With all the basics learned off by heart it is amazing what calculations can be done mentally, including dividing 2-digit numbers by 1-digit. When the numbers get harder a standard method of division will be used accurately and efficiently.
The latest two sets of worksheets we have published are for the brightest children in Year 6 as they look at the long division method with either whole numbers or fractions as remainders.
Learning to use the long division method became rather unfashionable in recent years, partly because it is hard to learn and has only appeared infrequently in the Year 6 SATS. However, it is a major target in the new Maths Programme of Study.