NCERT Solutions Class 3 Maths Chapter 4 Vacation with My Nani Maa

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 3 · M AT H S

NCERT Solutions + ×
Chapter 4: Vacation
with My Nani Maa

NCERT Textbook — Maths Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

29 – 43 15 56 English

Every question Step by step Exam ready
Activities, in-text questions The working shown, not Written to match how
and all exercises. just the final answer. marks are awarded.

Solutions, notes, sample papers & more at 70 pages

l h h e c i i h i A aS m · NCERT So ut ons
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C L A SS 3 · M AT H S · M AT H S M E L A
NCERT So ut ons — C apt r 4: Va at on w t My Nan
l i h e c i i h i

Maa
Nandini and Chirag spend their holidays at their Nan Maa s house While counting marbles balushahi
i ʼ . , ,

stamps ants radishes and apples they learn to a an su tra t on tens frames on a bead string called a
, , , dd d b c ,

ginladi on a number grid on a number line and with bundles of sticks
, , .

T E XT B OOK B OOK PAGE S
Ma h Mela Cla
t s ss 3 29  43

S EC T I ONS QU E ST I ONS
15 56

M EDI UM
English

Let us Do — Page 29
Nan Maa s ma
i ʼ gic trick

Q1 Can you tell what the trick is?

I shall tell you the number of marbles you have hidden.

on the table handkerchief

In the bookʼs first picture there are 15 marbles on the table. After the child hides some, 11
marbles are left in the open. Nani Maa says, “You have 4 under your handkerchief.ˮ

The trick is subtraction. Nan Maa nows t i k he total. She takes away the marbles she can see.

15 − 11 = 4 marbles are hidden.

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About the book: The third picture shows only 7 marbles. Use the first two pictures:
15 in all, 11 on the table.

− Exp anat on
l i

Why The a ble d
: go away. They are only in two places — on the table
m r s o not

and under the cloth. So the two parts together make the total.

Q2 Perform the trick with your friends. Write the numbers of hidden seeds in the table
below.

TOTAL SEEDS SEEDS ON THE TABLE HIDDEN SEEDS

15 12

17 10

19 8

20 9

23 7

27 12

The book prints two tables; both are shown here as one.

Hidden seeds Total seeds Seeds on the table
 

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TOTAL SEEDS SEEDS ON THE TABLE HIDDEN SEEDS

15 12 3

17 10 7

19 8 11

20 9 11

23 7 16

27 12 15

The hidden seeds are filled in.

15 − 12 = 3 17 − 10 = 7 19 − 8 = 11

20 − 9 = 11 23 − 7 = 16 27 − 12 = 15

− Exp anat on
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Why Seed : he table and hidden seeds together make the total. So the
s on t

hidden ones are the total minus the ones you can see.

For the parent or teacher: The bookʼs note says: say a number between 1 and
9; the child quickly says the number that makes it 9. Repeat with 10 and 20.

n-text Questions — Page 30
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Ba us a n the two boxes
co m
m.
l h hi i

as e
How mcaonymdo we have in total? g l
Q1
m . a
ase
agl
Nandini s box Chirag s box
m
ʼ ʼ

. co ag
e m
g l as
a

co m
em.
m l as
.co
Two tens frames. Each frame has ten small boxes.
a g
se m
g l a
a A NSW E R
om a s
agl
n total they have 12 balushahi.
. c
I

ra s ram to Nanem
Mov rom Chi
a s n s ram Now on ram s a u t n an ar t

agl
e 3 f gʼ f e fill di iʼ f e. e f e i f ll e d 2 e lef .

m
full ten
.coe
two mor
m
a se
.com a g l
m
ase
agl
se m
com g l a
m . a
ase
Ten dots fill the first frame and two dots go in the next frame.

agl
7 + 5 = 10 + 2 = 12
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
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a

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Q2 Draw the number of dots.

Nandini s box ʼ Chirag s boxʼ

Two tens frames. Each frame has ten small boxes.

Two empty tens frames, as printed in the book.

Draw 12 dots: fill the first frame with 10 dots, then draw 2 dots in the second frame.

full ten two more

Ten dots fill the first frame and two dots go in the next frame.

10 + 2 = 12 dots

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Q3 7 Balushahi  5 Balushahi = .......... Balushahi

Nandini s box
ʼ Chirag s box
ʼ

Two tens frames. Each frame has ten small boxes.

7 Balushahi + 5 Balushahi = 12 Balushahi

C ount on from 7 8, 9, 10, 11, 12.

Q4 Nandini: We bought the same number of balushahi from the shop. Did you eat some of
them?
Chirag: Hahahaha! I did eat some.
How many did he eat? .......... Balushahi

Nandini s box
ʼ Chirag s box
ʼ

Two tens frames. Each frame has ten small boxes.

