know the concept of transaction for example by exchanging a coin for an item during role-play
know 1:1 correspondence in everyday situations with adult prompting
know the concept of ‘many’
know the concept of ‘few’
know number names and can use them in everyday situations
can make sets of one and lots of objects with support
can experience and demonstrate an understanding of 1:1 correspondence in everyday situations
can take ‘one’ in a learned situation eg a biscuit
can watch and listen to an adult demonstrating use of number names in everyday situations
can join in with familiar number rhymes and songs
can indicate one object
can experience 1:1 correspondence in everyday
can indicate two objects
can touch objects one at a time as an adult counts
can indicate which group contains ‘lots’
can indicate which group contains ‘one’
can make sets of one and lots of objects with support
Upon completing Step Three pupils:
know the number names to 5 and can say them in the correct order in a song or by joining in with the teacher
know the concept of numbers up to 5 and can demonstrate this by putting together the right number of objects when asked
know the concept of more / less
can identify the big or small object from a set of two
can sort objects according to a stated characteristic
can copy and continue simple patterns using real-life materials
know key vocabulary e.g. number, how many, count, same number as etc.
know and can match sets of numerals to 5
can indicate one to five using fingers
can take part in number activities reciting numbers one to five
can count five objects either in a line or arranged randomly
can join in rote counting to 5
can create sets of 3
can demonstrate an awareness of none / zero / nothing / nil
can join in rote counting to 5
can join in rote counting to 10
can ‘purchase’ an item in value up to 5p, by counting out in 1p coins
can make sets of up to 5 on request
can count reliably to 5
can make an identical set of numbers to 5
can compare sets to identify more
can compare sets to identify less
Upon completing Step Four pupils:
know that the last number counted represents the total number of the count
know and can recognise numerals 0–10
know that the number of objects in a set is not affected by their size and position
can identify how many objects there are in a group of up to 10 objects, recognising smaller objects on sight and counting the objects in larger groups up to 10
can use real-life materials to add and subtract 1 from a group of objects and indicate how many are now present
can join in rote counting beyond 10
can estimate a small number and check by counting
can write numerals 0–5 (with some inaccuracies)
are beginning to count objects to 10 including objects placed randomly
can count onwards from a small number to 10
are beginning to estimate a small number and check by counting
can, with an adult prompt, combine two small sets and count the total
can with an adult, take away a number of objects from a set and count the remainder
can, in a practical setting, add one or take away one from a set
Upon completing Step Five pupils:
know most numbers to 10
know how to record numbers to 10
know and can use language such as ‘more’ or ‘less’ to compare two numbers
know the vocabulary ‘add’ and ‘take away’ and can use it in practical situations
know that if they count out objects arranged in different ways the amount will be the same
know addition means combining groups of objects
know subtraction means taking objects away from a group
can count objects reliably to 10 including objects placed randomly
can label sets with numerals 0–10
can observe number relationships and patterns in the environment and use them to derive facts
can find one more or one less than a number from 1–10
can select two groups of objects to make a given total of objects
can combine two sets and count the total
can subtract from a set and count the remainder
can count repeated groups of the same size
can share objects into equal groups and count how many in each group
can solve subtraction problems involving numbers up to 10
can solve addition problems involving numbers up to 10
can read and order ordinal numbers
can find the position of an object using ordinal numbers up the 5th
can find the position of an object using ordinal numbers up the 10th
can solve addition problems by counting on
can find numbers to 10 on a number line
can use objects to find the difference between two numbers
Upon completing Step Six pupils:
know the mathematical symbols of + - and =
know the composition of numbers to 5 and a developing ability to recall number bonds to and within 5 (e.g. 2 + 2 = 4 and 3 + 1 =4)
know number bonds up to 10
can read and write numbers in numerals from 0 to 9
can solve number problems involving the addition and subtraction of single-digit numbers up to 10
can demonstrate an understanding that the total number of objects changes when objects are added or taken away
can count to 20, demonstrating that the next number in the count is one more and the previous number is one less
can rote count to 100 in 1s
can rote count to 100 in 10s
can use number bonds up to 10 to solve mental calculations involving addition
can recognise and read numbers up to 20 in different cross curricular contexts
can write numbers up to 20 in different cross curricular contexts
are beginning to understand place value in 2 digit numbers
can answer a range of addition and subtraction problems
know that 0 is none or zero
can use my number skills to collect data and record it in a pictogram or block graph
Upon completing Stage One pupils:
know the language of: equal to, more than, less than (fewer), most, least
know how to count in multiples of two
know how to count in multiples of five
know how to count in multiples of ten
can count to and across 100, forwards beginning with 0 or 1, or from any given number
can count, read and write numbers to 100 in numerals
can identify and represent numbers using objects and pictorial representations including the number line
can read and write numbers from 1 to 20 in words
can write mathematical statements involving addition (+), subtraction (–) and equals (=) signs
can solve one-step problems that involve addition and subtraction by doing missing number problems
can add and subtract one-digit and two-digit numbers to 20, including zero
can solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations
