NCERT Solutions Class 4 Maths Chapter 3 Patterns Around Us
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NCERT Solutions Class 4 Maths Chapter 3 Patterns Around Us – Text
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Page 1
F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T
C L A S S 4 · M AT H S
NCERT Solutions
Chapter 3: Patterns Around Us
NCERT Textbook — Math Mela
BOOK PAGES SECTIONS QUESTIONS MEDIUM
34 – 38 6 23 English
Solutions, notes, sample papers & more at 61 pages
C L A S S 4 · M AT H S
NCERT Solutions
Chapter 3: Patterns Around Us
NCERT Textbook — Math Mela
BOOK PAGES SECTIONS QUESTIONS MEDIUM
34 – 38 6 23 English
Solutions, notes, sample papers & more at 61 pages
Page 2
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
CLASS 4 · MATHS · MATH MELA
NCERT Solutions — Chapter 3: Patterns Around Us
This chapter shows that a pattern makes counting easy. Trees in blocks, cups in piles, sweets in a plus and a
cross, coins in rows of two — every picture can be counted in groups instead of one by one. Counting in twos
leads to the big idea of the chapter: even and odd numbers.
TEXTBOOK BOOK PAGES
Math Mela (Class 4) 34 – 38
SECTIONS QUESTIONS
6 23
MEDIUM
English
Let Us Count — Page 34
Page 1 of 61
CLASS 4 · MATHS · MATH MELA
NCERT Solutions — Chapter 3: Patterns Around Us
This chapter shows that a pattern makes counting easy. Trees in blocks, cups in piles, sweets in a plus and a
cross, coins in rows of two — every picture can be counted in groups instead of one by one. Counting in twos
leads to the big idea of the chapter: even and odd numbers.
TEXTBOOK BOOK PAGES
Math Mela (Class 4) 34 – 38
SECTIONS QUESTIONS
6 23
MEDIUM
English
Let Us Count — Page 34
Page 1 of 61
Page 3
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Let Us Count
Q1 How many coconut trees does Gundappa have? ___________ How do you know?
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
ANSWER
Page 2 of 61
Let Us Count
Q1 How many coconut trees does Gundappa have? ___________ How do you know?
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
ANSWER
Page 2 of 61
Page 4
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
Gundappa has 81 coconut trees.
Do not count the trees one by one. The picture is already made of square blocks, so count a
block first.
Page 3 of 61
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
Gundappa has 81 coconut trees.
Do not count the trees one by one. The picture is already made of square blocks, so count a
block first.
Page 3 of 61
Page 5
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
One block = 3 rows of 3 trees
m l as
.co
3 + 3 + 3 = 9 trees in one block
m a g
l a se
g
The blocks stand in 3 rows, 3 blocks in each row
a3 + 3 + 3 = 9 blocks
co m
. ag
One row of blocks = 9 + 9 + 9 = 27 trees
e m
All three rows = 27 + 27 + 27 = 81 trees
g l as
a
m
How do you know? I counted one block, found 9 trees, and then added the blocks. Because
co
m.
every block looks the same, I did not have to count each tree.
o m l a se
Why it.chappens: When things are planted in equal groups, you
a g only need to count
m
se group and then add that group again and again.
g l a
one
a
om a s
. c agl
Tip: A farmer plants trees in rows so that a bullock cart or a water pipe can pass
s
between them. The rows also make
e mthe trees easy to count.
a
agl
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 4 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
One block = 3 rows of 3 trees
m l as
.co
3 + 3 + 3 = 9 trees in one block
m a g
l a se
g
The blocks stand in 3 rows, 3 blocks in each row
a3 + 3 + 3 = 9 blocks
co m
. ag
One row of blocks = 9 + 9 + 9 = 27 trees
e m
All three rows = 27 + 27 + 27 = 81 trees
g l as
a
m
How do you know? I counted one block, found 9 trees, and then added the blocks. Because
co
m.
every block looks the same, I did not have to count each tree.
o m l a se
Why it.chappens: When things are planted in equal groups, you
a g only need to count
m
se group and then add that group again and again.
g l a
one
a
om a s
. c agl
Tip: A farmer plants trees in rows so that a bullock cart or a water pipe can pass
s
between them. The rows also make
e mthe trees easy to count.
a
agl
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 4 of 61
Page 6
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q2 Gundappa has plucked 5 coconuts from each tree. How many coconuts has he
plucked?________
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
ANSWER
Page 5 of 61
Q2 Gundappa has plucked 5 coconuts from each tree. How many coconuts has he
plucked?________
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
ANSWER
Page 5 of 61
Page 7
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
He has plucked 405 coconuts.
Every tree gives the same 5 coconuts, so count block by block again.
Page 6 of 61
Top View
Gundappa’s coconut grove, seen from the top. The trees stand in square blocks.
He has plucked 405 coconuts.
Every tree gives the same 5 coconuts, so count block by block again.
Page 6 of 61
Page 8
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
One block has 9 trees
Coconuts from one block = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45
2 blocks = 45 + 45 = 90
4 blocks = 90 + 90 = 180
8 blocks = 180 + 180 = 360
9 blocks = 360 + 45 = 405 coconuts
So Gundappa has plucked 405 coconuts in all.
Why it happens: Each tree gives the same number, so we can add 5 again and again
instead of counting one coconut at a time.
Check it yourself: Skip-count the trees in fives — 5, 10, 15, 20 … If you say it 81
times you will end at 405.
Page 7 of 61
One block has 9 trees
Coconuts from one block = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45
2 blocks = 45 + 45 = 90
4 blocks = 90 + 90 = 180
8 blocks = 180 + 180 = 360
9 blocks = 360 + 45 = 405 coconuts
So Gundappa has plucked 405 coconuts in all.
Why it happens: Each tree gives the same number, so we can add 5 again and again
instead of counting one coconut at a time.
Check it yourself: Skip-count the trees in fives — 5, 10, 15, 20 … If you say it 81
times you will end at 405.
Page 7 of 61
Page 9
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q3 Muniamma makes plates and cups.
The cups Muniamma has made, put into six piles.
Number of cups = ____________
ANSWER
Page 8 of 61
Q3 Muniamma makes plates and cups.
The cups Muniamma has made, put into six piles.
Number of cups = ____________
ANSWER
Page 8 of 61
Page 10
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co a g
l a se
a g
co m
em . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag
co m
m .
m as e
.co a g l
se m
a
The cups Muniamma has made, put into six piles.
a g l
There are 60 cups.
se m
comonce and write the number down. g l a
.