Chi rag ate 2 balushahi.
Both bought the same number. Nandini still has 7 and Chirag has 5.

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7−5=2

Q5 7 Balushahi  5 Balushahi = .......... Balushahi

Nandini s box
ʼ Chirag s box
ʼ

Two tens frames. Each frame has ten small boxes.

7 Balushahi − 5 Balushahi = 2 Balushahi

Count back 5 from 7 6, 5, 4, 3, 2.

n-text Questions — Page 31
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Boo s or Nan Maa, L t us Do an t
k f i e d he Car Gam
d e

Q1 Chirag got 9 story books for Nani Maa and Nandini got 7 puzzle books for Nani Maa.
How many total books did the children get for Nani Maa?
.......... Books + .......... Books = .......... Books

story books puzzle books

The dots show the two kinds of books in tens frames.

9 Books + 7 Books = 16 Books

Mov e 1 d ot to fill the first frame. Now it is a full ten, and 6 dots are left.

full ten six more

Move one dot across: the first frame becomes a full ten.

9 + 7 = 10 + 6 = 16

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co m
m.
Q2 Use the tens frame to solve the following.

m as e
l
(a) 6  8  .............

m .co
(b) 5  10  ............. a g
l a se (c) 9  6  .............
ag (d) 18  9  .............

co m
e m . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se
a g Two empty tens frames, as printed in the book.

m a s
m .co agl
se
g l a
a
(a) 6 + 8 = 14 (6 + 4 = 10, 4 more)

co m
(b) 5 + 10 = 15 (one full ten and 5)
m .
m as e
.co
(c) 9 − 6 = 3
a g l
s m 18 − 9 = 9 (18 − 8 = 10, 10 − 1 = 9)
e(d)
gl a
a
se m
− Exp anat on
com g l a
. a
l i

em what is left.
one frame to ten first, then csount
a
agl
Fill

Why A e f a e h
: at one glance how far a number is from ten. That
om
t ns r m s ows

makes adding and taking away quick.
. c
s e m
m a
e m . co agl
g l as
a c
m .
m a s e
e m . co agl
g l as
a

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Q3 Make four sets of number cards with numbers 1 to 10. Shuffle and spread out all cards
facing down. Take turns with your friends to open one card at a time. When you open,
look at your card, and the cards that are already opened. If any three cards make an
addition or a subtraction statement, you can keep all three cards. Else, put it down
opened. For example, Nandini opens 4. The numbers 2 and 6 are already opened. So,
Nandini can keep all three cards: 2, 4 and 6. The game continues till all cards are
opened. Whoever collects the greatest number of cards wins the game.

2

4 6

ards lie face down. Three cards are open: 2, 4 and 6.
C

Sample turn: Nan n op ns 4. T di i e he c ar s an
d 2 d 6 ar op n
e e . 2  4  6, so she keeps all three
car s
d .

Ot r s ts t at wor
he e h k: 3, 5, 8 3  5  8 1, 9, 10 2, 5, 7.

− Exp anat on
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Ma ke 40 c ar sd — f our sets of 1 to 10. In each turn, open one card and look at all the open
car sd .

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Why Whe : bers add to make the third, they also give a subtraction: 2
n two num

+ 4  6 and 6  4  2. That is why the three cards go together.

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The stamp collection on the ginladi

Q1 Nandini and Chirag have got their stamps to show to their friends and Nani Maa.
Children: Look, Nani Maa. We have collected 15 stamps.
Nani Maa: Let me give you some more. Here are 7 more.
How many stamps do they have now?

15 Stamps + 7 Stamps = 22 Stamps

Or 15 + 7 = 22

The y now have 22 stamps. Start at bead 15 on the ginladi and move 7 beads ahead.

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The b ook shows three ways on the ginladi. All three reach 22

7
Way 1  seven jumps of 1

15 22

5 1 1
Way 2  a jump of 5, then two jumps of 1

15 20 22

10 1 1 1
Way 3  a jump of 10, then three jumps back of 1

15 22 25

The three ways Nandini, Chirag and Nani Maa used on the ginladi.

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Why A big j
: and then a small correction lands on the same bead. The path
ump

may change, the answer does not.

Q2 Nandini and Chirag have 22 stamps. Nani Maaʼs brother gives them his collection of 30
stamps. How many stamps do they have now?
22 Stamps + .......... Stamps = .......... Stamps
Or 22  .......... = ..........

A plain ginladi. The beads are tied in groups of ten.

22 Stamps + 30 Stamps = 52 Stamps

Or 22 + 30 = 52

s three tens. From 22, make three jumps of 10 22
30 i   
32 42 52.

10 10 10

22 32 42 52

Three jumps of ten carry the bead from 22 to 52.

