Today I want to share a bit about the method I consider to be the best for teaching multiplication. Now most of us know long multiplication, which is a pretty good algorithm, but I find that kids mostly have no understanding of what they are doing. You also might have seen the Chinese method of multiplication, which is a lot of fun for smaller numbers, but gets a bit complicated for bigger numbers and involves mostly counting rather than promote understanding of the concept.
The method I find best for understanding is the area method (also called the box method). I like it specifically because it combines different areas of maths and it can be extended very well into algebraic multiplication and factorisation.
The basic concept is to see every multiplication problem as finding the area of a rectangle. The basic concept of area can easily be explained as finding out how many 1x1 blocks fit inside a shape.
Multiplication problems then turn into area problems.
To make it easier, you can split the length and breadth to divide into smaller rectangles.
Add the areas of all the smaller rectangles to find the area of the big rectangle and thus the answer to the multiplication problem.
Using this method, you can also teach how to do 'shortcut' techniques for multiplication e.g. finding numbers that make 10; 100; 1000 or making a bigger rectangle and subtracting smaller ones from it.
From here, it is very easy to show the distribution property, which says that a × (b+c) = a × b + a × c or a × (b−c) = a × b − a × c
When algebra is introduced, it transitions well into a way to calculate the product of two binomials. Also, showing the square of a binomial as an actual square helps to remember to calculate the middle terms.
From here, factorisation is just the opposite: determining the dimensions when the area is given. This is done by splitting the expression into the 'boxes' and then finding the greatest common factor for every row and column.
I love the versatility of this method and the way that it can be used from very simple multiplication to algebraic expressions.
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