## 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.

· 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__