The UK National Curriculum now specifies that:
Pupils should be taught to:
Year 6 (UK KS2 age 10-11)
- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
- divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
- divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
Appendix 1 of the KS2 document includes the examples below and states that “the examples of formal written methods for all four operations illustrate the range of methods that could be taught. It is not intended to be an exhaustive list, nor is it intended to show progression in formal written methods. For example, the exact position of intermediate calculations (superscript and subscript digits) will vary depending on the method and format used. For multiplication, some pupils may include an addition symbol when adding partial products. For division, some pupils may include a subtraction symbol when subtracting multiples of the divisor.
And at KS3 (UK age 11-14) we are reminded that students should be able to “use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative”.
The Mathematics documents can all be found on this page.
From MathsOnline, comes a clear step by step demonstration of long multiplication, (uses html). Each step is clearly explained. Long Division is also very clearly illustrated and for your older students we can extend to Algebraic Long Division. Refreshing the page generates a new example each time.
Mathisfun explains long division very clearly and additionally offers questions and worksheets. Similar resources are available for Long Multiplication and for Algebraic long division.
From Sums Mathematics (requires Flash) come many useful activities including activities to illustrate formal methods of long multiplication and division. Choose Multiplication or Division under Numbers and Calculations from the top menu. All demonstrations are very clear and show the methods step by step. You can choose to watch examples and/or try examples of your own; choose Option 1 or 2. See the images below.