28. Sonu and Monu went for travelling. Their aunt gave
them a milk bottle of 10 litres of milk. Sonu consumed
1
of milk. Monu consumed the remaining milk.
4
a) How much milk did Sonu drink?
b) What fraction of total quantity and how many litres
of milk did monu drink?
(3)
Answers
Answer:
There have been continuous efforts to make teaching-learning processes interesting and effective.
There have been efforts to understand the objects of having different disciplines in the school syllabus and
to understand and explain nature of each subject. Yet in teachers and children a reflection on clarity and
good understanding does seem to be evident. This is particularly true about mathematics.
If you were to pose the question, “What is mathematics?”, the answers would range from counting
objects, displaying numbers, doing number operations, lines, making shapes and so on. A few answers
might differ from the ones cited above, but these would be largely the things mentioned.
Before we go ahead, let us try and understand what all happens when we are attempting to solve
a problem in mathematics. For example, “A bus travels a distance of 35 kilometers in 1 hour. How far will
it travel in 6 hours?”
Here, time is an abstract concept. We have defined an interval as the unit of this abstract concept
and expressed large time intervals in terms of these units. Similarly, for distance, we have defined a unit,
which then helps us quantify it.
In the next step we explore the relationship between these two units of time and distance. We have
stated, “ The bus travels a distance of 35 kilometres in 1 hour”. This defines a relationship, which we
translate in term of an operation-for instance, either addition or multiplication.
Let us consider another example. A kilogram of rice costs Rs. 16. How much will 54 kilograms of
rice cost?
In this example, we have again defined a unit for quantity of rice, and expressed the total quantity
in terms of the unit. The same can be observed while solving problems related to area, etc. It is clear from
these examples that mathematics is not just limited to counting or operations on numbers. In the same way,
mathematics of shapes and lines is about exploring and establishing the relationships between them. Further,
while we include the concept of measurement for use, the sorting, classification searching for and establishing
their properties, constitute important facets of mathematics.
When a child begins learning mathematics, in order to express abstract ideas understand operations
as well as simple problems faced in daily life, it becomes necessary to use concrete (real physical) objects.
However, this dependence on real objects progressively decreases as mathematical skills develop.
Children then begin to build arguments. Their ability to deal with abstractions increases. They
begin to abstract arguments from their daily life, and translate abstractions into reality. They also begin to
seek solutions to problems of their own accord using various methods. This whole process helps children