The cups stand in six piles. Count each pile
a
a s em
PILE gl
a1ST 2ND 3RD 4TH 5TH 6TH
com
Number of cups 11 10 9 9 10 11
m .
m ase
co agl
The piles match from the two ends, so add the matching pairs.
m .
ase
a g l
.c
s e m
m a
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 9 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co a g
l a se
a g
co m
em . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag
co m
m .
m as e
.co a g l
se m
a
The cups Muniamma has made, put into six piles.
a g l
There are 60 cups.
se m
comonce and write the number down. g l a
.
The cups stand in six piles. Count each pile
a
a s em
PILE gl
a1ST 2ND 3RD 4TH 5TH 6TH
com
Number of cups 11 10 9 9 10 11
m .
m ase
co agl
The piles match from the two ends, so add the matching pairs.
m .
ase
a g l
.c
s e m
m a
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 9 of 61
Page 11
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
11 + 11 = 22
10 + 10 = 20
9 + 9 = 18
22 + 20 = 42
42 + 18 = 60 cups
Why it happens: Adding two equal numbers is easy, so pairing the tall pile with the
tall pile keeps the sum simple.
Tip: Put a small mark on the top cup of a pile once you have counted it. Then you will
not count the same pile twice.
Page 10 of 61
11 + 11 = 22
10 + 10 = 20
9 + 9 = 18
22 + 20 = 42
42 + 18 = 60 cups
Why it happens: Adding two equal numbers is easy, so pairing the tall pile with the
tall pile keeps the sum simple.
Tip: Put a small mark on the top cup of a pile once you have counted it. Then you will
not count the same pile twice.
Page 10 of 61
Page 12
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q4 How many coconut laddoos are there in the trays? ____________
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
ANSWER
Page 11 of 61
Q4 How many coconut laddoos are there in the trays? ____________
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
ANSWER
Page 11 of 61
Page 13
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
There are 36 coconut laddoos.
In one tray the laddoos sit on the two slanting lines. They make a cross like the letter X.
The X has 4 arms
Each arm has 3 laddoos
3 + 3 + 3 + 3 = 12 laddoos in one tray
All the trays are laid out the same way, and there are 3 trays
12 + 12 + 12 = 36 laddoos
Page 12 of 61
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
There are 36 coconut laddoos.
In one tray the laddoos sit on the two slanting lines. They make a cross like the letter X.
The X has 4 arms
Each arm has 3 laddoos
3 + 3 + 3 + 3 = 12 laddoos in one tray
All the trays are laid out the same way, and there are 3 trays
12 + 12 + 12 = 36 laddoos
Page 12 of 61
Page 14
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Why it happens: The three trays hold the same pattern, so we count one tray and
then add it three times.
Tip: The middle place of the tray is not a laddoo — a white peda sits there. Do not
count it with the laddoos.
Page 13 of 61
Why it happens: The three trays hold the same pattern, so we count one tray and
then add it three times.
Tip: The middle place of the tray is not a laddoo — a white peda sits there. Do not
count it with the laddoos.
Page 13 of 61
Page 15
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
How many milk pedas are there in the trays? ____________
e
Q5
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com l a
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
. a g
m
ase
ANSWER
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 14 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
How many milk pedas are there in the trays? ____________
e
Q5
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com l a
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
. a g
m
ase
ANSWER
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 14 of 61
Page 16
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
There are 39 milk pedas.
In one tray the white pedas make a plus sign (+) — one line going down and one line going
across.
The down line has 7 pedas
The across line has 7 pedas
7 + 7 = 14
But the middle peda lies on both lines, so it was counted twice
14 − 1 = 13 pedas in one tray
3 trays = 13 + 13 + 13 = 39 pedas
Page 15 of 61
One tray of Muniamma’s sweets. Three such trays are stacked, all laid out the same way.
There are 39 milk pedas.
In one tray the white pedas make a plus sign (+) — one line going down and one line going
across.
The down line has 7 pedas
The across line has 7 pedas
7 + 7 = 14
But the middle peda lies on both lines, so it was counted twice
14 − 1 = 13 pedas in one tray
3 trays = 13 + 13 + 13 = 39 pedas
Page 15 of 61
Page 17
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Why it happens: The two lines cross at the middle. The sweet at the crossing
belongs to both lines, so we count it only once.
Check it yourself: One tray holds 12 laddoos and 13 pedas — that is 25 sweets.
Three trays hold 25 + 25 + 25 = 75 sweets, and 36 + 39 = 75 as well.
Patterns with Money — Page 35
Page 16 of 61
Why it happens: The two lines cross at the middle. The sweet at the crossing
belongs to both lines, so we count it only once.
Check it yourself: One tray holds 12 laddoos and 13 pedas — that is 25 sweets.
Three trays hold 25 + 25 + 25 = 75 sweets, and 36 + 39 = 75 as well.
Patterns with Money — Page 35
Page 16 of 61
Page 18
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Patterns with Money
TRY THIS
Q1 How much money? ________ (the first arrangement)
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
ANSWER
Page 17 of 61
Patterns with Money
TRY THIS
Q1 How much money? ________ (the first arrangement)
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
ANSWER
Page 17 of 61
Page 19
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
This pattern is worth ₹80.
Do not add coin by coin. Sort the coins by their value first.
COIN HOW MANY VALUE
₹10 4 10 + 10 + 10 + 10 = ₹40
₹5 4 5 + 5 + 5 + 5 = ₹20
₹20 1 ₹20
40 + 20 = 60
60 + 20 = ₹80
Why it happens: Coins of the same value add up quickly, so grouping the same
coins together saves work.
Page 18 of 61
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
This pattern is worth ₹80.
Do not add coin by coin. Sort the coins by their value first.
COIN HOW MANY VALUE
₹10 4 10 + 10 + 10 + 10 = ₹40
₹5 4 5 + 5 + 5 + 5 = ₹20
₹20 1 ₹20
40 + 20 = 60
60 + 20 = ₹80
Why it happens: Coins of the same value add up quickly, so grouping the same
coins together saves work.
Page 18 of 61
Page 20
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Tip: There are 9 coins here — 8 in the ring and 1 in the middle. Counting the coins
m as e
l
and counting the money are two different jobs.
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 19 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Tip: There are 9 coins here — 8 in the ring and 1 in the middle. Counting the coins
m as e
l
and counting the money are two different jobs.
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 19 of 61
Page 21
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q2 How much money? ________ (the second arrangement)
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are
small silver coins.
ANSWER
Page 20 of 61
Q2 How much money? ________ (the second arrangement)
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are
small silver coins.
ANSWER
Page 20 of 61
Page 22
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are small silver
coins.
The notes and the ₹5 coins come to ₹100. Then add the four small corner coins.
