
Year 3

Year 4

Year 5

Year 6

Place Value:
Counting

Children will:
 count from 0 in multiples of 4, 8, 50 and 100.
 find 10 or 100 more or less than a given number.

Children will:
 count in multiples of 6, 7, 9, 25 and 1000.
 Children will count backwards through zero to include negative numbers.

Children will:
 count forwards or backwards in steps of powers of 10 for any given number up to 1000000
 count forwards and backwards with positive and negative whole numbers, including through zero.


Place Value:
Represent

Children will:
 identify, represent and estimate numbers using different representations
 read and write numbers up to 1000 in numerals and in words

Children will:
 identify, represent and estimate numbers using different representations
 read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

Children will:
 read, write (order and compare) numbers to at least 1000000 and determine the value of each digit
 read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Children will:
 read, write (order and compare) numbers up to
 10 000 000 and determine the value of each digit.

Place Value:
Use Place Value and Compare

Children will:
 recognise the place value of each digit in a threedigit number (hundreds, tens, ones)
 compare and order numbers up to 1000

Children will:
 find 1000 more or less than a given number
 recognise the place value of each digit in a fourdigit number (thousands, hundreds, tens and ones)
 order and compare numbers beyond 1000

Children will:
 (read, write) order and compare numbers up to
1 000 000 and determine the value of each digit.

Children will:
 (read, write) order and compare numbers up to
10 000 000 and determine the value of each digit.

Place Value:
Problems and Rounding

Children will:
 solve number problems and practical problems involving these ideas.

Children will:
 round any number to the nearest 10, 100 or 1000.
 Solve number and practical problems that involve all of the above and with increasingly large positive numbers.

Children will:
 Interpret negative numbers in context.
 Round any number up to
 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000.
 solve number problems and practical problems that involve all of the above.

Children will:
 round any whole number to a required degree of accuracy.
 use negative numbers in context, and calculate intervals across zero.
 solve number and practical problems that involve all of the above.

Addition and Subtraction: Recall, Represent, Use

Children will:
 estimate the answer to a calculation and use inverse operations to check answers.

Children will:
 estimate and use inverse operations to check answers to a calculation.

Children will:
 use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.


Addition and Subtraction:
Calculations

Children will:
 add and subtract numbers mentally, including:
 a threedigit number and ones
 a three digit number and tens
 a three digit number and hundreds
 add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction.

Children will:
 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.

Children will:
 add and subtract whole numbers with more than 4 digits, including formal written methods (columnar addition and subtraction)
 add and subtract numbers mentally with increasingly large numbers.

Children will:
 perform mental calculations, including with mixed operations and large numbers.
 use their knowledge of the order of operations to carry out calculations involving the four operations.

Addition and Subtraction:
Solve Problems

Children will:
 solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction.

Children will:
 solve addition and subtraction twostep problems in contexts, deciding which operations and methods to use and why.

Children will:
 solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.
 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign.

Children will:
 solve addition and subtraction multistep problems in contexts, deciding which operations and methods to use and why.

Multiplication and Division:
Recall, Represent, Use

Children will:
 recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.

Children will:
 recall multiplication and division facts for multiplication tables up to 12 x 12.
 use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers.
 recognise and use factor pairs and commutativity in mental calculations.

Children will:
 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
 know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers.
 establish whether a number up to 100 is a prime and recall prime numbers up to 19.
 recognise and use square numbers and cube numbers, and the notation for squared and cubed.

Children will:
 identify common factors, common multiples and prime numbers.
 use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Multiplication and Division:
Calculations

Children will:
 write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for twodigit numbers times onedigit numbers, using mental and progressing to formal written methods.

Children will:
 multiply twodigit and threedigit numbers by a onedigit number using formal written layout.

Children will:
 multiply numbers up to 4 digits by a one or twodigit number using a formal written method, including long multiplication for twodigit numbers.
 multiply and divide numbers mentally drawing upon known facts.
 divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context.
 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000.

Children will:
 multiply multidigit numbers up to 4 digits by a twodigit whole number using the formal written method of long multiplication.
 divide numbers up to 4 digits by a twodigit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.
 divide numbers up to 4 digits by a twodigit number using the formal written method of short division where appropriate, interpreting remainders according to the context/
 perform mental calculations, including with mixed operations and large numbers.

Multiplication and Division:
Solve Problems

Children will:
 solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects and connected to m objects.

Children will:
 solve 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 and connected to m objects.

Children will:
 solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes.
 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Children will:
 solve problems involving addition, subtraction, multiplication and division.

Multiplication:
Combined Operations



Children will:
 solve problems involving addition, subtraction, multiplication and division and a combination of these including understanding the meaning of the equals sign.

Children will:
 use their knowledge of the order of operations to carry out calculations involving the four operations.

Fractions:
Recognise and Write

Children will:
 count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing onedigit numbers or quantities by 10.
 recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators.
 recognise and use fractions as numbers: unit fractions and nonunit fractions with small denominators.

Children will:
 count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.

Children will:
 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.


Fractions:
Compare

Children will:
 recognise and show, using diagrams, equivalent fractions with small denominators.
 compare and order unit fractions, and fractions with the same denominators.

Children will:
 recognise and show, using diagrams, families of common equivalent fractions.

Children will:
 compare and order fractions whose denominators are all multiples of the same number.

Children will:
 use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
 compare and order fractions, including fractions >1.

Fractions:
Calculations

Children will:
 add and subtract fractions with the same denominator within one whole.

Children will:
 add and subtract fractions with the same denominator.

Children will:
 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.

Children will:
 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.
 divide proper fractions by whole numbers.

Fractions:
Solve Problems

Children will:
 solve problems that involve all of the above.

Children will:
 solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including nonunit fractions where the answer is a whole number.



Decimals: Recognise and Write


Children will:
 recognise and write decimal equivalents of any number of tenths or hundredths.
 recognise and write decimal equivalents to ¼ ½ ¾

Children will:
 read and write decimal numbers as fractions.
 recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.

Children will:
 identify the value of each digit in numbers given to three decimal places.

Decimals:
Compare


Children will:
 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.

Children will:
 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.


Decimals:
Calculations and Problems


Children will:
 find the effect of dividing a one or twodigit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.

Children will:
 solve problems involving number up to three decimal places.

Children will:
 multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.
 multiply onedigit numbers with up to two decimal places by whole numbers.
 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.

Fractions, Decimals and Percentages


Children will:
 solve simple measure and money problems involving fractions and decimals in two decimal places.

Children will:
 recognise the per cent symbol (%) and understand that per cent related to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal.
 solve problems which require knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

Children will:
 associate a fraction with division and calculate decimal fraction equivalents for a simple fraction.
 recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Ratio and Proportion




Children will:
 solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.
 solve problems involving the calculation of percentages and the use of percentages for comparison.
 solve problems involving similar shapes where the scale factor is known or can be found.
 solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Algebra

Children will:
 solve problems, including missing number problems.



Children will:
 use simple formulae.
 generate and describe linear number sequences.
 express missing number problems algebraically.
 Find
