Acquiring Number Sense - 2

The skills described in the previous chapter would get strengthened by the following facts regarding relations between numbers & the four operations.


 * 1) Properties of Addition
 * 2) 5 + 4 = 6 + 3 = 7 + 2 (Reducing one number & increasing other by the same amount)
 * 3) Properties of Subtraction
 * 4) 5 – 4 = 6 – 5 = 7 -6 (Increasing or decreasing both numbers by the same amount)
 * 5) Relations between Addition & Subtraction
 * 6) If 3 + 4 = 7 then 7 – 3 = 4 Or 7 – 4 = 3
 * 7) If 5 – 3 = 2 then 2 + 3 = 5 and 5 – 2 = 3
 * 8) Properties of Multiplication
 * 9) 8 X 4 = 16 X 2 OR 7 X 6 = 14 X 3 (increasing one number by a factor and reducing the other by the same factor)
 * 10) Multiplication & Addition
 * 11) 8 X 4 = 8 + 8 + 8 + 8 OR 4 + 4 + 4 + 4 + 4 + 4 + 4 +4
 * 12) Division
 * 13) 8 ÷ 2 = 16 ÷ 4 (Increasing or reducing both numbers by the same factor)
 * 14) If 8 ÷2 = 4 then 8 = 4 X 2 (Relation between multiplication & division)
 * 15) If 9 ÷2 = 4 R1 then 4 X 2 + 1 = 9 (Relation between division with remainder & multiplication)
 * 16) Operations with Odd & Even numbers
 * 17) Even + even = Even, Even + Odd = Odd, Odd + Odd = Even
 * 18) Even X Even = Even, Even X Odd = Even, Odd X Odd = Odd
 * 19) End digits of products


 * 1) Divisibility by numbers from 2 to 9
 * 2) Relation between squares of consecutive numbers
 * 3) 8^2 = 7^2 + 7 + 8
 * 4) (n + 1 ^2 = n^2 + n + ((n + 1)
 * 5) Difference between squares of any 2 numbers
 * 6) 9^2 – 6^2 = (9 + 6) X (9 – 6)

It is important that children develop a strong understanding of numbers and their relationships before we ask them to compute. These will not develop unless students have time to explore or if the focus is on speed.