MONEY HOW MANY VALUE
₹10 notes 6 10 + 10 + 10 + 10 + 10 + 10 = ₹60
₹5 coins 8 5 × 8 = ₹40
small silver coins 4 read them in your book
60 + 40 = ₹100
then add the four corner coins
The four corner coins are printed very small, so their number cannot be read clearly. Look at the
four corner coins in your own book. If each one is a ₹1 coin, the pattern is worth 100 + 4 = ₹104.
If each one is a ₹2 coin, it is worth 100 + 8 = ₹108.
Page 21 of 61
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are small silver
coins.
The notes and the ₹5 coins come to ₹100. Then add the four small corner coins.
MONEY HOW MANY VALUE
₹10 notes 6 10 + 10 + 10 + 10 + 10 + 10 = ₹60
₹5 coins 8 5 × 8 = ₹40
small silver coins 4 read them in your book
60 + 40 = ₹100
then add the four corner coins
The four corner coins are printed very small, so their number cannot be read clearly. Look at the
four corner coins in your own book. If each one is a ₹1 coin, the pattern is worth 100 + 4 = ₹104.
If each one is a ₹2 coin, it is worth 100 + 8 = ₹108.
Page 21 of 61
Page 23
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Why it happens: The border, the corners and the middle are three neat groups.
Adding one group at a time is easier than adding eighteen pieces of money one by
one.
Tip: Notes are counted the same way as coins. A ₹10 note and a ₹10 coin are worth
exactly the same.
Page 22 of 61
Why it happens: The border, the corners and the middle are three neat groups.
Adding one group at a time is easier than adding eighteen pieces of money one by
one.
Tip: Notes are counted the same way as coins. A ₹10 note and a ₹10 coin are worth
exactly the same.
Page 22 of 61
Page 24
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q3 How did you count them? Discuss in class.
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
Page 23 of 61
Q3 How did you count them? Discuss in class.
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
Page 23 of 61
Page 25
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co ₹10 ₹10 a g
ase
agl
co m
m . ag
l a se
ag
₹5 ₹5 ₹5 ₹5
₹10
₹10
co m
e m.
m ₹5las
.co
₹5 ₹5 ₹5
ag
a sem
agl
₹10 m ₹10 a s
em
. co agl
a s
agl
The second money pattern — six ₹10 notes make a border. The four corner coins are
small silver coins.
co m
m .
as e
. com a g l
s em
ANSWER
gl a
a
se m
com g l a
m . a
ase
agl
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 24 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co ₹10 ₹10 a g
ase
agl
co m
m . ag
l a se
ag
₹5 ₹5 ₹5 ₹5
₹10
₹10
co m
e m.
m ₹5las
.co
₹5 ₹5 ₹5
ag
a sem
agl
₹10 m ₹10 a s
em
. co agl
a s
agl
The second money pattern — six ₹10 notes make a border. The four corner coins are
small silver coins.
co m
m .
as e
. com a g l
s em
ANSWER
gl a
a
se m
com g l a
m . a
ase
agl
co m
m .
m ase
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 24 of 61
Page 26
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
Page 25 of 61
₹5
₹10 ₹10
₹5 ₹20 ₹5
₹10 ₹10
₹5
The first money pattern — eight coins placed in a ring around one coin.
Page 25 of 61
Page 27
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are small silver
coins.
Here are three good ways to tell the class how you counted. Any of them is correct.
1. Group the same coins. Put all the ₹10 coins together, all the ₹5 coins together, and so on.
Find the value of each group, then add the groups.
2. Follow the shape. In the first picture, go round the ring and then take the middle coin. In
the second picture, take the border of notes first, then the corners, then the block of coins in
the middle.
3. Skip-count. For the ₹5 coins say 5, 10, 15, 20, 25, 30, 35, 40. For the ₹10 notes say 10, 20, 30,
40, 50, 60.
First pattern: 40 + 20 + 20 = ₹80
Second pattern: 60 + 40 = ₹100, and then the four corner coins
Why it happens: The money was laid out in a pattern on purpose. A pattern tells
your eye where one group ends and the next begins, so you do not lose your place.
Page 26 of 61
₹10 ₹10
₹5 ₹5 ₹5 ₹5
₹10
₹10
₹5 ₹5 ₹5 ₹5
₹10 ₹10
The second money pattern — six ₹10 notes make a border. The four corner coins are small silver
coins.
Here are three good ways to tell the class how you counted. Any of them is correct.
1. Group the same coins. Put all the ₹10 coins together, all the ₹5 coins together, and so on.
Find the value of each group, then add the groups.
2. Follow the shape. In the first picture, go round the ring and then take the middle coin. In
the second picture, take the border of notes first, then the corners, then the block of coins in
the middle.
3. Skip-count. For the ₹5 coins say 5, 10, 15, 20, 25, 30, 35, 40. For the ₹10 notes say 10, 20, 30,
40, 50, 60.
First pattern: 40 + 20 + 20 = ₹80
Second pattern: 60 + 40 = ₹100, and then the four corner coins
Why it happens: The money was laid out in a pattern on purpose. A pattern tells
your eye where one group ends and the next begins, so you do not lose your place.
Page 26 of 61
Page 28
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Try This: Ask your friend to count the same picture a different way. You should both
reach the same amount — the way of counting may change, the money cannot.
Q4 Arrange play money of amounts 1, 2, 5, and 10 to show `36, `125, and `183. Ask your
peers to tell how much it is.
ANSWER
Take out your play notes and coins of ₹1, ₹2, ₹5 and ₹10. Work in this order.
1. Use as many ₹10 as you can without going over the amount.
2. Then use ₹5, then ₹2, then ₹1 to finish it off.
3. Lay the money out in a neat pattern — a row, a ring or a square.
4. Ask a friend to count it and say the amount out loud.
Sample answer:
AMOUNT ₹10 ₹5 ₹2 ₹1 CHECK
₹36 3 1 0 1 30 + 5 + 1 = 36
₹125 12 1 0 0 120 + 5 = 125
₹183 18 0 1 1 180 + 2 + 1 = 183
Other ways are also right. For ₹36 you could take 3 tens and 3 twos, because 30 + 6 = 36.
Why it happens: Starting with the biggest note keeps the pile small, so your friend
has less to count.
Check it yourself: Count your own arrangement twice, in two different orders. If
both counts give the same amount, you have made it correctly.
Two Ways — Page 35
Page 27 of 61
Try This: Ask your friend to count the same picture a different way. You should both
reach the same amount — the way of counting may change, the money cannot.
Q4 Arrange play money of amounts 1, 2, 5, and 10 to show `36, `125, and `183. Ask your
peers to tell how much it is.
ANSWER
Take out your play notes and coins of ₹1, ₹2, ₹5 and ₹10. Work in this order.
