Number, Place Value and Calculation Progressions:

Number and Place Value

Knowledge Progression in Maths at Foundation Stage

Early Learning Goals for Mathematics

Numbers

Ear

ly Y

ears

Fo

un

dat

ion

Sta

ge

Count reliably with numbers from one to 20

Selects the correct numeral to represent 1 to 5, then 1 to 10 objects

Records, using marks that they can interpret and explain

Place numbers from one to twenty in order

Say which number is one more or one less than a given number up to 20

Use counting and place value to solve problems with adult support and guidance

Knowledge and Skills Progression for Number and Place Value at Key Stage 1

Counting Represent Use Place Value and Compare

Problems and Rounding

Yea

r 1

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number

count numbers to 100 in numerals; count in multiples of twos, fives and tens

identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

read and write numbers from 1 to 20 in numerals and words.

given a number, identify one more and one less

Yea

r 2

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

read and write numbers to at least 100 in numerals and in words

identify, represent and estimate numbers using different representations, including the number line

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

find 10 more or less than a given number

compare and order numbers from 0 up to 100; use <, > and = signs

identify the multiple of ten a number is closest to in value (pre-rounding to the nearest 10)

use place value and number facts to solve problems.

Knowledge and Skills Progression for Number and Place Value at Lower Key Stage 2

Counting Represent Use Place Value and Compare

Problems and Rounding

Yea

r 3

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

identify, represent and estimate numbers using different representations

read and write numbers up to 1000 in numerals and in words

read Roman numerals to 12, and recognise the numerals for 50 and 100

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

find 100 more or less than a given number

compare and order numbers up to 1000

round any number to the nearest 10 or 100

solve number problems and practical problems involving number and place value skills.

Yea

r 4

count in multiples of 6, 7, 9, 25 and 1000

count backwards through zero to include negative numbers

identify, represent and estimate numbers using different representations to 100,000

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

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

find 1000 more or less than a given number

order and compare numbers beyond 1000

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

Knowledge and Skills Progression for Number and Place Value at Upper Key Stage 2

Counting Represent Use Place Value and Compare

Problems and Rounding

Yea

r 5

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

count forwards and backwards with positive and negative whole numbers, including through zero

count in steps of -1, -2, -5, -10 and -25

read and write numbers to at least 1 000 000 and determine the value of each digit

read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

order and compare numbers to at least 1 000 000 and determine the value of each digit

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 number and place value knowledge and skills

interpret negative numbers in context, including through zero

Yea

r 6

read and write numbers up to 10 000 000 and determine the value of each digit

order and compare numbers up to 10 000 000 and determine the value of each digit

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 number and place value knowledge and skills

Number, Place Value and Calculation Progressions:

Addition and Subtraction

Knowledge Progression in Maths at Foundation Stage

Early Learning Goals for Mathematics

Numbers

Ear

ly Y

ears

Fo

un

dat

ion

Sta

ge

Read, write and interpret simple mathematical statements involving addition (+), subtraction (–) and equals (=) signs

with adult support and guidance.

Using quantities and objects, add and subtract two single-digit numbers and count on or back to find the answer

Solve problems, using addition and subtraction with adult support and guidance

Knowledge and Skills Progression for Addition and Subtraction at Key Stage 1

Recall, represent and use Calculations Solve problems Y

ear

1

read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs

represent and use number bonds and related subtraction facts within 20 e.g. 9+7=16, 16-7=9, 7=16-9

add and subtract one-digit and two-digit numbers to 20, including zero, showing proficiency in these stages:

o ones and ones

o a teens and ones

o a two-digit number and tens

understand the effect of adding or subtracting zero.

solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = [ ] – 9.

use practical contexts and associated terms (put together; add; altogether; total; difference between; distance between; more than; less than…)

Yea

r 2

recall and use addition and subtraction facts to 20 fluently

derive and use related facts up to 100 in multiples of 10 e.g. 3+7=10 so 30+70=100

derive and use related facts up to 100 to the next multiple of 10 e.g. [ ] + 21= 30 or 54 + [ ] = 60

show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

add and subtract numbers using concrete objects, pictorial representations, and mentally, including:

o a two-digit number and ones

o a two-digit number and tens

o two two-digit numbers

adding three one-digit numbers

Find small differences

solve problems with addition and subtraction:

o using concrete objects and pictorial representations, including those involving numbers, quantities and measures

applying their increasing knowledge of mental and written methods

recognise and use the inverse relationship between addition & subtraction and use this to check calculations and solve missing number problems.

Knowledge and Skills Progression for Addition and Subtraction at Lower Key Stage 2

Recall, represent and use Calculations Solve problems

Yea

r 3

estimate the answer to a calculation and use inverse operations to check answers

e.g. using rounding

derive and use related facts to 100 e.g. 93+7=100 and 35+65=100

add and subtract numbers mentally, including:

o a three-digit number and ones

o a three-digit number and tens

o a three-digit number and hundreds

add and subtract numbers with up to three digits, using formal written methods including expanded method of columnar addition and subtraction

solve problems, including missing

number problems, using number facts,

place value, and more complex addition

and subtraction.

