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E1) I have a three-year-old friend. He has a lot of toy cars to play with. Playing with him once, I divided the cars into two sets. One set was more spread out and had 14 cars in it. The other set had 15 cars, but they were placed more closely. He had the choice of taking the set with more cars. He made the correct choice. From this, which of the following statements would you deduce? What are the reasons for your choice?
a) He can count upto 20.
b) He can perceptually distinguish between large sets.
c) He just made the choice by chance, and may not be able to repeat it.
d) He may be able to do a lot of things with cars, but not with other objects.
As a child gets older, she moves from an intuitive understanding of number to a level higher than that of recognising numbers by mere perception. A good way of enabling the older among the pre-operational children to make connections, see relationships, and thereby, increase their mathematical understanding, is to involve them in games played with a small number of objects in which they have to 'add' and 'take away' objects.
The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(
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