Numbers and the number system
2. Pupils should be taught to:
Counting
 count on and back in tens or hundreds from any two or threedigit number; recognise and continue number sequences formed by counting on or back in steps of constant size from any integer, extending to negative integers when counting back
Number patterns and sequences
 recognise and describe number patterns, including two and threedigit multiples of 2, 5 or 10, recognising their patterns and using these to make predictions; make general statements, using words to describe a functional relationship, and test these; recognise prime numbers to 20 and square numbers up to 10 x 10; find factor pairs and all the prime factors of any twodigit integer
Integers
 read, write and order whole numbers, recognising that the position of a digit gives its value; use correctly the symbols <, >, =; multiply and divide any integer by 10 or 100 then extend to multiplying and dividing by 1000; round integers to the nearest 10 or 100 and then 1000; order a set of negative integers, explaining methods and reasoning; multiply and divide decimals by 10 or 100
Fractions, percentages and ratio
 understand unit fractions [for example, onethird or oneeighth] then fractions that are several parts of one whole [for example, twothirds or fiveeighths], locate them on a number line and use them to find fractions of shapes and quantities
 understand simple equivalent fractions and simplify fractions by cancelling common factors; compare and order simple fractions by converting them to fractions with a common denominator, explaining their methods and reasoning
 recognise the equivalence between the decimal and fraction forms of one half, quarters, tenths and hundredths; understand that 'percentage' means the 'number of parts per 100' and that it can be used for comparisons; find percentages of whole number quantities, using a calculator where appropriate
 recognise approximate proportions of a whole and use simple fractions and percentages to describe them, explaining their methods and reasoning
 solve simple problems involving ratio and direct proportion
Decimals
 understand and use decimal notation for tenths and hundredths in context [for example, order amounts of money, round a sum of money to the nearest £, convert a length such as 1.36 metres to centimetres and vice versa]; locate on a number line, and order, a set of numbers or measurements; then recognise thousandths (only in metric measurements)
 round a number with one or two decimal places to the nearest integer or tenth; convert between centimetres and millimetres or metres, then between millimetres and metres, and metres and kilometres, explaining methods and reasoning.
