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TEACHING
Measurement
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A PRACTICAL
APPROACH
Measurement
Measurement occupies a unique position in the curriculum, for various reasons. As it is an
essential everyday activity in human life, children are naturally exposed to measurement in
various situations at home and elsewhere. Also, measurement overlaps both with numbers
and geometry. It involves spatial dimensions as well as counting. In measurement, one is
measuring one attribute in terms of another attribute. Also one is expressing a non-discrete
quantity in terms of discrete numbers. Since there are different ways of measuring the given
length or mass, the choice of the measure is dependent on the purpose that needs to be
served. Children need to understand that some contexts require precision to a fine degree
while some require approximate figures. A strong foundation in measurement concepts
leads to a better understanding of decimal numbers in particular.
The focus of the teaching of measurement needs to be more on developing a proper
concept of measuring rather than on practising measuring activities. As the topic is
developed, children need to begin to appreciate under what situations measurement can be
used, and the suitability of different measures in different situations. It is also important to
create activities to the extent possible which have an inbuilt task in them, a task which is
sufficiently interesting and challenging for the children to take up with enthusiasm.
I have focussed only on length, weight and capacity in this article. Measurement includes
many other measures as well: measurement of time, of temperature, of speed and so on. I
shall go into these in a subsequent piece.
Measurement activities often require tools which may be limited in supply. Also typically the
activities require children to cooperate (like holding a rope tight or bringing two things
together). It is best to organise children in groups of four and set each group a task.
Young children require both experience and maturity to understand measurement concepts.
The awareness of quantity and appropriate language associated with that happens
simultaneously. Words such as big, small, more and less are learnt at a very early age.
However, they may take time to understand the principle of conservation of quantity or
number. It is dependent on the experiential understanding and maturity of the child and
develops slowly and varies from child to child. Also, they may hold false assumptions about
weight or volume. For instance, they may believe that between two objects, the one that
looks larger also weighs more. Or they may think that a taller container can hold more than
a shorter container. However, a teacher can quicken the pace of development by exposing
the children to meaningful activities and guiding them along by getting them to articulate
their observations and ideas. Through conversation, a teacher can clear some of the
misconceptions and help the child to acquire right understanding. The principle of
conservation is a prerequisite in developing an understanding of the principles of
measurement.
Keywords: Measurement, length, height, weight, capacity, size, comparison, estimation
ACTIVITIES
Preliminary activities for young children (3 to 5 year olds):
To understand the attribute of LENGTH:
Materials: Straws, used sketch pens, ice-cream sticks or
toothpicks, coloured paper strips or wooden rods of
different lengths, coloured ropes or shoe laces of
different lengths, pencils, beads and rope for threading.
Selection of materials is to be done carefully so that
children can focus on one attribute. Large 2-D shapes
and 3-D objects can be introduced at a later point as
they have more than one measure (length, width and
height).
Language to be introduced: long, short, tall, longest,
shortest, thick, thin, wide, narrow, distance - related
words (far, near).
Comparison of two objects of the same type: Let
children compare two standing objects like two trees or
two children standing on level ground to identify the
taller and the shorter. Since the objects stand at the
same level, there is no scope for confusion. Let them
now do the same for two sticks or two paper strips to
identify the longer and the shorter. An advantage of
measuring strips is that they can be placed one over the
other. To compare the strips, the children will need to
bring them close to each other. At this point, the
teacher must check to see that the child has placed the
strips so that the lower ends have the same starting
point. If not, the teacher will need to help the child
understand that in order to compare lengths, the
objects must be aligned at the starting point.
Comparison of more than two objects: Given a set of
objects (pencils, chalks, paper strips, sticks and so on)
with different lengths, they can arrange the objects in
order of their length. Children can make bead chains
and hang them in length order. Note that bead chains
provide an opportunity to make numerical comparisons
too: The blue bead chain is two beads longer than the
red bead chain.
Task 2: Ask children to form groups of four and have
each group stand in height order.
Task 3: Sorting activity: Materials: Coloured straws or
crayons of four different lengths as shown in the picture
shown in Figure 1, with a few of each size. Ask the
children to sort the straws or crayons into groups of
equal length.
Introduce the words 'wide' and 'narrow' in various
contexts: Opening and closing the door, pointing to the
gap (wide and narrow); or wide/narrow paper strip.
