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

Addition and subtraction, calculations

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