1. Use as many ₹10 as you can without going over the amount.
2. Then use ₹5, then ₹2, then ₹1 to finish it off.
3. Lay the money out in a neat pattern — a row, a ring or a square.
4. Ask a friend to count it and say the amount out loud.
Sample answer:
AMOUNT ₹10 ₹5 ₹2 ₹1 CHECK
₹36 3 1 0 1 30 + 5 + 1 = 36
₹125 12 1 0 0 120 + 5 = 125
₹183 18 0 1 1 180 + 2 + 1 = 183
Other ways are also right. For ₹36 you could take 3 tens and 3 twos, because 30 + 6 = 36.
Why it happens: Starting with the biggest note keeps the pile small, so your friend
has less to count.
Check it yourself: Count your own arrangement twice, in two different orders. If
both counts give the same amount, you have made it correctly.
Two Ways — Page 35
Page 27 of 61
Page 29
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
TWO WAYS
Q1 Shirley and Shiv arranged their coins in the following ways. Write the number of
coins in the triangles.
3 5
Shirley’s coin packs. Two triangles are already filled in.
4
Shiv’s coin packs. One triangle is already filled in.
ANSWER
Page 28 of 61
TWO WAYS
Q1 Shirley and Shiv arranged their coins in the following ways. Write the number of
coins in the triangles.
3 5
Shirley’s coin packs. Two triangles are already filled in.
4
Shiv’s coin packs. One triangle is already filled in.
ANSWER
Page 28 of 61
Page 30
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
.co a g
a s em
agl 3 5
m a s
.co agl
Shirley’s coin packs. Two triangles are already filled in.
se m
g l a
a
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m 4 as e
. c o a g l
se m
g l a Shiv’s coin packs. One triangle is already filled in.
a c
m .
Count each pack and write the number in its triangle.
m a s e
Shirley’s packs, from left to right:
e m . co agl
g l as
3 11 17 1 7
a
5
co m
m .
m as e
.co
a g l Page 29 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
em.
m l as
.co a g
a s em
agl 3 5
m a s
.co agl
Shirley’s coin packs. Two triangles are already filled in.
se m
g l a
a
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m 4 as e
. c o a g l
se m
g l a Shiv’s coin packs. One triangle is already filled in.
a c
m .
Count each pack and write the number in its triangle.
m a s e
Shirley’s packs, from left to right:
e m . co agl
g l as
3 11 17 1 7
a
5
co m
m .
m as e
.co
a g l Page 29 of 61
Page 31
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
3 11 17 1 7 5
Shirley’s packs with every triangle filled in.
Shiv’s packs, from left to right:
4 14 12 6 8
4 14 12 6 8
Shiv’s packs with every triangle filled in.
Page 30 of 61
3 11 17 1 7 5
Shirley’s packs with every triangle filled in.
Shiv’s packs, from left to right:
4 14 12 6 8
4 14 12 6 8
Shiv’s packs with every triangle filled in.
Page 30 of 61
Page 32
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Count a pack by rows of two. For Shirley’s longest pack: 2, 4, 6, 8, 10, 12, 14, 16 and then one
more coin alone, which makes 17.
Why it happens: Both children put their coins two in a row. Shiv’s packs always end
with a full row of two. Shirley’s packs always end with one coin sitting alone.
Did you know? Shirley has 3 + 11 + 17 + 1 + 7 + 5 = 44 coins, and Shiv has 4 + 14 + 12
+ 6 + 8 = 44 coins. They have exactly the same number of coins, arranged in two
different ways.
In-text Questions — Page 36
Page 31 of 61
Count a pack by rows of two. For Shirley’s longest pack: 2, 4, 6, 8, 10, 12, 14, 16 and then one
more coin alone, which makes 17.
Why it happens: Both children put their coins two in a row. Shiv’s packs always end
with a full row of two. Shirley’s packs always end with one coin sitting alone.
Did you know? Shirley has 3 + 11 + 17 + 1 + 7 + 5 = 44 coins, and Shiv has 4 + 14 + 12
+ 6 + 8 = 44 coins. They have exactly the same number of coins, arranged in two
different ways.
In-text Questions — Page 36
Page 31 of 61
Page 33
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Even numbers and odd numbers
MATH TALK
Q1 Describe Shiv’s arrangement and write his numbers.
4
Shiv’s coin packs. One triangle is already filled in.
ANSWER
4
Shiv’s coin packs. One triangle is already filled in.
Shiv’s arrangement: he puts his coins two side by side, row after row. Every row is full. When he
finishes a pack, no coin is left alone.
His numbers are:
Page 32 of 61
Even numbers and odd numbers
MATH TALK
Q1 Describe Shiv’s arrangement and write his numbers.
4
Shiv’s coin packs. One triangle is already filled in.
ANSWER
4
Shiv’s coin packs. One triangle is already filled in.
Shiv’s arrangement: he puts his coins two side by side, row after row. Every row is full. When he
finishes a pack, no coin is left alone.
His numbers are:
Page 32 of 61
Page 34
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
4, 14, 12, 6, 8
Written from the smallest to the biggest: 4, 6, 8, 12, 14.
Every one of them can be split into pairs:
4 = 2 pairs
6 = 3 pairs
8 = 4 pairs
12 = 6 pairs
14 = 7 pairs
Why it happens: A number that fills every row of two can be shared equally
between two children. Such numbers are called even numbers.
Tip: To test any number, keep taking away 2. If you end at 0, the number is even.
Page 33 of 61
4, 14, 12, 6, 8
Written from the smallest to the biggest: 4, 6, 8, 12, 14.
Every one of them can be split into pairs:
4 = 2 pairs
6 = 3 pairs
8 = 4 pairs
12 = 6 pairs
14 = 7 pairs
Why it happens: A number that fills every row of two can be shared equally
between two children. Such numbers are called even numbers.
Tip: To test any number, keep taking away 2. If you end at 0, the number is even.
Page 33 of 61
Page 35
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Describe Shirley’s arrangement and write her numbers.
e
Q2
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
m.
3 5
m as e
.co
Shirley’s coin packs. Two triangles are already filled in.
a g l
se m
g l a
a
s
ANSWER
m a
m .co agl
l a se
a g
com
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
3
m . 5
m as e
.co a g l
m
Shirley’s coin packs. Two triangles are already filled in.
l a se
ag Shirley’s arrangement: she also puts her coins two side by side. But in every pack the last row
.c
has only one coin. One coin is always left over.
s e m
m a
Her numbers are:
e m . co agl
g l as
3, 11, 17, 1, 7, 5 a
co m
m .
m as e
.co
a g l Page 34 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Describe Shirley’s arrangement and write her numbers.
e
Q2
m l as
m .co a g
l a se
a g
co m
e m . ag
g l as
a
co m
m.
