What are you like at multiplications? Chances are if you’re a mere mortal 2, 5s and 10s won’t seem too taxing. But when it comes to figuring out what 42×21 is, you may wish somebody had shown you the Japanese multiplication method in school.
This genius Japanese multiplication method of drawing lines and dots is supposed to make doing multiplications so much easier, quicker and – wait for it – fun. But does it work? Can you learn how to do it without any technical help or going back to the classroom (you know, when that’s finally allowed!)?
Home-schooling mum Laura Davies got out her colouring pens to give it a go and this is how she got on.
What is Japanese multiplication?
Although it looks a little bit like a magic trick, and in some way it is, this method is all about substituting numbers for lines. Japanese multiplication is also referred to as stick or line multiplication.
Did you know : In ancient times chopsticks were used to visualise the method – long before we studied it in school!
So how does it work?
Japanese multiplication is about completing a multiplication problem by drawing a few lines and counting the points where the other lines join to give you the answer. Sounds much too easy, right?
I plucked the numbers 13 x 21 out of the air to test myself. Well, even I can work out 10 x 10!
What you need to remember is that numbers are represented using place value. In this sum, 13 means one 10 and three ones; 21 means two 10s and one one. Got it?
Let’s draw!
Now the fun bit. The drawing.
For every number, you draw the corresponding number of lines on a piece of paper or a whiteboard.
Begin with the first number in the sum which here is 13.
Draw a diagonal line and leave a little space. Then draw lines for the second digit in parallel, here it is 3. Try using a different colour pen for each line – it can make it easier to see your method.
So for the number 13 I got this:
The blue line represents one ten and the three lines represent three ones.
Now, draw the lines for the second number, in this case, the number 21.
Again this should be drawn diagonally, but this time, draw it in the opposite direction to your other lines.
You should be left with a rough diamond shape, with the coloured lines crossing at the four corners.
Once you’ve drawn it, you then need to break up the diamond into three separate zones where the lines meet.
Either using a ruler or free-hand, draw a loop around the section nearest to the left side. That’s where the blue and orange lines join.
Then, moving right, draw a loop around the centre section. The red and blue are at the top, and the orange and green are at the bottom.
Finally, draw around the lines that are closest to the right side.
This is where the green and red lines meet.
Now it’s counting time
Using a different colour pen, mark a dot where each line joins in each zone.
Start from the left and work in a clockwise direction and count how many dots (joins) there are.
Write the numbers next to each point of your diamond. You should be left with four numbers inside your three yellow zones.
Each zone is broken down to the number of hundreds, tens and ones
Fun tip: You could try using coloured lollipop sticks or even chopsticks to add interest. As long as you follow the same formula you can do it anyhow or anywhere – you could even do it on the beach and draw lines in the sand using a stick and collect pebbles to mark your join dots. The possibilities are endless. Pretty cool isn’t it!
Now for some simple addition
Your middle yellow section should still have two numbers in it – one and six.
Now it’s time for some adding up. So 1 + 6 = 7 (that much I know!). This will be your number for your middle zone.
At this point, you may be feeling a bit confused with all these numbers flying around. But trust me, there’s no need! Try circling each number in your three yellow zones to make it easier.
In this case, you should end up with 273.
And just like that you have your answer!
13 x 21 = 273. Simples!
I’ve got to say that once you get your head around it, this ancient Japanese method is brilliant.
If only all maths tricks were as easy to remember!
By visualising the maths problem you only need to add up instead of multiply.
What do the experts say?
Award-winning online maths tutor Maths-Whizz love it! The sums wizards there say that at first, it may appear to be like something out of a magic show.
Dr Junaid Mubeen, former Countdown champion and Director of Education at Maths-Whizz, said: “Maths should never feel mystical to the point of confusion. And while magicians may never reveal their tricks, we think it’s essential to lift the lid on just why these strange methods work. It’s the only way to fully appreciate them!
“The Japanese method is a great way for your child to test their understanding of a particular method. It’s one thing to know how to carry out a procedure (like long multiplication), but this is only useful when your child knows why that method works. Once they make these connections between symbolic and visual methods, they’ll be able to apply their full toolkit of procedures in different situations.
“Your child – or you! – will learn to evaluate which method is most appropriate for a given problem. For example, the Japanese multiplication method becomes very inefficient when dealing with larger numbers – just try 9×8 and suddenly you find yourself counting 72 different intersections.
“Not nearly as efficient as other multiplication methods!”