Young children enjoy physical activities and they can
demonstrate the meanings of these words by opening
their eyes ('wide open', 'tightly shut'), parting their
fingers, etc.
Provide opportunities for checking other forms of
lengths like width and thickness. Again, ensure that they
Comparison of two objects of different types: Let
them compare the lengths of a pen and scale, chalk and
duster, a pencil and scissors.
Task 1: Give each child a straw and ask the children to
get an object as long as the straw. They may find a
pencil, a book, a leaf or a broom stick. In the process of
locating the object, they would have tested it against
many objects and acquired practice in comparing
lengths of objects.
Figure 1
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have aligned the objects correctly. Let them compare the
widths of two note books, widths of two pencil boxes,
etc. Encourage them to use appropriate words: The
English notebook is wider than the Math note book or
His pencil box is narrower than her pencil box , etc. Let
them compare the width of a chalk box and a pencil
box, width of a duster and ruler.
Similarly introduce words like thick and thin by pointing
to a thick book and a thin book, and a thick line and a
thin line. They can observe the different fingers on their
hand and describe them in terms of these words.
Task 4: Let each group of students collect four sticks
and use the words thick, thin, thicker than, thinner
than, as thick as, in between, etc to describe them. Let
them arrange the sticks in order of thickness.
Comparisons of objects with more than one
attribute: In the case of 2-D shapes and 2-D objects,
comparisons can be made based on different attributes.
The text book is longer and wider than the note book.
The door is taller than the window, but the window is
wider than the door. The bench is wider than the
table, but the table is taller than the bench. And so on.
The teacher may pose a problem: Is there a box in
which I can keep the duster? Let the children
experiment with various boxes in the class and give
reasons for why it will fit or why it will not. Can it fit
into the chalk box? No, the chalk box is not long
enough. Can the duster fit into the pencil box? Yes, it
can as the box is longer than the duster and wider than
the duster. Many more questions of this kind can be
posed. Can the book go into this bag? Will the map fit
in this space?
Children take great pleasure in filling slightly damp sand
into containers and inverting them to get sand moulds.
This is potentially an excellent opportunity to bring out
concepts related to shape and capacity. Once the children
have made several sand moulds with different objects on
the ground, an interesting question to pose is: Identify
the container used to make each mould. Secondly,
moulds come in interesting shapes based on the
containers used: cylinders, cones, truncated cones,
cuboids and cubes. Children can describe these shapes in
their own way. Thirdly, a discussion can ensue on finding
the bigger mould.
Let children compare capacities of two containers by
filling one with sand and then pouring out the same
sand into the other container. Let them repeat this
activity with different containers. Initiate a conversation
with the child to check whether the child has realised
that if the sand does not fill the second container, then
the second one has greater capacity. And if it overflows,
then the first one has greater capacity.
It is quite common for young children to think that a tall
container has greater capacity than a short container. It
is only through experiences of filling and testing that
they begin to realise that this may not always be true.
Usage of transparent containers makes it easier for
children to see the capacities of different containers.
Give children two plastic containers of equal height, one
with a narrow base and one with a broad base. Let
them fill each one with a cupful of water. Ask: Why is
the height of the water in one more than in the other?
Let them understand that the size of the base is more in
one than in the other. Devise more such experiments to
remove misconceptions.
To understand the attribute of CAPACITY/
VOLUME:
Materials: Large tub or a decent sized sand pit, cups of
different sizes, narrow tall containers, wide short
containers, discarded transparent plastic bottles,
transparent plastic bowls, cardboard boxes of different
sizes, sand, beads, cubes and boxes, bricks or wooden
blocks. Bucket, mugs, funnel, sieve and water.
Children need to experience activities involving filling,
pouring, packing, fitting and emptying to understand
the principles involving capacity. With small children we
do not use the words volume or capacity. Instead we
pose questions such as: Does this hold more than
that?
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Figure 2
To understand the attribute of WEIGHT:
Materials: Large tub, few cups or mugs of same size,
small cardboard boxes, sand, water, beads, used pens,
leaves, chalk pieces, different objects of varying weights.
Let children pick up one object in one hand and one in
the other to compare their weights.
Let children play around with filling a cup with various
materials such as sand, chalk pieces, stones etc, and ask:
Which material is the heaviest?
