Teaching Sequence

Work through this resource material in the following sequence:

10 minutes

Tune In: Making Multiples

10 minutes

Find Out: The Vedic Method

10 minutes

Take Action: Give it a go!

Tune In: Making Multiples

Ask your students. How do we multiply? Some small numbers you might have memorised, like your times tables. What is 2 x 3? 6! Once we start getting into bigger numbers, we start to apply methods we know. Let’s look at 16 x 4. When you do this sum, how do you do it? Your students might have a variety of answers! They might say:

4 x 10 is 40, and 4 x 6 is 24, 40 plus 24 is 64
double 16 is 32, and double 32 is 64
16 is nearly 15, 15 x 4 is 60, plus 4 more ones is 64

There are LOTS of different ways we can do multiplication, and today we are going to look at some very cool and very old tricks for doing multiplication with BIG numbers. These come from Vedic maths which was developed more than 2500 years ago. There are 16 sutras in Vedic math, but we’re only going to look at a couple of tricks today.

Find Out: The Vedic Method

Step 1

How easy is it to multiply by 11? Until you get to 9 x 11 (99), it’s pretty easy, but once you’re past that, it gets a bit trickier. But here is a cool trick. Choose a double-digit number to multiply by 11 For this example, we’ll choose 27, so we want to figure out 27 x 11. On the board, write down 27 with a space between the two and the seven like so:

2

7

What is 2 plus 7? 9! So write 9 in the middle:

2

9

7

And there’s the answer, 27 x 11 = 297

Step 2

Ahhhh, but what if our two numbers add up to more than 10? For example, 48 x 11? Not a problem start the same way:

4

8

4 plus 8 is 12, so write down the 2 and carry the 10:

4 +1

2

8

And there is your answer:

5

2

8

48 x 11 is 528.

Step 3

Neat! But sometimes, we need to multiply numbers by something other than 11. Here is a trick we can use for any 2-digit by 2-digit multiplication. It’s sometimes called the vertically and crosswise method. We multiply vertically, crosswise, and then vertically against (the dots represent number places).

Let’s take a look. Choose a sum, for example, 23 x 12. We start by multiplying vertically, so 2 x 3 is 6…

And then we multiply crosswise, where 2 x 2 is 4, and 1 x 3 is 3. 4 + 3 is 7

And lastly, we go vertically again, so 2 x 1 = 2

And 23 x 12 is 276. Easy peasy! And just like before, if we have multiples that result in numbers greater than 10, we can just carry the 10s across.

So 51 x 38 = 1938.

Step 4

Let your students work individually or in pairs to give this method a go. They can check their answers either using another method of multiplication they are familiar with or a calculator. Start with something easy (low numbers), and then see how large they can go with this method.

Learning Support: You can write out the individual sums next to the main problem so students can see how you work through it step by step.

Step 5

Ok, one last multiplication trick from Vedic maths! This is useful for multiplying numbers that are close to base 10 (i.e. 1, 10, 100, 100 etc.), for example, 102 x 107.

102
x 107

Both of these numbers are very close to 100. What do you need to do to 100 to get 102? Add 2! Write this in the right column.

102	+02
x 107	+07

Multiply these two numbers together ( 2 x 7)

102	+02
x 107	+07
	14

Next, we complete the sums that are on the diagonal like so:

So 102 + 7, and 107 + 2 (Hint: they will have the same value!) = 109

102	+02
x 107	+07
109	14

And there is your answer 102 x 107 = 10914

It works much the same for numbers below 100 as well:

97	-03
x 93	-07
90	21

97 x 93 + 9021

How interesting is that?

Take Action: Give it a go!

Step 1.

Let’s explore this last trick! Ask your students to try and answer these questions:

Does it work for 4-digit numbers? (base 1000 e.g. 1002 x 1009)
Does it work for 5-digit numbers? (base 10,000 e.g. 10008 x 10005)
Does it work for square numbers? (103 x 103)
Does it work when one number is above 100, and one number is below 100? (e.g. 97 x 104)

(Hint: There is a trick to making this last sum work. If you end up with a negative number after your multiplication sum, you need to subtract it from the base you are using, in this case 100)

97	-03
x 104	+04
	(100) -12
101	88

97 x 104 = 10188

Reflection

As a class, create posters explaining the different tricks of Vedic maths that we have explored.

Multiplication Methods: Vedic

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