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

• Add and subtract whole numbers with more than 4 digits.
• 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 (example, 12 462 – 2300 = 10 162)
• Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

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

• Compare and order fractions whose denominators are all multiples of the same number.
• 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, for example, 2 fifths + 4 fifths = 6 fifths = 1 and 1 fifth.
• 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 decimal numbers as fractions, for example, 0.71 = 71 hundredths.
• 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.
• Solve problems involving number up to three decimal places.
• Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal.
• Solve problems which require knowing percentage and decimal equivalents of one half, one quarter, one fifth, two fifths, four fifths and those fractions with a denominator of a multiple of 10 or 25.

Measurement

• Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre).
• Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints.
• Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres.
• Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm²) and square metres (m²) .
• Estimate the area of irregular shapes.
• Estimate volume, for example using 1 cm³ blocks to build cuboids (including cubes) and capacity, for example using water.
• Solve problems involving converting between units of time.
• Use all four operations to solve problems involving measure, for example, length, mass, volume, money using decimal notation, including scaling.

• 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 (total 360°);
  • angles at a point on a straight line and half a turn (total 180°);
  • other multiples of 90°.
• Use the properties of rectangles to deduce related facts and find missing lengths and angles.
• Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

• 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.

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

• 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.

• Multiply multi-digit numbers up to 4 digits by a two-digit whole number.
• 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 number 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 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.
• Perform mental calculations, including with mixed operations and large numbers.
• Identify common factors, common multiples and prime 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.
• Solve problems involving addition, subtraction, multiplication and division.
• Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

• 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, for example, 1 quarter × 1 half = 1 eighth.
• Divide proper fractions by whole numbers, for example, one third ÷ 2 = one sixth.
• Associate a fraction with division and calculate decimal fraction equivalents, for example, 0.375 for a simple fraction, for example three eighths.
• Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three 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.
• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

• Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.
• Solve problems involving the calculation of percentages, for example, of measures, and such as 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

• 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 to up to three decimal places.
• Convert between miles and kilometres.
• 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 standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units, for example, mm³ and km³.

• Draw 2D shapes using given dimensions and angles.
• Recognise, describe and build simple 3D shapes, including making nets.
• Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons.
• Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.
• 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.

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