Properties of Numbers 1

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Each number has certain properties and it also has arithmetic relations with other numbers. Exploring the properties and relations of numbers would give students a good foundation of Number Sense and fluency in operations. In this chapter we would explore properties.

But most of these properties are taught only as abstract concepts. Primary children would understand and remember them if presented and explored visually through activities using concrete materials like tokens.

Before we proceed, we need to understand what an array is. An array is an arrangement of tokens in columns &amp; rows as shown below. Children are familiar with this idea through assemblies &amp; PT classes. The following array has 3 rows with 4 tokens in each row. For example this array can be described as a 3 by 4 or 4 by 3 array.



Even &amp; Odd

The given number of tokens should be arranged in rows, with each row having 2 tokens. Each subsequent row should be below the top one.

If all the tokens are used up, the number is Even. If there is a token left, then the number is Odd. It would also become clear that for any Odd number, of any magnitude, only 1 token would be left.

Usually in a 2 digit number such as 56, it is taught that the number is even because the number in the Units Place, in this case 6, is even. No one asks about why the number in the Tens place, in this case 5, which is odd, is not considered. Representing the number in bundles and sticks will reveal that all bundles (in the decimal system) are even (as they can be shared equally among 2 persons) and hence bundles need not be taken into account. Only the number in the Units place needs to be considered.

Composite (Rectangle) Numbers

If a given number can be arranged, if necessary, after several tries, into a rectangular array, like the above, then the number is Composite. Its factors would be the Number of Rows and the Number of tokens in a Row. Initially, they can be called Rectangle Numbers.

Any child can, after some trial &amp; error, can find that 12 can be arranged in a 3X4 and 2X6 array. IN later years, she can find out that these are the factors of 12.

If a rectangular array has 3 tokens in a row, adding more tokens in the rows (in sets of 3) would give multiples of 3 &amp; thus lead to multiplication facts of 3 and the multiplication table for 3!

Prime (Line) Numbers

If a given number cannot be arranged, even after several tries, into a rectangular array, then the number is Prime. The only way it can be arranged is in One Row with all the tokens in that row or One column. It resembles a Line and can initially be called Line Numbers.

7 can only be arranged in a line. In later years they can be introduced to the term &lsquo;prime&rsquo;.

Properties of Individual Numbers

Apart from these general properties, individual numbers have a number of interesting properties on which a huge number of books have been written.

For example 2 is the only even prime. 6 is the smallest Perfect Number.

4 is the only number which can be represented with the same two numbers in 3 different ways. 2 + 2, 2 X 2, 2 ^ 2.

16 is the only number which can be expressed as exponential relations between 2 unique numbers in two ways. 2^4 & 4^2

< 7.6 Number Names – Indian Tradition | Topic Index | 8.2 Properties of Numbers 2 >