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Long Multiplication - with a Splash of Colour

Long multiplication probably lives long in our memories as one of the most traditional mathematical methods we learnt at primary school and not a particularly colourful experience.

If you haven't already, read my blog from last week about the Grid Method and not jumping into Long Multiplication too quickly. Long Multiplication needs lots of ground work to support mathematical understanding.


I have to admit, before I attended university to study children's development and learning as part of my teacher training, I hadn't used Long Multiplication for many years. Calculators had been my 'go-to' at every opportunity and I lacked confidence in my ability in maths. You can imagine the instant sinking feeling I felt when my first maths lesson at university, consisted of an arithmetic test with Long Multiplication (and other methods i'd long since forgotten). I suddenly realised, I never actually knew why I was carrying out any of the steps in the calculation and inadvertently missed one step, leading to a wrong answer. That flippin zero again! Comfortingly, many of my peers didn't understand the method either. There was talk of milk bottles on doorsteps and other unfathomable tips. We were all totally confused by how the method worked. Those that correctly answered the question, couldn't explain why it worked either. Thank goodness our lecturer enlightened us.


These experiences taught me that children need to understand the principles of maths, not follow meaningless processes. Processes are forgotten when there is no understanding behind them and they are not used regularly. Children who rely purely on processes in maths are unlikely to be able to decipher whether their answers are realistic either.


After more than fifteen years teaching Long Multiplication to hundreds of children, the use of colour has to be the biggest tool I have discovered in helping children understand the meaning behind each step of the calculation and how the Place Value of each digit is vital.


The Expanded Method of Long Multiplication

One of first steps to teaching Long Multiplication, in a way children understand, is to showcase each of the steps by expanding the calculation into a list. I use one colour to show all the multiplication steps by the 'Ones' digit (5) and a different colour to show all the the multiplication steps by the 'Tens' digit (2).


Again, the Expanded Method is just an interim method for understanding and not one to stick with. The most efficient method for multiplying large numbers is Long Multiplication.

Long Multiplication

Using two different coloured pens or pencils helps children to visualise the Place Value of each digit in this method. This is a 'stabilisers' approach to learning this method. It provides an opportunity for understanding, paving the the way for progress, application and confidence.


No tricks, no strange stories, just maths taught for understanding. Children won't need the colours forever but they will love using them.


Happy Multiplying.








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