Progression in fractions, decimals, percentages - new ...



Progression: Fractions (decimals Y4+; percentages Y5+)

Programme of study (statutory requirements)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Fractions |Fractions |Fractions |Fractions (including decimals) |Fractions (including decimals and percentages) |Fractions (including decimals and percentages) |

| | | | | | |

|Pupils should be |Pupils should be taught |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |

|taught to: |to: | | |compare and order fractions whose denominators are all | |

| | |count up and down in tenths; |recognise and show, using diagrams, |multiples of the same number |use common factors to simplify fractions; use common|

|recognise, find and |recognise, find, name |recognise that tenths arise |families of common equivalent fractions |identify, name and write equivalent fractions of a given |multiples to express fractions in the same |

|name a half as one of |and write fractions 1/3,|from dividing an object into 10|count up and down in hundredths; recognise |fraction, represented visually, including tenths and |denomination |

|two equal parts of an |1/4, 2/4 and 3/4 of a |equal parts and in dividing |that hundredths arise when dividing an |hundredths |compare and order fractions, including fractions >1 |

|object, shape or |length, shape, set of |one-digit numbers or quantities|object by a hundred and dividing tenths by |recognise mixed numbers and improper fractions and convert |add and subtract fractions with different |

|quantity |objects or quantity |by 10 |ten |from one form to the other and write mathematical statements|denominators and mixed numbers, using the concept of|

| | |recognise, find and write |solve problems involving increasingly |> 1 as a mixed number (for example, 2/5 + 4/5 = 6/5 = 11/5) |equivalent fractions |

|recognise, find and |write simple fractions |fractions of a discrete set of |harder fractions to calculate quantities, |add and subtract fractions with the same denominator and |multiply simple pairs of proper fractions, writing |

|name a quarter as one |for example, 1/2 of 6 = |objects: unit fractions and |and fractions to divide quantities, |denominators that are multiples of the same number |the answer in its simplest form (for example, 1/4 × |

|of four equal parts of|3 and recognise the |non-unit fractions with small |including non-unit fractions where the |multiply proper fractions and mixed numbers by whole |1/2 =1/8) |

|an object, shape or |equivalence of 2/4 and |denominators |answer is a whole number |numbers, supported by materials and diagrams |divide proper fractions by whole numbers (for |

|quantity |1/2 |recognise and use fractions as |add and subtract fractions with the same |read and write decimal numbers as fractions (for example, |example, 1/3 ÷ 2 = 1/6 ) |

| | |numbers: unit fractions and |denominator |0.71 = 71/100) |associate a fraction with division and calculate |

| | |non-unit fractions with small |recognise and write decimal equivalents of |recognise and use thousandths and relate them to tenths, |decimal fraction equivalents (for example, 0.375) |

| | |denominators |any number of tenths or hundredths |hundredths and decimal equivalents |for a simple fraction (for example, 3/8) |

| | |recognise and show, using |recognise and write decimal equivalents to |round decimals with two decimal places to the nearest whole |identify the value of each digit in numbers given to|

| | |diagrams, equivalent fractions |¼, ½, 3/4 |number and to one decimal place |three decimal places and multiply and divide numbers|

| | |with small denominators |find the effect of dividing a one- or |read, write, order and compare numbers with up to three |by 10, 100 and 1000 giving answers up to three |

| | |add and subtract fractions with|two-digit number by 10 and 100, identifying|decimal places |decimal places |

| | |the same denominator within one|the value of the digits in the answer as |solve problems involving number up to three decimal places |multiply one-digit numbers with up to two decimal |

| | |whole (for example, 5/7 + 1/7 =|ones, tenths and hundredths |recognise the per cent symbol (%) and understand that per |places by whole numbers |

| | |6/7) |round decimals with one decimal place to |cent relates to “number of parts per hundred”, and write |use written division methods in cases where the |

| | |compare and order unit |the nearest whole number |percentages as a fraction with denominator 100, and as a |answer has up to two decimal places |

| | |fractions, and fractions with |compare numbers with the same number of |decimal |solve problems which require answers to be rounded |

| | |the same denominators |decimal places up to two decimal places |solve problems which require knowing percentage and decimal |to specified degrees of accuracy |

| | |solve problems that involve all|solve simple measure and money problems |equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a |recall and use equivalences between simple |

| | |of the above |involving fractions and decimals to two |denominator of a multiple of 10 or 25 |fractions, decimals and percentages, including in |

| | | |decimal places | |different contexts |

Notes and guidance (non-statutory)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Fractions |Fractions |Fractions |Fractions (including decimals) |Fractions (incl. decimals and percentages) |Fractions (incl. decimals and percentages) |

| | | | | | |

|Pupils are taught |Pupils use fractions as |Pupils connect tenths to place |Pupils should connect hundredths to tenths |Pupils should be taught throughout that percentages, |Pupils should practise, use and understand the |

|half and quarter as|‘fractions of’ discrete and|value, decimal measures and to |and place value and decimal measure. |decimals and fractions are different ways of expressing |addition and subtraction of fractions with different|

|‘fractions of’ |continuous quantities by |division by 10. | |proportions. |denominators by identifying equivalent fractions |

|discrete and |solving problems using | |They extend the use of the number line to | |with the same denominator. They should start with |

|continuous |shapes, objects and |They begin to understand unit |connect fractions, numbers and measures. |They extend their knowledge of fractions to thousandths and |fractions where the denominator of one fraction is a|

|quantities by |quantities. They connect |and non-unit fractions as | |connect to decimals and measures. |multiple of the other (for example, ½ + 1/8 = 5/8) |

|solving problems |unit fractions to equal |numbers on the number line, and|Pupils understand the relation between | |and progress to varied and increasingly complex |