Yea

r 4

estimate and use inverse operations to check answers to a calculation

derive and use related facts to 1000 e.g. 300+700=1000 350+650=1000

add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction (+ money / decimals) where appropriate

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

Knowledge and Skills Progression for Addition and Subtraction at Upper Key Stage 2

Recall, represent and use Calculations Solve problems

Yea

r 5

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

derive and use related facts to a whole with one decimal place compliments e.g. 3.1+6.9=10

add and subtract whole numbers with more than 4 digits (and decimals with up to 3 dp), including using formal written methods (columnar addition and subtraction)

add and subtract numbers mentally with increasingly large numbers

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

derive and use related facts to a whole with one decimal place compliments e.g. 3.1+6.9=10

Yea

r 6

use estimation (including rounding to the nearest 20/50 if appropriate to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

derive and use related facts to a whole with two decimal place compliments e.g. 3.17+6.83=10

perform mental calculations, including with mixed operations and large numbers

add and subtract any set of whole numbers and decimals using an appropriate written method

Understand how brackets affects calculations

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

use estimation (including rounding to the nearest 20/50 if appropriate to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

derive and use related facts to a whole with two decimal place compliments e.g. 3.17+6.83=10

Number, Place Value and Calculation Progressions:

Multiplication and Division

Knowledge Progression in Maths at Foundation Stage

Early Learning Goals for Mathematics

Numbers

Ear

ly Y

ears

F

ou

nd

atio

n S

tag

e

Solve problems, including doubling, halving and sharing with adult support and guidance

Knowledge and Skills Progression for Multiplication and Division at Key Stage 1

Recall, represent and use Calculations Solve problems

Yea

r 1

recall and use doubles and halves numbers 1-10

Count in multiples of ones, twos, fives

and tens(PV)

Make connections between arrays,

number patterns, and counting in twos, fives and tens

Alongside the practical problem solving

begin to recognise and understand

operation signs x, ÷ and in readiness for

number sentences

solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Yea

r 2

recall and use doubles and halves

numbers 1-20

recall and use multiplication and

division facts for the 2, 5 and 10

multiplication tables, including

recognising odd and even numbers

count in steps of 2, 3, and 5 from 0, and

in tens from any number, forward and

backward(PV)

begin to count in multiples of 100 and 50 to 1000

show that multiplication of two numbers can be done in any order (commutative) e.g. 3x5=5x3 and division of one number by another cannot

calculate mathematical statements for

multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

begin to relate multiplication and division to fractions

e.g. ½ is the same as ÷2

solve problems involving

multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems

in contexts

begin to understand the concept of remainders in practical problems-ie these are left over and cannot be shared fairly

Knowledge and Skills Progression for Multiplication and Division at Lower Key Stage 2

Recall, represent and use Calculations Solve problems

Yea

r 3

recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

connect 2, 4 and 8x through doubling

recall doubles of 10 and use these to derive doubling facts of multiples of 10 up to double 100

count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number(PV)

count in steps of 20s, 200s and 500s to 1000

write and calculate 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

understand remainders in the context of division- i.e. this is left over/remaining

solve 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

understand scaling a number by a scale factor of 3 as making the number (or measurement) 3 times larger

link scaling to the understanding of multiplication e.g. 6+6+6 = 6x3

understand remainders in the context of division- i.e. this is left over so it cannot be shared fairly

Yea

r 4

recall multiplication and division facts for multiplication tables up to 12 × 12

use place value, known and derived facts e.g. 600÷3=200 to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers choosing the best order to do it

understand the effect on place value when you multiply whole numbers by 10 and 100 in derived related facts above

recognise and use factor pairs and commutativity in mental calculations

count in multiples of 1000(PV), 5000 and 2000 to 10000

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

divide numbers up to 2 and 3 digits by a one-digit number using the informal methods moving onto formal written method of short division

understand remainders in the context of division- i.e. this is left over so it cannot be shared fairly and record as ‘r3’

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 are connected to m objects.

Knowledge and Skills Progression for Multiplication and Division at Upper Key Stage 2

Recall, represent and use Calculations Solve problems Combined Operations

Yea

r 5

identify multiples and

factors, including finding all factor pairs of a number, and common factors of two numbers

know and use the vocabulary

of prime numbers, prime factors and composite (non-prime) numbers

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

recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)

multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

Count in steps of powers of

10 including 10,000s, and 100,000s to 1,000,000(PV)

multiply numbers up to 4

digits by a one- or two-digit number using a formal written method, including long multiplication for two-

digit numbers

multiply and divide numbers

mentally drawing upon known facts

divide numbers up to 4 digits by a one-digit number using the formal written method of

short division and interpret remainders appropriately for the context

Begin to express remainders in different ways e.g. 98÷4=24r2 and 24½

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.

solve problems involving

addition, subtraction, multiplication and division and a combination of these, including understanding the

meaning of the equals sign

Yea

r 6

identify common factors,

common multiples and prime

numbers

find prime factors of 2 digit

numbers, and test for prime

numbers beyond 100

use estimation (linked to

rounding and related facts) to check answers to

calculations and determine, in the context of a problem, an appropriate degree of accuracy

multiply multi-digit numbers up to 4 digits by a two-digit

whole number using the formal written method of

long multiplication

divide numbers up to 4 digits by a two-digit 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

begin to express remainders in different ways e.g. 98÷4=24r2 or 24½ or 24.5/£24.50

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

perform mental calculations, including with mixed

operations and large numbers

solve problems involving addition, subtraction,

multiplication and division

use their knowledge of the order of operations to carry

out calculations involving the four operations