# Year 5-Programme of Study (Level 5)

__Number__

## Number & Place Value

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

## Addition & Subtraction

- add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
- add and subtract numbers mentally with increasingly large numbers
- use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

## Multiplication & Division

· 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 (nonprime) numbers · establish whether a number up to 100 is prime and recall prime numbers up to 19 · 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 (Including decimals)

· compare and order fractions whose denominators are all multiples of the same number · identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths · recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, ] · 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 · 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.

__Measurement__

· 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 · 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 · estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water] · 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.

__Geometry__

## Properties of Shapes

· identify 3-D shapes, including cubes and other cuboids, from 2-D representations · 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 360^{o }) · angles at a point on a straight line and 2 1 a turn (total 180^{o }) · other multiples of 90^{o} · 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.

## Position and Direction

· 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.

__Statistics__

· solve comparison, sum and difference problems using information presented in a line graph complete, read and interpret information in tables, including timetables.