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Pupil Asset - NC Maths 2017 - Exemplifications

Number

Statement Beginning Developing EmbeddedYear 6: Number and place value

Reads, writes, orders and compares numbers up to 10 000 000 and determines the value of each digit.

Reads, writes, orders and compares numbers up to 10 000 000 and uses knowledge of place value to solve simple problems e.g. which number is larger 75 000 or 700 500?

Demonstrates an understanding of place value, including large numbers and decimals.

Reads, writes, orders and compares numbers up to 10 000 000 and uses knowledge of place value to solve more complex problems.

Rounds any whole number to a required degree of accuracy.

Correctly rounds numbers to common integers e.g. 10, 50, 100, 500 (dependent on context).

Correctly rounds numbers to any given integer to a required degree of accuracy.

Uses knowledge of rounding to make accurate estimations and to solve word problems involving rounding.

Uses negative numbers in context, and calculates intervals across zero.

Solves simple calculations involving negative numbers e.g. How many more degrees warmer is 5°c than -5°c?

Solves more abstract calculations involving negative numbers e.g. 5 + (-7) = -2

Spontaneously uses knowledge of negative numbers to solve mathematical problems in other subjects e.g. Science.

Solves number and practical problems that involve all of the above.

Solves one and two step problems involving place value, rounding and negative numbers.

Solves multi-step problems involving place value, rounding and negative numbers.

Solves and poses multi-step problems involving place value, rounding and negative numbers.

Year 6: Number - addition and subtraction

Solves addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Solves addition and subtraction multi-step problems in contexts, sometimes deciding which operations and methods to use (may sometimes need support to choose appropriate methods).


Solves addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and evaluating chosen methods in terms of effectiveness.

Performs mental calculations, including those with mixed operations and large numbers.

Solves numerical mental calculations, including those with mixed operations and large numbers, e.g. 10x3 + 20x5 = 130

Calculate mentally, using efficient strategies such as manipulating expressions using commutative and distributive properties to simplify the calculation

Solves numerical mental calculations and word problems, including those with mixed operations and large numbers, e.g. A farmer has 20 sheep in each field and 5 fields. If each sheep has four legs, how many legs is that altogether?

Year 6: Number - multiplication and division

Multiplies multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.

Calculates multi-digit numbers up to 4 digits by a two-digit whole number using the formal method of long multiplication (may need additional jottings to support and/or reference to grid method)

Multiplies multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.

When presented with a word problem, spontaneously uses formal written method of long multiplication to solve problem.

Divides numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interprets remainders as whole number remainders, fractions, or by

With prompting, divides multi-digit whole numbers by up to 2 digit numbers using the formal method of short and long division as appropriate (may need additional jottings to

Divides multi-digit whole numbers by up to 2 digit numbers using the formal method of short and long division as appropriate. Interprets remainders as whole number remainders,

When presented with a word problem, spontaneously uses formal written method of short and long division (as appropriate) to solve problem.

rounding, as appropriate for the context. support and/or reference to chunking method). fractions, or by rounding, as appropriate for the context.

Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context.

With prompting, divides multi-digit whole numbers by up to 2 digit numbers using the formal method of short and long division as appropriate (may need additional jottings to support and/or reference to chunking method).

Divides multi-digit whole numbers by up to 2 digit numbers using the formal method of short and long division as appropriate. Interprets remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.

When presented with a word problem, spontaneously uses formal written method of short and long division (as appropriate) to solve problem.

Identifies common factors, common multiples and prime numbers.

With prompting, identifies common factors, multiples and prime numbers from a given set of numbers.

Independently identifies common factors, multiples and prime numbers.

Identifies common factors, multiples and prime numbers and solves problems involving these numbers.

Uses their knowledge of the order of operations to carry out calculations involving the four operations.

Carries out straightforward calculations, using knowledge of order and involving all four operations.

Uses knowledge of the order of operations to carry out calculations involving the four operations, including the use of brackets.

Uses knowledge of the order of operations to carry out complex calculations involving the four operations, including the use of brackets and missing number/operation problems.

Solves problems involving addition, subtraction, multiplication and division.

Solves problems involving addition, subtraction, multiplication and division using appropriate methods.

Use formal methods to solve multi-step problems using all four operations and appropriate methods.

Poses and solves complex problems involving all four operations choosing and justifying the use of appropriate methods.

Uses estimation to check answers to calculations and determines, in the context of a problem, an appropriate degree of accuracy.

With prompting, uses estimation to explain why a given answer is incorrect.

Independently checks own work, using estimations to identify any incorrect answers and correcting them as necessary.

Spontaneously uses estimation to predict answers prior to calculation, thus making fewer mistakes, whilst also checking answers and correcting them as necessary.

Year 6: Number - Fractions (Decimals & Percentages)

Uses common factors to simplify fractions; uses common multiples to express fractions in the same denomination.

Pupil can simplify fractions where the numerator and denominator can be halved to find equivalents and can double denominators to express fractions in the same denomination.

Pupil can identify common denominator in simple fractions and can use this to simplify fractions and express fractions in the same denomination. e.g. 2/3, 5/12

Pupil can identify common denominator in more complex fractions, including mixed fractions and can use this to simplify fractions and express fractions in the same denomination.

Compares and orders fractions, including fractions > 1.

Identifies larger of two presented fractions and can order simple fractions (e.g. with the same denominator) on a number line.

Compares and orders fractions, including those > 1 and fractions where denominators differ e.g. 4/5, 2/3, 6/8.

Confidently compares and orders any given fraction and can apply this knowledge to word problems involving the ordering of fractions.

Adds and subtracts fractions with different denominators and mixed numbers, using the concept of equivalent fractions.

Adds and subtracts fractions with different denominators, but only at a simple level e.g. having/doubling to find common denominator.

Calculates using fractions, decimals or percentages. Identifies common denominator and uses this to solve addition and subtraction calculations.

Pupil applies knowledge of manipulating fractions to solve addition and subtraction calculations including word problems in different contexts.

Multiplies simple pairs of proper fractions, writing the answer in its simplest form.

Multiplies simple pairs of proper fractions, writing the answer in its simplest form.

Calculates using fractions, decimals or percentages. Identifies common denominator and uses this to solve multiplication calculations.

Pupil applies knowledge of manipulating fractions to solve multiplication calculations including word problems in different contexts.

Divides proper fractions by whole numbers.With visual supports e.g. diagrams and prompting, divides proper fractions by whole numbers.

Calculate using fractions, decimals or percentages.

Applies knowledge of dividing proper fractions by whole numbers to solve numerical calculations and word problems.

Associates a fraction with division and calculates decimal fraction equivalents.

With prompting, explains, with diagrams as necessary, how fractions are associated with division and can divide whole numbers with to show fractions of numbers.

Confidently explains how fractions are associated with division and can divide whole numbers successfully to show fractions of numbers.

Confidently explains how fractions are associated with division coherently enough to effectively create a ‘how to’ guide/poster to teach another peer.

Identifies the value of each digit in numbers given to three decimal places and multiplies and divides numbers by 10, 100 and 1000 giving answers up to three decimal places.

With visual supports, e.g. place value grid, identifies the value of each digit in numbers given to three decimal places and multiplies and divides numbers by 10, 100 and 1000 giving answers up to three decimal places.

Identifies the value of each digit in numbers given to three decimal places and multiplies and divides numbers by 10, 100 and 1000 giving answers up to three decimal places.

Use knowledge of place value to solve word problems involving the multiplication and division of numbers by 10, 100 and 1000.

Multiplies one-digit numbers with up to two decimal places by whole numbers.

Multiplies one-digit numbers with up to two decimal places by whole numbers, using grid method (may require prompting).

Multiplies one-digit numbers with up to two decimal places by whole numbers, choosing either grid or formal method.

Multiplies one-digit numbers with up to two decimal places by whole numbers, using formal method.

Solves problems which require answers to be rounded to specified degrees of accuracy.

Solve one step problems which require answers to be rounded to specified degrees of accuracy.

Solves multi-step problems which require answers to be rounded to specified degrees of accuracy.

Poses and answers problems which require answers to be rounded to specified degrees of accuracy.

Recalls and uses equivalences between simple fractions, decimals and percentages, including those in different contexts.

