The pupils are working on a broad curriculum in mathematics including: place value; addition and subtraction; multiplication and division; fractions, decimals and percentages; measurement, geometry and statistics. Their Homework Booklets support all the areas below. They are learning all multiplication and division facts up to and including 12 x12.

Number - number and place value

Pupils read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit. They count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000. Pupils interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0. In Year 5 they round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000. Pupils solve number problems and practical problems that involve all of the above. They read Roman numerals to 1,000 (M) and recognise years written in Roman numerals.

Number - addition and subtraction

In Year 5, pupils add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) with increasingly large numbers. They use rounding to check answers to calculations and solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Number - multiplication and division

Pupils identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers. They know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers. They establish whether a number up to 100 is prime and recall prime numbers up to 19. Pupils 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. They 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. They multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000. In Year 5, pupils recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³). They solve problems involving multiplication and division, including using their knowledge of factors, scaling and multiples, squares and cubes.

Number - fractions (including decimals and percentages)

In their work on fractions, pupils compare and order fractions whose denominators are all multiples of the same number. They 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. They 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 and read and write decimal numbers as fractions. Pupils recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents. They round decimals with 2 decimal places to the nearest whole number and to 1 decimal place. Pupils read, write, order and compare numbers with up to 3 decimal places and solve problems involving number up to 3 decimal places. In Year 5, they recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction. They then solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4 , 1/5 , 2/5 , 4/5 and those fractions with a denominator of a multiple of 10 or 25.

Measurement

In measurement, pupils convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]. They understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints. They measure and calculate the perimeter of composite rectilinear shapes in centimetres/metres and calculate/compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes. Pupils estimate volume and capacity; solving problems involving converting between units of time. They use all four operations to solve problems involving measure using decimal notation, including scaling.

Geometry - properties of shapes

Pupils identify 3-D shapes, including cubes and other cuboids, from 2-D representations. They know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles; draw given angles, and measure them in degrees (°C). They can identify:

• angles at a point and 1 whole turn (total 360°)
• angles at a point on a straight line and half a turn (total 180°)
• other multiples of 90°
• 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.

Geometry - position and direction

Pupils 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

Year 5 pupils solve comparison, sum and difference problems using information presented in a line graph. They complete, read and interpret information in tables, including timetables.