The following question is taken from my website Diagnostic Questions. Here you will find 1000s of free, high quality maths multiple choice diagnostic / hinge questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.
I’ll admit it from the start – I hate this method of written multiplication. I have heard it called “Chinese” and also attributed to Napier (surely he cannot be happy with this), but whatever you want to call it, I am not a big fan.
Don’t get me wrong, I have seen many students use the algorithm extremely effectively. And I will also concede that if you have lower achieving students who struggle with other methods of written multiplication, then this is viable option to enable them to get questions correct.
But do they, or indeed any student who uses the method, really know what they are doing?
Well, I wrote this question to find out.
Here is my thinking behind each of the answers:
Answer A) could imply a student simply sees the 1 as a 1
Answer B) is correct (I think!)
Answer C) could be a result of the student seeing the 0 below the 1, and hence believing it stands for 10. Or, as one of my students confidently explained, it is 10 because it is in the “tens column” underneath the 2 in 626
Answer D) could be a result of the student seeing the 1010 in the bottom row, and hence thinking the first 1 is 1000, or simply imply a complete misunderstanding of this confusing algorithm.
When Diagnostic Questions has the feature to collect students’ responses from all over the world (and their accompanying explanations), I will be fascinated to see the results of questions like this. This is all coming soon! 🙂
In the meantime, I would love to hear the response of your students when presented with this question.
And I guess there is a wider point for discussion here… does it really matter?
Does it matter that students don’t really know what they are doing with this algorithm, so long as they are getting it right. Well, in my opinion, yes it does. If students don’t understand what each of the numbers in the grid mean, then not only does this fail to cement their knowledge of place value which is fundamental to success with numbers, but this algorithm will then be added to a long list of rules that they have to remember in maths – rules that are abstract, meaningless, and magically seem to arrive at the right answer. And abstract, meaningless algorithms are easily forgotten, muddled up and misapplied.
Oh, and if you are interested, I am a Grid Method man, through and through 🙂
Worst thing I’ve ever read. This method is by far the most efficient method for multiplying large numbers. The grid method is a very poor way of doing so due to adding lots of unnecessary zeros with students only needing to miss one zero somewhere to get completely the wrong answer.
This method also places each digit into the correct place value automatically with each diagonal being units, tens, hundreds and so on. This can be clearly explained to students so that they DO understand the method.
It is also better than the column method as students don’t need to add zeros when multiplying by different powers of ten and you only need to carry your addition at the end rather than carrying multiple times throughout.
When selecting a method for my students I always try to use the one with the lowest possible number of ways the students can make a mistake and for multiplication it is this method by a long way.
I’m aware this article is from 2014 and I’d be interested to know whether you’ve changed your opinion since.