can read and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
can identify one more given a starting number
can identify one less given a starting number
can read and write numbers from 1 to 20 in numerals
can solve one-step problems involving division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher
can represent and use number bonds and related subtraction facts within 20
can recognise, find and name a quarter as one of four equal parts of an object
can solve one-step problems involving multiplication by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher
can recognise, find and name a quarter as one of four equal parts of a shape
can recognise, find and name a quarter as one of four equal parts of a quantity
Upon completing Stage Two pupils:
know how to count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
know the place value of each digit in a two-digit number (tens, ones)
know and can use addition and subtraction facts to 20 fluently, and derive and use related facts up to100
know that addition of two numbers can be done in any order (commutative)
know that subtraction of one number from another cannot be done in any order
know, can recall and use multiplication facts for the 2, 5 and 10x tables, including recognising odd and even numbers
know, can recall and use division facts for the 2, 5 and 10x tables, including recognising odd and even numbers
know that multiplication of two numbers can be done in any order (commutative)
know that division of one number by another cannot be done in any order
know that a fraction can be represented as ½ with a numerator and denominator or as one half
know the equivalence of fractions such as ½ and 2/4
know and can write simple fractions such as ½ of 6 = 3
can add and subtract numbers using concrete objects, pictorial representations, and mentally, including two two-digit numbers
can identify, represent and estimate numbers using different representations, including the number line
can compare and order numbers from 0 up to 100; use <, > and = signs
can add numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and tens
can subtract numbers using concrete objects, pictorial representations, and mentally, including a two digit number and tens
can read and write numbers to at least 100 in numerals and in words
can add numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and ones
can subtract numbers using concrete objects, pictorial representations, and mentally, including a two-digit number and ones
can solve problems with addition and subtraction by applying my increasing knowledge of mental methods
can add numbers using concrete objects, pictorial representations, and mentally, including three one-digit numbers
can use place value and number facts to solve problems
can use the inverse relationship between addition and subtraction to check calculations and solve missing number problems
can solve problems with addition and subtraction by applying my increasing knowledge of written methods
can subtract numbers using concrete objects, pictorial representations, and mentally, including three one-digit numbers
can recognise the inverse relationship between addition and subtraction
can solve problems with addition and subtraction involving numbers using concrete objects and pictorial representations
can solve problems with addition and subtraction involving measures using concrete objects and pictorial representations
can solve problems with addition and subtraction involving quantities using concrete objects and pictorial representations
can solve problems involving multiplication and division using multiplication and division facts including problems in contexts
can calculate mathematical statements for division within the multiplication tables
can write mathematical statements for division within the multiplication tables using the division (÷) and equals (=)
can calculate mathematical statements for multiplication within the multiplication tables
can write mathematical statements for multiplication within the multiplication tables using the multiplication (×), and equals (=) signs
can interpret and construct simple tally charts, pictograms, block diagrams and simple tables
can solve problems involving multiplication and division involving multiplication including problems in contexts
can solve problems involving multiplication and division using materials and arrays including problems in contexts
can solve problems involving multiplication and division using repeated addition including problems in contexts
can solve problems involving multiplication and division using mental methods including problems in contexts
Upon completing Stage Three pupils:
know how to count on from 0 in multiples of 4 and 8
know how to count on from 0 in multiples of 50 and 100
know that tenths arise when we divide an object into 10 equal parts and we divide numbers or quantities by 10
know how to count in tenths
know, can recall and use x and ÷ facts for the 3, 4 and 8 multiplication tables
know how to add and subtract fractions with common denominators
know how to compare unit fractions with a common denominator
know and can show equivalent fractions using diagrams
can compare and order numbers up to 1000
can add and subtract ones, tens and hundreds to a 3-digit number mentally
can find 10 or 100 more than a 3 digit number
can find 10 or 100 less than a 3 digit number
can add numbers with up to 3 digits using columnar addition
can subtract numbers up to 3 digits using formal columnar methods
can order unit fractions with a common denominator
can recognise and find fractions of sets of objects
can subtract fractions with common denominators
can read and write numbers up to a thousand in words
can read and write numbers up to a thousand in numerals
can recognise the value of each digit in a 3-digit number
can write and calculate mathematical statements for x using known facts for 2 digit and 1 digit numbers using mental methods
can write and calculate mathematical statements for x using known facts for 2 digit and 1 digit numbers using written methods
can write and calculate mathematical statements for ÷ using known facts for 2 digit and 1 digit numbers using mental methods
can write and calculate mathematical statements for x using known facts for 2 digit and 1 digit numbers using written methods
can estimate the answer to a calculation