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Stamps of famous persons and of monuments

Q1 They now have 52 stamps. Nandini and Chirag count and find that they have 37
stamps with faces of famous persons and the remaining with pictures of monuments.
How many stamps with pictures of monuments do they have?
52 Stamps  37 Stamps = .......... Stamps
Or 37 Stamps + .......... Stamps  52 Stamps

A plain ginladi. The beads are tied in groups of ten.

52 Stamps − 37 Stamps = 15 Stamps

Or 37 Stamps + 15 Stamps = 52 Stamps

The y have 15 monument stamps. Nandiniʼs way: jump back 2, then 10, then 3. 2  10  3  15.

3 10 2

37 40 50 52

Nandiniʼs way on the ginladi: she jumps back from 52.

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co m
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Q2 They have 15 stamps with pictures of monuments. Can you find other ways of doing it?

m as e
.co a g l
se m
g l a
a

. com ag
plain ginladi eTm
a s he beads are tied in groups of ten

agl
A . .

co m
m.

m as e
l
Yes. Two other ways:
.co a g
a s em
a gl 1: 52 − 30 = 22, then 22 − 7 = 15
Way

s
Way 2: count up from 37: 37 + 3 = 40, 40 + 12 = 52. 3 + 12 = 15
m a
m .co agl
l a se
g
− Exp anat on
a
l i

Why Taki g a a 37 i
: n e go or in two goes removes the same num
w y n on
. c omber of
stamps. So the answer is the same. Counting up from 37 to 52 m
s e also gives the
. pm
gcao between them. gla a
m
ase
agl For the parent or teacher: The bookʼs note asks you to encourage different
se m
com a
ways of jumping on the number line and to revise skip counting.

. ag l
m
ase
agl

co m
m .
m as e
.co a g l
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Q3 Children: Nani Maa, we have 52 stamps now. Next time when we come, we will have
75 stamps!
How many more stamps will they need? Figure it out using the number line.
.......... Stamps + .......... Stamps = .......... Stamps
Or, .......... + .......... = ..........

A plain ginladi. The beads are tied in groups of ten.

T y will need 23 more stamps.
he

52 Stamps + 23 Stamps = 75 Stamps

Or, 52 + 23 = 75

From 52, jump 8 to reach 60, then jump 15 to reach 75. 8  15  23.

8 15

52 60 75

ounting on from 52 up to 75 on the ginladi.
C

Let us o — Page 34
D

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Jumping on the ginladi, and the ants under the leaves

Q1 1. Solve using a ginladi.
(a) 34  6 (b) 23  12 (c) 33  5 (d) 42  15

A plain ginladi. The beads are tied in groups of ten.

(a) 34 + 6 = 40
(b) 23 + 12: 23 + 10 = 33, 33 + 2 = 35

(c) 33 − 5: 33 − 3 = 30, 30 − 2 = 28

(d) 42 − 15: 42 − 10 = 32, 32 − 5 = 27

− Exp anat on
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On t he gi nladi, first jump the tens, then the ones. For 42  15 you can also go 32  2  30,
then 30  3  27.

Why The bead a e ied i g
: s f e . Jumping a whole group of ten is
r t n roups o t n

quicker than counting bead by bead.

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Q2 2. A frog is jumping on the ginladi. He is at 7. He wants to jump 10 beads at a time. Mark
the beads that he will jump on and write the numbers.

7

The frog is sitting on the 7th bead.

T he frog jumps on 17, 27, 37, 47, 57, 67, 77, 87 and 97.

7 17 27 37 47 57 67 77 87 97

E very jump of 10 lands on a bead whose number ends in 7.

Ea ch j ump adds 10. The 7 at the end never changes.

Q3 3. The frog again jumps forward by 10 each time. Mark all the places where the frog
will land.

23

The frog is now on the 23rd bead.

T he frog starts at 23 and lands on 33, 43, 53, 63, 73, 83 and 93.

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23 33 43 53 63 73 83 93

E ach landing bead ends in 3.

Ea ch j ump adds 10. The 3 at the end stays the same.

Q4 4. The grasshopper jumps backward by 10 each time. Mark all the beads that the
grasshopper will jump on and write the numbers.

76

The grasshopper is on the 76th bead.

T rasshopper starts at 76 and jumps on 66, 56, 46, 36, 26, 16 and 6.
he g

6 16 26 36 46 56 66 76

Jumping back by 10 each time, every bead ends in 6.

Ea ch j ump back takes away 10. The 6 at the end stays the same.

