Year 4

We can divide a two-digit number or a three-digit number by a one-digit number using efficient written methods

Year 4 Unit 12b

What we are learning:

Once we know our tables, long division is not as difficult as it sometimes looks.
If the answer to the division is within our tables knowledge we should know the answer, e.g. 81 ÷ 9 is 9 or 56 ÷ 8 is 7. If the calculation takes us beyond the range of our tables knowledge we need an efficient written method to work out the answer.
For example, if we have 96 ÷ 4 this is well beyond 10 x 4 = 40 or even 12 x 4 = 48, which we know.
We can set the division out like this. We know we are trying to find out how many times 4 will ‘go into’ 96.

The first stage is to ask ourselves how many times 4 will go into 96 by using
multiples of 10. We know that 4 x 10 = 40, 4 x 20 = 80 and 4 x 30 = 120.
Since 120 is too big we know that 4 goes into 96 twenty times, which is 80.
We set it out like this:

Note that the 2 is in the tens column and represents the 20 that we have
multiplied by 4 to get 80. We can now take the 80 away from 96 to see how
many we have left to divide like this:

We can now ask how many times 4 will go into 16. We know from our tables
that 4 x 4 = 16. We put the 4 at the top to make the ‘quotient’ (answer),
insert the 16 underneath (as we now that 4 x 4 = 16) and we take this away
to see if there is a remainder.

Now we can see that 4 (the divisor) goes into 96 (the dividend) exactly 24
times (the quotient) and there is no remainder.
We can extend this method to divide a three-digit number by a one-digit
number.
For example, if we have 767 ÷ 3 we set it out the same way:

This time 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

Activities you can do at home:

First try dividing two-digit numbers by a one-digit number using the examples on the activity sheet provided.

Once your child is confident with these, move on to dividing three-digit numbers by a one-digit number.

Good questions to ask and discuss:

Can you explain what the following are: divisor, dividend, quotient, and remainder?
Pick a number in the division calculation on the page that you have finished together and ask Where does this number come from? What part does it play in the calculation? This will get your child to explain part of the process to you to ensure s/he understands all parts of it.

If your child:

Can’t explain what s/he is doing and gets confused part way through the process
Work on a simpler calculation to re-establish the method.
Go back to the beginning of the calculation and talk through each stage together. Long division is one of the calculations with the most stages in it, so it is not surprising that children get confused sometimes. By talking it
through you will quickly see whether they understand what they are doing.