Year 6

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We can divide whole numbers by two-digit numbers using efficient written methods

Year 6 Unit 11b

What we are learning:

When we come to dividing whole numbers by a two-digit number we use the same method as before, but we need to estimate multiples of the two-digit divisors as we don’t know our 23 times tables, for example!
If we need to divide 897 by 23 we set it out like this:

The first stage is to ask ourselves whether we can multiply 23 by multiples of 100. The answer is ‘no’ as 23 x 100 is 2300, and we only have 897 to divide.
We therefore use multiples of 10.

We know that 23 x 10 is 230
23 x 20 is 460 (23 x 2 x 10)
23 x 30 is 690 (23 x 3 x 10) = this works as it is under 897
23 x 40 is 920 (23 x 4 x 10) = too many
We might need to make jottings to remember this information, which should be encouraged. There is no need to hold everything in our heads.

We can now record the next stage of the calculation like this:

We have entered a zero in the hundreds column of the quotient (answer) as we could not use multiples of 100. We have entered a 3 in the tens column of the quotient, representing the 30 x 23 and have entered 690 (30 x 23) under the dividend of 896. We then take 690 away from 896 to see how much we have left to divide.

Now we see how many times we can divide 23 into 207 using multiples up to 10.
Again we use our tables knowledge and make jottings.
We know that 23 x 10 is 230. Although this is too many it is only just too large so we try 23 x 9. We should be able to work this out mentally as 9 x 3 = 27 and 9 x 20 = 180. 180 + 27 = 207. This is exactly right so we can complete the calculation like this:

We entered the 9 into the quotient and 207 (9 x 23) under the remaining dividend. When we subtract it we find that it goes exactly and there is no remainder.
The answer to 897 ÷ 23 is therefore 39
If we wish, we can check this by multiplying 39 x 897 on a calculator.

Activities you can do at home:

Try the divisions on the Activity Sheet. Remember to make jottings as you do the calculations.
Talk through each stage of the calculation and use the correct terms (dividend, divisor and quotient).

Good questions to ask:

Why do we use multiples of 100 or 10 first?
How does knowing our tables help us with long division?
How does being able to use multiples of 10 help us?

If your child:

Finds it difficult to work out multiples of 1 or 10 for two-digit numbers, e.g. 35 x 4 or 35 x 60
Make jottings to work them out, set them out as long multiplications or even use a calculator to maintain the pace of the division sum. To learn long division children will need to see and understand the process without being slowed down too much by calculations that contribute to it.

Extension Activity

Please use this activity when you think your child understands the unit of work. It will deepen and extend your child’s understanding of this unit.


Extension activity (PDF)

Extension activity answers (PDF)