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co m
m.
Q5
e
Some ants are carrying big leaves to their homes. They will eat these leaves in the
m l as
.co
rainy season. Nani Maa can tell how many ants there are without looking under the
a g
enmyou also tell how many ants there are under the leaves? Fill the answers in the
leaves.
a s
a gl C a
boxes provided.

co m
e m . ag
l as
1 to 40

1 2 3 4 a g 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

co m
m.
41 to 72

m as e
.co g l
41 42 43 44 45 46 47 48 49 50 51 52 65 66 67 68 69 70 71 72

em a
l a s 72 to 100

ag 72 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

m a s
m .co agl
l a se
g
nts stand on every number. A leaf hides some of them; the white box is where the number
a
A

goes.

co m
m .
m as e
.oxco s t 21 12 an 11 l
T m a g
e
las
he b e ge , d .

ag
Leaf 1 (ants 5 to 25): 25 − 4 = 21
se m
Leaf 2 (ants 53 to 64): 64 − 52 = 12 com g l a
m . a
e
a=s 11
g l
Leaf 3 (ants 73 to 83): 83 − 72
a

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
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1 to 40

21
1 2 3 4 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 to 72

12
41 42 43 44 45 46 47 48 49 50 51 52 65 66 67 68 69 70 71 72

72 to 100

11
72 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

The number of ants hidden under each leaf.

− Exp anat on
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Why The a : a d in counting order. So you do not need to look under a leaf.
nts st n

The last number you see before the leaf and the first number after it tell you
which ants are hidden.

n-text Questions — Page 35
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Jump tables, and Adding and Subtracting Smartly with the Number Grid

Q1 5. Fill in the tables by jumping as instructed.

Jump 5 Jump 6 Jump 9

34 56 87 28 59 73 29 12 93
39 82 34 67 38 84
66 71
39

E ach arrow means one jump. Follow the arrow to the next box.

Jump 5 Jump 6 Jump 9

34 56 87 28 59 73 29 12 93
39 61 82 34 65 67 38 21 84
44 66 71 30
39

The new numbers are shown in yellow boxes.

Jump 5: 56 + 5 = 61, 39 + 5 = 44

Jump 6: 59 + 6 = 65

Jump 9: 12 + 9 = 21, 21 + 9 = 30

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Follow each arrow and add the jump. Check with the printed numbers: 61  5  66, 65  6
= 71, 30  9  39.

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Tip: The arrow on the right side of each table points upwards 82  5  87, 67 
6  73, 84  9  93.

Q2 Let us play a grid game. Each player takes turns rolling two dice to make a two-digit
number, and moves the counter by the number they have made. They can choose to
move forward or backward. The first to reach a number between 91 and 100 is the
winner!

91 92 93 94 95 96 97 98 99 100

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80

61 62 63 64 65 66 67 68 69 70

51 52 53 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

31 32 33 34 35 36 37 38 39 40

21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

The number grid. The bottom row starts at 1 and the top row ends at 100.

Sample turn: My ount r s on 28. T
c e i he dice show 4 and 3, so I make 43. I go 4 rows up to 68,
then 3 boxes right to 71.

28 + 40 = 68, 68 + 3 = 71

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− Exp anat on
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On row up t
e he g id ir s 10. One box to the right is 1. You may also choose 34, or move
ba war
ck d.

For the parent or teacher: The bookʼs note says: if you cannot go forward,
move backward. If neither is possible, roll again.

n-text Questions — Page 36
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Moving the counter on the number grid

Q1 Chirag: Nandini is at 23. She has got 11 on the dice. She thinks of two ways of moving
to 34.
A jump from 23 to 34 is .......... steps.

Way 1  one row up  10, then one box right  1
1
 

10 33 34

23

Way 2  one box right  1, then one row up  10
 

34 10

23 24
1

Nandiniʼs two ways of moving from 23 to 34 on the grid.

ump from 23 to 34 is 11 steps.
A j

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co m
e m.
Way 1: 23 + 10 = 33, 33 + 1 = 34
m l as
.co
Way 2: 23 + 1 = 24, 24 + 10 = 34
m a g
l a se
g
10 + 1 = 11
a

co m
e on the dice. m . ag
Nandini: Chirag is at 19. He gets s
la
Q2 54
Help him move his counter atogthe correct number.

co m
m.
e 99
m l as
.co
91 92 93 94 95 96 97 98 100
a g
se m 81
l a
82 83 84 85 86 87 88 89 90
a g
71 72 73 74 75 76 77 78 79 80

om a s
61 62 63 64
m .c65 66 67 68 69 70
agl
l a se
51 52 53
ag 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

. 39com
e m
as
31 32 33 34 35 36 37 38 40

. com21 agl 28
m
ase
22 23 24 25 26 27 29 30

agl 11 12 13 14 15 16 17 18 19 20

se m
1 2 3 4
c o m5 6 7 8 9 10
g l a
m . a
The number gra e
ids The bottom row starts at and the top row ends at
a g l . 1 100.

co m
m .
e
agmʼs counter goes to 73.
ro
g l as
m .cs t ns an a
Chi

se ones. Go 5 rows up from 19 to 69. Then go 4 boxes on to 73.
gla
54 i 5 e d 4

a c
m .
19 + 50 = 69, 69 + 4 = 73
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Q3 1. Use the number grid to answer the following. Show your thinking by drawing arrows
in the grid.
(a) Nandini is at 45. She gets 34. She will land on ..........

