Multiplication


 * __ Multiplication __**

Ruth Davidson, Laura Pendlebury, Vanessa Kent and Hannah McDowell

There are two methods which can be used to calculate multiplications in Key Stage 1 and 2: the **grid method,** and the **vertical method.**

__ The Grid Method __ When using the grid method, you need to break up the numbers into hundreds, tens and units. Each number has to be multiplied separately and the answers of these sums added together to produce a final answer. For example: 32x45
 * **// x //** || **// 30 //** || **// 2 //** ||
 * **// 40 //** || **// 1200 //** || **// 80 //** ||
 * **// 5 //** || **// 150 //** || **// 10 //** ||

1200 + 80 + 150 + 10 = **__1440__**

Here is a useful video which demonstrates how to do the grid method clearly:

media type="youtube" key="7_2fiYzEf8A" height="315" width="420"

Once the expanded method has been mastered and understood, you can move onto the vertical method.

__ The Vertical Method __ When using the vertical method, it is necessary to line up the units, tens, hundreds and thousands underneath each other and multiply each digit. You must start with the units. For example: 852x5 Start by multiplying the 5 by 2 to give 10:
 * **//__ H __//** || **//__ T __//** || **//__ U __//** ||
 * **// 8 //** || **// 5 //** || **// 2 //** ||
 * **// x //** || **// 1 //** || **// 5 //** ||
 * ||  || **// 0 //** ||

Next, multiply the 5 by 5, adding the carried over 1 to give 26: Now multiply the 5 by 8, adding on the 2 carried over from the tens column, to give 42: So, 852x5= 4260 It is important to remember that if you are multiplying a number by 10, for example 45x43, to use the same vertical method as above but to break it down into two parts: 45x3 and 45x40, before adding the two answers together:
 * **//__ H __//** || **//__ T __//** || **//__ U __//** ||
 * **// 8 //** || **// 5 //** || **// 2 //** ||
 * **// X //****// 2 //** ||  || **// 5 //** ||
 * || **// 6 //** || **// 0 //** ||
 * **//__ Thou __//** || **//__ H __//** || **//__ T __//** || **//__ U __//** ||
 * || **// 8 //** || **// 5 //** || **// 2 //** ||
 * **// x //** ||  ||   || **// 5 //** ||
 * **// 4 //** || **// 2 //** || **// 6 //** || **// 0 //** ||


 * **//__ Thou __//** || **//__ H __//** || **//__ T __//** || **//__ U __//** ||
 * ||  || **// 4 //** || **// 5 //** ||
 * ||  || **// 4 //****// 1 //** || **// 3 //** ||
 * **// x //** ||

**// 1 //** ||

**// 3 //** ||

**// 5 //** ||
 * ** 1 ** || **// 2 //****// 8 //** || **// 0 //** || **// 0 //** ||

** 1 ** ||

**// 9 //** ||

**// 3 //** ||

**// 5 //** ||

So 45x43 = 1935

__ Another Alternative __ Another method, possibly the easiest method of multiplication, is the Gelosia method. It is also fairly quick. It is not generally recommended however because it does not teach place value but could be used as a last resort for those students who are really struggling to grasp the other methods of multiplication.

Firstly, take a large square and divide it into 4. Each of the 4 small squares need to be split diagonally, as shown below.



Make sure the numbers start at the bottom left corner, following round clockwise. The example used here is for 83 x 26.

Step 2: Multiply each possible combination and put the answer in the section that corresponds to the numbers you have multiplied, with the tens going in the right triangle and the units going in the left. For example, the bottom left square would be 8 x 2, and the answer is 16 and so is written in as 1, 6. The example below demonstrates this clearly.

Step 3: add together the numbers in each diagonal row. The first row at the top contains only the number 8, so write 8 at the side. Diagonal row underneath it contains 6, 1, 8 so add these to make 15. Write the 5 at the side and carry the 1 to the next row. The 3rd row now has 1 (which you just carried over), 6 and 4, add these to make 11. Again, put the units (1) at the side and carry the tens (1) to to the next row. The final diagonal row has 1 (which you carried over) plus 1. Add these to make 2. The diagram below illustrates all of the above calculations:

You can now read the answer, starting from the bottom left and going round anti-clockwise which reads as 2158. So 83 x 26 = 2158.

__**Resources**__

Here are a few links to some useful teaching resources:

Interactive Whiteboards: [|Multiplication ITP] [|Interactive whiteboard explanation and examples] [|Interactive whiteboard grid method examples]

Songs: media type="youtube" key="cwkgNf69ihY" height="315" width="420"

__**Generate Your Own Work Sheet (useful for differentiation and assessment)**__ []
 * __ References __**

**[]** - accessed 5/10/2011

[] - accessed 4/10/2011

[] Woodlands Primary School Website - accessed 04/10/2011