Which is the
lightest?
Children may have notions about length and weight or
volume and weight which are incorrect. Give
simultaneously opposite examples as given below to
prevent and clear any misconceptions that may arise
with regard to weight.
A larger object does not always weigh more.
Give children a large balloon and a tennis ball. Let them
compare their weights and see that even though the
balloon is larger in size, it weighs less. Also, give two
other objects where the larger object does weigh more,
say a thick book and a thin one.
A larger quantity does not always weigh more.
Fill a large packet either with cotton or saw dust. Fill a
smaller packet with sand so that the weight of the sand
packet is more than the sawdust packet. Let children lift
both objects and find out which has greater weight.
Objects of the same length may have different
weights.
Give children different objects of the same length, say a
paper strip and a wooden or metal rod. Let them pick
up the objects one in each hand and compare the
weights. Do the same with more pairs of objects of the
same length.
Figure 3
Weight of a larger number of one type of object is
not always more than the weight of a smaller
number of some other type of object.
Give children five balloons or table-tennis ('ping pong')
balls and a cricket ball. Let them compare the weights of
both and see. Let them realise that a greater number
does not necessarily imply more weight.
Tie a rope from one end of the class to another with a
basket hanging from it as shown in figures 3 and 4. Pull
it taut. Let children experiment with placing different
objects in the basket to find the heaviest and the
lightest.
Measuring activities for 5 to 7 year
olds:
Measurement of LENGTH with 5 to 7 year
olds: Comparisons of objects which need another
object to be used as a measure:
Task 5: Is the cupboard in the class wider than the
door?
This requires comparison of objects which are fixed and
cannot be placed next to each other.
Questions of this kind require the use of another object
to be used as a measure, say a string. The cupboard is
first measured with a string and a blue mark is made on
the string marking the endpoint. Then the same string is
used to measure the door and a red mark is made on it
at the new endpoint. From the two marks we can
determine which one is the wider object. Or two strings
can be used and laid next to each other for comparison.
Children can be encouraged to use their feet or arms to
make comparisons of fixed objects. Example: The width of
the classroom steps is longer than my foot, and the width
of the steps on the slide is shorter than my foot.
Figure 4
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Task 6: Who has the biggest head? Let children work
in pairs and use a string to measure the length
around the forehead. They can mark the strings and
lay them out straight for comparison.
The level of accuracy needed in measurement depends
very much on the context. In many of our day to day
activities, we use non-standard units (NSUs) routinely as
we need only approximate values. By approaching
measurement through the usage of NSUs, the
measurement concept becomes clear to young children.
A scale with numbers and fine divisions can be better
appreciated by the child when he or she constructs the
scale and marks the numbers on it.
Pose a task: Is the length of the class more than the
width? If so, by how much?
Children select a unit available in the class like a straw to
measure the length of the room and the width of the
room in terms of number of straws and determine
which is bigger. Selection of the unit should be
attempted by the child on his/her own. He/she needs to
develop the skill of choosing the right unit. It is only
through trial and error that the child begins to realise
that a large unit will not give a useful answer, while a
very small unit will make the number large and
unwieldy. Later, guide the children to use straws or
wooden blocks for measuring longer lengths and icecream sticks or paper clips for measuring smaller
lengths. Beads can be used for measuring very small
lengths but they tend to roll.
While they measure with NSUs the teacher needs to
watch out for the following:
Do the children know where to begin and end? Have
they left any gap at the start, or is it aligned
correctly?
Have the children placed the units one after another
without gaps or overlaps?
Have they managed to form a reasonably straight
line or has the line become curved?
If the teacher notices that any of the above conditions
have not been met satisfactorily, he/she should initiate a
discussion or demonstrate to them why it would give an
incorrect result. Also, while using straws and sticks an
uncovered space might result at the end. Teacher can
help them to do rounding.
I once asked a group of preschool children, varying in
ages from 3 to 5, to make the longest possible train in
the class using blocks. It was very interesting to see the
engagement that ensued. One child began to form a
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line of blocks from the middle of the room. Soon they
laid out a string of blocks and reached one end of the
room. Just as they thought they had finished another
child noticed that they had started from the middle and
that they could extend it in the other direction too.
Quickly more blocks were picked off the shelf and
unloaded to complete the train to the other end as well.