91 92 93 94 95 96 97 98 99 100

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80

61 62 63 64 65 66 67 68 69 70

51 52 53 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

31 32 33 34 35 36 37 38 39 40

21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

The number grid. The bottom row starts at 1 and the top row ends at 100.

She will land on 79.
A rrows: 3 rows up from 45 to 75, then 4 boxes right to 79.

45 + 30 = 75, 75 + 4 = 79

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Q4 (b) Chirag is at 75. He gets 56. He will land on ..........

91 92 93 94 95 96 97 98 99 100

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80

61 62 63 64 65 66 67 68 69 70

51 52 53 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

31 32 33 34 35 36 37 38 39 40

21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

The number grid. The bottom row starts at 1 and the top row ends at 100.

He will land on 19.
G oing forward 56 goes past 100, so he moves backward. Arrows: 5 rows down from 75 to 25,
then 6 boxes left to 19.

75 − 50 = 25, 25 − 6 = 19

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Q5 (c) Nandini is at 30. She gets 66. She will land on ..........

91 92 93 94 95 96 97 98 99 100

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80

61 62 63 64 65 66 67 68 69 70

51 52 53 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

31 32 33 34 35 36 37 38 39 40

21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

The number grid. The bottom row starts at 1 and the top row ends at 100.

She will land on 96.
A rrows: 6 rows up from 30 to 90, then 6 more to 96.

30 + 60 = 90, 90 + 6 = 96

96 i s between 91 and 100, so this move wins the grid game!

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Q6 (d) Chirag is at 89. He gets 63. He will land on ..........

91 92 93 94 95 96 97 98 99 100

81 82 83 84 85 86 87 88 89 90

71 72 73 74 75 76 77 78 79 80

61 62 63 64 65 66 67 68 69 70

51 52 53 54 55 56 57 58 59 60

41 42 43 44 45 46 47 48 49 50

31 32 33 34 35 36 37 38 39 40

21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10

The number grid. The bottom row starts at 1 and the top row ends at 100.

He will land on 26.
G oing forward 63 goes past 100, so he moves backward. Arrows: 6 rows down from 89 to 29,
then 3 boxes left to 26.

89 − 60 = 29, 29 − 3 = 26

− Exp anat on
l i

For the parent or teacher: The bookʼs note asks you to use different words for
adding (more, added to, total, sum) and for taking away (take away, difference,
less, reduce), and to let children try such jumps with other numbers.

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co m
m.
Magic Sums — Page 37
m ase
.co
Nani Maaʼs number puzzles and the magic square
a g l
a s em
aQg1 l Nandini and Chirag find some puzzles that Nani Maa had solved.
Observe the numbers. What do you notice?

co m
e m . ag
g l as
a

co m
m.
m .co
m 5 2 8 aglas15
e

l a se
a g
s
3 ase
m 1 .co
m
6 10 agl
a

agl

co m
m 9 4 7 glase 20 m .
m .co a
ase
agl
se m
17 7m 21 l a
m .co ag
ase
agl
m
The puzzle Nani Maa had already solvedm
.co
m l a se
co
.

e m . ag
g l as
a c
.
s e m
omits right: 5  2  8  15.
numbers from 1 to 9 are used, each only once.
a
Each row adds up to the numbe. rcon agl
All

s m
enum
Each column adds up to a
l ag
the ber below it: 5  3  9  17.

co m
m .
m ase
.co

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− Exp anat on
l i

Rows: 15 + 10 + 20 = 45

Columns: 17 + 7 + 21 = 45

Why The : rows and the columns use the same nine numbers, and 1  2  3  …
 9  45.

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Q2 Fill the boxes below. In each puzzle, all numbers 1  9 are there. The numbers in each
row add up to the number in the box on the right. The numbers in each column add up
to the number in the box below. (first puzzle)

5 8 16

22

1 4 7

11 16 18

The first puzzle, as printed.

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3 5 8 16

7 9 6 22

1 2 4 7

11 16 18

The completed first puzzle.

Top row: 16 − 5 − 8 = 3 Bottom row: 7 − 1 − 4 = 2
Column 1: 11 − 3 − 1 = 7 Column 2: 16 − 5 − 2 = 9

Column 3: 18 − 8 − 4 = 6 Check: 7 + 9 + 6 = 22 ✓

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Q3 Fill the boxes below. In each puzzle, all numbers 1  9 are there. The numbers in each
row add up to the number in the box on the right. The numbers in each column add up
to the number in the box below. (second puzzle)

3 12

5 15

7 4 18

7 15 23

The second puzzle, as printed.

