those three pieces to weigh
firewood of all weights — from 1 kg to 9 kg.
Here is how Abdu weighed 1 kg of firewood —
The s
Ah! hi
h t of t .
weig kg
l e is 1
bun d
143
200
g
1kg
Rationalised 2023-24
200
g
1kg
✤ Now you show how Abdu will use these stone pieces to
weigh —
6 kg
5 kg 2 kg
a) 4 kg of firewood
b) 3 kg of firewood
200
g
1kg
c) 7 kg of firewood
144
200
g
1kg
Rationalised 2023-24
200
g
1kg
Post Office
Have you ever been to a post office? _________
What different things do people go there for?
How much does a postcard cost? _________
How much does an inland letter cost? _________
Postal Rates
1kg
i) 20 grams or less 5.00
ii) For every additional 2.00
200
g
20 grams
Parcel weighing -
i) 50 grams or less 5.00
ii) For every additional 3.00
50 grams
145
200
1kg g
Rationalised 2023-24
200
g
1kg
3. Read the weight shown in the picture. Find out the cost of
sending a parcel of that weight.
200 250
150 30
0
0
10 35
0
50
in gm
146
200
g
1kg
Rationalised 2023-24
200
g
1kg
Am I Fit or Fat?
The chart shows the height and weight of children between
6 and 10 years old.
1kg
Now, you also fill the table by finding out the age, height and
weight of any five friends.
200
g
Can you make my
Name Age Height Weight health chart?
My health
chart too!
147
200
g
1kg
Rationalised 2023-24
200
g
1kg
1kg
1kg
200
g
How many oranges?
148
200
g
1kg
Rationalised 2023-24
13 Fields and Fences
I need a fence
around my field.
How much wire
should I buy?
Rahmat needs to find the length of the boundary of the field. Can
you find it from this picture? See the length of each side written
near it.
9 metre
15
m
9 metre
et
re
0 1 2 3 4 5 6 7 8 9 10 11 12 0 13 1 14 2 15 3 4 5 6 7 8 9 10 11 12 13 14 15
21 metre
Uhm---m! The
boundary is
54 metres long.
149
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I should also
do the same
for my field.
Ganpat
15
m
m
15
150
Rationalised 2023-24
Practice Time
1. Here are pictures of some more fields. Find out which one has
the longest boundary.
a) 6 metre
15
re
m
et
et
m
re
Boundary = __________ metre
15
24 metre
6 metre
3 metre
b)
6 metre
9 metre
6 metre
Boundary = __________ metre
12 metre
12
c) m
etr
re
e
et
m
15 metre
9 metre
re 15
et m
m et
d) 15 re
re re
et et
m m
15 15
Boundary = __________ metre
9 metre
151
Rationalised 2023-24
100 m 2. Chandu's father is called the
'young old man' in his village.
At 70 years of age, he is fully
fit. Do you know his secret?
m
m
150
He goes for a walk around the
150
1 m 50 cm
50 cm
50 cm
1 m 50 cm
152
Rationalised 2023-24
Activity
1. Find out the length of the boundary of these shapes. (Hint :– You
can use a thread)
A B
C D
153
Rationalised 2023-24
3. How many different shapes can you make by joining
two squares? Draw them on the squared sheet given
below. How long is the boundary of each shape?
154
Rationalised 2023-24
Practice Time
3 cm
1. A square has a boundary of
12 cm.
3 cm
3 cm
a) From the corner of this
square, a small square of A B
side 1 cm is cut off. Will the 3 cm
boundary of B be less or 3 cm
more? Find its length.
b) If you cut a 1 cm square to
3 cm
3 cm
get shape C, what will be the
length of the boundary of C? A C
3 cm
Square New shape
E
D
5 cm
1 cm
155
Rationalised 2023-24
3. A hockey field is 91 metres 40 cm long and 55 metres wide.
How long is the boundary of the field?
EN
D
ST
AR
T
Valsamma runs faster than
Usha. But still she loses
the race. Can you guess
why? ______________
END
ST
AR
T
156
Rationalised 2023-24
School Garden
The students of Class III and IV thought of making a vegetable
garden. They chose a place which looked like this.