Since they had not lined the blocks against the wall,
their train was not absolutely straight. When I asked
'how many bogies are there in your train?, with great
enthusiasm they counted off in chorus and found it to
be 114 bogies. The counting itself did not go smoothly
as the younger ones were uncertain about some
numbers. But the older ones corrected them, and they
finally arrived at the correct number. I then asked them:
How many bogies long is the room? They took some
time to respond and this time it was the older ones who
saw the correspondence between their train and the
length of the room and answered correctly.
Measurement of curved lines: Let children use small
units like ice-cream sticks or paper clips and measure the
length of curved lines or length around a circular shape.
Whose shape has the biggest round? How much
bigger is this flower pot than the other?
Figure 5
As children go through the experience of measuring
lengths with NSUs they need to absorb certain essential
principles involved. One principle is that they need to use
the same unit repeatedly while measuring one object.
Secondly to make comparisons between two lengths they
need to use the same unit for measuring both. Thirdly
they begin to see that measurement with a larger unit will
result in a smaller count and measurement with a smaller
unit will result in a larger count. They will later be able to
appreciate that the choice of the measuring unit depends
on the level of accuracy that is needed.
The teacher can devise activities which lead to an
understanding of measurement processes and skills.
Materials: A long strip, three measuring units of
different length (chalk, tooth pick, straw).
Let children measure the long strip with each unit. They
will see that when they measure with straws they get a
small number, when they measure with a chalk they get
a larger number and when they measure with a
toothpick they get a still larger number.
Body lengths: Let children work in pairs. One child lies
on the floor, and the other traces the outline of his body
with a chalk. Let each child measure the length of his
body using straws or sketch pens.
Help them to record the information. Similar activities
can be done by tracing the foot or palm of each child
and selecting a suitable measurement unit.
Using body measures as NSUs: Children now begin to
measure lengths using the foot as a unit of
measurement. They also use hand span and paces,
though this requires greater motor co-ordination to get
it right. Sports and games activities provide many
measurement opportunities.
Figure 7
Show them why aligning the starting end of an object
with zero facilitates reading of information. At the same
time, expose them to measuring lengths of objects
which are not aligned, as shown in Figure 7, so that
they understand the need to subtract the first number
from the second number in order to determine the
length of the object.
Measurement of CAPACITY for 5 to 7 year olds:
Materials: tub, plastic bottles, plastic containers (some
with small base and some with large base), cups or
glasses, cardboard boxes (all these items should be of
different sizes), plastic or wooden cubes for fitting into
the boxes, sand and water.
Task 7: Mark a circle on the ground outside or in the
veranda of the school. Let children take turns to stand in
the circle and throw a stick, one by one. Let them
measure the distance thrown using feet or paces.
Figure 8
Figure 6
Constructing Rulers of different units: Let children
build cardboard rulers using a straw or ice-cream stick
as a unit, as shown in Figure 6. Let them number the
markings as '1 straw' or '1 stick.' This will help them
understand that '1' points to the place where one straw
ends and the second one begins. Children often make
errors in measuring by not aligning an object with zero
on the scale as they do not understand that the number
'1' is at the end point of the measuring unit.
Children can compare the capacities of two or more
containers by filling the containers with sand measured
with a cup and count the number of cupfuls each one
holds. Ask questions which require them to apply their
understanding: Does this cup hold double of that
cup? Will the container fill up if I pour one more
cupful?
Let each group of four children select one large
container and three differently sized cups for measuring
the capacity of the container. Ask questions which will
require them to reason out their answers. How many
small cupfuls of sand did you use to fill the bowl?
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How many big cupfuls of sand did you use to fill the
bowl? Why did you get a smaller number? Point to a
size which is in-between and ask: What will happen if
you use this cup? Point to a bowl which is smaller in
size than the one measured and ask: How many small
cupfuls of sand will this hold?
They can measure the capacities of their water bottles.
Children's water bottles come in various shapes and
sizes, and as they measure them they will see that
objects which look different in size and shape may have
the same capacity. They can also measure the capacities
of their tiffin boxes by filling it with cubes.
Measurement of WEIGHT for 5 to 7 year olds:
Materials: Give children a collection of objects and ask
them to pick up pairs of objects which are similar in
weight.
