Band 1 Band 2
2014-2015
FRACTION STATEMENTS
Band 1 Recognise, find and name a half as one of two equal parts of an object, shape or quantity
Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity
Understand halving as splitting an object, shape or quantity into two equal parts. Find half of a shape or object. Find half of a quantity practically. Know some halves of numbers e.g. halves of numbers to 10. Recognise, find and name a half as one of two equal parts of an object, shape or quantity. Understand quartering as splitting an object, shape or quantity into four equal parts. Find quarter of a shape or object. Find quarter of a quantity practically. Know some halves and quarters of numbers e.g numbers to 20. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
Band 2 Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity
Understand the notation of a unit fraction and identify that the numerator indicates the number of equal parts that a shape, object or quantity is to be divided in two. Begin to find non-unit fractions of shapes or quantities when working practically.
Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2
Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity. Find a unit fraction e.g. half, quarter, third) of shapes, objects and quantities. Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.
2014-2015
FRACTION STATEMENTS
Band 3 count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
Understand the fractional notation for one tenth and understand that a tenth is found by dividing a shape or object in to ten equal parts or dividing a quantity by ten. Find one tenth of shapes, quantities, objects or measures. Combine tenths of shapes, quantities, objects or measures to find two tenths, three tenths etc. Know decimal equivalence for one tenth, then other tenths.
recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10. Find any non-unit fraction e.g. thirds, quarters, fifths, sixths) of a shape, measure or quantity by using an understanding of the denominator and numerator. Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators. Understand halves and quarters as numbers. Count in halves and quarters using a number line. Find any simple unit fraction e.g. , half, third, quarter, fifth, sixth of a shape, measure or quantity by using an understanding of the denominator. Understand halves as numbers. Count in halves using a number line to support. Count in halves and quarters. Count in other fractions with small denominators using number lines.
Recognise and show, using diagrams, equivalent fractions with small denominators
Add and subtract fractions with the same denominator within one whole e.g. 5/7 + 1/7 = 6/7
Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators. Compare unit fractions through direct comparison on diagrams. Recognise and show, using diagrams, equivalent fractions with small denominators. Practically add and subtract fractions of the same denominator within one whole. Add and subtract fractions with the same denominator within one whole e.g. for example, 5/7 + 1/7 = 6/7
2014-2015
FRACTION STATEMENTS
Compare and order unit fractions, and fractions with the same denominators Solve fraction problems
Order unit fractions through direct comparison on diagrams. Solve fraction problems.
Band 4 Recognise and show, using diagrams, families of common equivalent fractions
Create fraction families for fractions with small denominators through division by 2. Work practically to identify equivalence. Create fraction families for fractions with small denominators through division by 3 or 5. Work practically to identify equivalence.
Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
Recognise and show, using diagrams, families of common equivalent fractions. Understand the notation for one hundredth and understand that a hundredth is found by dividing a shape or object in to 100 equal parts or division of a quantity by 100. Find one hundredth of shapes, quantities, objects or measures. Find hundredths of shapes, quantities, objects or measures. Know that a hundredth is one tenth divided by ten. Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number Add and subtract fractions with the same denominator Recognise and write decimal equivalents of any number of tenths or hundredths
Recognise and write decimal equivalents to 1/4, 1/2, 3/4
Know the decimal equivalence of tenths and hundredths e.g. know that 20 hundredths or two tenths and can be written as 0.2. Recognise and write decimal equivalents of any number of tenths or hundredths. Know that five tenths is equivalent to one half, identify that 0.5 is equal to one half. Know that 25 hundredths is equivalent to one
2014-2015
FRACTION STATEMENTS quarter and identify that 0.25 is the same as one quarter.
Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
Recognise and write decimal equivalents to 1/4, 1/2, 3/4 Understand the effect of dividing a single digit number by 10 or 100 and record the value using decimal notation. Understand the effect of dividing a two digit number by 10 and record the value using decimal notation. Find the effect of dividing a one or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
Round decimals with one decimal place to the nearest whole number Compare numbers with the same number of decimal places up to two decimal places
Compare and order numbers with one decimal place. Compare numbers with the same number of decimal places up to two decimal places.
Solve simple measure and money problems involving fractions and decimals to two decimal places
2014-2015
FRACTION STATEMENTS
Band 5 Compare and order fractions whose denominators are all multiples of the same number
Create equivalent fractions through multiplication or division of the denominator. Convert two fractions to like terms in order to compare them. 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 e.g. 2/5 + 4/5 = 5/6 = 1 1/5
Convert improper fractions to mixed numbers and vice versa. Convert the solution to addition of fractions from improper fractions to mixed numbers. Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number e.g. for example, 2/5 + 4/5 = 5/6 = 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
Multiply unit and non-unit fractions by whole numbers where the solution is less than one whole. Multiply non-unit fractions by whole numbers where solutions are greater than one whole and express the solution as mixed numbers. Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagram.