About the book: This puzzle cannot be filled as printed: the last row would need a
second 7. The 4 in the last row should be 9.

Page 33 of 70

ase
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a g l A aS m · NCERT So ut ons
gl e l i

co m
em.
m l as
m .co a g
l a se
a g
1 3 .com 8 12
ag
a sem
agl
4 5 6 15
m .
e
com
m l as
m .co a g
l a se
a g
2 7 .com 9 18
agl
a s
se m
g l a
a

co m
7 15 23 e m .
m l as
m .co a g
l a se
ag
se m
cozzmle works if the last g l a
How the second pu
m . is read as 9.
a
ase
4

− Exp anat on
l i
agl

co m
m .
m as e
l
Rows: 1 + 3 + 8 = 12, 4 + 5 + 6 = 15, 2 + 7 + 9 = 18
c o
. Columns: 1 + 4 + 2 = 7, 3 + 5 + 7 = 15, 8 + 6 + 9 = 23 a g
se m
g l a
a c
s printed, the last row needs 18  7  4  7, but 7 is already used. Also the last column
m .
s e
A

must make 23, but even 9  8  4 mam a
o agl
kes only 21. With 9 in place of 4, every row and

. c
column wor ks.

se m
g l a
a

co m
m .
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.co

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Why E e : ber from 1 to 9 may be used only once. A puzzle that needs the
v ry num

same number twice cannot be right.

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Q4 Fill the boxes below. In each puzzle, all numbers 1  9 are there. The numbers in each
row add up to the number in the box on the right. The numbers in each column add up
to the number in the box below. (third puzzle)

6 10

19

9 16

10 12 23

The third puzzle, as printed.

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1 3 6 10

4 7 8 19

5 2 9 16

10 12 23

One way to complete the third puzzle.

Column 3: 23 − 6 − 9 = 8

Top row: 10 − 6 = 4 = 1 + 3

Middle row: 19 − 8 = 11 = 4 + 7

Bottom row: 16 − 9 = 7 = 5 + 2

− Exp anat on
l i

Check the columns: 1  4  5  10, 3  7  2  12, 6  8  9  23.

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Did you know? This puzzle has one more answer: 1 3 6 / 7 4 8 / 2 5 9 also fits
every row and column.

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a g l A aS m · NCERT So ut ons
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coomf the
Add the numbers in the blue boxes and the numbers in the red boxes in ea.ch
m
Q5
a se
com l
puzzles. What do you find?
. a g
m
ase
agl

co m
e m . ag
5 a g l as2 8 15
co m
em.
m l as
m.co 3 1 6 a g
10
l a se
a g
m a s
.co agl
9 aglasem4 7 20

com
m .
e
.co
m 17 7 21 aglas
a sem
agl
se m
com g l a
m . a
ase
agl
The puzzle Nani Maa had already solved.

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 ase
.co

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5 8 16

22

1 4 7

11 16 18

The first puzzle, as printed.

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3 12

5 15

7 4 18

7 15 23

The second puzzle, as printed.

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6 10

19

9 16

10 12 23

The third puzzle, as printed.

The bl ue boxes and the red boxes both add up to 45 in every puzzle.

PUZZLE RED BOXES BLUE BOXES

Nan Maaʼs
i 15  10  20  45 17  7  21  45

First 16  22  7  45 11  16  18  45

Sec ond 12  15  18  45 7  15  23  45

T r hi d 10  19  16  45 10  12  23  45

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− Exp anat on
l i

Why The ed b e add all i e
: r ox sbers row by row. The blue boxes add the
nn num

same nine numbers column by column. And 1  2  3  …  9  45.

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co m
m.
Q6 Nani Maa was doing something in the newspaper. Nandini and Chirag looked into what
as e
om l
she was doing.
Maem . c
gic magic magic a g
s
glaWi h n mbe o
!!!

a
t u rs 1 t 9

Add the numbers in a line
m
From left to right
And from top to bottom . co ag
em
Did you find the magic?
No w, try r f om igh o lef agl
r
as
tt t

And from bottom to top
Isnʼt it magical?
co m
The e i ome hing mo e ome hing mo e em.
m n mbe on he diagonal as
r ss t r ,s t r

Addohe
. c t u rs t
a g l
e m
I n i magical
las Nandini: Nani Maa, What is so magical about this Square?
s ʼt t ?

ag
m a s
m .co agl
l a se
ag
m

m .co
m 2 7 a g l as 6
e m . co

l a se
ag
se m
com a

agl
9 ase
m .
5 1 ag l

co m
m .
m as e

ag l a se m.co
4 3 a g l
8 .c
s e m
m a
e m . co agl
g l as
a
The square Nani Maa was making in the newspaper.

co m
m .
m ase
.co

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The magic: every row, every column and both corner-to-corner lines add up to 15.