Recalls and uses equivalences between simple fractions, decimals and percentages e.g. halves, quarters, tenths.

Recognises the relationship between fractions, decimals and percentages and express them as equivalent quantities, including those in different contexts.

Uses and applies knowledge of equivalences between fractions, decimals and percentages to solve problems, knowing which form is appropriate for context.

Year 6: Ratio & ProportionSolves problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

Solve simple problems involving the relative sizes of two quantities

Solves problems, including word problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

Use knowledge of ratios to solve equivalent ratio problems e.g. Are these ratios equivalent? 4:5 and 12:15?

Solves problems involving the calculation of percentages.

Solves simple problems involving the calculation of percentages e.g. What is 15% of £84.00

Calculate using fractions, decimals or percentages Solves more complex problems involving the calculation of percentages e.g. If an item costs £84 after a 15% reduction, what was the original cost?

Solves two or more step problems involving the calculation of percentages e.g. Which is the best deal? 15% off £85 or 20% off £105?

Solves problems involving the use of percentages for comparison.

Solve one step problems involving the use of percentages for comparison.

Solves multi-step problems involving the use of percentages for comparison.

Poses and answers problems involving the use of percentages for comparison.

Solves problems involving similar shapes where the scale factor is known or can be found.

Solves simple numerical problems involving similar shapes where the scale factor is known or can be found.

Solves problems, including simple word problems, involving similar shapes where the scale factor is known or can be found.

Solves a range of problems, using all four operations and including multi-step word problems, involving similar shapes where the scale factor is known or can be found.

Solves problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Solves simple numerical problems involving unequal sharing and grouping using knowledge of fractions and multiples. May need to use simple diagrams as jottings.

Solves problems, including simple word problems, involving unequal sharing and grouping using knowledge of fractions and multiples and appropriate jottings.

Solves a range of problems, including multi-step word problems, involving unequal sharing and grouping using knowledge of fractions and multiples, using jottings where necessary.

Year 6: AlgebraUses simple formulae. With prompting and/or practical resources/

diagrams, substitute values into a simple Substitute values into a simple formula to solve problems.

Solves a range of simple algebraic problems using all four operations.

formula to solve problems.

Generates and describes linear number sequences.

Finds the common difference and the next two numbers in simple linear number sequences.

Generates and describes linear number sequences.

Uses knowledge of linear number sequences to find the nth term in a basic linear number sequence.

Expresses missing number problems algebraically.

Solves simple missing number problems algebraically, e.g. 20-X=4 what is X ?

Solves missing number problems algebraically e.g. 4 X + 9 = 21 what is X ?

Uses knowledge of missing number problems to solve word problems.

Finds pairs of numbers that satisfy an equation with two unknowns.

Finds pairs of numbers that satisfy a simple equation with two unknowns

Finds pairs of numbers that satisfy an equation with two unknowns, e.g. (3 X+8) = (4Î³+12), what could X and y be?

Finds pairs of numbers that satisfy an equation with two unknowns, including those with mixed operations, e.g. (3 X+8) = (4Î³-10), what could X and y be?

Enumerates possibilities of combinations of two variables.

Quickly and automatically recalls pairs of whole numbers that make 10, 20, 100.

Quickly and automatically recalls pairs of whole numbers that make 10, 20, 100, 1000, 10 000 etc.

Uses knowledge of number bonds to solve problems e.g. How many numbers can you find that have a sum of 100 and that can both be rounded to 50?

Year 5: Number and place value

Reads, writes, orders and compares numbers to at least 1 000 000 and determines the value of each digit.

Reads, writes, orders and compares numbers up to 1 000 000 and uses knowledge of place value to solve simple problems e.g. which number is larger 75 000 or 700 500.

Demonstrates an understanding of place value, including large numbers and decimals.

Reads, writes, orders and compares numbers up to 1 000 000 and uses knowledge of place value to solve more complex problems.

Counts forwards or backwards in steps of powers of 10 for any given number up to 1 000 000.

Counts forwards and is beginning to count backwards in steps of powers of 10 for any given number up to 1 000 000.

Counts forwards and backwards in steps of powers of 10 for any given number up to 1 000 000.

Confidently and quickly counts forwards and backwards in steps of powers of 10 for any given number up to 1 000 000.

Interprets negative numbers in context, counts forwards and backwards with positive and negative whole numbers, including through

Begins to develop fluency with counting forwards and backwards with positive and negative whole numbers.

Interprets negative numbers in context, counts forwards and backwards with positive and negative whole numbers, including through

Confidently and quickly reasons with negative numbers in context and is beginning to solve simple calculations involving negative numbers.

zero. zero.

Rounds any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000.

Rounds any number up to 1 000 000 to the nearest 10, 100 and 1000.

Rounds any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000.

Confidently and quickly rounds any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000.

Solves number problems and practical problems that involve all of the above.

Solves one and two step problems involving place value, rounding and negative numbers up to 1 000 000.

Solves multi-step problems involving place value, rounding and negative numbers up to 1 000 000.

Solves and poses multi-step problems involving place value, rounding and negative numbers up to 1 000 000.

Read Roman numerals to 1000 (M) and recognises years written in Roman numerals.

Confidently reads Roman numerals to 100 (C) and is beginning to recognise and use numbers to 1000 (M)

Reads Roman numerals to 1000 (M) and recognises most years written in Roman numerals.

Confidently reads Roman numerals to 1000 (M) and recognises and writes years in Roman numerals. Uses knowledge of Roman numerals to solve mathematical problems.


Adds and subtracts whole numbers with more than 4 digits, including using formal written methods.

With prompting, adds and subtracts using the formal methods of addition and subtraction (may need additional jottings to support and/or use of number line method).

Adds and subtracts multi-digit numbers including those with more than 4 digits using the formal written methods of addition and subtraction.

When presented with a word problem, spontaneously uses formal written method for addition or subtraction to solve problem.

Adds and subtracts numbers mentally with increasingly large numbers.

Solves mental calculations, including those which cross 100s/1000s, applying compensation methods where required e.g. 361 + 246 = 361 + 250 -4.

Solves mental calculations, including more complex problems such as missing number calculations e.g. 609 + ___ = 957

Solves multi-step mental calculations, involving increasingly large numbers.

Uses rounding to check answers to calculations and determines, in the context of a problem, levels of accuracy.

With prompting, uses rounding to the nearest 10, 50, 100 and 500 to check answers to calculations, making changes where necessary.

Uses rounding to check answers to calculations and determines, in the context of a problem, levels of accuracy. Makes changes where necessary.

Spontaneously uses rounding mentally, prior to solving calculation to estimate and then check answers to calculations determining levels of accuracy.


EOY6: Solves addition and subtraction multi-step problems in contexts, sometimes deciding which operations and methods to use (may sometimes need support to choose appropriate methods).

EOY6: Solves addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

EOY6: Solves addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and evaluating chosen methods in terms of effectiveness.

Year 5: Number - multiplication and divisionIdentifies multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.

Identifies some multiples and factors, including finding some factor pairs of a number and common factors of two numbers.

Identifies most multiples and factors, including finding all factor pairs of a number and common factors of two numbers.

Confidently and quickly identifies all multiples and factors including finding all factor pairs of a number and common factors of two numbers.

Knows and uses the vocabulary of prime numbers, prime factors and composite (non-prime) numbers.

Knows and uses some of the vocabulary of prime numbers, prime factors and composite numbers.

Knows and uses most of the vocabulary of prime numbers, prime factors and composite numbers.

Confidently and quickly knows and uses all of the vocabulary of prime numbers, prime factors and composite numbers.

Establishes whether a number up to 100 is prime and recall prime numbers up to 19.

With prompting or visual supports, establishes whether a number up to 100 is prime and recalls some prime numbers up to 19.

Establishes whether a number up to 100 is prime and recalls prime numbers up to 19.

Confidently and quickly establishes whether a number up to 100 is prime and recalls prime numbers up to 19. Begins to extend for larger numbers.

Multiplies numbers up to 4 digits by a one- or two-digit number using a formal written method,

Multiplies numbers up to 4 digits by a one- or two-digit number using formal written methods

Multiplies numbers up to 4 digits by a one- or two-digit number using a formal written method,

When presented with a word problem, spontaneously uses formal written method of

including long multiplication for two-digit numbers.

for multiplication (may need additional jottings to support and/or reference to grid method).

including long multiplication for two-digit numbers. long multiplication to solve problem.