Read and write decimal numbers as fractions e.g. 0.71 = 71/100 Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
Understand one thousandth as a whole divided in to 1000 parts. Recognise the decimal notation for one thousandth. Recognise the decimal notation to thousandths for equivalence to tenths and hundredths. Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
2014-2015
FRACTION STATEMENTS
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
Understand per cent as meaning number of parts per hundred. Relate simple percentages to hundredths and find such percentages of quantities with and understanding of fractions e.g. know that 50% is equivalent to half, so find 50% of a quantity by finding a half. Relate simple percentages to hundredths and find such percentages of quantities such as 10%, 40%, 60% etc. 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 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25
2014-2015
FRACTION STATEMENTS
Band 6 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 e.g. 1/4 × 1/2 = 1/8
Order mixed numbers and fractions where denominators are within the same fraction families and conversion to like denominators is obvious. Multiply simple fractions using pictorial representations and arrays. Compare and order fractions, including fractions > 1. Add and subtract mixed numbers and fractions where denominators are within the same fraction families and conversion to like denominators is obvious. Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. Multiply decimal numbers with one decimal place by single digit whole numbers, using mental methods or formal written methods where appropriate. Multiply fractions using pictorial representations and arrays, understanding how common denominators are illustrated by these diagrams.
Divide proper fractions by whole numbers e.g. 1/3 ÷ 2 = 1/6
Multiply simple pairs of proper fractions, writing the answer in its simplest form e.g. for example, 1/4 × 1/2 = 1/8 Divide simple fractions by whole numbers using pictorial representations and arrays. Divide proper fractions by whole numbers e.g. for example, 1/3 ÷ 2 = 1/6
Associate a fraction with division and calculate decimal fraction equivalents e.g. 0.375 for a simple fraction e.g. 3/8 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
Multiply decimal numbers with two decimal places by single-digit whole numbers, using mental methods or formal written methods where appropriate. Multiply one-digit numbers with up to two
2014-2015
FRACTION STATEMENTS
Use written division methods in cases where the answer has up to two decimal places
decimal places by whole numbers. Extend understanding of formal methods for division to answers with one decimal place. 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
FRACTION STATEMENTS
Band 1 Recognise, find and name a half as one of two equal parts of an object, shape or quantity
Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity
Understand halving as splitting an object, shape or quantity into two equal parts. Find half of a shape or object. Find half of a quantity practically. Know some halves of numbers e.g. halves of numbers to 10. Recognise, find and name a half as one of two equal parts of an object, shape or quantity. Understand quartering as splitting an object, shape or quantity into four equal parts. Find quarter of a shape or object. Find quarter of a quantity practically. Know some halves and quarters of numbers e.g numbers to 20. Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
Band 2 Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity
Understand the notation of a unit fraction and identify that the numerator indicates the number of equal parts that a shape, object or quantity is to be divided in two. Begin to find non-unit fractions of shapes or quantities when working practically.
Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2
Recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity. Find a unit fraction e.g. half, quarter, third) of shapes, objects and quantities. Write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2.
2014-2015
FRACTION STATEMENTS
Band 3 count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
Understand the fractional notation for one tenth and understand that a tenth is found by dividing a shape or object in to ten equal parts or dividing a quantity by ten. Find one tenth of shapes, quantities, objects or measures. Combine tenths of shapes, quantities, objects or measures to find two tenths, three tenths etc. Know decimal equivalence for one tenth, then other tenths.
recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10. Find any non-unit fraction e.g. thirds, quarters, fifths, sixths) of a shape, measure or quantity by using an understanding of the denominator and numerator. Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators. Understand halves and quarters as numbers. Count in halves and quarters using a number line. Find any simple unit fraction e.g. , half, third, quarter, fifth, sixth of a shape, measure or quantity by using an understanding of the denominator. Understand halves as numbers. Count in halves using a number line to support. Count in halves and quarters. Count in other fractions with small denominators using number lines.
Recognise and show, using diagrams, equivalent fractions with small denominators
Add and subtract fractions with the same denominator within one whole e.g. 5/7 + 1/7 = 6/7
Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators. Compare unit fractions through direct comparison on diagrams. Recognise and show, using diagrams, equivalent fractions with small denominators. Practically add and subtract fractions of the same denominator within one whole. Add and subtract fractions with the same denominator within one whole e.g. for example, 5/7 + 1/7 = 6/7
2014-2015
FRACTION STATEMENTS
Compare and order unit fractions, and fractions with the same denominators Solve fraction problems
Order unit fractions through direct comparison on diagrams. Solve fraction problems.