Building a sense of weight: Give children some
identical cardboard boxes each containing an object
which they have handled before (examples: chalk,
duster, crayon box, tennis ball, stapler, punch), of
different weights. Mention the names of the objects
used. Let children pick up each box in turn and guess
the object in the box based on the weight.
Hanger balance: Build a hanger balance as shown in
Figures 9 and 10 for children to compare weights of
different small objects.
should use the knowledge and experiences that children
already possess with regard to usage of length, weight
and capacity. Children would have already witnessed
usage of length while buying cloth, when they visit a
tailor, while buying shoes, height chart in a doctor's
clinic, etc. They would have experienced weights while
buying vegetables and sweets, on packaged products,
in a doctor's clinic, in baking activities, etc. They would
have experienced capacity while having cool drinks,
buying milk or oil, drinking water cans, metre readings
of petrol consumption, etc.
Measuring activities for 7 to 9 year
olds
Measurement of LENGTH for 7 to 9 year olds:
Need for standard units: Select a long object in the
classroom, say the blackboard or a wall, for measuring
its length. Ask different children to measure it using
hand spans. The teacher can also measure using his or
her hand span. It will be noticed that slightly different
answers are obtained. Discuss with the children the
reasons for such differences. Point out the difficulties
that can arise if we had to ask a carpenter to make a
frame for the board and we specified the dimensions
using NSUs. Bring in the need for standard units as
measures.
Sense of centimetre: Now one can make the transition
to the standard units of centimetre and metre. Show a
centimetre ruler to the children and help them
understand the markings. Typically, the zero mark is a
little off the edge of the ruler. The teacher must explain
this so that the children clearly see that the cm length
begins at the zero mark.
Figure 9
Figure 10
With older children in the primary school, the teacher
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Normal rulers come with millimetre markings as well. If
one wishes to avoid teaching millimetres at this stage, it
is good to prepare and keep centimetre rulers in the
class, so that one can introduce millimetres at a later
point. During the days when wooden rulers were
available, I used the back of the ruler to create cm
markings. However, if children are curious and ask
about the smaller divisions within the centimetre
markings, the teacher can explain about millimetres as
well. Let the children count the divisions and see that 10
millimetres makes a centimetre, and that a millimetre is
useful for very small lengths. However, while recording
measurements they can write lengths as 1 cm and 5
mm, or 15 mm. Decimal notation can be taught later.
Construct a ruler with only centimetres marked: Even
though children have rulers of their own, it is still
worthwhile to get children to build rulers with cm
markings and number the markings as 1 cm, 2 cm, etc.
In the act of constructing and making markings and
labelling them, their understanding of a measuring scale
and its divisions becomes clearer.
Figure 11
Let them now observe a normal ruler and describe it in
terms of the main divisions they see, how each division
is further divided into subdivisions, the numbering on
the ruler, etc. Verify whether they understand this
completely and whether they are able to use it correctly.
Let children measure various objects in their bag,
recording the information in a table form. Some
questions are always big hits with children: Who has
the widest smile? Who has the longest nose? Who
has the longest palm? While measuring length, ensure
that children do not confuse length with area measure.
Length is a linear measure whereas area is a surface (2D) measure.
Building estimation skills using body measures: Let
children find and look for cm sized parts in their body.
Ask: Which finger nail is about 1 cm wide? Once that
is clearly established, they can learn to use their sense of
a centimetre to estimate lengths of other small objects.
Practice activities: Children can be given coloured
streamers to cut 1 cm pieces without measuring. They
can later make a collage and hang it in the class. Toilet
roll paper can also be used for cutting and estimation
activities involving bigger lengths like 10, 15, 30 cm.
Let them go on a cm hunt and find natural objects
which are about a cm long.
Shoe size: Let them measure their foot size and see
how it corresponds with their shoe size.
Footprints: Make children into groups of four. Using old
newspapers, each group can print their footprints using
poster colour. Other groups have to match the footprint
with the right person.
Let children collect some small objects like screws, pen
caps, chalk pieces, bottle caps, etc. Let them make a
table listing these objects and write their estimations
before checking and writing the actual measurements
next to them.
Construction activities: Measurement becomes
meaningful when children are given construction tasks
for which they need to use measurements. Create a box
to hold a given object. Make a paper T-shirt for a friend,
using a newspaper. Create a streamer decoration for the
classroom. Make a rangoli design in the centre of the
floor.