Multiplies and divides numbers mentally drawing upon known facts.

Multiplies and divides numbers mentally up to 12x12 using knowledge of times tables. Uses knowledge of place value to derive further number facts e.g. 7 x 6 = 42 so 70 x 60 = 4200

Uses a range of strategies to multiply and divide numbers mentally. E.g. uses knowledge of place value to work out inverse calculations such as 7 x 6 = 42 so 7 x 12 = 84 so 840 / 7 = 120.

Uses a range of strategies to solve simple problems involving multiplication and division of numbers mentally.

Divides numbers up to 4 digits by a one-digit number using the formal written method of short division and interprets remainders appropriately for the context.

With prompting, divides numbers up to 4 digits by a one-digit number using the formal written method for short division (may need additional jottings to support and/or reference to chunking method)

Divides numbers up to 4 digits by a one-digit number using a formal written method for short division and interprets remainders appropriately.

When presented with a word problem, spontaneously uses formal written method of short division to solve problem.

Multiplies and divides whole numbers and those involving decimals by 10, 100 and 1000.

Confidently multiplies and divides whole numbers by 10, 100 and 1000 and is beginning to do so accurately with decimals.

Multiplies and divides whole numbers and those involving decimals by 10, 100 and 1000.

Confidently and quickly multiplies and divides whole numbers and those involving decimals by 10, 100 and 1000 mentally as well as written as appropriate to context.

Recognises and uses square numbers and cube numbers, and the notation for squared (2) and cubed (3).

Understands what a square number is and can recognise and use them with the correct notation (2).

Understands what a square and cube number is and can recognise and use them with the correct notations (2), (3).

Can use knowledge of square and cube numbers to teach another peer. Can recognise and use square numbers and cube numbers with larger numbers (e.g. beyond 100).

Solves problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.

Solves one and two step problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.

Solves multi-step problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.

Solves and poses complex problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.

Solves problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign.

Solves one and two step problems involving all four operations including combinations of these.

Solves multi-step problems involving all four operations including combinations of these.

Solves and poses complex problems involving all four operations including combinations of these.

Solves problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Solves one and two step problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Solves multi-step problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Solves and poses complex problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Year 5: Number - Fractions (Decimals & Percentages)Compares and orders fractions whose denominators are all multiples of the same number.

Identifies larger of two presented fractions whose denominators are multiples of the same number.

Compares and orders fractions whose denominators are all multiples of the same number (e.g. 1/5s, 1/10s, 1/20s, 1/50s).

Compares and orders fractions whose denominators are all multiples of the same number (range of denominators).

Identifies, names and writes equivalent fractions of a given fraction, represented visually, including tenths and hundredths.

Identifies, names and writes simple equivalent fractions of a given fraction.

Identifies, names and writes equivalent fractions of a given fraction, represented visually, including tenths and hundredths.

Identifies, names and writes equivalent fractions of a range of given fractions.

Recognises mixed numbers and improper fractions and converts from one form to the other and writes mathematical statements > 1

Recognises mixed numbers and improper fractions and converts from one form to the other.

Recognises mixed numbers and improper fractions and converts from one form to the other and writes mathematical statements > 1

Confidently uses mixed numbers and improper fractions in a range of ways.

as a mixed number. as a mixed number.

Adds and subtracts fractions with the same denominator and denominators that are multiples of the same number.

Adds and subtracts fractions with the same denominator or different denominators that share a simple equivalence e.g. 2/6 + 1/3 = 1/3 + 1/3.

Adds and subtracts fractions with the same denominator and denominators that are multiples of the same number.

Adds and subtracts fractions with denominators that are multiples of the same number. Begins to add and subtract with mixed denominators.

Multiplies proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Begins to multiply proper fractions and mixed numbers by whole numbers, supported by provided materials and diagrams. May need adult support.

Multiplies proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Multiplies proper fractions and mixed numbers by whole numbers, supported by chosen materials and own drawn diagrams.

Reads and writes decimal numbers as fractions.

Reads and writes decimal numbers as fractions to two decimal places/100ths e.g. 0.72 = 72/100

Reads and writes decimal numbers as fractions up to three decimal places/1000ths e.g. 0.374 = 374/1000

Reads and writes any given decimal number as a fraction.

Recognises and uses thousandths and relates them to tenths, hundredths and decimal equivalents.

Using visual resources e.g. place value grid, identifies the larger of two presented numbers (including a mixture of tenths, hundredths and thousandths).

Recognises and uses thousandths and relates them to tenths, hundredths and decimal equivalents.

Orders numbers involving a mixture of tenths, hundredths, thousandths and decimal equivalents.

Rounds decimals with two decimal places to the nearest whole number and to one decimal place.

Using a number line or alternative visual resources, rounds decimals with two decimal places to the nearest whole number.

Rounds decimals with two decimal places to the nearest whole number and to one decimal place.

Uses knowledge of rounding to solve simple problems e.g. what is the smallest number (to 2 decimal places) that can be rounded to 3.4? What is the largest?

Reads, writes, orders and compares numbers with up to three decimal places.

Identifies larger of two presented numbers with up to three decimal places.

Reads, writes, orders and compares numbers with up to three decimal places.

Reads, writes, orders and compares numbers with up to three decimal places, including a mixture of these e.g. order the following: 3.4, 3.044, 3.04, 3.444

Solves problems involving number up to three decimal places.

Uses appropriate resources e.g. number line, place value grid, solves simple problems involving numbers up to three decimal places.

Solves problems involving numbers up to three decimal places.

Solves multi-step problems involving numbers up to three decimal places.

Recognises the per cent symbol (%) and understands that per cent relates to ‘number of parts per hundred’, and writes percentages as a fraction with denominator 100, and as a decimal.

Recognises % symbol and has a basic understanding that % relates to ‘number of parts per hundred’.

Understands that % relates to ‘number of parts per hundred’ and writes percentages as a fraction with denominator 100, and as a decimal.

Explains to an adult or peer what % means. Writes percentages as a fraction (with denominator 100, and as a decimal) and vice versa.

Solves 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.

Can match up 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.

Solves 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.

Solves problems, including words problems, which require knowing percentage and decimal equivalents.


Counts in multiples of 6, 7, 9, 25 and 1000.Count forward from 0 in multiples of 6, 7, 9, 25 and 1000, using this to solve simple problems e.g. can complete the sequence 7, 14, 21 etc.

Counts forwards and backwards from any number in multiples of 6, 7, 9, 25 and 1000, using this to solve problems e.g. 99, 90, 81, __, __, 54, 45

Reasons with multiples of 6, 7, 9, 25 and 1000 to solve problems e.g. complete a Venn Diagram showing a multiple of 6/a multiple of 9.

Finds 1000 more or less than a given number.Finds 1000 more or less for any number where other place value boundaries are not crossed e.g. 543 + 100 2254 - 1000

Finds multiples of 1000 more or less than any number.

Reasons with their understanding of +/- 1000 to solve problems.

Counts backwards through zero to include negative numbers.

Counts backwards from 10 through 0 to -10, following a simple chant.

Counts backwards from 10 through 0 to -10, demonstrating an understanding of how the number system pivots around 0 e.g. can locate negative numbers on a number line. e.g. can continue to count back in 2s from 8, 6, 4, 2, 0, __, __, __

Applies the logic of negative numbers to a wider range of contexts e.g. count backwards in 100s from 400 into the negative numbers.

Recognises the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

Identifies the thousands, hundreds, tens and unit digit in four-digit numbers, including where 0 is used as a place holder. e.g. Can say how many hundreds there are in 1324. e.g. Can write the number two thousand, three-hundred and seven in digits.

Uses an understanding of thousands, hundreds, tens and units to solve problems e.g. with 4 digits, makes the smallest/ largest/number you can or the number closest to a given number.

Uses an understanding of ThHTUs to reason e.g. Find four numbers between 1000 and 2000 with digits that add up to 7.

