Volume

Converting units

Pupils should be taught to:

• convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

• understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

• solve problems involving converting between units of time

• use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling.

Negative numbers

Pupils should be taught to:

• interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

Decimals 

Pupils should be taught to:

• read and write decimal numbers as fractions [for example, 0.71 = ]

• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

• round decimals with two decimal places to the nearest whole number and to one decimal place

• read, write, order and compare numbers with up to three decimal places

• solve problems involving number up to three decimal places

Position and direction

Pupils should be taught to:

• identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed.

Angles 

Pupils should be taught to:

• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

• draw given angles, and measure them in degrees (o)

• identify:

  • angles at a point and one whole turn (total 360o)

  • angles at a point on a straight line and a turn (total 180o)

  • other multiples of 90o

• use the properties of rectangles to deduce related facts and find missing lengths and angles

• distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Statistics

Pupils should be taught to:

• solve comparison, sum and difference problems using information presented in a line graph

complete, read and interpret information in tables, including timetables.read and write decimal numbers as fractions [for example, 0.71 = ]

Measurement - Perimeter and Area 

Pupils should be taught to:

• measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

• calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

Number - Fractions (including decimals and percentages)

• read and write decimal numbers as fractions [for example, 0.71 = ]

• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

• round decimals with two decimal places to the nearest whole number and to one decimal place

• read, write, order and compare numbers with up to three decimal places

• solve problems involving number up to three decimal places

• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal

• solve problems which require knowing percentage and decimal equivalents of , , , , and those fractions with a denominator of a multiple of 10 or 25.

Multiplication and division

• multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

• multiply and divide numbers mentally drawing upon known facts

• divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

• multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Fractions

• add and subtract fractions with the same denominator and denominators that are multiples of the same number

• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Place Value

Pupils should be taught to:

• read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

• count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

• round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

• solve number problems and practical problems that involve all of the above

• read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Multiplication and division 

Pupils should be taught to:

• identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

• know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

• establish whether a number up to 100 is prime and recall prime numbers up to 19

• multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

• recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)

• solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Pupils should be taught to:

• read and write decimal numbers as fractions [for example, 0.71 = ]

• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

• round decimals with two decimal places to the nearest whole number and to one decimal place

• read, write, order and compare numbers with up to three decimal places

• solve problems involving number up to three decimal places