3 5
m as e
.co
Shirley’s coin packs. Two triangles are already filled in.
a g l
se m
g l a
a
s
ANSWER
m a
m .co agl
l a se
a g
com
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
3
m . 5
m as e
.co a g l
m
Shirley’s coin packs. Two triangles are already filled in.
l a se
ag Shirley’s arrangement: she also puts her coins two side by side. But in every pack the last row
.c
has only one coin. One coin is always left over.
s e m
m a
Her numbers are:
e m . co agl
g l as
3, 11, 17, 1, 7, 5 a
co m
m .
m as e
.co
a g l Page 34 of 61
Page 36
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Written from the smallest to the biggest: 1, 3, 5, 7, 11, 17.
6 → 3 pairs 7 → 3 pairs, 1 left
Making pairs: 6 pairs off fully, 7 always leaves one out.
Each of her numbers is some pairs and then one extra:
3 = 1 pair + 1
5 = 2 pairs + 1
7 = 3 pairs + 1
11 = 5 pairs + 1
17 = 8 pairs + 1
1 = no pair at all, just 1
Why it happens: A number that leaves one out cannot be shared equally between
two children. Such numbers are called odd numbers.
Tip: Shiv’s numbers and Shirley’s numbers sit next to each other on the number line:
1, 2, 3, 4, 5, 6 … one odd, one even, turn by turn.
Page 35 of 61
Written from the smallest to the biggest: 1, 3, 5, 7, 11, 17.
6 → 3 pairs 7 → 3 pairs, 1 left
Making pairs: 6 pairs off fully, 7 always leaves one out.
Each of her numbers is some pairs and then one extra:
3 = 1 pair + 1
5 = 2 pairs + 1
7 = 3 pairs + 1
11 = 5 pairs + 1
17 = 8 pairs + 1
1 = no pair at all, just 1
Why it happens: A number that leaves one out cannot be shared equally between
two children. Such numbers are called odd numbers.
Tip: Shiv’s numbers and Shirley’s numbers sit next to each other on the number line:
1, 2, 3, 4, 5, 6 … one odd, one even, turn by turn.
Page 35 of 61
Page 37
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q3 Identify numbers between 1 and 20 as even or odd. You may draw the pairing
arrangement of the numbers.
Odd Even
The two boxes printed in the book, waiting to be filled.
ANSWER
Odd Even
The two boxes printed in the book, waiting to be filled.
Try to make pairs out of each number. If one is left out, the number is odd.
Page 36 of 61
Q3 Identify numbers between 1 and 20 as even or odd. You may draw the pairing
arrangement of the numbers.
Odd Even
The two boxes printed in the book, waiting to be filled.
ANSWER
Odd Even
The two boxes printed in the book, waiting to be filled.
Try to make pairs out of each number. If one is left out, the number is odd.
Page 36 of 61
Page 38
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Odd Even
1, 3, 5 2, 4, 6
7, 9, 11 8, 10, 12
13, 15, 17 14, 16, 18
19 20
The same two boxes, filled in.
ODD 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
EVEN 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Here is the pairing for two of them:
6 → 3 pairs 7 → 3 pairs, 1 left
Making pairs: 6 pairs off fully, 7 always leaves one out.
There are 10 odd numbers and 10 even numbers from 1 to 20. They take turns: 1 odd, 2 even, 3
odd, 4 even …
Page 37 of 61
Odd Even
1, 3, 5 2, 4, 6
7, 9, 11 8, 10, 12
13, 15, 17 14, 16, 18
19 20
The same two boxes, filled in.
ODD 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
EVEN 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Here is the pairing for two of them:
6 → 3 pairs 7 → 3 pairs, 1 left
Making pairs: 6 pairs off fully, 7 always leaves one out.
There are 10 odd numbers and 10 even numbers from 1 to 20. They take turns: 1 odd, 2 even, 3
odd, 4 even …
Page 37 of 61
Page 39
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Why it happens: Every time we add 1 to a number, the coin that was left alone gets
a partner, or a new coin is left alone. So even and odd must keep changing turn by
turn.
Tip: If the question means only the numbers strictly between 1 and 20, leave out 1
and 20. You then get 9 odd numbers and 9 even numbers.
Q4 Do you think all numbers in the times-2 table are even?
ANSWER
Yes. Every number in the times-2 table is an even number.
2×1=2 2×2=4 2×3=6 2 × 4 = 8 2 × 5 = 10
2 × 6 = 12 2 × 7 = 14 2 × 8 = 16 2 × 9 = 18 2 × 10 = 20
Look at the ones digit of each answer: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0. It is always 0, 2, 4, 6 or 8 — so
every answer is even.
Why it happens: The times-2 table is made by taking 2s. 2 × 7 means 7 pairs of
coins. Pairs can never leave a single coin out, so the answer must be even.
Check it yourself: Lay out 2 × 9 = 18 buttons as nine rows of two. Not one button is
left alone.
Crayons Arrangement — Page 37
Page 38 of 61
Why it happens: Every time we add 1 to a number, the coin that was left alone gets
a partner, or a new coin is left alone. So even and odd must keep changing turn by
turn.
Tip: If the question means only the numbers strictly between 1 and 20, leave out 1
and 20. You then get 9 odd numbers and 9 even numbers.
Q4 Do you think all numbers in the times-2 table are even?
ANSWER
Yes. Every number in the times-2 table is an even number.
2×1=2 2×2=4 2×3=6 2 × 4 = 8 2 × 5 = 10
2 × 6 = 12 2 × 7 = 14 2 × 8 = 16 2 × 9 = 18 2 × 10 = 20
Look at the ones digit of each answer: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0. It is always 0, 2, 4, 6 or 8 — so
every answer is even.
Why it happens: The times-2 table is made by taking 2s. 2 × 7 means 7 pairs of
coins. Pairs can never leave a single coin out, so the answer must be even.
Check it yourself: Lay out 2 × 9 = 18 buttons as nine rows of two. Not one button is
left alone.
Crayons Arrangement — Page 37
Page 38 of 61
Page 40
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
Crayons Arrangement
co m
em.
m l as
Q1
.co
Circle the odd numbers and put a square around each even number. Use the
m a g
l a se
crayons arrangement, if needed.
a g
co m
e m . ag
5
aglas
8 36 69
odd even
co m
em.
m l as
m .co a g
l a se 22 51 30 38
a g
m a s
m.co agl
37
l a se 52 43
a g
co m
m
The eleven numbers printed on page 37. Two of them are already marked in the book.
.
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
em . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 39 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
Crayons Arrangement
co m
em.
m l as
Q1
.co
Circle the odd numbers and put a square around each even number. Use the
m a g
l a se
crayons arrangement, if needed.
a g
co m
e m . ag
5
aglas
8 36 69
odd even
co m
em.
m l as
m .co a g
l a se 22 51 30 38
a g
m a s
m.co agl
37
l a se 52 43
a g
co m
m
The eleven numbers printed on page 37. Two of them are already marked in the book.