Orders and compares numbers beyond 1000. Orders a series of numbers beyond 1000 from Order numbers beyond 1000 by, for example, Solve problems with numbers beyond 1000

smallest to biggest/lowest to highest.positioning numbers on a number line or by using =, < and > to write or complete mathematical expressions.

e.g. using the digits 1 2 3 and 4, find all the ways of completing this statement: 2000 + ___ < 5000

Identifies, represents and estimates numbers using different representations.

- Represents four-digit numbers using digits and resources e.g. build 1341 from Cuisenaire. - Begins to show some awareness of numbers beyond 1000 when estimating e.g. says whether the population of their local area is closer to 100 or 1000.

- Represent four-digit numbers in different ways e.g. identifies that the following numbers are the same: Th H T U 2 2 2 0 1 12 0 20 - Begins to show greater accuracy in estimating e.g. says whether the population of their local area is closer to 100, 1000 or 10 000.

Use their confidence with estimating and representing four-digit numbers to help solve problems e.g. re-distributes values to aid mental calculation.

Rounds any number to the nearest 10, 100 or 1000.

Can round TU numbers to the nearest 10, HTU numbers to the nearest 100 and ThHTU numbers to the nearest 1000.

Can estimate answers to four operation questions by rounding TU numbers to the nearest 10, HTU numbers to the nearest 100 and ThHTU numbers to the nearest 1000.

Rounds to an increasing degree of accuracy, taking into account the context of the problem e.g. rounds the number of children in school to the nearest 10 when calculating how many coaches are needed for a school trip, appreciating that it will not be appropriate to round down in this case.

Read Roman numerals to 100 (I to C) and knows that over time, the numeral system changed to include the concept of zero and place value.

Can read and write Roman numerals to represent numbers 1 to 10 and each multiple of 10 to 100. Pupil appreciates there is no need for a 0 to hold the place of the units in these numbers.

Can read and write Roman numerals to C (100), combining numerals to represent the tens and to represent units. Pupils can identify ways in which the Roman system differs from our contemporary number system, including the absence of the 0 concept.

Solve mathematical problems in the context of Roman numerals.

Solves number and practical problems that involve all of the above and with increasingly large positive numbers.

Solves basic number and practical problems that involve all of the above and with some large positive numbers.

Solves number and practical problems that involve all of the above and with increasingly large positive numbers.

Solves more complex number and practical problems that involve all of the above and with increasingly large positive numbers.


Adds and subtracts numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.

- Add and subtract numbers up to 4 digits using columnar methods that may require some intermediate calculation (i.e. some borrowing or carrying). - Where appropriate, will make use of mental strategies, either because the numbers are small or because they lend themselves to mental calculation e.g. 340 + 210 =

- Add and subtract numbers up to 4 digits using columnar methods where intermediate calculation is required (i.e. borrowing and carrying). - Where appropriate, will make use of a range of mental strategies such as treating a subtraction as a difference question or applying derived number facts e.g. 3 + 7 = 10 so 3 + 6 = 9 so 232 + 160 = 202 + 190

- Uses their understanding of columnar methods to solve problems e.g. infers a missing digit from otherwise complete columns involving numbers up to 4 digits. - Where appropriate, will make use of a range of mental strategies to challenge more challenging problems e.g. when adding 3 or more numbers.

Estimates and uses inverse operations to check answers to a calculation.

Estimates answers to addition, subtraction multiplication and division questions by rounding TU numbers to the nearest 10, HTU numbers to the nearest 100 and ThHTU numbers to the nearest 1000.

- Rounds to a greater degree of accuracy when estimating the answer to questions e.g. rounds ThHTU numbers to the nearest 10 or 100. - Uses the inverse to check their answer to an addition or subtraction question.

Uses a wider range of estimating strategies such as reasoning whether the estimated answer will be greater or less than the actual answer, and by approximating by how much.

Solves addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Solves two-step addition and subtraction problems such as ‘Dan buys an apple for 35p and a bag of oranges for 80p. How much change does it get from £2?

Solves two-step addition and subtraction problems where the required operation is fairly obvious e.g. ‘Amy buys 250ml of orange juice. She gives Sasha 93ml and Becky 76 ml. How

Solves addition and subtraction problems with more than 2 steps e.g. ‘Amy buys three cereal bars at 45p each and four drinks for 36p each. How much change does she get from a £5

much juice does Amy have left?’ note?’ Year 4: Number - multiplication and division

Recalls multiplication and division facts for multiplication tables up to 12 Ã— 12.

Recall multiplication facts for the 6, 7, 9, 11 and 12 times tables up to 12 times.

Recall or derive associated division facts for the 6, 7, 9, 11 and 12 times tables up to 12 x 12. Use this to solve problems e.g. ‘A minibus carries 12 children. How many minibuses are needed to take 132 children to the zoo?’

Use their knowledge of the times tables up to 12 x 12 to solve multiplication and division problems e.g. ‘Guess my number. It’ s digit add up to 15 have a product of 56’ .

Uses place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers.

Uses the inverse and place value to derive x and facts e.g. 15 x 10 = 15 x 100; Knows a x 0 = 0; a x 1 = a; b 1 = b.

Uses inverse and place value in the context of other number facts to derive x and facts e.g. 7 x 6 = 42 so 70 x 6 = 420 70 x 60 = 4200 42 7 = 6 420 7 = 60 - Multiplies 3 numbers together, demonstrating the effect of multiplication on place value e.g. 90 x 40 = 9 x 4 = 36 36 x 100 = 3600

Uses their knowledge of the inverse, place value and derived number facts to reason.

Recognises and uses factor pairs and commutativity in mental calculations.

Recognises factor pairs such as 4 and 7 for 28. - Uses commutativity to aid mental multiplication e.g. 2 x 7 x 5 is easier as 2 x 5 x 7 =

Uses factor pairs and commutativity, including in combination, to aid mental multiplication e.g. 20 x 15 = 2 x 10 x 15 = 10 x 15 x 2 =

Uses their knowledge of factor pairs and commutativity to reason e.g. Simon buys 5 crates with 16 boxes of 9 cakes in. How many cakes?’ 5 x 16 x 9 = 5 x 2 x 8 x 9 = 5 x 8 x 9 x 2 = 5 x 8 = 40 40 x 9 = 54 360 x 2 = 720

Multiplies two-digit and three-digit numbers by a one-digit number using formal written layout.

Multiples TU x U or HTU x U using either a formal written layout or an adhoc method such as partitioning which progresses to a formal method.

Multiples TU x U and HTU x U using a formal written layout such as Grid Method.

Can use their knowledge of TU x U and HTU x U by a formal written method to solve problems e.g. complete an otherwise answered multiplication grid.

Solves problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

- Use the distributive law to solve problems such as ‘Kate has 7 boxes with 13 cakes in each. How many cakes does Kate have in total?’ 10 x 7 = 70 3 x 7 = 21 + = 91 - Solves simple integer scaling and correspondence problems e.g. Max uses 2 bags to store 10 footballs. How many bags will Claire need to store 20 footballs?

- Solve problems involving addition and multiplication, applying the distributive law where applicable e.g. ‘Sasha buys three cereal bars for 45p each and four drinks for 36p each. How much does she spend in total?’ - Solves integer scaling and correspondence problems e.g. ‘To make 4 cupcakes you need 200g of flour and 50g of sugar. How much flour and sugar do you need to make 8 cupcakes?’

- Solves more challenging problems involving multiplication and addition, applying the distributive law appropriately. - Solves more complex integer scaling problems including those expressed as word problems’ .

Divides two-digit and three-digit numbers by a one-digit number using formal written layout.

Divides TU U using formalised methods such as chunking on an ENL.

Divides TU U or HTU U using formalised methods such as chunking on an ENL.

Can use their knowledge of TU U and HTU U to solve problems.


Recognises and shows, using diagrams, families of common equivalent fractions.

Can show equivalences using pre-determined resources e.g. with a fraction wall or by shading grids divided into an appropriate number of equal ‘parts’, can determine that 3/15 is equivalent to 1/5.

Can show equivalent fractions using resources, including quantities e.g. 1/7 and 2/14 of 28 are both 4. Might use times tables, multiples and factors to help find equivalences e.g. 3/4 x 3 = 9/12

Solves problems involving equivalent fractions.

