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Math Help: How Do You Multiply Using the Grid Method? Partition the Units, Tens and Hundreds to Make It Simpler

I have been a teacher for a few years now and I know how hard the job is. I write articles to help teachers come up with great ideas.

What Do I Need to Know Before I Learn This Method?

There is some basic mathematical knowledge that is essential for you to progress to the grid method:

  1. Times table knowledge is essential for any kind of maths. (I knew a girl in year 6 who was amazing with her times tables and used this to gain a level 5 in her SATs, even though she wasn't a natural mathematician.)
  2. You need a good understanding of place value in order to partition the numbers.

Grid Method: What Is It?

The grid method is a preferred method for multiplying numbers that are too big for a lot of primary school children to access through times tables.

In primary schools, we teach times tables in a variety of ways so children have a good understanding of what it means to multiply. The next step from this is the grid method, usually taught in year 3 for the first time, for multiplying bigger numbers.

I tend to think of it as a foolproof method for working out large multiplications, as each step is easily checked later for silly mistakes.

Skill 1: Times Tables

Your times table knowledge is vital when working with multiplication. The better you know them, the easier you will find any multiplication you come across.

There are plenty of ways to practice your times tables, and there are plenty of websites that can help you too, so I recommend you do just that to become a good mathematician.

Here is a multiplication grid to remind you of your times table facts:

A multiplication grid. Try completing a blank multiplication grid yourself to practice, and then you can check your answers here.

A multiplication grid. Try completing a blank multiplication grid yourself to practice, and then you can check your answers here.

Times Tables Can Help When Working Out Multiplication Facts of Large Numbers or Even Decimal Numbers

What you need to remember is that times table facts will help you when multiplying with large numbers or even small numbers.

Here are some examples of what I mean:

  • 30 x 3 = 90, because I know 3 x 3 = 9.
  • 80 x 4 = 360, because I know 8 x 4 = 36.
  • 70 x 7 = 490, because I know 7 x 7 = 49.

I knew the time tables as shown, and with this, I counted how many zeros there are in the original multiplication. In this case, there was one, so I had to multiply the times table fact I knew by one 10.

  • 300 x 3 = 900, because I know 3 x 3= 9
  • 800 x 4 = 3600, because I know 8 x 4 = 36
  • 700 x 7 = 4900, because I know 7 x 7 = 49

I knew the times table as shown, and with this, I counted how many zeros there are in the original multiplication. In this case, there were two, so I had to multiply the times table fact I knew by two 10s, or by 100.

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This can work for multiplying by decimals, too:

  • 0.3 x 3 = 0.9, because I know 3 x 3 = 9.
  • 0.8 x 4 = 3.6, because I know 8 x 4 = 36.
  • 0.7 x 7 = 4.9, because I know 7 x 7 = 49.

In these cases, I know the times table facts, and then I counted how many digits there are past the decimal point, in this case, one. So I had to divide the times table fact by one 10.

  • 0.03 x 3 = 0.09, because I know 3 x 3 = 9
  • 0.08 x 4 = 0.36, because I know 8 x 4 = 36
  • 0.07 x 7 = 0.49, because I know 7 x 7 = 49

Here I know the times table facts, and then I counted how many digits there are past the decimal point, in this case, two. So I had to divide the times table fact by two 10s, or by 100.

Skill 2: What Do You Mean by Place Value?

In maths we only have ten digits, the numbers 0-9. These make up the whole number system, so for this to work successfully it means that one particular digit can take the value of different values.

For example:

  • The in the number 123, the 3 represents the value of three units.
  • If you take the number 132, the 3 represents the value of three tens.
  • With the number 321, the 3 here, represents the value of three hundreds.
  • And so on and so on.

In order for us to start to understand place value teachers use place value headings in their teaching:

Place value chart

Place value chart

We use the place value headings like, units, tens and hundreds to help us do sums and to be able to tell which number is larger or smaller than others.

If we look at a number, say 45, we say that it has two digits. If we took the number 453, we say it has three digits. It is the position of the number that tells us the value of the digit:

  • 45: The 5 is in the units column so its value is 5 units.
  • 453: The 5 is in the tens column so its value is 5 tens, or 50.
Partitioning

Partitioning

How Do I Use Place Value to Help Me?

When using the grid method you need to partition numbers so you know the value of each digit. We do a lot of work in KS1 to help children here.

So for example:

  • 45 = 40 + 5

The number 45 can be broken into two parts, or partitioned. We can think of it as 40 plus 5. The reason this is so, is because we can see the value of the 4 is 4 tens or 40. The value of the 5 is 5 units or in other words, 5.

This is the way we partition any number when using the grid method:

  • 89 = 80 + 9
  • 143= 100 + 40 + 3
  • 4872 = 4000 + 800 + 70 + 2
  • 81243= 80000 + 1000 + 200 + 40 + 3
  • 738922 = 700000 + 30000 + 8000 + 900 + 20 + 2

This is a common test question in the year 6 SATs. "Can you write this number down 7032?" This tests place value knowledge because there are no hundreds in this number, so you need a place holder which is 0. This is where a lot of children go wrong when it comes to place value. But remember that this 0 means there is no value for this digit.

