Exemplification
Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement
multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication

Look at longmultiplication calculations containing errors, identify the errors and determine how they should be corrected.

Solve problems such as:Printing charges for a book are 3p per page and 75p for the cover. I paid £4.35 to get this book printed. How many pages are there in the book? Write down the calculations that you did. Seeds are £1.45 for a packet. I have £10 to spend on seeds. What is the greatest number of packets I can buy?
divide numbers up to 4 digits by a twodigit 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

Every day a machine makes 100 000 paper clips, which go into boxes. A full box has 120 paper clips. How many full boxes can be made from 100 000 paper clips?
Each paper clip is made from 9.2 centimetres of wire. What is the greatest number of paper clips that can be made from 10 metres of wire?

A DJ has two different sized storage boxes for her CDs. Small boxes hold 15 CDs. Large boxes hold 28 CDs. The DJ has 411 CDs. How could the DJ pack her CDs?
solve problems involving multiplication and division
use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy
Children should be able to:

Give the best approximation to work out 4.4 × 18.6 and explain why. Answer questions such as: roughly, what answer do you expect to get? How did you arrive at that estimate? Do you expect your answer to be greater or less than your estimate? Why?
perform mental calculations, including with mixed operations and large numbers

Use mental strategies to calculate in their heads, using jottings and/or diagrams where appropriate. For example, to calculate 24 × 15, they multiply 24 × 10 and then halve this to get 24 × 5, adding these two results together. They record their method as (24 × 10) + (24 × 5). Alternatively, they work out 24 × 5 = 120 (half of 24 × 10), then multiply 120 by 3 to get 360.
identify common factors, common multiples and prime numbers

Children should be able to answer questions such as:

How can you use factors to multiply 17 by 12?

Start from a twodigit number with at least six factors, e.g. 72. How many different multiplication and division facts can you make using what you know about 72? What facts involving decimals can you derive?

What if you started with 7.2? What about 0.72?

Which three prime numbers multiply to make 231?

use their knowledge of the order of operations to carry out calculations involving the four operations

Children should be able to find answers to calculations such as 5.6 ⬜ = 0.7 or 3 × 0.6, drawing on their knowledge of number facts and understanding of place value. They should be able to approximate, use inverses and apply tests of divisibility to check their results.

Children should know the square numbers up to 12 × 12 and derive the corresponding squares of multiples of 10, for example 80 × 80 = 6400.