Rows: 2 + 7 + 6 = 15, 9 + 5 + 1 = 15, 4 + 3 + 8 = 15

Columns: 2 + 9 + 4 = 15, 7 + 5 + 3 = 15, 6 + 1 + 8 = 15

Diagonals: 2 + 5 + 8 = 15, 6 + 5 + 4 = 15

− Exp anat on
l i

Why The i e
: bers add up to 45. They sit in three rows with the same
nn num

total. 15  15  15  45, so each row makes 15.

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Q7 Fill the blanks to complete the Magic square

3
9
6
The magic square to be completed.

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8 3 4
1 5 9
6 7 2
The completed magic square.

very line must make 15, and the middle box is 5, as in Nani Maaʼs square.
E

Middle column: 15 − 3 − 5 = 7 Middle row: 15 − 5 − 9 = 1

First column: 15 − 1 − 6 = 8 Top row: 15 − 8 − 3 = 4

Bottom row: 15 − 6 − 7 = 2

− Exp anat on
l i

Check the diagonals: 8  5  2  15 and 4  5  6  15. The bookʼs note says the teacher
can make similar puzzles for children.

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n-text Questions — Page 38
I

Nan Maa s ra s
i ʼ di h field s

Q1 Nani Maa has plucked 25 red radishes and 36 white radishes. Nandini starts by
drawing the problem on the ground.
Nandini: Estimate the total number of radishes. ............

red radish white radish
25 36

Nandiniʼs drawing of the problem on the ground.

The e r ar about 60 radishes
e .

36 is close to 35. 25 + 35 = 60

− Exp anat onl i

An estimate is a quick, close guess. Any answer near 60 is a good estimate. The exact
answer is 61.

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co m
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Q2 Nani Maa has plucked 25 red radishes and 36 white radishes. How many total radishes

m as e
l
has she plucked?
.co a g
em36 ..........
25 red radishes  36 white radishes = .......... radishes

a s
gl
25
a
 

m
.co
25 red radishes 36 white radishes
ag
asem
agl

dis.hc
Bundles of ten sticks and loose sticks for the two kinds of ram
om
m as e
.

.co a g l
a s em
a gAlNSW E R
m a s
25 red radishes + 36 white radishes = 61 radishes
m .co agl
l a se
25 + 36 = 61
ag
undles: 2  3  5. Sticks: 5  6  11  1 bundle and 1 stick. So 6 bundles and 1 m
co
stick  61.
.
B

e m
m l as
m.co a g
l a se 6 bundles and 1 stick  61
ag
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 .
Eleven loose sticks make one more bundle and one stick is left
m a s e
co agl
.

m .
as e
− Exp anat on
l i

a g l
Nan n oes it on the number line: 25  5  30, then 10, 10, 10 to 60, then 1  61.
m
di i d

. co
e m
m l as
.co a g
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5 10 10 10 1

0 10 20 30 40 50 60 70 80 90 100

Nandiniʼs jumps on the number line.

Why Te l : e sticks always make one new bundle. That is why the tens digit
n oos

goes up from 5 to 6.

Q3 Find other ways of solving the same problem on the number line.

0 10 20 30 40 50 60 70 80 90 100

A number line from to 0 100.

Two ot he r ways. Both reach 61.

Way 1: 25 + 30 = 55, 55 + 6 = 61

Way 2: start at 36. 36 + 20 = 56, 56 + 5 = 61

30 6

0 10 20 30 40 50 60 70 80 90 100

Two shorter ways to reach the same answer.

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− Exp anat onl i

Why 36 ca be b ke i
: 30 and 6, or 25 into 20 and 5. However you split
n ro n nto

the numbers, you still reach 61.

n-text Questions — Page 39
I

T he b ox of 100 vegetables

Q1 Nani Maa puts tomatoes and carrots in a box and writes 100 on it.
Nandini: I remember she had put 65 tomatoes.
Chirag: We need not count the carrots.
Nandini draws the given problem.
Your estimation of carrots ............

100

65 tomatoes ? carrots

The whole box holds 100 vegetables.

About 30 to 35 carrots.

65 is close to 70. 70 + 30 = 100

So t he e r ar a tt
e li le more than 30 carrots.

− Exp anat onl i

T ox as on y tomato s an arrots so w at v r s not a tomato s a arrot T
he b h l e d c , h e e i i c . he exact
answ r s T oo s not as s
e i 35. r n to s ar ow t y ma t r u ss
he b kʼ e k child e h e h he de hei g e .

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Q2 Circle the bundle of sticks that shows the correct number of carrots.