Counts up and down in hundredths; recognises that hundredths arise when dividing an object

Counts up and down in tenths and hundredths e.g. 1, 99/100ths, 98/100ths etc. Recognises

Continues a simple sequence of hundredths e.g. 30/100ths, 60/100ths etc. Makes

Continues more complex sequences such as counting back from 5 in 50/100s. Has a deeper

by one hundred and dividing tenths by ten. that dividing an object by 100 is give you 1/100th.

associations between fractions and division e.g. 1/10th 10 = 1/100th 3/10th = 30/100th

understanding of the association between fractions and division e.g. If 3 cakes are shared between 100 people, 1 person can have 1/100 of each cake or 3/100 of one.

Solves problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number.

Solve one-step problems involving non-unit fractions e.g. Simon and Claire have 20 rabbits. They sell 3/5. How many rabbits do they sell?

Solve two-step problems involving non-unit fractions e.g. Simon and Claire have 24 sweets. Claire eats 2/6. How many sweets are left?

Solves more complex problems involving non-unit fractions e.g. I have a bag of 30 sweets. I eat 2/6 and my friend eats 1/3. Have we eaten more or less than half of our bag of sweets?’

Add and subtracts fractions with the same denominator.

Adds and subtracts a wider range of unit and non-unit fractions with the same denominator e.g. 4/7 + 2/7 = 6/7 7/8 -4/8 = 3/8

Adds and subtracts a wider range of non-unit fractions, identifying where these represent more than 1 whole e.g. 5/8 + 6/8 = 11/8 11/8 -7/8 = 4/8

Can solve more complex addition and subtraction of fraction problems e.g. can add and subtract fractions with different denominators using their knowledge of equivalence to reason a suitable method e.g. 2/6 + 1/3 = 1/3 + 1/3 =

Recognises and writes decimal equivalents of any number of tenths or hundredths.

Can match 1/10 to 0.1, 2/10 to 0.2, 3/10 to 0.3 etc.

Can match 100/100 to 1, 99/100 to 0.99, 98/100 to 0.98 etc. They are believing some flexibility e.g. recognising the equivalence between 0.7, 0.70 and 7/10, 70/100

Reasons with equivalences between fractions and decimals to help solve problems e.g. 0.25 = ¼ so 0.25 2 = 0.125 1/4 2 = 1/8 1/8 = 0.125

Recognises and writes decimal equivalents to 1/4, 1/2, 3/4.

Recognises some landmark equivalents e.g. that 1/2 is 0.5.

Recognises a range of landmark equivalents e.g. 1/4 is 0.25; 1/5 is and 3/4 is 0.75. Uses to solve simple problems.

Uses their knowledge of fraction and decimal equivalences to reason.

Finds 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.

Understands the effect on place value of dividing by 10 e.g. 5 10 = 0.5 and knows this is equivalent to 5/10th.

Understands the effect on place value of dividing by 10 and 100 e.g. 36 10 = 3.6 36 100 = 0.36 which is equivalent to 36/100ths.

Uses the effect of dividing numbers by 10 and 100 and fraction equivalence to help solve problems.

Rounds decimals with one decimal place to the nearest whole number.

Round U.th to the nearest whole number, using < 0.5 and = or > 0.5.

Round U.th to the nearest whole number, using this to answer simple problem solving questions e.g. Rounded to the nearest whole number, it is 21oC in Adam’ s room. What is the highest and lowest temperature it could be?

Use rounding of U.th to the nearest whole numbers to solve more challenging problems.

Compares numbers with the same number of decimal places up to two decimal places.

Compares numbers one decimal place, drawing analogies with fractions where appropriate e.g. orders 0.3 and 0.6.

Compares numbers with two decimal places e.g. orders 2.39, 2.61 and 2.34

Reasons when comparing numbers up to two decimal places e.g. orders 0.25, 5, 5.2 and 5.02.

Solves simple measure and money problems involving fractions and decimals to two decimal places.

Solve one-step problems involving decimals or non-unit fractions e.g. Simon and Claire have £20. They spend 3/5 of it. How much money did they spend?

Solve two-step problems involving decimals or non-unit fractions e.g. Simon and Claire have 60cm of ribbon. Claire uses 0.4 of the ribbon to wrap a present. How many cm of ribbon are left?

Solves more complex problems involving decimals and non-unit fractions e.g. Expressed as a fraction, how much of 60cm of would remain if 0.6 was used to wrap a present?


Counts from 0 in multiples of 4, 8, 50 and 100; finds 10 or 100 more or less than a given number.

- Count forward from 0 in multiples of 4, 8, 50 and 100, using this to solve simple problems e.g. can complete the sequence 8, 16, 24 etc. - Finds 10 and 100 more or less for any number up to 1000 as long as other place value boundaries are not crossed e.g. 435 + 10.

- Counts forwards and backwards from any number in multiples of 4, 8, 50 and 100, using this to solve problems e.g. 96, 88, __, __, 64. - Finds multiples of 10 and 100 more or less than any number up to 1000, including where other place value boundaries may be crossed e.g. 789 + 300 = 320 - 40 =

Reasons with multiples of 4, 8, 50 and 100 and their understanding of +/- 10 and 100 e.g. Completes a Venn Diagram for ‘A Multiple of 8’ / ‘> 10 more than 32’ .

Recognises the place value of each digit in a three-digit number (hundreds, tens, ones).

Identifies the hundreds, tens and unit digit in three-digit numbers, including where 0 is used as a place holder. e.g. Can say how many tens there are in 354. e.g. Can write the number three-hundred and seventy-two in digits.

Uses an understanding of hundreds, tens and units to solve problems e.g. with 3 digits, makes the smallest/ largest/number you can or the number closest to a given number.

Uses an understanding of HTUs to reason e.g. Find the numbers between 200 and 300 with digits that add up to 9.

Compares and orders numbers up to 1000. Orders a series of numbers from smallest to biggest/lowest to highest.

Order numbers up to 1000 by, for example, positioning numbers on a number line or by using =, < and > to write or complete mathematical expressions.

Use their understanding of order to solve problems with numbers up to 1000 e.g. using the digits 1 2 and 3 find all the ways of completing this statement: 200 + ___ < 500

Identifies, represents and estimates numbers using different representations.

Represents three-digit numbers using digits and resources e.g. build 254 from Cuisenaire slabs, rods and cubes. - Begins to show some awareness of numbers up to 1000 when estimating. e.g. Is the number of children in our school closer to 100 or 1000?

Represent three-digit numbers in different ways. e.g. identifies that the following numbers are the same: H T U 2 3 0 1 13 0 - Begins to show greater accuracy in estimating e.g. is the school population closest to 100, 500 or 1000.

Use their confidence with estimating and representing three-digit numbers to help solve problems e.g. re-distributes values to aid mental calculation.

Reads and writes numbers up to 1000 in numerals and in words. Can write numbers to 1000 in numerals. Can write numbers up to 1000 in numerals, in

words and transfer between the two.

Solve problems involving how numbers are expressed in numerals and words. e.g. If every vowel is worth 8 points and every consonant is worth 4, how many points is the number 84 worth when written in letters?

Solves number problems and practical problems involving these ideas.

Solves simple problems involving numbers skills learnt at the ‘Beginning’ of Year 3 number. e.g. A farmer loses 100 sheep from a herd of 435. How many are left? e.g. Use the

Solve problems involving number skills associated with ‘Developing’ the Year 3 expectations. e.g. Jack has £2 in 10p coins. How many 10p coins will Jack have after he

Solve more complex problems involving number skills associated with the Year 3 expectations for number. e.g. How many three-digit, even numbers can be made using the

heights of 4 children given in cm to order them from the tallest to the shortest. has spent 40p? digits 5, 2 and 1?

Solves number and practical problems that involve all of the above.

Solves simple problems involving numbers skills learnt at the ‘Beginning’ of Year 3 number. e.g. A farmer loses 100 sheep from a herd of 435. How many are left? e.g. Use the heights of 4 children given in cm to order them from the tallest to the shortest.

Solve problems involving number skills associated with ‘Developing’ the Year 3 expectations. e.g. Jack has £2 in 10p coins. How many 10p coins will Jack have after he has spent 40p?

Solve more complex problems involving number skills associated with the Year 3 expectations for number. e.g. How many three-digit, even numbers can be made using the digits 5, 2 and 1?