.
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
em . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 39 of 61
Page 41
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Page 40 of 61
Page 40 of 61
Page 42
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
1 2
3 4
5 6
7 8
9 10
11 12
13 14
Page 41 of 61
1 2
3 4
5 6
7 8
9 10
11 12
13 14
Page 41 of 61
Page 43
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
ANSWER
Page 42 of 61
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
ANSWER
Page 42 of 61
Page 44
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
5 8 36 69
odd even
22 51 30 38
37 52 43
The eleven numbers printed on page 37. Two of them are already marked in the book.
Look at the ones digit of each number and then mark it.
5 8 36 69
odd even
22 51 30 38
37 52 43
Every number marked: a ring for odd, a box for even.
Page 43 of 61
5 8 36 69
odd even
22 51 30 38
37 52 43
The eleven numbers printed on page 37. Two of them are already marked in the book.
Look at the ones digit of each number and then mark it.
5 8 36 69
odd even
22 51 30 38
37 52 43
Every number marked: a ring for odd, a box for even.
Page 43 of 61
Page 45
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
PUT A CIRCLE (ODD) 5, 51, 37, 43, 69
m ase
.co
PUT A SQUARE (EVEN)
a
8, 36, 22, 30, 38, 52
g l
a s em
a gl has already ringed 5 and boxed 8 for you. So you have to mark the other nine: 36, 69,
The book
22, 51, 30, 38, 37, 52, 43.
co m
ag
The crayon strip helps. Find the number on the crayon: if it is in the left column it is odd, if it is in
m .
e
the right column it is even.
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 44 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
PUT A CIRCLE (ODD) 5, 51, 37, 43, 69
m ase
.co
PUT A SQUARE (EVEN)
a
8, 36, 22, 30, 38, 52
g l
a s em
a gl has already ringed 5 and boxed 8 for you. So you have to mark the other nine: 36, 69,
The book
22, 51, 30, 38, 37, 52, 43.
co m
ag
The crayon strip helps. Find the number on the crayon: if it is in the left column it is odd, if it is in
m .
e
the right column it is even.
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 44 of 61
Page 46
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Page 45 of 61
Page 45 of 61
Page 47
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
1 2
3 4
5 6
7 8
9 10
11 12
Page 46 of 61
1 2
3 4
5 6
7 8
9 10
11 12
Page 46 of 61
Page 48
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
13 14
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
Why it happens: Tens always pair off by themselves, so only the ones digit decides.
52 is 5 tens and 2 ones; the 2 ones make one pair, so nothing is left over.
Tip: You never need to count a big number in twos. Just cover the tens with your
thumb and look at the last digit.
Page 47 of 61
13 14
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
Why it happens: Tens always pair off by themselves, so only the ones digit decides.
52 is 5 tens and 2 ones; the 2 ones make one pair, so nothing is left over.
Tip: You never need to count a big number in twos. Just cover the tens with your
thumb and look at the last digit.
Page 47 of 61
Page 49
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q2 Which numbers are even and which are odd? Discuss.
5 8 36 69
odd even
22 51 30 38
37 52 43
The eleven numbers printed on page 37. Two of them are already marked in the book.
ANSWER
5 8 36 69
odd even
22 51 30 38
37 52 43
Page 48 of 61
Q2 Which numbers are even and which are odd? Discuss.
5 8 36 69
odd even
22 51 30 38
37 52 43
The eleven numbers printed on page 37. Two of them are already marked in the book.
ANSWER
5 8 36 69
odd even
22 51 30 38
37 52 43
Page 48 of 61
Page 50
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
The eleven numbers printed on page 37. Two of them are already marked in the book.
co m
em.
com g l as
. a
em
EVEN NUMBERS 8, 22, 30, 36, 38, 52
a s
gl NUMBERS
aODD 5, 37, 43, 51, 69
com ag
Tell the class how you decided. This is the reason to give:
.
22, 30, 36, 38, 52 and 8 end in 2, 0, 6, 8,e2mand 8. Those digits are even, so the numbers are
g l as
even.
a
37, 43, 51, 69 and 5 end in 7, 3, 1, 9 and 5. Those digits are odd, so the numbers are odd.
co m
em.
m l as
52 → 5 tens and 2 ones → the 2 ones make 1 pair → even
. c o a g
s
51 →
e m5 tens and 1 one → that 1 one has no partner → odd
a
agl
m
Why it happens: Ten is 5 pairs, so every ten pairs off perfectly. Only the leftover
a s
ones can spoil the pairing.
m.co agl
l a se
a g
Did you know? This is why a car number plate, a house number or a bus number
can be called even or odd just by glancing at its last digit.
co m
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 49 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
The eleven numbers printed on page 37. Two of them are already marked in the book.
co m
em.
com g l as
. a
em
EVEN NUMBERS 8, 22, 30, 36, 38, 52
a s
gl NUMBERS
aODD 5, 37, 43, 51, 69
com ag
Tell the class how you decided. This is the reason to give:
.
22, 30, 36, 38, 52 and 8 end in 2, 0, 6, 8,e2mand 8. Those digits are even, so the numbers are
g l as
even.
a
37, 43, 51, 69 and 5 end in 7, 3, 1, 9 and 5. Those digits are odd, so the numbers are odd.
co m
em.
m l as
52 → 5 tens and 2 ones → the 2 ones make 1 pair → even
. c o a g
s
51 →
e m5 tens and 1 one → that 1 one has no partner → odd
a
agl
m
Why it happens: Ten is 5 pairs, so every ten pairs off perfectly. Only the leftover
a s
ones can spoil the pairing.
m.co agl
l a se
a g
Did you know? This is why a car number plate, a house number or a bus number
can be called even or odd just by glancing at its last digit.
co m
m .
m ase
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m as e
.co
a g l Page 49 of 61
Page 51
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Q3 Explore your textbook and find out what Shirley has seen. Draw a square on the
even numbers. Put a circle on the odd numbers.
ANSWER
36 37
left-hand page right-hand page
An open Maths book. The page number sits at the bottom of each page.
What Shirley has seen: in her Maths book every left-hand page has an even number and every
right-hand page has an odd number.
Do this yourself:
1. Open this book at any place and keep it flat.
2. Read the page number at the bottom of the left page — for example 36. Put a square on it.
3. Read the page number on the right page — 37. Put a circle on it.
4. Turn the page and do it again: 38 on the left, 39 on the right.
Left pages: 34, 36, 38, 40 … → all even
Right pages: 35, 37, 39, 41 … → all odd
Reading straight through: 34, 35, 36, 37, 38 → even, odd, even, odd, even
Why it happens: Every sheet of paper has two sides. The front side is a right-hand
page and the back side is the next left-hand page, so the numbers keep changing
turn by turn.
