# Exemplification

## Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

recall multiplication and division facts for multiplication tables up to 12 × 12

Children should be able to:

Pupils continue to practise recalling and using multiplication tables and related division facts to aid fluency.

*e.g. One orange costs nineteen pence. How much will three oranges cost?*

*What is twenty-one multiplied by nine?*

*How many twos are there in four hundred and forty?*

use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers

Children should be able to:

Pupils practise mental methods and extend this to three-digit numbers to derive facts, for example 200 × 3 = 600 into 600 ÷ 3 = 200.

*e.g. Divide thirty-one point five by ten.*

*Ten times a number is eighty-six. What is the number?*

recognise and use factor pairs and commutativity in mental calculations

Children should be able to:

Pupils write statements about the equality of expressions (e.g. use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations e.g. 2 x 6 x 5 = 10 x 6.

*e.g. Understand and use when appropriate the principles (but not the names) of the commutative, associative and distributive laws as they apply to multiplication:
*

*Example of commutative law* *8 × 15 = 15 × 8*

*Example of associative law* *6 × 15 = 6 × (5 × 3) = (6 × 5) × 3 = 30 × 3 = 90*

*Example of distributive law* *18 × 5 = (10 + 8) × 5 = (10 × 5) + (8 × 5) = 50 + 40 = 90*

solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

Children should be able to:

Pupils solve two-step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. This should include correspondence questions such as the numbers of choices of a meal on a menu, or three cakes shared equally between 10 children.

*e.g. 185 people go to the school concert. They pay £l.35 each.
How much ticket money is collected?*

*Programmes cost 15p each. Selling programmes raises £12.30. How many programmes are sold?*

Thanks Luke. The content in the orange boxes does not amount to an exhaustive list of all National Curriculum statements: the page is designed to give some examples of what children should be able to do in the broad curriculum area.