Adds and subtracts numbers mentally, including a three-digit number and ones. Add and subtract TU or HTUs and Us.

Add and subtract TU or HTUs and Us. Some mental strategies may be applied e.g. 186 + 8 = 186 + 4 + 4 = or 186 + 10-2 =

Apply their knowledge of mental strategies to solve more challenging problems such as missing number problems.

Add and subtracts numbers mentally, including a three-digit number and tens. Add and subtract TU or HTUs and 10.

Add and subtract TU or HTUs and 10s, including when crossing a hundreds boundary e.g. 320 - 40 = Some mental strategies may be applied e.g. 320 -20 -20 or 320 -70 + 30


Adds and subtracts numbers mentally, including a three-digit number and hundreds. Add and subtract TU or HTUs and 100.

Add and subtract TU or HTUs and 100s, including when crossing 1000 e.g. 999 + 100 = Some mental strategies may be applied e.g. 900 + 100 + 99


Adds and subtracts numbers with up to three digits, using formal written methods of columnar addition and subtraction.

Add and subtract numbers up to 3 digits using columnar methods where the need for intermediate calculations is not required (i.e. no borrowing or carrying). e.g. 324 + 275

Add and subtract numbers up to 3 digits using columnar methods that may require some intermediate calculation for addition (i.e. some ‘carrying the 1’ ). e.g. 324 + 285.

Uses their understanding of columnar methods to solve problems e.g. infers a missing digit from otherwise complete columns.

Estimates the answer to a calculation and uses inverse operations to check answers.

Can round TU numbers to the nearest 10 and HTU numbers to the nearest 100. - When given a number sentence, a pupil can find all inverses e.g. 23 + 9 = 32 so 9 + 23 = 32 32 -9 = 23 32 -23 = 9

- Can estimate answers to addition and subtraction problems by rounding TU numbers to the nearest 10 and HTU numbers to the nearest 100. - Can check answers by seeing whether the inverse is correct.

Can use more accurate estimation strategies such as rounding HTU to the nearest 10 or reasoning whether the estimated answer will be greater than or less than the actual answer.

Solves problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Solves simple problems such as 25 + ? = 46. In solving problems, can use known number facts to derive useful information e.g. 25 + 10 = 35 25 + 20 = 45 25 + 21 = 46 e.g. place value and inverses: 46 -20 -5 = 21.

Solves inverse problems such as ‘Tom has a number, adds 15, takes away 8 and gets 56. What was Tom’ s number?’ In solving problems, can use known number facts to derive useful information e.g. 64 -15 = 64 -20 + 5 = e.g. place value 49 + 15 = 49 + 10 + 5 =

Solve more challenging problems involving addition and subtraction, including missing number problems e.g. Using the following digits, complete the following number sentence and get as close as you can to 100. __ + __ + __ = 1 2 3 4 5 6

Year 3: Number - multiplication and divisionRecalls and uses multiplication and division facts for the 3, 4 and 8 multiplication tables.

Recalls or can calculate multiplication facts for the 3, 4 and 8 times table e.g. 2 x 3 =, 6 x 4 = and 8 x 8 =

Recalls or derives division facts from known multiplication facts e.g. 6 x 6 = 36 so 36 6 = 6. Uses some early understanding of factor pairs and commutativity to aid mental

Quickly recalls or derives multiplication and division facts for the 3, 4 and 8 times tables, using this knowledge to solve problems e.g. ‘List the multiples common to 4 and 3 that are

multiplication. May be limited to multiples of 10 where 10 is one of the factor pairs e.g. 30 x 4 = 3 x 10 x 4 = 3 x 4 x 10 =

less than 40’ . Uses a range of mental calculation strategies to improve fluency e.g. more extensive use of commutative principle and factor pairs e.g. 32 x 5 = 8 x 5 x 4 = 40 x 4 = 160

Writes and calculates mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods.

Reads and writes mathematical statements for multiplication and division such as U x U, TU x U, U U and TU U. Uses informal strategies such as repeated addition for x and repeated subtraction for , expressing remainders as whole numbers.

Deduces mathematical statements for multiplication and division from word problems: U x U, TU x U, UU and TU U. e.g. ‘Kate has 7 bags with 4 apples in. How many apples in total?’ With division, starts to recognise both metaphors (equal groups/ inverse multiplication). May start to formalise multiplication strategies e.g. using the Grid Method for TU x U and may start to formalise division strategies e.g. chunking on an ENL.

Solves more challenging multiplication and division word problems e.g. ‘I need to pack 22 cakes into boxes. I have boxes that hold 3 cakes, 4 cakes and 8 cakes. I need to use as few boxes as possible and have no spaces left over. What boxes should I use?’

Solves problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

Uses the inverse to solve simple missing number problems e.g. 6 x __ = 24. - Solve simple problems where n and m objects are connected e.g. ‘Sam has 4 rabbits. Claire has 3 times as many rabbits as Sam. How many rabbits does Claire have?’

- Solves more challenging missing number problems e.g. __ 4 = 6 r. 2 - Solve problems where n and m objects are connected.

Solve missing number problems expressed as word problems. Solve integer scaling problems such as ‘Max uses 3 bags to store 12 footballs. How many bags will Claire need to store 24 footballs?’


Counts up and down in tenths; recognising that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10.

Counts up and down in tenths e.g. 1, 9/10ths, 8/10ths etc. Divides shapes into equal tenths, identifying that e.g. 7 of these parts is 7/10ths of the whole.

Continues a simple sequence of tenths e.g. 2/10ths, 4/10ths etc. Divides shapes into equal tenths, making associations between fractions and division e.g. If a cake is shared between 10 people, each person gets 1/10th. If 2 cakes were shared between 10, each person would get 2/10ths.

Continues more complex sequences such as counting back from 3 in 6/10s. Has a deeper understanding of the association between fractions and division e.g. If 4 cakes are shared between 10 people, 1 person can have 1/10 of each cake which is the same as 4/10 of one.

Recognises, finds and writes fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators.

Knows to share a set of objects equally between the denominator. Can use this to derive unit and non-unit fractions e.g. 1/5th of 20 = 4 3/5th of 20 = 12

Uses known times tables to help recognise and find fractions of quantities e.g. 16 is in the 2, 4 and 8 times tables and so can be divided equally into halves, fourths and eighths.

Can solve problems relating to quantity and fractions e.g. ‘In my class of 24 pupils, 1/3 are boys. How many pupils are girls?’

Recognises and uses fractions as numbers: unit fractions and non-unit fractions with small denominators.

Knows that fractions are a way of expressing less than 1. Counts up and down through fractions with the same denominator e.g. 1/6, 2/6, 3/6 etc.

Uses fractions to express quantities that are less than one. Uses the <, > and = signs when ordering fractions or expressing equivalence.

Reads and writes fraction notations which express a number less than 1 e.g. in word problems and in answers to related questions.

Recognises and shows, using diagrams, equivalent fractions with small denominators.

Can derive simple equivalences using pre-determined resources e.g. with a fraction wall or by shading grids divided into an appropriate number of equal ‘parts’, can determine that Â½ is equivalent to 4/8 or that 2/6 is equivalent to 1/3.

Can derive equivalent fractions using resources, including quantities e.g. 1/3 and 2/6 of 12 are both 4 and so 1/3 and 2/6 are equivalent fractions.

Can derive equivalent fractions unaided e.g. reasons that in order to determine whether ¾, 9/12 and 2/3 are equivalent, they will need either grids or quantities that are divisible by 3, 4 and 12.

Adds and subtracts fractions with the same denominator within one whole.

Use practical resources to add and subtract fractions with the same denominator e.g. 2/8 + 4/8 = 6/8 e.g. 4/4 -1/4 = 3/4

Use knowledge of adding and subtracting fractions with the same denominator to solve word problems.

Can apply their knowledge to solve more complex fraction problems e.g. 1 -1/3 = 3/3 -1/3 e.g. 4/6 + 3/6 = 7/6, using practical resources if necessary, the learner realises this is ‘more than 1’ and can express the answer as ‘1 and one sixth’ .

Compare and order unit fractions, and fractions with the same denominators.

Can order the following fractions or position them on a number line: ¼, 1/3, ½, ¾ and 1.