Page 50 of 61
Q3 Explore your textbook and find out what Shirley has seen. Draw a square on the
even numbers. Put a circle on the odd numbers.
ANSWER
36 37
left-hand page right-hand page
An open Maths book. The page number sits at the bottom of each page.
What Shirley has seen: in her Maths book every left-hand page has an even number and every
right-hand page has an odd number.
Do this yourself:
1. Open this book at any place and keep it flat.
2. Read the page number at the bottom of the left page — for example 36. Put a square on it.
3. Read the page number on the right page — 37. Put a circle on it.
4. Turn the page and do it again: 38 on the left, 39 on the right.
Left pages: 34, 36, 38, 40 … → all even
Right pages: 35, 37, 39, 41 … → all odd
Reading straight through: 34, 35, 36, 37, 38 → even, odd, even, odd, even
Why it happens: Every sheet of paper has two sides. The front side is a right-hand
page and the back side is the next left-hand page, so the numbers keep changing
turn by turn.
Page 50 of 61
Page 52
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Try This: Check a story book and a newspaper too. You will find the same rule in
every printed book.
In-text Questions — Page 38
Even and odd numbers, page numbers and neighbours
MATH TALK
Q1 Identify which of the following numbers are even and which are odd. Explain your
reasoning.
30 78 300 415
46 67 154 99
The eight numbers printed on page 38.
Odd numbers : ____________ Even numbers : ____________
ANSWER
30 78 300 415
46 67 154 99
The eight numbers printed on page 38.
Look only at the last digit of each number.
Page 51 of 61
Try This: Check a story book and a newspaper too. You will find the same rule in
every printed book.
In-text Questions — Page 38
Even and odd numbers, page numbers and neighbours
MATH TALK
Q1 Identify which of the following numbers are even and which are odd. Explain your
reasoning.
30 78 300 415
46 67 154 99
The eight numbers printed on page 38.
Odd numbers : ____________ Even numbers : ____________
ANSWER
30 78 300 415
46 67 154 99
The eight numbers printed on page 38.
Look only at the last digit of each number.
Page 51 of 61
Page 53
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
30 78 300 415
46 67 154 99
even even even odd
even odd even odd
The same eight numbers, each one named.
ODD NUMBERS 67, 415, 99
EVEN NUMBERS 30, 46, 78, 300, 154
My reason, number by number:
30 ends in 0 — even. 46 ends in 6 — even. 78 ends in 8 — even.
300 ends in 0 — even. 154 ends in 4 — even.
67 ends in 7 — odd. 415 ends in 5 — odd. 99 ends in 9 — odd.
Why it happens: Every ten and every hundred can be split into pairs on its own. So
only the ones left over decide whether one is left alone.
Tip: A big number does not have to be an even number. 300 is big and even, 415 is
big and odd. Size has nothing to do with it.
Q2 Make two 2-digit numbers using the digits 1 and 6 without repetition.
ANSWER
The two numbers are 16 and 61.
Put 1 in the tens place and 6 in the ones place → 16
Put 6 in the tens place and 1 in the ones place → 61
‘Without repetition’ means you may not use the same digit twice. So 11 and 66 are not allowed.
Why it happens: With two different digits there are only two places to fill, so there
are only two ways to arrange them.
Page 52 of 61
30 78 300 415
46 67 154 99
even even even odd
even odd even odd
The same eight numbers, each one named.
ODD NUMBERS 67, 415, 99
EVEN NUMBERS 30, 46, 78, 300, 154
My reason, number by number:
30 ends in 0 — even. 46 ends in 6 — even. 78 ends in 8 — even.
300 ends in 0 — even. 154 ends in 4 — even.
67 ends in 7 — odd. 415 ends in 5 — odd. 99 ends in 9 — odd.
Why it happens: Every ten and every hundred can be split into pairs on its own. So
only the ones left over decide whether one is left alone.
Tip: A big number does not have to be an even number. 300 is big and even, 415 is
big and odd. Size has nothing to do with it.
Q2 Make two 2-digit numbers using the digits 1 and 6 without repetition.
ANSWER
The two numbers are 16 and 61.
Put 1 in the tens place and 6 in the ones place → 16
Put 6 in the tens place and 1 in the ones place → 61
‘Without repetition’ means you may not use the same digit twice. So 11 and 66 are not allowed.
Why it happens: With two different digits there are only two places to fill, so there
are only two ways to arrange them.
Page 52 of 61
Page 54
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Tip: 16 and 61 use the very same digits, but they are not the same number. The place
of a digit decides its value.
Q3 Identify the numbers as even or odd. Now choose any two digits and make 2-digit
numbers in such a way that the numbers are even.
ANSWER
First, name the two numbers you made from 1 and 6:
16 ends in 6 → even
61 ends in 1 → odd
Now pick two digits that will give even numbers both ways. Pick two even digits.
Sample answer: take the digits 2 and 4.
2 and 4 → 24 and 42
24 ends in 4 → even
42 ends in 2 → even
Other pairs that work: 4 and 6 give 46 and 64; 6 and 8 give 68 and 86; 2 and 8 give 28 and 82.
Why it happens: A number is even when its ones digit is even. If both digits are
even, then whichever one you put in the ones place, the number stays even.
Check it yourself: Try 3 and 5. You get 35 and 53 — both odd. Two odd digits can
never make an even 2-digit number.
Q4 Are there more even or odd numbers between 1 and 100?
ANSWER
Neither. There are just as many even numbers as odd numbers.
Page 53 of 61
Tip: 16 and 61 use the very same digits, but they are not the same number. The place
of a digit decides its value.
Q3 Identify the numbers as even or odd. Now choose any two digits and make 2-digit
numbers in such a way that the numbers are even.
ANSWER
First, name the two numbers you made from 1 and 6:
16 ends in 6 → even
61 ends in 1 → odd
Now pick two digits that will give even numbers both ways. Pick two even digits.
Sample answer: take the digits 2 and 4.
2 and 4 → 24 and 42
24 ends in 4 → even
42 ends in 2 → even
Other pairs that work: 4 and 6 give 46 and 64; 6 and 8 give 68 and 86; 2 and 8 give 28 and 82.
Why it happens: A number is even when its ones digit is even. If both digits are
even, then whichever one you put in the ones place, the number stays even.
Check it yourself: Try 3 and 5. You get 35 and 53 — both odd. Two odd digits can
never make an even 2-digit number.
Q4 Are there more even or odd numbers between 1 and 100?
ANSWER
Neither. There are just as many even numbers as odd numbers.
