Year 5
· 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, including using formal written methods (columnar addition and subtraction).
· Add and subtract numbers mentally with increasingly large numbers.
· 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, 2/5 + 4/5 = 6/5 = 1 1/5]
· 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.
· Read and write decimal numbers as fractions [for example, 0.71 = 71/100].
· 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 ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.
· 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) and 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 3-D shapes, including cubes and other cuboids, from 2-D representations.
· Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.
· Draw given angles, and measure them in degrees (o).
· Identify:
o angles at a point and one whole turn (total 360 degrees)
o angles at a point on a straight line and ½ a turn (total 180 degrees)
o other multiples of 90 degrees.
· 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.
Back
· 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, including using formal written methods (columnar addition and subtraction).
· Add and subtract numbers mentally with increasingly large numbers.
· 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, 2/5 + 4/5 = 6/5 = 1 1/5]
· 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.
· Read and write decimal numbers as fractions [for example, 0.71 = 71/100].
· 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 ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.
· 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) and 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 3-D shapes, including cubes and other cuboids, from 2-D representations.
· Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles.
· Draw given angles, and measure them in degrees (o).
· Identify:
o angles at a point and one whole turn (total 360 degrees)
o angles at a point on a straight line and ½ a turn (total 180 degrees)
o other multiples of 90 degrees.
· 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.
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