# Upper key stage 2

## Place value, counting

### 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

Autumn 1

### Year 6

• Consolidation throughout the year

## Place value, represent

### Year 5

• 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

Autumn 1

### Year 6

• Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit

Autumn 1

## Place value context and compare

### Year 5

• Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit

Autumn 1

### Year 6

• Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit

Autumn 1

## Place value, problems and rounding

### Year 5

• 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

Autumn 1

### Year 6

• 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

Autumn 1

## Addition and subtraction, recall, represent use

### Year 5

• Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

Autumn 2

### Year 6

• Consolidation throughout the year

### 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

Autumn 2

### Year 6

• 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

Autumn 2

## Addition and subtraction, solve problems

### Year 5

• 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

Autumn 2

### Year 6

• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Autumn 2

## Multiplication and division, recall, represent use

### 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)

Autumn 4

### 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

Autumn 2

## Multiplication and division, calculations

### Year 5

• 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.

Autumn 4, spring 1, summer 1

### Year 6

• 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

Autumn 2

## Multiplication and division, solve problems

### Year 5

• 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

Autumn 4, spring 1

### Year 6

• Solve problems involving addition, subtraction, multiplication and division.

Autumn 2 (consolidation throughout the year)

## Multiplication and division, combined operations

### Year 5

• Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

Spring 1

### Year 6

• Use their knowledge of the order of operations to carry out calculations involving the four operations

Autumn 2

## Fractions, recognise and write

### 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. 2/5 + 4/5  = 6/5  or 1 1/5)

Spring 2

### Year 6

• Consolidation throughout the year

## Fractions, compare

### Year 5

• Compare and order fractions whose denominators are all multiples of the same number

Spring 2

### Year 6

• Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• Compare and order fractions, including fractions > 1

Autumn 3

## Fractions, calculations

### Year 5

• 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

Spring 3

### Year 6

• 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 = 1/8)
• Divide proper fractions by whole numbers (ie. 1/3 ÷ 2 = 1/6)

Autumn 3

## Fractions, solve problems

### Year 6

• Consolidation throughout the year

## Decimals, recognise and write

### Year 5

• Read and write decimals as fractions (for example 0.71 = 71/100)
• Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

Spring 3

### Year 6

• Identify the value of each digit in numbers given to three decimal places

Spring 1

## Decimals, compare

### Year 5

• 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

Spring 3

### Year 6

• Consolidation throughout the year

## Decimals, calculations and problems

### Year 5

• Solve problems involving number up to three decimal places

Summer 1

### Year 6

• Multiply and divide numbers by 10, 100 and 1000 giving answers up to 3 decimal places
• Multiply one-digit numbers with up to two decimal places by whole numbers
• Use written division methods in cases where the answer has up to two decimal places
• Solve problems which require answers to be rounded to specified degrees of accuracy

Spring 1

## Fractions, decimals and percentages

### Year 5

• 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 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25

Spring 3

### Year 6

• Associate a fraction with division and calculate decimal fraction equivalents (ie. 0.375 is equal to 3/8 and 3 ÷ 8)
• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Spring 1 and 2

## Ratio and proportion

### 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

Spring 6

## Algebra

### Year 6

• 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

Spring 3

## Measurement: using measures

### 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

Summer 1, 4 and 6

### Year 6

• 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

Spring 4

## Measurement: money

### Year 5

• Use all four main operations (+, -, x, ÷) to solve problems involving measure and specifically in this context, money

Summer 1

### Year 6

• Consolidation throughout the year

## Measurement: time

### Year 5

• Solve problems involving converting between units of time

Summer 4

### Year 6

• 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

Summer 4

## Measurement: perimeter, area, volume

### Year 5

• 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

Autumn 5, summer 5

### Year 6

• 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)

Spring 5

## Geometry: 2D shapes

### 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

Summer 2

### 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

Summer 1

## Geometry: 3D shapes

### Year 5

• Identify 3D shapes, including cubes and other cuboids, from 2D representations

Summer 2

### Year 6

• Recognise, describe and build simple 3D shapes, including making nets

Summer 1

## Geometry: Angles and lines

### Year 5

• 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°

Summer 2

### Year 6

• 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

Summer 1

## Geometry: position and direction

### Year 5

• 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

Summer 3

### Year 6

• 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

Autumn 4

## Statistics: present and interpret

### Year 5

• Complete, read and interpret information in tables, including timetables

Autumn 3

### Year 6

• Interpret and construct pie charts and line graphs and use these to solve problems

Summer 3

## Statistics: solve problems

### Year 5

• Solve comparison, sum and difference problems using information presented in a line graph

Autumn 3

### Year 6

• Calculate and interpret the mean as an average

Summer 3