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Developing an understanding in number 8. Strategies for division a)    Dividing by one      Any given number of objects divided into groups of one will result in that number of single groups.            6 ÷ 1 = 6        b)    Dividing by two      The result is half the number being divided.        One half of 18 is 9       18 ÷ 9 = 2        c)    Dividing by ten      Here groups of ten are formed from a given quantity. The answer is obtained by disregarding the zero on the quantity.        50 ÷ 10 = 5        180 ÷ 10 = 18   (extension)   d)    Dividing by four      Halving twice will give the answer.        28 ÷ 4 = ?        half of 28 is 14       half of 14 is 7       e)    Dividing by nine      The answer is obtained by adding one to the tens digit of the number being divided.        36 ÷ 9 = 4   (3 + 1)   54 ÷ 9 = 6   (5 + 1)   f)    Dividing a number by itself      For example,\Given 8 objects, make a group of 8'.      Only one group can be formed.          8 ÷ 8 = 1   g)    Other useful division strategies      Children should realise that multiplication facts can be used to solve unknown division facts.        56 ÷ 7 = ?     The child should ask: '7 multiplied by what makes 56? 7 eights make 56.'   7 x 8 = 56   so 56 ÷ 7 = 8     The tens digit in each two-digit answer is one less than the number of nines.   5 x 9 = 45     3 x 9 = 27     6 x 9 = 54        Repeated subtraction        12 ÷ 2 = ?       Begin with 12 blocks. How many times can two blocks be taken from the pile? The answer is 6 times.   12 ÷ 2     12, 10, 8, 6, 4, 2, 0   12 ÷ 2 = 6       Note: Division by zero is impossible. This can be illustrated using knowledge of multiplication facts.   Consider 5 ÷ 0 = . If this is rewritten as a multiplication sentence, it becomes 0 x = 5. No matter what number is placed in the box, the resulting sentence is 0 = 5, which is a false statement. Therefore 5 ÷ 0 has no answer.   Some properties of zero can be summarised as:   • Any number x 0 = 0         For example, 2 x 0 = 0   • 0 ÷ any number = 0         For example, 0 ÷ 2 = 0   • Any number ÷ 0 has no answer.

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