Page 53 of 61
Page 55
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
Even: 2, 4, 6, 8 … 98, 100 → 50 numbers
m l as
.co
Odd: 1, 3, 5, 7 … 97, 99 → 50 numbers
m a g
l a se
g
50 + 50 = 100
a
co m
You can see it best by writing the numbers two in a row, as the crayon in the book does.
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 54 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
e m.
Even: 2, 4, 6, 8 … 98, 100 → 50 numbers
m l as
.co
Odd: 1, 3, 5, 7 … 97, 99 → 50 numbers
m a g
l a se
g
50 + 50 = 100
a
co m
You can see it best by writing the numbers two in a row, as the crayon in the book does.
e m . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
m ase
.co
a g l Page 54 of 61
Page 56
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Page 55 of 61
Page 55 of 61
Page 57
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
1 2
3 4
5 6
7 8
9 10
11 12
Page 56 of 61
1 2
3 4
5 6
7 8
9 10
11 12
Page 56 of 61
Page 58
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
13 14
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
The left column holds every odd number and the right column holds every even number. Both
columns have the same length, so the two kinds are equal in number.
Why it happens: Numbers go odd, even, odd, even … in turn. In any run that starts
at 1 and ends at an even number, each odd number has exactly one even partner
just after it.
Page 57 of 61
13 14
15 16
17 18
19 20
...
99 100
The crayon in the book, with the numbers 1 to 100 written two in a row.
The left column holds every odd number and the right column holds every even number. Both
columns have the same length, so the two kinds are equal in number.
Why it happens: Numbers go odd, even, odd, even … in turn. In any run that starts
at 1 and ends at an even number, each odd number has exactly one even partner
just after it.
Page 57 of 61
Page 59
Class 4 Maths Chapter 3 Patterns Around Us AglaSem · NCERT Solutions
Tip: If you leave out 1 and 100 and take only the numbers strictly between them, you
get 49 odd and 49 even — still the same many of each.
Q5 Shiv wonders if both the numbers, before and after an even number, will be odd.
What do you think? Check and discuss.
ANSWER
Shiv is right. The number just before an even number and the number just after it are both
odd.
Check it with a few numbers:
BEFORE EVEN NUMBER AFTER
7 (odd) 8 9 (odd)
19 (odd) 20 21 (odd)
45 (odd) 46 47 (odd)
99 (odd) 100 101 (odd)
Shirley had already noticed the other half of the same rule: the numbers before and after an
odd number are both even. For example 6, 7, 8.
… 6 7 8 9 10 11 12 …
even odd even odd even odd even
Why it happens: Adding one coin to an even group leaves one coin alone, and
taking one coin away from an even group also leaves one alone. So both neighbours
must be odd.
Check it yourself: Take 10 pebbles and make 5 pairs. Add one pebble — it has no
partner. Take two away from 10 — you get 8 again, still all in pairs.
Page 58 of 61
Tip: If you leave out 1 and 100 and take only the numbers strictly between them, you
get 49 odd and 49 even — still the same many of each.
Q5 Shiv wonders if both the numbers, before and after an even number, will be odd.
What do you think? Check and discuss.
ANSWER
Shiv is right. The number just before an even number and the number just after it are both
odd.
Check it with a few numbers:
BEFORE EVEN NUMBER AFTER
7 (odd) 8 9 (odd)
19 (odd) 20 21 (odd)
45 (odd) 46 47 (odd)
99 (odd) 100 101 (odd)
Shirley had already noticed the other half of the same rule: the numbers before and after an
odd number are both even. For example 6, 7, 8.
… 6 7 8 9 10 11 12 …
even odd even odd even odd even
Why it happens: Adding one coin to an even group leaves one coin alone, and
taking one coin away from an even group also leaves one alone. So both neighbours
must be odd.
Check it yourself: Take 10 pebbles and make 5 pairs. Add one pebble — it has no
partner. Take two away from 10 — you get 8 again, still all in pairs.
Page 58 of 61
Page 60
as e
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Choose any 10 numbers in order without skipping any (consecutive numbers). Write
e
Q6
m l as
.co
whether they are even or odd below each number. What do you notice? Discuss.
a g
se m
g l a
a
20 21
co m
e m . ag
g l as
a
The strip of ten circles in the book. The first two are filled in.
co m
em.
ANSWER .co
m g l as
em a
a s
agl
m a s
.co agl
20 21
se m
g l a
a
co m
The strip of ten circles in the book. The first two are filled in.
m .
o m l a se
g any number.
.c has started the strip at 20 and 21. Carry on without skipping
a
se m
The book
g l a
a
se m
23 .com g l a
20 21 22
em
24 25 26 27 28 29
a
a s
even odd agl odd even
even odd even odd even odd
co m
m .
e
The strip filled in, with each number named below it.
m l as
.co a g
a s em NUMBER
gl
20 21 22 23 24 25 26 27 28 29
a c
m .
e
EVEN OR ODD even odd even odd even odd even odd even odd
m a s
What I notice:
e m . co agl
g l as
a
Even and odd come turn by turn — never two evens together and never two odds together.
Out of the ten numbers, 5 are even and 5 are odd.
co m
m .
m as e
.co
a g l Page 59 of 61
Class 4 Maths Chapter 3 Patterns Around Us
a g l AglaSem · NCERT Solutions
co m
m.
Choose any 10 numbers in order without skipping any (consecutive numbers). Write
e
Q6
m l as
.co
whether they are even or odd below each number. What do you notice? Discuss.
a g
se m
g l a
a
20 21
co m
e m . ag
g l as
a
The strip of ten circles in the book. The first two are filled in.
co m
em.
ANSWER .co
m g l as
em a
a s
agl
m a s
.co agl
20 21
se m
g l a
a
co m
The strip of ten circles in the book. The first two are filled in.
m .
o m l a se
g any number.
.c has started the strip at 20 and 21. Carry on without skipping
a
se m
The book
g l a
a
se m
23 .com g l a
20 21 22
em
24 25 26 27 28 29
a
a s
even odd agl odd even
even odd even odd even odd
co m
m .
e
The strip filled in, with each number named below it.
m l as
.co a g
a s em NUMBER
gl
20 21 22 23 24 25 26 27 28 29
a c
m .
e
EVEN OR ODD even odd even odd even odd even odd even odd
m a s
What I notice:
e m . co agl
g l as
a
Even and odd come turn by turn — never two evens together and never two odds together.
Out of the ten numbers, 5 are even and 5 are odd.
co m
m .
m as e
.co
a g l Page 59 of 61
Document Details
| Board / Org | NCERT |
| Exam | Class 4 |
| Type | Solution |
| Pages | 49 |
| Language | english |
| Updated | 13 Oct 2026 |