# 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

### 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