Band 4 Recognise and show, using diagrams, families of common equivalent fractions
Create fraction families for fractions with small denominators through division by 2. Work practically to identify equivalence. Create fraction families for fractions with small denominators through division by 3 or 5. Work practically to identify equivalence.
Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
Recognise and show, using diagrams, families of common equivalent fractions. Understand the notation for one hundredth and understand that a hundredth is found by dividing a shape or object in to 100 equal parts or division of a quantity by 100. Find one hundredth of shapes, quantities, objects or measures. Find hundredths of shapes, quantities, objects or measures. Know that a hundredth is one tenth divided by ten. Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number Add and subtract fractions with the same denominator Recognise and write decimal equivalents of any number of tenths or hundredths
Recognise and write decimal equivalents to 1/4, 1/2, 3/4
Know the decimal equivalence of tenths and hundredths e.g. know that 20 hundredths or two tenths and can be written as 0.2. Recognise and write decimal equivalents of any number of tenths or hundredths. Know that five tenths is equivalent to one half, identify that 0.5 is equal to one half. Know that 25 hundredths is equivalent to one
2014-2015
FRACTION STATEMENTS quarter and identify that 0.25 is the same as one quarter.
Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
Recognise and write decimal equivalents to 1/4, 1/2, 3/4 Understand the effect of dividing a single digit number by 10 or 100 and record the value using decimal notation. Understand the effect of dividing a two digit number by 10 and record the value using decimal notation. Find the effect of dividing a one or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
Round decimals with one decimal place to the nearest whole number Compare numbers with the same number of decimal places up to two decimal places
Compare and order numbers with one decimal place. Compare numbers with the same number of decimal places up to two decimal places.
Solve simple measure and money problems involving fractions and decimals to two decimal places
2014-2015
FRACTION STATEMENTS
Band 5 Compare and order fractions whose denominators are all multiples of the same number
Create equivalent fractions through multiplication or division of the denominator. Convert two fractions to like terms in order to compare them. 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 e.g. 2/5 + 4/5 = 5/6 = 1 1/5
Convert improper fractions to mixed numbers and vice versa. Convert the solution to addition of fractions from improper fractions to mixed numbers. Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number e.g. for example, 2/5 + 4/5 = 5/6 = 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
Multiply unit and non-unit fractions by whole numbers where the solution is less than one whole. Multiply non-unit fractions by whole numbers where solutions are greater than one whole and express the solution as mixed numbers. Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagram.
Read and write decimal numbers as fractions e.g. 0.71 = 71/100 Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
Understand one thousandth as a whole divided in to 1000 parts. Recognise the decimal notation for one thousandth. Recognise the decimal notation to thousandths for equivalence to tenths and hundredths. Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.
2014-2015
FRACTION STATEMENTS
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
Understand per cent as meaning number of parts per hundred. Relate simple percentages to hundredths and find such percentages of quantities with and understanding of fractions e.g. know that 50% is equivalent to half, so find 50% of a quantity by finding a half. Relate simple percentages to hundredths and find such percentages of quantities such as 10%, 40%, 60% etc. 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 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25
2014-2015
FRACTION STATEMENTS
Band 6 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 e.g. 1/4 × 1/2 = 1/8
Order mixed numbers and fractions where denominators are within the same fraction families and conversion to like denominators is obvious. Multiply simple fractions using pictorial representations and arrays. Compare and order fractions, including fractions > 1. Add and subtract mixed numbers and fractions where denominators are within the same fraction families and conversion to like denominators is obvious. Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. Multiply decimal numbers with one decimal place by single digit whole numbers, using mental methods or formal written methods where appropriate. Multiply fractions using pictorial representations and arrays, understanding how common denominators are illustrated by these diagrams.
Divide proper fractions by whole numbers e.g. 1/3 ÷ 2 = 1/6
Multiply simple pairs of proper fractions, writing the answer in its simplest form e.g. for example, 1/4 × 1/2 = 1/8 Divide simple fractions by whole numbers using pictorial representations and arrays. Divide proper fractions by whole numbers e.g. for example, 1/3 ÷ 2 = 1/6
Associate a fraction with division and calculate decimal fraction equivalents e.g. 0.375 for a simple fraction e.g. 3/8 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
Multiply decimal numbers with two decimal places by single-digit whole numbers, using mental methods or formal written methods where appropriate. Multiply one-digit numbers with up to two
2014-2015
FRACTION STATEMENTS
Use written division methods in cases where the answer has up to two decimal places
decimal places by whole numbers. Extend understanding of formal methods for division to answers with one decimal place. 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
