Year 6

We can divide whole numbers by a one-digit number using efficient written methods

Year 6 Unit 11a

What we are learning:

We are revisiting division that we did in Year 5 Unit 15a.
For example, if we have 767 ÷ 3 we set it out like this:

We start by dividing with multiples of 100. We know that 3 x 100 = 300, 3 x 200 = 600 and 3 x 300 = 900, so 3 will go into 767 200 times. We put the 200 into the hundreds column like this and take the 600 away from our dividend.

Having divided with multiples of 100 we can now use multiples of 10. We know that 3 x 50 is 150 which works and that3 x 60 is 180 which is too big. We insert the 50 into the tens column and take the 150 away from the dividend
that is left like this:

Finally we can divide the 17 by 3 and complete the division to leave a remainder of 2

The answer (quotient) is therefore 255 remainder 2
If we want to divide a four-digit number by a one-digit number we use a similar method, except that we have to divide using multiples of 1000 first.
For example, if we want to divide 9328 by 4 we set it out like this:

We start dividing with multiples of 1000. We know that 4 x 1000 is 4000 and 4 x 2000 is 8,000 and 4 x 3,000 is 12,000. We only have 9,000 so we can only use 4 x 2000 and insert the 8000 into the thousands column like this and then take it away from the dividend to see what we have left to divide:

We now have 1328 to divide by 4 so we use multiples of 100. We know that 4 x 100 = 400, 4 x 200 = 800, 4 x 300 = 1200. 4 x 400 = 1600 which is too big so we put the 300 into the quotient in the hundreds column, insert the 1200
and take it away from the remaining dividend to see what we have left to divide.

We now have 128 to divide by 4 using multiples of 10. We know that 4 x 30 is 120 and 4 x 40 so we put the 30 into the tens column of the quotient insert the 120 and take it away from the remaining dividend like this:

Finally we can divide the remaining 8 by 4 and take away:

The answer, or quotient for the division is therefore 2332

Activities you can do at home:

Try the divisions on the Activity Sheet together. Talk each one through step by step to ensure that your child understands each stage.
It is possible to learn to do long division by a ‘mechanical’ method. This is when your child can do the ‘sum’ but cannot explain why they are doing it this way or what each number means in the calculation. Whilst this will work, it is not as secure as fully understanding the process.

Good questions to ask:

When might we need to use division in everyday life?
Think about sharing the cost of shopping or bills between friends

If your child:

Gets confused by the layout and process of long division
Repeat some simpler examples, e.g. a two-digit number divided by a one-digit number, e.g. 87 ÷ 3 and talk about it thoroughly before moving on to a three-digit number divided by a one-digit number, e.g. 566 ÷ 4. Once these are
secure increase the complexity by dividing four or five –digit numbers by one-digit numbers.