Approaches and methodologies

Some activities with odd and even numbers

When children have a conceptual understanding of multiplication as repeated addition or grouping, the multiplication sign can be introduced as meaning ’sets of’.

The children can be given a worksheet with the multiplication facts arranged in table form and asked to fill in as many of the facts as they can from memory. Reference should be made to previous work done by the children, for example patterns on the hundred square. After filling in the multiplication table from memory the children can discuss with the teacher what strategies they used to help them fill in the products they did not know. Initially the most common strategy for working out an unknown fact is counting on from a known fact: for example, 3 x 6 = 18, so 4 x 6 is 18 + another 6. Some children will use skip-counting from memory or count on their fingers.

In exploring multiplication patterns children will notice that odd and even patterns appear, and this can provide scope for interesting investigations; for example will the final digit in the x2 facts be odd or even? What about x4? or x3?

These investigations can lead to further work on odd and even. Children can work in pairs with one child being ‘odd’ and one child ‘even’. They each throw a die and get a point each time an odd or even number is thrown. They will soon notice that there is an equal chance of either of them winning as there are three even and three odd numbers on the die. This can be extended by using two dice. The initial response may be that the result will be the same (equal chance of winning). The children will soon realise that you must add the totals of each die, as it is the total that scores the point. After the experimentation and guesswork it is interesting to record and discuss all the possible combinations of the two dice throws.

Odd totals
1 + 2 = 3
1 + 4 or 2 + 3 = 5
1 + 6 or 2 + 5 or 3 + 4 = 7
3 + 6 or 4 + 5 = 9
6 + 5 = 11
Number of possibilities: 9

Even totals
1 + 1 = 2
1 + 3 or 2 + 2 = 4
1 + 5 or 2 + 4 or 3 + 3 = 6
2 + 6 or 3 + 5 or 4 + 4 = 8
4 + 6 or 5 + 5 = 10
6 + 6 = 12
Number of possibilities: 12.