Upper key stage 2

Place Value

Year 5

Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
Count forwards and backwards with positive and negative whole numbers, including through zero
Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
Read Roman numerals to 1000 (M) and recognise years written in Roman numerals
Interpret negative numbers in context
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

Year 6

Consolidation throughout the year
Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
Round any whole number to a required degree of accuracy
Use negative numbers in context and calculate intervals across zero
Solve number and practical problems that involve all of the above

Addition and Subtraction

Year 5

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
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Solve problems involving the four main operations (sometimes combined) including understanding the equals sign

Year 6

Consolidation throughout the year
Perform mental calculations, including with mixed operations and large numbers
Use their knowledge of the order of operations to carry out calculations involving the four operations
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Multiplication and Division

Year 5

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
Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
Multiply numbers by up to 4 digits by a one-digit 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.
Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

Year 6

Identify common factors, common multiples and prime numbers
Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
Perform mental calculations, including with mixed operations and large numbers
Solve problems involving addition, subtraction, multiplication and division.
Use their knowledge of the order of operations to carry out calculations involving the four operations

Fractions, Decimals and Percentages

Year 5

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 (ie. + = or 1
Compare and order fractions whose denominators are all multiples of the same number
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 decimals 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
Recognise the percent symbol (%) and understand that percent relates to ‘the number of parts per 100’ and write percentages as a fraction with a denominator of 100 and as a decimal
Solve problems which require knowing percentages and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25

Year 6

Consolidation throughout the year
Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
Compare and order fractions, including fractions > 1
Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest form (ie. ¼ x ½ = )
Divide proper fractions by whole numbers (ie. ÷ 2 = )
Identify the value of each digit in numbers given to three decimal places
Associate a fraction with division and calculate decimal fraction equivalents (ie. 0.375 is equal to and 3 ÷ 8)
Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Ratio and Proportion, Algebra

Year 6

Solve problems involving the relative sizes of two quantities where the missing values can be found by using integer multiplication and division facts
Solve problems involving the calculation of percentages (ie. 15% of 360) and the use of percentages for comparison
Solve problems involving similar shapes where the scale factor is known or can be found
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Use simple formulae
Generate and describe linear number sequences
Express missing number problems algebraically
Find pairs of numbers that satisfy an equation with two unknowns
Enumerate possibilities of combinations of two variables

Measurement

Year 5

Convert between different units of metric measure (ie. Km to m, l to ml etc.)
Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
Use all four operations to solve problems involving measure (ie. Length, mass, volume, money) using decimal notation, including scaling
Use all four main operations (+, -, x, ÷) to solve problems involving measure and specifically in this context, money
Solve problems involving converting between units of time
Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
Calculate and compare the area of rectangles (including squares), use standard units (cm² and m²) and estimate the area of irregular shapes
Estimate volume (for example using 1cm³ blocks to build cuboids (including cubes))and capacity

Year 6

Consolidation throughout the year
Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice-versa, using decimal notation up to three decimal places
Convert between miles and kilometres
Use, read, write and convert between standard units, converting measurements of time from a smaller unit of measure to a larger unit and vice-versa
Recognise that shapes with the same areas can have different perimeters and vice versa
Recognise when it is possible to use formulae for area and volume of shapes
Calculate the area of parallelograms and triangles
Calculate, estimate and compare volume of cubes and cuboids using standardised units, including cubic centimetres (cm²) and cubic metres (m³) and extending to other units (ie. mm³ or km³)

Geometry

Year 5

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles
Use the properties of rectangles to deduce related facts and find missing lengths and angles
Identify 3D shapes, including cubes and other cuboids, from 2D representations
Know angles are measured in degrees
Estimate and compare acute, obtuse and reflex angles
Draw given angles and measure them in degrees
Identify angles at a point and one whole turn (360°)
Identify angles at a point on a straight line and ½ turn (180°)
Identify other multiples of 90°
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

Year 6

Draw 2D shapes using given dimensions and angles
Compare and classify geometric shapes based on their properties and sizes
Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
Recognise, describe and build simple 3D shapes, including making nets
Find unknown angles in any triangles, quadrilaterals and regular polygons
Recognise angles where they meet at a point, are on a straight line or are vertically opposite and find missing angles
Describe positions on the full coordinate grid (all four quadrants)
Draw and translate simple shapes on the coordinate plane and reflect them in the axes

Statistics

Year 5

Complete, read and interpret information in tables, including timetables
Solve comparison, sum and difference problems using information presented in a line graph

Year 6

Interpret and construct pie charts and line graphs and use these to solve problems
Calculate and interpret the mean as an average