NCERT Textbook: How Big, How Heavy | Mathematics for Class 5: NCERT PDF Download

 Page 1


1kg
200
g
1kg
200
g
187
Sarikacollectsthingslikemarbles,coins,erasers
etc.Shetakessomewaterinaglassandmarksthe
levelofwateras'0'.
How Big? How Heavy?
See, each marble pushes up
some water. Right? That is
because it takes up some space
which is its volume.
Childrenwillneedmoreexercisestocomparethevolumeofsolidbodiesbyguessingandby
informal measurement (using marbles, coins, matchboxes, etc.) before they begin to use
formalmeasuressuchaslitresandcubiccentimetres.
Shedrops5marblesintheglass.Shemarks
thenewlevelofwateras5marbles.
14
If I drop 5
marbles in this
glass, can you
guess what will be
the level of water?
I think
this much.
Oh, how did
you guess! Do
you know the
of a
marble?
volume
I just made a guess
about how much
water will be
pushed up by the
marbles. How do you
find the volume?
Reprint 2024-25
Page 2


1kg
200
g
1kg
200
g
187
Sarikacollectsthingslikemarbles,coins,erasers
etc.Shetakessomewaterinaglassandmarksthe
levelofwateras'0'.
How Big? How Heavy?
See, each marble pushes up
some water. Right? That is
because it takes up some space
which is its volume.
Childrenwillneedmoreexercisestocomparethevolumeofsolidbodiesbyguessingandby
informal measurement (using marbles, coins, matchboxes, etc.) before they begin to use
formalmeasuressuchaslitresandcubiccentimetres.
Shedrops5marblesintheglass.Shemarks
thenewlevelofwateras5marbles.
14
If I drop 5
marbles in this
glass, can you
guess what will be
the level of water?
I think
this much.
Oh, how did
you guess! Do
you know the
of a
marble?
volume
I just made a guess
about how much
water will be
pushed up by the
marbles. How do you
find the volume?
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
Name of the thing Its volume (nearly
how many marbles?)
188
WhichhasMoreVolume?
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
Now make a guess. Do you think the volume of 10 five-rupee
coins will be more than that of 10 marbles?
Guess the volume of each of these:
A ball is nearly __________ marbles.
An eraser is nearly __________ marbles.
A lemon is nearly __________ marbles.
A pencil is nearly __________ marbles.
A potato is nearly __________ marbles.
‘ ’
Now put each thing inthemeasuring glassandcheckyourguess.
Trywithdifferentthingslikeamatchbox,astone,etc.andfillthetable.
Now make your own measuring glass using 35 marbles.
Take a glass of water and mark the level of water as 0 . Then put in 5 marbles
andmarkthelevelofwater as 5 M.
Again drop 5 marbles and mark the level of water as 10 M. Likewise make the
markingsfor15M,20M,25 M, 30 M and 35 M.
D
D
D
D
D
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
Page 3


1kg
200
g
1kg
200
g
187
Sarikacollectsthingslikemarbles,coins,erasers
etc.Shetakessomewaterinaglassandmarksthe
levelofwateras'0'.
How Big? How Heavy?
See, each marble pushes up
some water. Right? That is
because it takes up some space
which is its volume.
Childrenwillneedmoreexercisestocomparethevolumeofsolidbodiesbyguessingandby
informal measurement (using marbles, coins, matchboxes, etc.) before they begin to use
formalmeasuressuchaslitresandcubiccentimetres.
Shedrops5marblesintheglass.Shemarks
thenewlevelofwateras5marbles.
14
If I drop 5
marbles in this
glass, can you
guess what will be
the level of water?
I think
this much.
Oh, how did
you guess! Do
you know the
of a
marble?
volume
I just made a guess
about how much
water will be
pushed up by the
marbles. How do you
find the volume?
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
Name of the thing Its volume (nearly
how many marbles?)
188
WhichhasMoreVolume?
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
Now make a guess. Do you think the volume of 10 five-rupee
coins will be more than that of 10 marbles?
Guess the volume of each of these:
A ball is nearly __________ marbles.
An eraser is nearly __________ marbles.