can use inverse operations to check answers
can add and subtract amounts of money to give change, using £ and p in practical contexts
can solve problems, using number facts and/or place value
Upon completing Stage Four pupils:
know place value up to 10000
know how to count in multiples of 6, 7, 9, 25 and 1000
know Roman numerals 1-100
know that the number system changed over time to include 0
know and can recall multiplication and division facts for multiplication tables up to 12 x 12
know that hundredths arise when dividing an object into 100 equal parts and we divide numbers or quantities by 100
know how to write and recognise decimal equivalents of any number of tenths or hundredths
know how to write a recognise decimal equivalents of ¼ , ½ and ¾
know and can show families of common equivalent fractions
know how to add and subtract fractions with the same denominator beyond one whole
know how to count up and down in hundredths
can count back in stated multiples including negative numbers and through 0
can round numbers to the nearest 10, 100 and 1000
can use column methods for addition and subtraction up to 4 digits
can estimate answers and use inverse to check calculations
can solve two-step problems in different contexts, deciding which methods to use and explain reasoning
can use place value, known and derived facts to multiply and divide mentally
can use the rules of arithmetic to multiply and divide (associative, commutative and distributive)
can multiply two-digit and three-digit numbers by a one-digit number using formal written layout
can solve two step problems in context
can recognise and show, using diagrams, families of common equivalent fractions
can find non-unit fractions of quantities
can round, compare and order decimals to 2.d.p
can interpret and present discrete and continuous data using appropriate graphical methods, including barcharts and time graphs
can solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs
Upon completing Stage Five pupils:
know how to count forwards or backwards in steps of powers of 10 for any given number up to 1000000
know, use and understand the properties of numbers including–multiples, factors, prime numbers, prime factors and composite numbers
know, can identify, name and write equivalent fractions including decimals of a given fraction, represented visually, including tenths and hundredth
know the per cent symbol and that per cent relates to ‘number of parts per hundred’
know how to write percentages as hundredths and as decimals
know how to compare and order fractions whose denominators are all multiples of the same number
know how to add and subtract fractions whose denominators are all multiples of the same number
know how to convert mixed numbers and improper fractions from one to the other and use them in mathematical statements such as 2/5 + 4/5 = 6/5 = 1 1/5
know that thousands arise when we divide an object into 1000 equal parts and we divide numbers or quantities by 1000
understand place value up to 1000000
understand negative numbers in context
can round numbers up to 100000
can use column methods for addition and subtraction using numbers with than 4 digits
can estimate answers and use inverse and rounding to check accuracy of calculations
can add and subtract mentally using increasingly large numbers
can solve multi-step problems in different contexts, including decimals, deciding which methods to use and explain reasoning
can multiply and divide numbers up to 4 digits using written calculations. Interpret remainder in a context
can multiply and divide numbers mentally drawing upon known facts
can multiply and divide whole numbers and decimals by 10, 100 and 1000
can recognise and use square and cube numbers and associated notation
can solve problems with all 4 operations involving using knowledge of cube, squares, multiples, scaling and simple rates
can multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
can round, order and compare decimals to 3.d.p
can solve problems which require knowing percentage and decimal equivalents of ½, ¼,1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25
can solve comparison, sum and difference problems using information presented in a line graph
Upon completing Stage Six pupils:
know place value and can recognise the value of each digit up to 10000000 and am able to read and write them, round, order and compare
know how to round any whole number to a required degree of accuracy
know how to use the formal written method of long multiplication and can use it to multiply multi-digit numbers up to 4 digits by a two-digit whole number
know how to use the formal written method of long division and can use it to divide numbers up to 4 digits by a two-digit whole number, and interpret remainders as appropriate
know how to use common factors to simplify fractions and use common multiples to express fractions with the same denominator
know how to compare and order fractions including fractions greater than one whole
know how to add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
know how to multiply simple pairs of proper fractions
know how to divide proper fractions by whole numbers
can use negative numbers in context and calculate intervals across zero
can solve number and practical problems that involve whole and negative numbers
can solve multi-step problems in different contexts, including decimals, deciding which methods to use and explain reasoning
can perform mental calculations, including with mixed operations and large numbers
can use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
can simplify, compare, and order fractions, including fractions > 1
can use all 4 operations to solve problems involving fractions and decimals (including mixed numbers)
can calculate decimal fraction equivalents e.g.3/8= 0.375
can multiply (proper fractions) and divide (by whole numbers) and write answers in simplest form
can multiply one-digit numbers with up to two decimal places by whole numbers
can use simple formulae
can generate and describe linear number sequences
can express missing number problems algebraically
can find pairs of numbers that satisfy an equation with two unknowns
can enumerate possibilities of combinations of two variables
can interpret and construct pie charts and line graphs and use these to solve problems
can calculate and interpret the mean as an average