A B C D

The four choices of bundles and sticks printed in the book.

r
Ci cle g roup C (the third one): 3 bundles and 5 sticks = 35.

100 − 65 = 35 carrots

A = 30, B = 34, C = 35, D = 52

Q3 Solve the above problem on the number line.

0 10 20 30 40 50 60 70 80 90 100

A number line from to 0 100.

Count up from 65 to 100 jump 5 to 70, then 30 to 100.

5 30

0 10 20 30 40 50 60 70 80 90 100

Counting on from 65 to 100.

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5 + 30 = 35, so 100 − 65 = 35 carrots

Q4 ......... tomatoes and ......... carrots total ......... vegetables ......... + .........  100

100

65 tomatoes ? carrots

The whole box holds 100 vegetables.

65 tomatoes and 35 carrots total 100 vegetables

65 + 35 = 100

100

65 tomatoes 35 carrots

The two parts of the box of 100.

The two parts together make the whole box.

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co m
m.
Q5 .........tomatoes taken out from a box of 100 vegetables, leaves ......... carrots 100 

m as e
.co l
......... = .........
a g
se m
g l a
a 100

co m
65 tomatoes
e m . ? carrots
ag
g l as
a
The whole box holds 100 vegetables.

co m
em.
A NSW E R com g l as
m . a
ase
agl 65 tomatoes taken out from a box of 100 vegetables, leaves 35 carrots
m a s
.co agl
100 − 65 = 35

a s em
w o an on pagrtl w ta t at part away to n t
If we know the h
a
le d e , e ke h fi d he other part.

co m
m .
n-text Questions — Page 40
m as e
.co l
I

a g
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 .
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.co

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P u n t r p app s
l cki g he i e le

Q1 Nani Maa asks Nandini and Chirag to pluck the ripe apples. Woho! So many of them.
Nandini: I collected 85 apples.
Chirag: I plucked 67 apples.
Let us see how many total apples we have collected.
Nandini: 80 and 20 is 100. So they would be more than 100 in all.
Draw a box diagram for the problem below.

Nandini Chirag
85 apples 67 apples

What the two children said they had plucked.

?

85 67

A box diagram the two parts are known and the whole is not
: .

Draw one long box with two parts. Write 85 Nandini) in one part and 67 Chirag) in the other.
Write ? above the whole box for the total.

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Q2 How many apples in all?

85 app sle 67 app sle

The two collections shown in bundles of ten and loose sticks.

85 + 67 = 152 apples

Bundles: 8  6  14. Sticks: 5  7  12, that is 1 more bundle and 2 sticks. 15 bundles and 2
sticks. Ten bundles make 100, so 100  50  2  152.

− Exp anat on
l i

Why Te :icks make a bundle and ten bundles make a hundred. That is how
n st

the number grows past 100, as Nandini guessed.

n-text Questions — Page 41
I

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W o oh c t
llec ed more apples?

Q1 Try finding out the answer on the number line below.
85 Apples  67 Apples = .......... Apples
85  67  ..........

70 80 90 100 110 120 130 140 150 160 170

The number line printed in the book, from 70 to 170.

85 Apples + 67 Apples = 152 Apples

85 + 67 = 152

Start at 85. Jump 60 to 145, then 5 to 150, then 2 to 152.

60 5 2

70 80 90 100 110 120 130 140 150 160 170

Three jumps take 85 up to 152.

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Q2 Who collected more, Nandini or Chirag? How much more?
Chirag draws a box diagram for the problem. The book also shows Nandiniʼs apples 8
bundles and 5 sticks), Chiragʼs apples 6 bundles and 7 sticks) and a box “How much
more?ˮ with two circles to fill.

85

67 ?

Chirag s box diagram
ʼ : 85 is the whole, 67 is one part.

Nandini o c t
llec ed more, 18 apples more.

85 − 67 = 18 (1 bundle and 8 sticks)

Count up from 67 67  3  70, 70  15  85. 3  15  18.

85

67 18

The missing part is 18.

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co m
m.
Q3 ................ collected ......... apples more than ................ .

m as e
.co a g l
se m
g l a 85
a
m
.co
67 ?

ag
Chirag s bgoxladiagram
sem
ʼ
a : 85 is the whole, 67 is one part.

co m
e m.
m as
.co a g l
a s em collected 18 apples more than Chirag.
gl
Nandini
a
m a s
.co agl
85  67  18

se m
− Exp anat on
g l a
a
l i

For the parent or teacher: The bookʼs note asks you to make more sumch
co
problems and let children draw and solve them with things found .at home, like

m a s em
.c o
stick s or stones. l ag
s e m
a
agl
se m
com g l a
n-text Questions — Page 42 m. a
ase
I

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

com
m .
m ase
.co

a g l Page 59 of 70