Several circles can be drawn through a point. How many can be drawn through two points, or three points, or.…?

i)Work on this problem and note down the processes you use.

ii)Did the properties of mathematics, mentioned in Sec.1.3, show up while you were developing your arguments? If so, in what way?

When we

(i)Estimate quantity, and/or

(ii)Look for relationships, and/or

(iii)Observe patterns

we are doing mathematics. List examples of these three activities occurring in each of the following situations.

a)Saba lives in Jaipur, and has to reach Delhi on 23rd March by 10:00A.M;

b)Suresh is planning to knit a sweater for his sister.

Lata wants to put up a swing on the tree in front of her house. To put up the swing she needs a rope and an appropriate branch of the tree. Does she need, or use, any mathematics in the process of choosing them? Explain your answer.

A friend of mine said, “I’m just a housewife. I don’t know maths, and I don’t do maths.” I strongly disagreed with her, giving her several examples of mathematics that she is doing all the time without realising it. Can you give four examples of different topics of mathematics she would be applying at home?

Think of a card game and an outdoor sport that you or your friends play. Write down what mathematics is used while playing them.

In a discussion among primary school teachers, many of them said that mathematics is a study of numbers and how to use them for calculation. Do you agree with this? Give reasons for your answer.

Would you say that the number system developed through the process of abstraction? If so, how?

Historically, it is said, that the concept of zero was invented in ancient India. How has this concept helped in developing a better way for symbolically representing numbers?

Which subject is not hierarchically structured? Give reasons for your choice.

Prove, or disprove, the statement that every counting number is greater than or equal to the sum of its proper factors. (e.g., the proper factors of 6 are 2, 3 and 2+3 = 5.)

In what way does the unambiguity of mathematical statements make mathematics powerful?

List at least two examples of a mathematical term being used loosely in ordinary conversation. Give reasons for your choice.

Write down two hierarchical chains in mathematics. You can look for examples related to number operations and shape.