Can order a wider range of unit fractions, including non-unit fractions which share the same denominator e.g. order Â¼, 1/5 and 1/3 from smallest to largest. e.g. order 3/5, 1/5 and 5/5 from largest to smallest.

Can solve problems involving comparing and ordering fractions, including non-unit fractions with different denominations e.g. order 1/8, 4/8, and 1/3 from smallest to largest.

Solves problems that involve all of the above.Solve simple one-step problems involving fractions e.g. Simon has 18. He eats 1/3. How many sweets does Simon eat?

Solves problems involving fractions using mathematical functions associated with the Year 3 ‘Developing’ expectations e.g. ‘I have 15 sweets. 1/3 are green and the rest are red. How many red sweets do I have?’

Solve more complex problems involving fractions e.g. ‘I have 20 sweets. If I eat 1/5 and give 1/4 to my friend, how many sweets will I have left?’


Counts in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward.

Count in 2s, 5s and 10s from 0 and use counting strategies to solve problems e.g. count the number of chairs in a diagram when the chairs are organised into 7 rows of 5 by counting in 5s.

Counts forwards and backwards in 2s, 3s and 5s and in 10s from any number and uses this to solve problems e.g. identifies missing numbers on a number line descending in 3s.

Uses counting in steps to reason when solving problems e.g. recognising that 20 and 65 are multiples of 5, finds the difference between 20 and 65 by counting from 20 in 5s.

Recognises the place value of each digit in a two-digit number (tens, ones).

Demonstrate an understanding of place value, though may still need to use apparatus to support them e.g. by stating the difference in T and 1s between 77 and 33 as 40 and 4.

Partition two digit numbers into different combinations of Ts and 1s. The may include using apparatus e.g. 23 is the same as 2 Ts and 3 1s which is the same as 1 T and 13 1s.

Uses place value to reason e.g. partitions 64 into 50 and 14 to aid mental calculation.

Identifies, represents and estimates numbers using different representations, including the number line.

Estimates accurately to around 30. Can count out items in order to represent a given number up to 100.

Estimates accurately to around 100. Can represent numbers to 100 using apparatus and on an ENL e.g. given 10s, is able to locate where 33 and 74 would go.

Reasons with estimation and representing numbers.

Compares and orders numbers from 0 up to 100; use <, > and = signs.

Compare and order numbers to 100 e.g.by writing number statements such as 35 < 53 and 42 > 36.

Compare and order a group of numbers. Begin to use < and > alongside = to create mathematical statements, illustrating that they understand the meaning of = e.g. 22 < 31 -8 22 = 31 -9

Show reasoning when comparing numbers and using <, > and =. e.g. 23 + ? > 27

Reads and writes numbers to at least 100 in numerals and in words.

Read and write numbers correctly in numerals up to 100 e.g. can write the numbers 14 and 41 correctly.

Read and write numbers correctly in words e.g. 37, thirty-seven

Reason with numbers expressed as numerals and words e.g. write five different numbers as words and then order them from the longest to

shortest.

Uses reasoning about place value and number facts to solve problems.

Solves simple problems e.g. What is the biggest and smallest number you can make with a 3 and 6?

Solve simple problems with a broader scope e.g. Make as many 2 digit numbers as you can from a 3, 5 and a 7 and put them in order from the smallest to the biggest.

Reasons with place value and other aspects of number e.g. Find the two-digit number with 1 odd and 1 even digit that add up to 5.


Solves problems with addition and subtraction using concrete objects and pictorial representations, including those involving numbers, quantities and measures.

Solve simple addition and subtraction problems e.g. Jack has 25p and Susan has 41p, how much money do they have altogether?

Can solve addition and subtraction problems where the operation is less clear e.g. Jack has 25p and Susan has 41p. How much more money does Susan have than Jack?

Solve problems that involve more than one step. e.g. Jack has 35p in his purse and 23p in his piggy bank. Susan has a 50 coin. How much more money does Jack have than Susan?

Solves problems with addition and subtraction applying their increasing knowledge of mental and written methods.

Solve simple addition and subtraction problems e.g. Jack has 25p and Susan has 41p, how much money do they have altogether?

Can solve addition and subtraction problems where the operation is less clear e.g. Jack has 25p and Susan has 41p. How much more money does Susan have than Jack?

Solve problems that involve more than one step. e.g. Jack has 35p in his purse and 23p in his piggy bank. Susan has a 50 coin. How much more money does Jack have than Susan?

Recalls and uses addition and subtraction facts to 20 fluently, and derives and uses related facts up to 100.

Use number bonds and related subtraction facts within 20 e.g. 18 = 9 + ? 15 = 6 + ?

Use number bonds and related subtraction facts within 100 e.g. uses 3 + 6 = 9 to help solve 30 + ? = 90 43 + ? = 49

Use number bonds to reason e.g. Use 30 + 70 = 100 to derive 34 + ? = 90

Adds and subtracts numbers using concrete objects, pictorial representations, and mentally, including a 2-digit number and 1's.

Add and subtract a two-digit number and ones e.g. 23 + 5 = Demonstrate their method using concrete apparatus or pictorial representations. Can add TU and U mentally.

Can add and subtract TU and U numbers mentally where no regrouping is required.

Can add and subtract a two-digit and a one digit number mentally where regrouping is required e.g. 52 -9

Adds and subtracts numbers using concrete objects, pictorial representations, and mentally, including a 2-digit number and 10's.

Add and subtract a two-digit number and tens e.g. 46 + 20 = Demonstrate their method using concrete apparatus or pictorial representations.

Add and subtract a two-digit number and 10s mentally e.g. 87 -40 =

Can add and subtract a three-digit number and 10s where regrouping is required e.g. 123 -30 =

Adds and subtracts numbers using concrete objects, pictorial representations, and mentally, including two 2-digit numbers.

Add and subtract 2 two-digit numbers within 100 where no regrouping is required e.g. 23 + 14 = Can add 2 two-digit numbers mentally where no regrouping is required.

Add 2 two-digit numbers within 100 e.g. 48 + 35 (regrouping required). Subtract 2 two-digit numbers where there is no regrouping required e.g. 74 -33 = Demonstrate their method using concrete apparatus and pictorial representations. Can add and subtract 2 two-digit numbers mentally where no regrouping is required.

Can add and subtract 2 two-digit numbers mentally where regrouping is required e.g. 52 -27 e.g. 91 -73

Adds and subtracts numbers using concrete objects, pictorial representations, and mentally, including adding 3 single-digit numbers.

Add and subtract 3 single digit numbers using concrete objects and pictorial representations.

Add and subtract 3 single digit numbers mentally.

Reason about addition e.g. the sum of 3 odd numbers will always be odd.

Shows that addition of two numbers can be done in any order and subtraction of one number from another cannot.

Identifies number sentences that do and do not make sense e.g. 3 + 6 = 9 6 + 3 = 9 9 -6 = 3 6 -9 = 3

Can produce the 4 correct variations of an +/- number sentence e.g. 3 + 6 = 9 6 + 3 = 9 9 -6 = 3 9 -3 = 6

Reasons with commutatively to help solve problems.

Recognises and uses the inverse relationship between addition and subtraction and use this

Use the inverse relationship between addition and subtraction to answer simple missing

Recognise the inverse relationships between addition and subtraction and use

Solve more complex number problems e.g. 14 + ? -3 = 17 e.g. 14 + ? = 15 + 27

to check calculations and solves missing number problems. number problems e.g. 12 + ? = 19 ? + 30 = 53 this to check calculations and work out

missing number problems e.g. ? -14 = 28.Year 2: Number - multiplication and division

Recalls and uses multiplication and division facts for the 2, 5 and 10 multiplication tables.

Recall multiplication and division facts for the 2s, 5s and 10s.

Recall and use multiplication and division facts for the 2s, 5s and 10s to solve simple problems.

Use multiplication facts to make deductions outside known multiplication n facts e.g. 18 x 5 cannot = 92 because multiples of 5 end in 0 or 5.

Calculates mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division () and equals (=) signs.

Reads and interprets, multiplication and division statements, recognising x, and =

Writes multiplication and division statements for simple problems. e.g. make 7 groups from 35 blocks and write 35 5 = 7.

