What is our aim when teaching children multiplication? Firstly they should be able to judge which situations they need to multiply in, and the numbers that are to be multiplied secondly, they would be able to do long multiplication, i.e., one multi-digit number multiplied by another, with understanding what is involved. To enable children to do this, the following sequence may be followed. We list all the stages from the beginning.
1) Developing the meaning of multiplication.
a) Grouping of equal numbers of objects.
b) Adding equal groups.
c) Skip counting.
d) Practising early multiplication facts - framing multiplication tables.
2) Understanding and using the language of multiplication as well as the symbolic method of recording multiplication facts.
3) Understanding and applying the distributive law of multiplication with respect to addition.
Multiplication and Division
4) Learning the algorithm of multiplication - recording in columns as 3x4 = 12
5) Introduction to the multiplication of larger numbers - two-digit number with a one digit number without carry-over, e.g., 12 , and with can-over, e.g., 13.
6) Extending the algorithm to multiply a two-digit number by. a two-digit number:
i) By splitting one of them, e.g., 23 x 12 = (23 x 2) + (23 x lo),
ii) Without carry-over,
iii) With carry-over.
7) Developing a deeper feel for why the algorithm works.
8) Multiplication of a three digit number by
i) a one-digit number,
ii) a two-digit number.
Let us now consider the problems children face in learning division, and possible ways of improving the situation.