Sense of metre: Show them a metre ruler and
demonstrate usage of it in measuring a few objects in
the class. It is good to cut and keep a few 1 metre
pieces of rope for measurement activities. Let the
children use it for measuring arm length, height, etc.
They can describe these measures in terms of my arm is
less than a metre, my leg is less than a metre, my
height is more than a metre.
Building estimation skills using body
measures:
Demonstrate that the distance from one shoulder to the
tip of the opposite arm is roughly a metre (for an
'average' adult). They can now begin to use this as a
rough measure in various estimation activities.
On a daily basis, pose questions about the lengths of
new objects inside or outside the class which require
them to use their sense of cm and metre. To reinforce
the sense of how large is a metre, ask questions such as:
Guess the length of a cycle and a car. Guess the width
of a road. They can later measure the width of a
narrow road and a broad road, and the width and
length of a car.
More on metres:
Materials: Measuring tapes, metre rulers.
By class 5, they can measure lengths of paths from the
school gate to the school, or the length of the school
veranda, or the road in front of the school. At this point
one needs to discuss rounding to the nearest whole
figure.
They should also be given tasks which require them to
measure lengths in parts and add them like total length
around a building or a garden bed. They can also be
given broken up tasks so that pairs of children measure
lengths from opposite directions and add them to arrive
at the total figure.
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Different routes: Ask the children to think of the various
paths they can take from the school gate to their
classroom. Let them guess the length of these routes.
They can then measure these lengths and share their
measurements in class.
Children of primary school find it difficult to develop a
sense of kilometre. However, sports events which involve
running on 50 m, 100 m and 200 m tracks will help
children develop a sense of these measures.
Task 8: Given a simple local map depicting lengths in
kilometres, children will be able to work out the lengths
of the shortest routes connecting various pairs of places.
Foot and inches: Since many measurements are done
using feet and inches as measures (rather than metre
and cm), children can be taught these in a subsequent
year once they thoroughly understand cm and metre.
Building estimation skills using body measures: Let
children use the knowledge of their own height to
estimate the heights of various objects in the class. Get
them to articulate how they think about it. They may
say: this seems to be double my height or This is
slightly more than half my height or This is close to my
height, etc.
glass, teacup, spoon, water bottle): Let children fill a
tumbler using a 100 ml measure and check its capacity.
Let them also fill a tea cup and a spoon with
appropriate measuring units and check their capacity.
As 1 litre bottles are widely used, children are quite
familiar with them. They can also measure a bath mug
and a small bucket. Once they are completely familiar
with the capacities of these objects, they will be able to
use this knowledge for estimating the capacities of
other containers.
Create a calibrated bottle: Let children use a standard
transparent bottle. They can fill it with 100 ml measure
and mark on the bottle with a marker pen. They can
record in multiples of 100 or 250, 500, 750, etc.
Let children use cubes to fill different cardboard boxes
(toothpaste box, soap box) and compare capacities of
these boxes.
Task 10: Building boxes with interlocking cubes or plain
cubes: Give each group of children 36 cubes.
One challenge could be to
build open boxes with
them. What is the
maximum capacity of these
boxes? Another challenge
can be to make all the
Let them estimate height of the door, height of the class
room, height of the tube light, bench, chair, height of
the flag pole, etc. This can be followed by actual
measurement activities using a foot ruler or a metre
scale.
Task 9: Match object and length.
Prepare a set of object cards and length cards. Object
cards can have labels and pictures of familiar objects and
animals with varying heights (dog, elephant, coconut
tree, table, stool, flower pot, doorstep ) and the length
cards can have possible heights in metres, centimetres.
Figure 13
Figure 12
Children will have to use their sense of length to match
these cards.
Measurement of CAPACITY for 7 to 9 year olds:
Materials: Litre bottles, half litre bottles, 100 ml, 50
ml, 250 ml measuring cups, measuring spoons, 5 ml
and 10 ml measuring caps of medicine bottles,
normal glass, standard cup, paper cups, spoon,
bucket and bathing mug, containers with labels
showing capacity, sand, water, cardboard boxes,
cubes
Building sense of capacity of everyday objects (drinking
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Figure 14
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possible types of cuboids with them to see how many
differently shaped cuboids can be made from the same
number of cuboids.