Reasons with multiplication and division statements e.g. can recognise the relationship between +/- and x/ and simplify addition statements as multiplication statements: 10 + 10 + 10 + 5 + 5 = 3 x 10 + 2 x 5 = 4 x 10.

Shows that multiplication of two numbers can be done in any order and division of one number by another cannot.

Identifies number sentences that do and do not make sense e.g. 7 x 5 = 35; 5 x 7 = 35; 35 5 = 7; 7 35 = 5

Can produce the 4 correct variations of an x/· number sentence e.g. 7 x 5 = 35 5 x 7 = 35 35 5 = 7 35 7 = 5 Demonstrate commutativity as necessary.

Reason with commutativity to help solve problems.

Solves problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

Solve simple x and problems where the operation is clear and aided by pictures. e.g. Tom and Ben share out 18 sweets. How many do they get each?

Use multiplication and division facts for the 2s, 5s and 10s to solve simple problems. e.g. share 40 cherries between 10 and write 40 10 = 4 e.g. Altogether six 5p coins makes 30p.

Solve word problems that involve more than one step e.g. which is more, 4 packets of 5 or 3 packets of 10 biscuits? Determine remainder given known facts e.g. Given 15 5 =3 has a remainder of 0, deduce 16 5 will have a remainder of 1.

Recognises odd and even numbers and explains how you know a particular number is odd or even.

Recognise or list odd and even numbers.

Use knowledge of odd or even numbers in problem solving contexts e.g. number sorting machines, investigating statements like ‘The sum of two even numbers is always an even number’ .

Reason about odd and even e.g. the sum of 3 odd numbers will always be odd.

Makes connections between multiplication and division by 2 and doubling and halving, using these to reason about problems and calculations.

Recall doubles and halves to 20 e.g. double 2 is 4, double 5 is 10 and half of 18 is 9.

Use knowledge of doubles and halves to solve problems e.g. 16 2 = 10 2 = 5; 62 = 3 . 8 8

Reason about doubling and halving e.g. investigate the question ‘If you halve an even number, will you always get an odd number as the answer?’

Year 2: Number - Fractions (Decimals & Percentages)Recognises, finds, names and writes fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity.

Identify, name and write ½, 1/3 and ¼ of a shape, length or quantity. Know that all parts must be equal parts of the whole.

Identify name and write 1/3, ¼, 2/4, ¾ and knows that all parts must be equal parts of the whole.

Reasons with fractions e.g. uses pictorial representations to investigate whether two ¼s are bigger than 1/3.

Writes simple fractions for example, 1/2 of 6 = 3 and recognises the equivalence of 2/4 and 1/2.

Find ½, 1/3, ¼ of an amount. Find ½, 1/3, ¼, 2/4 and ¾ of an amount and write the statements ½ of x = y. Appreciate that ½ and 2/4 are equivalent.

Reasons with fractions of amounts and simple equivalences. e.g. Can find and compare fractions of amounts e.g. ¼ of £20 = £5 and ½ of £8 = £4 so ¼ of £20 is greater than ½ of £8.

Year 1: Number and place valueCounts to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

Rote counts from 0 to 100 forwards and can count on from any given number

Counts to and across 100 forwards and backwards from any given number.

Confidently counts to and across 100 from any given number with no errors or prompting.

Counts, reads and writes numbers to 100 in numerals; counts in multiples of twos, fives and tens.

Reads numbers up to 50 correctly. Writes numbers up to 50, but may show reversals or inconsistencies. Recites 2 and 10 times table (from start).

Consistently reads numbers correctly to 100. Writes mostly accurately up to 100. Recites 2, 5 and 10 times table (from start).

Confidently and accurately reads and writes numbers up to 100 I numerals. Continues 2, 5 and 10 times tables from a given multiple.

Given a number, identifies one more and one less.

When given a group of objects, up to 10, says one more and one less.

Given a number, up to 20, says one more and one less.

Given a number up to 50, says one more and one less.

Identifies and represents numbers using objects and pictorial representations including the number line, and uses the language of: equal to, more than, less than (fewer), most, least.

Identifies and represents numbers up to 10. Uses language of more than/less than.

Identifies and represents numbers up to 20. Uses language of more than/less than; most/least and equal to.

Identifies and represents numbers up to 50 using own number line. Uses language of more than/less than; most/least and equal to; fewer/fewest.

Reads and writes numbers from 1 to 20 in numerals and words.

Reads and writes numbers to 20 in numerals and can write some in words.

Reads and writes numbers to 20 in numerals and can write most in words.

Reads and writes numbers to 20 and can write all accurately in words.

Year 1: Number - addition and subtractionReads, writes and interprets mathematical statements involving addition (+), subtraction (â“) and equals (=) signs.�

Reads and writes simple sums involving numbers up to 10.



Represents and uses number bonds and related subtraction facts within 20.

Knows by heart number bonds to 10. Can complete missing number problems e.g. 3 + ___ = 10

Knows by heart number bonds to 20. When given number bond, can write related subtraction fact i.e. If 6 +14 = 20, 20 -Â __ = 6

Confidently knows number bonds to 20 and can write related subtraction facts for any given pair.

Adds and subtracts one-digit and two-digit numbers to 20, including zero.

Given appropriate and concrete resources (e.g. cubes), adds and subtracts 1 and 2 digit numbers to 10.

Chooses available resources (e.g. cubes, number lines), to add and subtract 1 and 2 digit numbers to 20, including zero.

Can draw own number lines to add and subtract 1 and 2 digit numbers. In some cases, can do mentally.

Solves one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = n -9.

Solves problems involving numbers up to 10 with appropriate resources. Can solve missing number problems up to 10.



Year 1: Number - multiplication and divisionSolves one-step problems involving multiplication and division, by calculating the answer using concrete objects etc. with the support of the teacher.

In practical situations can work out answer to simple multiplication problems e.g. how many sweets will we need to give everybody on the blue table 2 sweets.

Using concrete objects can solve simple multiplication and division problems e.g. I have 8 sweets; how many will each person get if I share them between 4 people?

Solves simple one-step problems involving multiplication and division, by calculating the answer using concrete object.

Recalls multiplication facts for the 10 times Recites 10 times table and begins to count in Recalls most multiplication facts for the 10 Confidently recalls multiplication facts for all of

table and uses them to derive division facts, counting in steps of 10 to answer questions. steps of 10 to answer questions.

times table and uses them to derive most division facts, counting in steps of 10 to answer simple questions.

the 10 times table and uses them to derive division facts, counting in steps of 10 to answer questions.

Recalls and uses doubling and halving facts for numbers up to double 10 and other significant doubles.

Recalls doubling facts for numbers up to double 10 and is starting to learn halving facts.

Recalls and uses doubling and halving facts for numbers up to double 10 and other significant doubles e.g. 50+50 = 100

Confidently uses doubling and halving facts for numbers up to double 10. Begins to see relationship between 2+2=4 and 20+20=40.

Recognises odd and even numbers to 20. Recognises odd and even numbers up to 10. Recognises odd and even numbers up to 20.Can explain the rules for odd and even numbers i.e. 2, 4, 6, 8, 0 = even, 1, 3, 5, 7, 9 = odd


Recognises, finds and names a half as one of two equal parts of an object, shape or quantity.

Experiments with folding paper shapes to see how they can be halved. Can share 10 objects equally between 2 people and recognise that each has one halve.

Colours in half of given simple shapes e.g. squares, rectangles and triangles. Can share up to 20 objects equally between 2 people and say how many each has in their half.

Colours in half of given more complex shapes e.g. triangles and regular polygons. Can explain what a half is and can give simple examples using concrete objects if necessary e.g. demonstrate using cubes.

Recognises, finds and names a quarter as one of four equal parts of an object, shape or quantity.

Experiments with folding paper shapes to see how they can be quartered. Can share 8 objects equally between 4 people and begin to use the term quarters.

Colours in quarters of given simple shapes e.g. squares, rectangles and triangles. Can share up to 20 objects equally between 4 people, recognising that each has a quarter.

Can identify if a shape has been coloured in correctly to show quarter. Can explain what a quarter is and give simple examples using concrete objects e.g. demonstrate using cubes.

web viewcorrectly rounds numbers to common integers e.g. 10, 50, 100, 500 (dependent on context)....

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