# 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 (cm
^{2}and m^{2}) and estimate the area of irregular shapes - Estimate volume (for example using 1cm
^{3}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 (cm
^{2}) and cubic metres (m^{3}) and extending to other units (ie. mm^{3}or km^{3})

## 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