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

a. 5 + 4 = 6 + 3 = 7 + 2 (Reducing one number & increasing other by the same amount)

2. Properties of Subtraction

a. 5 – 4 = 6 – 5 = 7 -6 (Increasing or decreasing both numbers by the same amount)

3. Relations between Addition & Subtraction

a. If 3 + 4 = 7 then 7 – 3 = 4 Or 7 – 4 = 3

b. If 5 – 3 = 2 then 2 + 3 = 5 and 5 – 2 = 3

3. Properties of Multiplication

a. 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)

b. Multiplication & Addition: 8 X 4 = 8 + 8 + 8 + 8 OR 4 + 4 + 4 + 4 + 4 + 4 + 4 +4

4. Division

a. 8 ÷ 2 = 16 ÷ 4 (Increasing or reducing both numbers by the same factor)

b. If 8 ÷2 = 4 then 8 = 4 X 2 (Relation between multiplication & division)

c. If 9 ÷2 = 4 R1 then 4 X 2 + 1 = 9 (Relation between division with remainder & multiplication)

5. Operations with Odd & Even numbers

a. Even + even = Even, Even + Odd = Odd, Odd + Odd = Even

b. Evan X Even = Even, Even X Odd = Even, Odd X Odd = Odd

6. End digits of products

7. Divisibility by numbers from 2 to 9

8. Relation between squares of consecutive numbers

a. 8^2 = 7^2 + 7 + 8

b. (n + 1 ^2 = n^2 + n + ((n + 1)

9. Difference between squares of any 2 numbers

a. 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.