Garden
Path
Garden 2
1
I think both
gardens are Quite possible!
equally big.
Let us find out if
you are right.
tax
❇ How will Neetu find out if the two gardens are equally big?
157
Rationalised 2023-24
Activity
1. Look at the table in your
classroom. Guess how many Math-
Magic books you can place on it.
(Remember — The books should
IC
AG
-M
not overlap. Do not leave gaps
TH
MA
GIC
between the books.)
IC
-MA
AG
TH
-M
MA
TH
MA
IC
AG
Write your guess here. __________
IC
-M
AG
TH
-M
IC
MA
TH
AG
MA
-M
TH
Now check if your guess was right.
IC
MA
AG
-M
TH
IC
MA
AG
How many books could you place?
-M
TH
MA
__________
What is the difference between
your guess and the actual number
of books? __________
2. Now look for another table.
a) Is this table bigger than the last table? Yes/No
b) Make a guess how many Math-Magic books can be kept on
this table. __________
c) Check if your guess was correct.
How many Math-Magic books could you keep? __________
d) The difference between the sizes of the two tables is
__________ books.
3. a) How many Math-Magic books can be covered with one
sheet of newspaper?
b) Try covering your Math-Magic book with half a sheet of
newspaper.
c) Can you cover your book with a smaller sheet?
158
Rationalised 2023-24
d) Find the smallest sheet which can cover your book. Check
if your friend used a smaller sheet than you did.
4. a) Which is the biggest leaf in this picture?
159
Rationalised 2023-24
5 . a) How many small squares of size 1
cm are there in this big green
square?
b) Can you think of a faster way to
know the total number of small
squares without counting each ?
160
Rationalised 2023-24
Puzzle: A House and the Well
Raghavan has a piece of land.
There are 4 houses on his land and in the middle there is a well.
He wants to divide this land equally among his four children.
Each should get one house and be able to use the well without
entering the other's land. Can you help him divide the land?
Give different colours to each one's share.
161
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14 Smart Charts
162
Rationalised 2023-24
From your table
Watching TV/listening to the radio...
❖ ________ children spend more than 6 hours in a week.
❖ ________ children spend no time at all.
❖ Most children spend ________ hours in a week.
❖ ________ children spend more than 3 hours.
Which Programme?
There are different types of programmes on TV or radio such as
cartoons, news, sports, music, plays, serials. Juhi's father likes
watching serials. Her mother likes sports. Juhi likes news
programmes.
(1) Ask people in your family to name one programme they like
and one programme they dislike. Make a table.
Mother
Father
163
Rationalised 2023-24
2) Find out from 20 friends the programmes they like and
dislike, and write in a table.
News
Serials
Cartoons
Comedy shows
Sports
Who is my friend?
164
Rationalised 2023-24
❖ Read the poem carefully and answer these questions:
a) Which word comes most often in the poem?
b) Which letter has been used most?
c) Which letter comes the least?
Food We Eat
Children were talking about what things they eat in the morning
— made of rice, wheat, maize, barley, etc.
tis ink
a t c hapa e t o dr f
Ie m I li k de o My favourite is
a d e fro m a
I eat rice and m t. But, I eat sattu arley. porridge made
things made whea rotis made b from ragi.
from rice. from maize.
165
Rationalised 2023-24
Find out from your classmates and fill the table:
Main food Number of persons
Rice
Wheat
Look at the table and tell:
❖ Most children eat food made from _____________.
❖ Compared to children who eat rice, those who eat wheat are
more/less/equal.
❖ Compared to those who eat wheat, children eating ragi are
more/less.
Preparing for the Class Drama
All children of a class are getting ready for a drama. Some
children are acting. Some are busy collecting the dresses. Some
are bringing tables and chairs to make the sets.
166
Rationalised 2023-24
The Drama Chart This shows 3
children
Number of
Children
167
Rationalised 2023-24
Some children had pasted their strips and
Madhu
made a chart like this.
R o h i t
Your chart should also look like this.