A lemon is nearly __________ marbles.
A pencil is nearly __________ marbles.
A potato is nearly __________ marbles.
‘ ’
Now put each thing inthemeasuring glassandcheckyourguess.
Trywithdifferentthingslikeamatchbox,astone,etc.andfillthetable.
Now make your own measuring glass using 35 marbles.
Take a glass of water and mark the level of water as 0 . Then put in 5 marbles
andmarkthelevelofwater as 5 M.
Again drop 5 marbles and mark the level of water as 10 M. Likewise make the
markingsfor15M,20M,25 M, 30 M and 35 M.
D
D
D
D
D
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
188
WhichhasMoreVolume?
Mollie used her measuring bottle to find the volume of five-rupee
coins. She found that
. So you can also use 9 five-rupee coins to make your
measuring bottle! Go ahead!
a) What is the volume of 6 marbles? ________ mL.
9 five-rupee coins push up 10 mL of
water
Useyourmeasuringbottletofindout:
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
In Class IV you made a measuring bottle for 250 mL.
Can you think of ways for making a measuring bottle which can
measure 10 mL, 20 mL, 30 mL, ………., 60 mL? Discuss with
your friend.
Tariq and Mollie made their measuring bottles.
Tariq had an injection. He used it to make his measuring
bottle. Mollie used an empty medicine bottle.
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
Page 4


1kg
200
g
1kg
200
g
187
Sarikacollectsthingslikemarbles,coins,erasers
etc.Shetakessomewaterinaglassandmarksthe
levelofwateras'0'.
How Big? How Heavy?
See, each marble pushes up
some water. Right? That is
because it takes up some space
which is its volume.
Childrenwillneedmoreexercisestocomparethevolumeofsolidbodiesbyguessingandby
informal measurement (using marbles, coins, matchboxes, etc.) before they begin to use
formalmeasuressuchaslitresandcubiccentimetres.
Shedrops5marblesintheglass.Shemarks
thenewlevelofwateras5marbles.
14
If I drop 5
marbles in this
glass, can you
guess what will be
the level of water?
I think
this much.
Oh, how did
you guess! Do
you know the
of a
marble?
volume
I just made a guess
about how much
water will be
pushed up by the
marbles. How do you
find the volume?
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
Name of the thing Its volume (nearly
how many marbles?)
188
WhichhasMoreVolume?
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
Now make a guess. Do you think the volume of 10 five-rupee
coins will be more than that of 10 marbles?
Guess the volume of each of these:
A ball is nearly __________ marbles.
An eraser is nearly __________ marbles.
A lemon is nearly __________ marbles.
A pencil is nearly __________ marbles.
A potato is nearly __________ marbles.
‘ ’
Now put each thing inthemeasuring glassandcheckyourguess.
Trywithdifferentthingslikeamatchbox,astone,etc.andfillthetable.
Now make your own measuring glass using 35 marbles.
Take a glass of water and mark the level of water as 0 . Then put in 5 marbles
andmarkthelevelofwater as 5 M.
Again drop 5 marbles and mark the level of water as 10 M. Likewise make the
markingsfor15M,20M,25 M, 30 M and 35 M.
D
D
D
D
D
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
188
WhichhasMoreVolume?
Mollie used her measuring bottle to find the volume of five-rupee
coins. She found that
. So you can also use 9 five-rupee coins to make your
measuring bottle! Go ahead!
a) What is the volume of 6 marbles? ________ mL.
9 five-rupee coins push up 10 mL of
water
Useyourmeasuringbottletofindout:
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
In Class IV you made a measuring bottle for 250 mL.
Can you think of ways for making a measuring bottle which can
measure 10 mL, 20 mL, 30 mL, ………., 60 mL? Discuss with
your friend.
Tariq and Mollie made their measuring bottles.
Tariq had an injection. He used it to make his measuring
bottle. Mollie used an empty medicine bottle.
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
1kg
200
g
1kg
200
g
b) What is the volume of 16 one-rupee coins? _________ mL.