|using shapes, |sharing and grouping, to |deduce relations between them, |non-unit fractions and multiplication and |Pupils connect equivalent fractions > 1 that simplify to |problems. |

|objects and |numbers when they can be |such as size and equivalence. |division of quantities, with particular |integers with division and other fractions > 1 to division |Pupils should use a variety of images to support |

|quantities. |calculated, and to |They should go beyond the [0, |emphasis on tenths and hundredths |with remainders, using the number line and other models, and|their understanding of multiplication with |

| |measures, finding fractions|1] interval, including relating| |hence move from these to improper and mixed fractions. |fractions. This follows earlier work about fractions|

|For example, they |of lengths, quantities, set|this to measure. |Pupils make connections between fractions | |as operators (fractions of), as numbers, and as |

|could recognise and|of objects or shapes. They | |of a length, of a shape and as a |Pupils connect multiplication by a fraction to using |equal parts of objects, for example as parts of a |

|find half a length,|meet 3/4 as the first |Pupils understand the relation |representation of one whole or set of |fractions as operators (fractions of), and to division, |rectangle. |

|quantity, set of |example of a non-unit |between unit fractions as |quantities. Pupils use factors and |building on work from previous years. This relates to |Pupils use their understanding of the relationship |

|objects or shape. |fraction. |operators (fractions of), and |multiples to recognise equivalent fractions|scaling by simple fractions, including fractions > 1. |between unit fractions and division to work |

| | |division by integers. |and simplify where appropriate (for | |backwards by multiplying a quantity that represents |

|Pupils connect |Pupils should count in | |example, 6/9 = 2/3 or 1/4 = 2/8). |Pupils practise adding and subtracting fractions to become |a unit fraction to find the whole quantity (for |

|halves and quarters|fractions up to 10, |They continue to recognise | |fluent through a variety of increasingly complex problems. |example, if ¼ of a length is 36cm, then the whole |

|to the equal |starting from any number |fractions in the context of |Pupils continue to practise adding and |They extend their understanding of adding and subtracting |length is 36 × 4 = 144cm). |

|sharing and |and using the 1/2 and 2/4 |parts of a whole, numbers, |subtracting fractions with the same |fractions to calculations that exceed 1 as a mixed number. |They practise calculations with simple fractions and|

|grouping of sets of|equivalence on the number |measurements, a shape, and unit|denominator, to become fluent through a | |decimal fraction equivalents to aid fluency, |

|objects and to |line (for example, 11/4, |fractions as a division of a |variety of increasingly complex problems |Pupils continue to practise counting forwards and backwards |including listing equivalent fractions to identify |

|measures, as well |12/4 (or 11/2), 13/4, 2). |quantity. |beyond one whole. |in simple fractions. |fractions with common denominators. |

|as recognising and |This reinforces the concept| | | |Pupils can explore and make conjectures about |

|combining halves |of fractions as numbers and|Pupils practise adding and |Pupils are taught throughout that decimals |Pupils continue to develop their understanding of fractions |converting a simple fraction to a decimal fraction |

|and quarters as |that they can add up to |subtracting fractions with the |and fractions are different ways of |as numbers, measures and operators by finding fractions of |(for example, 3 ÷ 8 = 0.375). For simple fractions |

|parts of a whole. |more than one. |same denominator through a |expressing numbers and proportions. |numbers and quantities. |with recurring decimal equivalents, pupils learn |

| | |variety of increasingly complex| | |about rounding the decimal to three decimal places, |

| | |problems to improve fluency. |Pupils’ understanding of the number system |Pupils extend counting from year 4, using decimals and |or other appropriate approximations depending on the|

| | | |and decimal place value is extended at this|fractions including bridging zero, for example on a number |context. Pupils multiply and divide numbers with up |

| | | |stage to tenths and then hundredths. This |line. |to two decimal places by one-digit and two-digit |

| | | |includes relating the decimal notation to | |whole numbers. Pupils multiply decimals by whole |

| | | |division of whole number by 10 and later |Pupils say, read and write decimal fractions and related |numbers, starting with the simplest cases, such as |

| | | |100. |tenths, hundredths and thousandths accurately and are |0.4 × 2 = 0.8, and in practical contexts, such as |

| | | | |confident in checking the reasonableness of their answers to|measures and money. |

| | | |They practise counting using simple |problems. |Pupils are introduced to the division of decimal |

| | | |fractions and decimal fractions, both | |numbers by one-digit whole number, initially, in |

| | | |forwards and backwards. |They mentally add and subtract tenths, and one-digit whole |practical contexts involving measures and money. |

| | | | |numbers and tenths. |They recognise division calculations as the inverse |

| | | |Pupils learn decimal notation and the | |of multiplication. |

| | | |language associated with it, including in |They practise adding and subtracting decimals, including a |Pupils also develop their skills of rounding and |

| | | |the context of measurements. They make |mix of whole numbers and decimals, decimals with different |estimating as a means of predicting and checking the|

| | | |comparisons and order decimal amounts and |numbers of decimal places, and complements of 1 (for |order of magnitude of their answers to decimal |

| | | |quantities that are expressed to the same |example, 0.83 + 0.17 = 1). |calculations. This includes rounding answers to a |

| | | |number of decimal places. They should be | |specified degree of accuracy and checking the |

| | | |able to represent numbers with one or two |Pupils should go beyond the measurement and money models of |reasonableness of their answers. |

| | | |decimal places in several ways, such as on |decimals, for example, by solving puzzles involving | |

| | | |number lines. |decimals. | |

| | | | | | |

| | | | |Pupils should make connections between percentages, | |

| | | | |fractions and decimals (for example, 100% represents a whole| |

| | | | |quantity and 1% is 1/100, 50% is 50/100, 25% is 25/100) and | |

| | | | |relate this to finding ‘fractions of’. | |

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Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

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