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I was discussing with other parents online, about the merits of various school Math multiplication approaches.

In the “Japanese Line method” you draw lines for each digit, and then count the intersections and add them up.

In the “Box-Method” you draw areas for each sub-product, and in “Longhand Multiplication” you just use the square grid to keep track in a table, without use of a diagram.

My main issue with the Line Method is that for problems like 97*98, you’ll be drawing a lot of lines .. its a lot of work even for 64×34 :

I also like the idea that Box Method starts with a physical / visual intuition – you can start children counting rows and columns, then progress to counting areas such as “How many 1ft square tiles do I need to tile the 3’x7′ kitchen floor ?”

Then you can discuss the distributive law a(b+c) and (a+b)(c+d) and explain the method behind longhand multiplication .. and then go on and show some handy tricks, such as using negative numbers to make less work, vis :

The above example, which does the same problem in 2 different ways, shows the kind of approach Jo Boaler recommends, called “Number Sense” – where students are encouraged to find their own way of doing a math problem.  The idea is that there are many valid ways to do it, and struggling to find your own way is a good thing [ even if you fail ], and students tend to engage more, and certainly recall more when they have actively discussed with other students.

The same Box Method diagram can lead onward naturally to algebra and quadratics.. and even the beginnings of calculus 🙂