Now solve these in your mind.
c) The volume of 24 marbles is _________ mL.
d) The volume of 32 one-rupee coins? _________ mL.
e) Mollie puts some five-rupee coins in the measuring bottle.
How many coins has she put in it:
if 30 mL water is pushed up? __________
if 60 mL water is pushed up? __________
First guess and then use your measuring bottle to find out the
volume in mL of some other things.
h
h
HowManyCanFitIn?
Thing Its volume (in mL)
Guess how many
litres of water your
body will push up?!
To make a measuring bottle, make children use a wide-mouthed and transparent bottle so
that markings can be made easily. The activity aims to develop measurement skills in
childrenandinvolvesbothmakingandhandlingapparatus(suchasmeasuringbottle)inthe
mathematicsclassroom.
1cm
1cm
This is a cube whose sides are of 1 cm each.
See, your Math-Magic book is 1 cm high. So
guess how many such centimetre cubes will
take the same space as your Math-Magic book?
190
MatchboxPlay
The activity 'How many can fit in' requires a sense of the size of a cm cube. For finding the
volume of different shapes, the teacher can make cm cubes and use matchboxes to make
different models. Tanu's stage or Mohan's model are examples where children calculate
volumeintermsofmatchboxes,whichmaylaterbeconvertedintocmcubes.
And it is about cm
wide. So cubes will
fit along the width.
___
___
Hey, my ath- agic
book is about ___ cm
long. So cubes
will fit along its length.
M M
___ cm
So total
cubes will fit n the
Math-Magic book.
___ cm
o
191
Reprint 2024-25
Page 5


1kg
200
g
1kg
200
g
187
Sarikacollectsthingslikemarbles,coins,erasers
etc.Shetakessomewaterinaglassandmarksthe
levelofwateras'0'.
How Big? How Heavy?
See, each marble pushes up
some water. Right? That is
because it takes up some space
which is its volume.
Childrenwillneedmoreexercisestocomparethevolumeofsolidbodiesbyguessingandby
informal measurement (using marbles, coins, matchboxes, etc.) before they begin to use
formalmeasuressuchaslitresandcubiccentimetres.
Shedrops5marblesintheglass.Shemarks
thenewlevelofwateras5marbles.
14
If I drop 5
marbles in this
glass, can you
guess what will be
the level of water?
I think
this much.
Oh, how did
you guess! Do
you know the
of a
marble?
volume
I just made a guess
about how much
water will be
pushed up by the
marbles. How do you
find the volume?
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
Name of the thing Its volume (nearly
how many marbles?)
188
WhichhasMoreVolume?
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
Now make a guess. Do you think the volume of 10 five-rupee
coins will be more than that of 10 marbles?
Guess the volume of each of these:
A ball is nearly __________ marbles.
An eraser is nearly __________ marbles.
A lemon is nearly __________ marbles.
A pencil is nearly __________ marbles.
A potato is nearly __________ marbles.
‘ ’
Now put each thing inthemeasuring glassandcheckyourguess.
Trywithdifferentthingslikeamatchbox,astone,etc.andfillthetable.
Now make your own measuring glass using 35 marbles.
Take a glass of water and mark the level of water as 0 . Then put in 5 marbles
andmarkthelevelofwater as 5 M.
Again drop 5 marbles and mark the level of water as 10 M. Likewise make the
markingsfor15M,20M,25 M, 30 M and 35 M.
D
D
D
D
D
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
Children can paste a paper strip on the glass and mark the level of water using a pen or a
pencil. imistodevelop senseoftheconceptofvolumethroughexamplesandhands
onactivitieswithoutgivingadefinitionofvolume.Comparingthingsonthebasisofvolumeis
moreabstractthencomparisonintermsoflengthorarea.
Thea a
Let's fill it with
sand or nails.
The matchbox
floats. How do I
find its volume?
188
WhichhasMoreVolume?
Mollie used her measuring bottle to find the volume of five-rupee
coins. She found that
. So you can also use 9 five-rupee coins to make your
measuring bottle! Go ahead!
a) What is the volume of 6 marbles? ________ mL.
9 five-rupee coins push up 10 mL of
water
Useyourmeasuringbottletofindout:
Yes, if we
make a
measuring
bottle.
