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

What do I need to know before I start to learn this method?

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

  1. Timetable knowledge is essential for any kind of maths. (I knew a girl in year 6, who was amazing with her timetables 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 prefered method of multiplying numbers bigger than they can access through timestables for a lot of primary school children.

In primary schools, we teach timetables in a variety of ways so children have a good understanding of what it means to multiply. The next step on 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 of working out large multiplications as each step is easily checked later for silly mistakes.

Skill 1: Timetables

Your timestable 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 timestables, 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 timestable facts:

How about completing a blank mulitiplication grid yourself to practice, and then you can check your answers here.

Multiplication grid
Multiplication grid | Source

Timestables can help when working out multiplication facts of large numbers or even decimal numbers:

What you need to remember is that timetable 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 3x3=9.
  • 80 x 4 = 360, because I know 8x4=36.
  • 70 x 7 = 490, because I know 7x7=49.

I knew the timetables as shown, and with this I counted how many 0's there are in the original multiplication. In this case there was 1, so I had to multiply the timestable fact I knew by one 10.

  • 300 x 3 = 900, because I know 3x3=9
  • 800 x 4 = 3600, because I know 8x4=36
  • 700 x 7 = 4900, because I know 7x7=49

I knew the tablestable as shown, and with this I counted how many 0's there are in the original multiplication. In this case there were 2, so I had to multiply the timestable fact I knew by two 10's, or by 100.

This can work for multiplying by decimals too though:

  • 0.3 x 3 = 0.9, because I know 3x3=9.
  • 0.8 x 4 = 3.6, because I know 8x4=36.
  • 0.7 x 7 = 4.9, because I know 7x7=49.

In these cases, I know the timestable facts, and then I counted how many digits past the decimal point to the first digit over 0, in this case one. So I had to divide the timestable fact by one 10.

  • 0.03 x 3 = 0.09, because I know 3x3=9
  • 0.08 x 4 = 0.36, because I know 8x4=36
  • 0.07 x 7 = 0.49, because I know 7x7=49

Here I know the timestable facts, and then counted how many digits past the decimal point I had to go to the first digit over 0, in this case two. So I had to divide the timetable fact by two 10's, or by 100.

Skill 2: What do you mean 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 | Source

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 | Source

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)

Now you have the skills it's time to know how to multiply using the grid method.

A fool proof method, because you can check each step easily, that you can use to multiply larger numbers than you use for your timestables.

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
 
 
 
 
 

123x12 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
 
 
 

20x10 =

 
 
 
 
X
100
20
3
10
100
200
 
2
 
 
 

3x10=

 
 
 
 
X
100
20
3
10
1000
200
30
2
 
 
 

100x2=

 
 
 
 
X
100
20
3
10
1000
200
30
2
200
 
 

20x2=

 
 
 
 
X
100
20
3
10
1000
200
30
2
200
40
 

3x2=

 
 
 
 
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 1: 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 2: 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 3: 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 4: 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 5: 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

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