Checking capacity through displacement: Place a
small bucket filled completely with water in a tub. Lower
a closed bottle into the bucket. Let the water which has
spilled out be collected carefully and poured into the
immersed bottle. What is noticed?
Measurement of WEIGHT for 7 to 9 year olds:
Use a rubber band and a clip along with a basket as
shown in figures 15 and 16. Let children select three
objects and guess the heaviest and lightest among
them. Children can now hang the objects from the
hooks and measure the lengths of the stretched rubber
band. Do they see a relationship between the weight of
the object and the length of the stretch?
Materials: Balance made by the children, real
balance if possible, 50 gm weight, 100 gm weight,
250 gm weight, 500 gm weight, 1 kg weight (it is
easy to put together some stones of equivalent
weights packed into cloth bags).
Let children measure the weights of many everyday
objects.
Let them build a sense of the weights of some objects
they use every day, weights of their tiffin box, water
bottle, notebook, biggest textbook, pencil box, pencil,
etc. They should use actual weights for the
measurements and record the results. Using knowledge
of these weights, they should be able to estimate the
weights of other objects in the class.
Game: Find a match! One child picks up any object, e.g.
a rubber ball, and asks the others: Find a match for the
rubber ball. The other children try to find another
object with a similar weight. They can later compare the
actual weights using the balance. Whoever comes
closest is the winner.
Home project: Let children look around in the house,
particularly the kitchen, and ask their parents to make a
list of items bought in gm, kg, litres, etc. Discuss the
need for smaller measures like gm in medicines and
cooking, and the need for larger measures like tonnes.
Building estimation skills: Estimation is a skill learnt
through trial and error. One learns from the feedback
one gets and the skill gets refined. Children use
estimation frequently in daily life. They may not even be
aware that they use estimation when they race or jump
or leap from one place to another, when they estimate
the length of paper needed to make a paper plane or
the time they need to complete their homework.
Build the estimation skills by specifying the measure of
one object to determine the measure of other objects. If
the weight of an orange is known, weights of other
fruits like apple, sweet lime, banana, lemon and
coconut can be estimated by comparing them mentally
and then multiplying or dividing by a suitable factor.
Similarly, if the height of the classroom is known, then
other heights like the height of the building, the flag
pole, the gate, the door, the black board can be
estimated. Another important approach used in
estimation is to estimate the length or weight of a small
portion of the actual object. Example: If one wants to
estimate the height of a book shelf with 6 divisions, one
will estimate the height of one division and then
multiply by the appropriate factor.
Activity: Find the unit used.
Create a worksheet or a set of cards which give
measures of various objects without specifying the unit
used. Let children use their sense of measure to decide
which unit has been used. Example: Rishi is 120 ___ tall;
weight of this apple is 125 ___; the handkerchief is 25
___ long; the shoe is 130 ___ long; this jug's capacity is
2000 ____.
Body awareness: Height: Class room can be a place
where the heights of children are recorded on the wall
(behind the door) with a pencil. Children can record
their height in centimetres, or feet and inches, in their
math notebook at the start of the year. They can check it
again half way through the year and at the end of the
year.
Weight: A weighing scale can be brought to the class at
the start of the year and children can record their
weight in their note book. They can repeat this activity
at the end of the year.
Figure 15
Figure 16
The Teacher can discuss the results. Correlation between
increase in height and weight can be observed in many
cases.
Vol. 4, No. 2, July 2015 | At Right Angles
11
Padmapriya Shirali
12
Padmapriya Shirali is part of the Community Math Centre based in Sahyadri School (Pune)
and Rishi Valley (AP), where she has worked since 1983, teaching a variety
of subjects mathematics, computer applications, geography, economics, environmental
studies and Telugu. For the past few years she has been involved in teacher outreach work. At
present she is working with the SCERT (AP) on curricular reform and primary level math
textbooks. In the 1990s, she worked closely with the late Shri P K Srinivasan, famed
mathematics educator from Chennai. She was part of the team that created the multigrade
elementary learning programme of the Rishi Valley Rural Centre, known as 'School in a Box'.
Padmapriya may be contacted at padmapriya.shirali@gmail.com
At Right Angles | Vol. 4, No. 2, July 2015