Teaching Sequence

Work through this resource material in the following sequence:

10 minutes

Tune In: Making Multiples

10 minutes

Find Out: The Russian Peasant 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 a very old (hundreds of years!) way of doing multiplication. This way is called the Russian Peasant Method, and all you have to do to multiply any two numbers is halve, double, and add. Let’s give it a go.

Find Out: The Russian Peasant Method

Step 1

Choose a double-digit multiplication sum and write it on the board horizontally. For example:

35

x

12

Step 2

To figure out the answer, we are going to halve the numbers on the left and double the numbers on the right. Let’s start with the left! What is half of 35? 17 and a half.

Halve		Double
35	x	12
17 ½

Now here’s the fun bit. We can actually just ignore that ½! Let’s cross it out and forget that it existed.

Halve		Double
35	x	12
17 ½

Much better. Let’s keep going. What is half of 17? 8 and a half! Let’s get rid of that cheeky half as well.

Halve		Double
35	x	12
17 ½
8½

Keep going down the list until we hit the number 1.

Halve		Double
35	x	12
17 ½
8½
4
2
1

Great. Now we know how far down we go, it’s time to do the other side. This time, instead of halving, let’s double it. What is double 12? 24! Keep going down the rows until you are level with the 1 in the halve column.

Halve		Double
35	x	12
17 ½		24
8½		48
4		96
2		192
1		384

Excellent. Now, let’s go back to the Halve column. Any even number in this column is a row we don’t need, so let’s cross it out.

Halve		Double
35	x	12
17 ½		24
8½		48
4		96
2		~~192~~
1		384

Great! This leaves 12, 24, and 384 in the double column. Let’s add them together…

12 + 24 + 384 = 420

Which means 35 x 12 = 420!

Take Action: Give It a Go!

Step 1

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 (ZZ x Y), and then see how large they can go with this method. Can they multiply one four-digit number by another?

Learning Support: Use objects (like MAB blocks) to represent the numbers visually. Let students manoeuvre the blocks to halve and double their numbers and check which ones are even and which would have fractions/remainers.

Step 2

Now they understand the method, let’s compare it to a method we currently use. Have students choose a complicated sum (for example, 327 x 192). They can time themselves using different mental methods and see which method works best for them.

Learning Extension: Here’s the big question, how does it work? It all comes down to binary. Remember when we crossed out the even numbers? Those represented 0s, and the odd numbers left over represented 1s. If we worked our way up the Halve column in our example above, we would have (in order) 100011, which is 35 in binary. That’s right, hundreds of years ago, Russian Peasants were using the language of today’s modern computers to do multiplication. For those students who want to dive deeper, use this video to kick off their understanding and ask them to create a visual or written explanation of how binary is used in this method.

Russian Multiplication - Numberphile

Reflection

As a class make posters explaining the Russian Peasant method of multiplication.

Multiplication Methods: Russian

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