Can you tell
me the volume
of 6 marbles
in mL?
189
1kg
200
g
1kg
200
g
YourMeasuringGlass
In Class IV you made a measuring bottle for 250 mL.
Can you think of ways for making a measuring bottle which can
measure 10 mL, 20 mL, 30 mL, ………., 60 mL? Discuss with
your friend.
Tariq and Mollie made their measuring bottles.
Tariq had an injection. He used it to make his measuring
bottle. Mollie used an empty medicine bottle.
I took 5 mL once
in my injection.
I filled it twice
to mark 10 mL
on my bottle.
I used this bottle
which measures
10 mL to make my
measuring bottle.
Reprint 2024-25
1kg
200
g
1kg
200
g
b) What is the volume of 16 one-rupee coins? _________ mL.
Now solve these in your mind.
c) The volume of 24 marbles is _________ mL.
d) The volume of 32 one-rupee coins? _________ mL.
e) Mollie puts some five-rupee coins in the measuring bottle.
How many coins has she put in it:
if 30 mL water is pushed up? __________
if 60 mL water is pushed up? __________
First guess and then use your measuring bottle to find out the
volume in mL of some other things.
h
h
HowManyCanFitIn?
Thing Its volume (in mL)
Guess how many
litres of water your
body will push up?!
To make a measuring bottle, make children use a wide-mouthed and transparent bottle so
that markings can be made easily. The activity aims to develop measurement skills in
childrenandinvolvesbothmakingandhandlingapparatus(suchasmeasuringbottle)inthe
mathematicsclassroom.
1cm
1cm
This is a cube whose sides are of 1 cm each.
See, your Math-Magic book is 1 cm high. So
guess how many such centimetre cubes will
take the same space as your Math-Magic book?
190
MatchboxPlay
The activity 'How many can fit in' requires a sense of the size of a cm cube. For finding the
volume of different shapes, the teacher can make cm cubes and use matchboxes to make
different models. Tanu's stage or Mohan's model are examples where children calculate
volumeintermsofmatchboxes,whichmaylaterbeconvertedintocmcubes.
And it is about cm
wide. So cubes will
fit along the width.
___
___
Hey, my ath- agic
book is about ___ cm
long. So cubes
will fit along its length.
M M
___ cm
So total
cubes will fit n the
Math-Magic book.
___ cm
o
191
Reprint 2024-25
1kg
200
g
1kg
200
g
HowManyCanFitIn?
Guess how many
litres of water your
body will push up?!
To make a measuring bottle, make children use a wide-mouthed and transparent bottle so
that markings can be made easily. The activity aims to develop measurement skills in
childrenandinvolvesbothmakingandhandlingapparatus(suchasmeasuringbottle)inthe
mathematicsclassroom.
1cm
1cm
This is a cube whose sides are of 1 cm each.
See, your Math-Magic book is 1 cm high. So
guess how many such centimetre cubes will
take the same space as your Math-Magic book?
190
Practicetime
__________ cm cubes.
2. Guess the volume of these things in cm cubes.
A matchbox is about _________ cm cubes.
A geometry box is about_______cm cubes.
An eraser is about__________cm cubes.
How will you check your guess? Discuss.
Tanu is making a stage with matchboxes.
She first puts 14 matchboxes like this in
the first layer.
1. A stage (platform) is made with 5 Math-Magic books. The
volume of this stage is the same as
h
h
h
MatchboxPlay
The activity 'How many can fit in' requires a sense of the size of a cm cube. For finding the
volume of different shapes, the teacher can make cm cubes and use matchboxes to make
different models. Tanu's stage or Mohan's model are examples where children calculate
volumeintermsofmatchboxes,whichmaylaterbeconvertedintocmcubes.
And it is about cm
wide. So cubes will
fit along the width.
___
___
Hey, my ath- agic
book is about ___ cm
long. So cubes
will fit along its length.
M M
___ cm
h Now if all these cubes are arranged in one line then how long
will that line be?______cm
So total
cubes will fit n the
Math-Magic book.
___ cm
o
191
Reprint 2024-25