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# Year 5

### We can multiply a three-digit or a four-digit number by a one-digit number using efficient written methods

#### What we are learning:

• We have covered the grid method for multiplying a two digit number by a one digit number. We can now shorten this into a more efficient written method but still keep a full understanding of what we are doing and what each stage means.
• First we’ll revisit the grid method to remind ourselves of each stage in the multiplication process when we are multiplying a two digit number by a one digit number.
• If we are multiplying 38×7 we can partition the 38 into 30+8 and then multiply each part by 7 as follows:

• We have to add 210 (30×7) and 56 (8×7) together to find the final answer of 266. The grid method works for all long multiplications and helps children understand what long multiplication is, but is not the most efficient method
of recording.
• Now we can shorten this grid method to a more efficient written method

• In this method we need to remember the value of each digit. We start by multiplying the 8 units by the 7, making 56. We record this as 6 units in the units column, and we carry the 50, or 5 tens into the tens column. We can then multiply the 30, or 3 tens by the 7 which gives is 21 tens, or 210. Before we record this we have to add on the 5 tens we have carried across, giving us a total of 26 tens, or 260. We record this in the hundreds and tens columns
as you can see, giving us the total answer of 266.
• With practice the efficient written method becomes routine, and the reasons why it works can still be understood – this forms the basis of longer multiplications that come next.
• Exactly the same process and format applies with four-digit numbers e.g. 2,354 x 6 =

#### Activities you can do at home:

Look at the Multiplication grid challenge and see if you can complete the examples provided. Make sure you are confident multiplying two digits by one digit (e.g. 45×7) before extending this to three digits by one digit (e.g.
345×8)
When your child becomes confident, extend the multiplications to include hundreds, e.g. 238×7

The first part of this calculation is the same as the model above. We multiply the 8 units by 7 and carry the 5 tens across. Then we multiply the 3 tens by the 7 but this time we carry the 2 hundreds across as we have more digits to
multiply. Finally we multiply the 2 hundreds by the 7 to make 14 hundreds, add on the 2 hundreds we have carried across to make 16 hundreds and record this.

Which method of multiplication do you find easiest – the grid method or the efficient method?
What makes it easy for you to understand?
What is more difficult about the other method?

Finds it difficult to remember how to record the process
Start with simple multiplications and discuss the value of each digit, i.e. the column that it is in. It is essential to understand the value of digits confidently to be able to complete long multiplications. Go through the calculations together and talk about what is happening at each stage.

##### ACTIVITY SHEETS

Activity sheet PDF