Teaching Sequence

Work through this resource material in the following sequence:

10 minutes

Tune In: Making Multiples

10 minutes

Find Out: The Chinese 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 really interesting way of representing multiplication visually using a very old Chinese method.

Find Out: The Chinese Method

Learning support: provide the students with strips of paper, bamboo skewers or other sticks and let them manipulate the physical materials to represent the equation.

Step 1

Let’s start with an easy sum, say 3 x 2. Start by drawing 3 lines to represent the 3:

And then cross them with 2 lines to represent the 2:

The intersections of the lines represent multiplication. Here we can see we have 6 intersections:

So 2 x 3 = 6. Easy right? Give your students an opportunity to try it with other single-digit multiplication.

Step 2

Let’s try it with larger numbers now, like 12 x 4. Just like before, we are going to draw lines to represent the number 12, however, now we group the numbers by their place. 12 is made up of 1 ten and 2 ones, so we draw it like this:

And, same as before, we draw 4 lines across to represent the 4.

Great! Now, let’s mark all the intersections:

In the first group (the tens), we have 4, and in the second group (the ones), we have 8.

So our answer is 48! 12 x 4 = 48.

But how does this work with two double-digit numbers? Let’s try 31 x 42. Let’s start with our 31:

And then add the 42:

Mark the intersections:

The column on the left is the hundreds column:

12

The middle column is the tens column::

10

And the right column is the ones column:

2

So we get:

Hundreds	Tens	Ones
12	10	2

Now we can’t keep the 10 in the tens column, so we carry the 1 over to the hundreds column and get:

Hundreds	Tens	Ones
13	0	2

31 x 42 = 1302

Step 3

Let’s give it a go! In pairs or small groups practice using this method.

Learning extension: Let the students try larger numbers. Can they make it work for four-digit numbers? Five? How far can they go?

Take Action: Give It a Go!

Step 1

The Chinese method of multiplication was the inspiration behind another method of multiplication, the lattice method. Let’s take a look at how this works. Let’s use the same two-digit by two-digit sum that we used in our last example, 31 x 42. Add your numbers to the outside of the lattice.