  • 108 = 100 + 8 (No tens)
  • 1087 = 1000 + 80 + 7 (No hundreds)
  • 10387 = 10000 + 300 + 80 + 7 (No thousands)

It’s Time to Learn How to Multiply Using the Grid Method

This is a foolproof method (because you can check each step easily) that you can use to multiply larger numbers than you use for your times tables.

How Do I Use the Grid Method?

The steps you should follow every time are?

  1. Partition each number into units, tens, hundreds etc. i.e. 12 = 10 + 2, 123 = 100+20+3
  2. Place the first partitioned number into the top row of the grid. Units, tens, hundreds etc. all take on column each.
  3. Next, place the second partitioned number into the first column of the grid. Units, tens, hundreds etc. all take a differnet row each.

 

This is the top row.

------>

This is the first column

 

 

 

 

123 x 12 Would Be Set Out Like This:

X

100

20

3

10

2

4. After you have set your grid up, you just need to use it as a multiplication grid and multiply each set of numbers up.

100 x 10 =

X

100

20

3

10

1000

 

 

2

 

 

 

20 x 10 =

X

100

20

3

10

100

200

2

3 x 10 =

X

100

20

3

10

1000

200

30

2

100 x 2 =

X

100

20

3

10

1000

200

30

2

200

20 x 2 =

X

100

20

3

10

1000

200

30

2

200

40

3 x 2 =

X

100

20

3

10

1000

200

30

2

200

40

6

Using the Column Method to Add up the Grids

1000

200

200

40

30

6

1476

5. The last thing you need to do to get the answer is to add up all the grids you have just worked out.

So it would be 1000+200+200+40+30+6

The best way to do this would be to add it in the column method (place each unit underneath each other, each ten underneath each other, each hundred underneath each other etc.) so you don't mix any of the values up and get the wrong answer, like adding 10 to 3 and getting 4, which is a mistake a lot of people do when they rush adding - so used properly this is another fool proof method.

Example One: 12 x 7 =

X

10

2

7

70

14

Then Add the Grids Up

70

14

84

In this example, I partitioned the 12 to make 10 and 2. This formed the top row of the grid method (although it doesn't matter if it was the first column, this is just the method I prefer.)

Then I placed the seven, I was multiplying 12 by, on the first column. So it was just a case of using this grid as a multiplication grid:

7x10 = 70 (because I know 7x1=7)

7x2 = 14

These answers were added to the table where it intersects the two numbers which are being multiplied.

The next step was to add these numbers using the column method to find the answer. So 70+14=84. So I know that 7x12 = 84.

Example Two: 32 x 13 =

X

30

2

10

300

20

3

90

6

300

20

90

6

416

In this example, I partitioned the 32 to make 30 and 2, and I partitioned 13, to make 10 and 3. I then placed these numbers in the grid.

I multiplied these numbers up using my timestable knowledge and placed the answers in the grid.

30 x 10 = 300 (because I know 3x1=3)

2 x 10 = 20 (because I know 2x1=2)

300 x 3 = 900 (because I know 3x3=9)

2 x 3 = 6

These answers were added up using the column method to find the answer for 32 x 13.

So I know that 32 x 13 = 416.

Example Three: 234 x 32 =

X

200

30

4

30

600

900

120

2

400

60

8

600

900

400

120

60

8

2088

I started off partitioning the numbers 234 and 32, to get 200 + 30 + 4, and 30 + 2. These were added to the grid.

I then used my timetable facts to work out the answers when these were multiplied:

200 x 30 = 600 (because I know 2x3=6)

200 x 2 = 400 (because I know 2x2=4)

30 x 30 = 900 (because I know 3x3=9)

30 x 2 = 60 (because I know 3x2=6)

4 x 30 = 120 (because I know 4x3=12)

4 x 2 = 8

I then added the answers up using the column method as shown opposite.

So I know that 234 x 32 = 2088

Example Four: 24 x 0.4 =

X

20

4

0.4

8

1.6

8.0

1.6

9.6

I first partitioned 24 to get 20 + 4. I then added this to the grid with 0.4 (this has one digit so can't be partitioned.)

I then used my timestable knowledge to help work out the answers:

20 x 0.4 = 8 (because I know 2x4=8)

4 x 0.4 = 1.6 (because I know 4x4=16)

I then used the column method to add these totals to find out that 24x0.4=9.6.

NOTE: if you make sure you write 8 as 8.0 in the column method, you can see straight away that you are not adding any tenths here and don't make a silly mistake of trying to add 8 to 6 because you didn't write down the digits in the correct column for their place value.

Example Five: 55 x 0.28 =

X

50

5

0.2

10

1

0.08

4

0.4

10.0

1.0

4.0

0.4

15.4

With my last example I partitioned 55 to make 50 +5, and partitioned 0.28 to make 0.2 + 0.08. These numbers where then added to the grid.

I then used my timestable knowledge to help me find the answers:

50 x 0.2 = 10 (because I know 5x2=10)

5 x 0.2 = 1 (because I know 5x2=10)

50 x 0.8 = 4 (because I know 5 x 8 = 40)

5 x 0.08 = 0.4 (because I know 5 x 8 = 40)

These values were added up using the column method, making sure I placed any 0's where I needed to for the tenths as in 10.0, 1.0, 4.0 so I didn't mix the numbers up because they were all in the correct place value columns.

So 55 x 0.28 = 15.4

Comments

Sarah on May 20, 2018:

Example 3: is wrong

allo on December 03, 2017:

8 * 4 is 32 m8

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