Ramesh
Chapati Chart
All children of a school take part in different clubs:
Drawing Club
168
Rationalised 2023-24
From the picture we can see that:
a) Half the children in the class take part in the Games Club.
b) One fourth of the children are members of the Garden Club.
c) The Drawing Club has one fourth of the children of the class.
If there are 200 students in the school, look at the above Chapati
Chart and tell the number of members in each club:
❖ The Games Club has ______ members.
❖ The Garden Club has ______ members.
❖ There are _____ members in the Drawing Club.
169
Rationalised 2023-24
If the number of children in the class is 28, then tell the number
of children
❖ who like to get wet in the rain __________
❖ who do not like to get wet in the rain __________
Milk 20
Coffee 10
Tea 10
Total Number of
children ________
170
Rationalised 2023-24
0425 – MATH MAGIC
ISBN 81-7450-698-5
Textbook for Class IV
First Edition
ALL RIGHTS RESERVED
March 2007 Chaitra 1928
q No part of this publication may be reproduced, stored in a retrieval
system or transmitted, in any form or by any means, electronic,
Reprinted mechanical, photocopying, recording or otherwise without the prior
January 2008 Magha 1929 permission of the publisher.
q This book is sold subject to the condition that it shall not, by way of
February 2009 Phalguna 1930 trade, be lent, re-sold, hired out or otherwise disposed of without
the publisher’s consent, in any form of binding or cover other than
January 2010 Magha 1931 that in which it is published.
November 2010 Kartika 1932 q The correct price of this publication is the price printed on this page,
Any revised price indicated by a rubber stamp or by a sticker or by
January 2012 Magha 1933 any other means is incorrect and should be unacceptable.
December 2012 Agrahayana 1934
December 2013 Agrahayana1935 OFFICES OF THE PUBLICATION
DIVISION, NCERT
December 2014 Agrahayana 1936
November 2017 Agrahayana 1939 NCERT Campus
Sri Aurobindo Marg
December 2018 Agrahayana 1940 New Delhi 110 016 Phone : 011-26562708
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January 2021 Pausa 1942 Hosdakere Halli Extension
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© National Council of Educational Maligaon
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Research and Training, 2007
Publication Team
Head, Publication : Anup Kumar Rajput
Division
` 65.00
Chief Production : Arun Chitkara
Officer
Rationalised 2023-24
TEXTBOOK DEVELOPMENT COMMITTEE
CHIEF ADVISOR
Amitabha Mukherjee, Director, Centre for Science Education and Communication (CSEC),
Delhi University, Delhi
MEMBERS
Anita Rampal, Professor, Department of Education, Delhi University, Delhi
Asha Kala, Primary Teacher, MCD School, Krishi Vihar, G.K. Part I, New Delhi
Asmita Varma, Primary Teacher, Navyug School, Lodhi Road, New Delhi
Bhavna, Lecturer, DEE, Gargi College, New Delhi
Dharam Parkash, Professor, CIET, NCERT, New Delhi
Hema Batra, Primary Teacher, CRPF Public School, Rohini, Delhi
Jyoti Sethi, Primary Teacher, The Srijan School, Model Town, Delhi
Kanika Sharma, Primary Teacher, Kulachi Hansraj Model School, Ashok Vihar, Delhi
Prakasan V.K., Lecturer, DIET, Malappuram, Tirur, Kerala
Preeti Chadha Sadh, Primary Teacher, Basic School, CIE, Delhi University, Delhi
Suneeta Mishra, Primary Teacher, N.P. Primary School, Sarojini Nagar, New Delhi
MEMBER–COORDINATOR
Inder Kumar Bansal, Professor, DEE, NCERT, New Delhi
Rationalised 2023-24
MATH-MAGIC
What is inside this book?
Foreword iii
1. Building with Bricks 1
2. Long and Short 13
3. A Trip to Bhopal 23
4. Tick-Tick-Tick 35
5. The Way The World Looks 52
6. The Junk Seller 60
7. Jugs and Mugs 69
8. Carts and Wheels 81
9. Halves and Quarters 94
10. Play with Patterns 107
11. Tables and Shares 120
12. How Heavy? How Light? 133
13. Fields and Fences 149
14. Smart Charts 162
Rationalised 2023-24