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Age | Patterns and Relationships | Sorting and Analysing |

Birth - 11 Months | Notices changes in number of objects/images or sounds in group of up to 3. | |

8 - 20 Months | Develops an awareness of number names through their enjoyment of action rhymes and songs that relate to their experience of numbers. Has some understanding that things exist, even when out of sight. | |

16 - 26 Months | Knows that things exist, even when out of sight. Beginning to organise and categorise objects, e.g. putting all the teddy bears together or teddies and cars in separate piles. Says some counting words randomly. | |

22 - 36 Months | Selects a small number of objects from a group when asked, for example, ‘please give me one’, ‘please give me two’. Recites some number names in sequence. Creates and experiments with symbols and marks representing ideas of number. Begins to make comparisons between quantities. Uses some language of quantities, such as ‘more’ and ‘a lot’. Knows that a group of things changes in quantity when something is added or taken away. | |

30 - 50 Months | Uses some number names and number language spontaneously. Uses some number names accurately in play. Recites numbers in order to 10. Knows that numbers identify how many objects are in a set. Beginning to represent numbers using fingers, marks on paper or pictures. Sometimes matches numeral and quantity correctly. Shows curiosity about numbers by offering comments or asking questions. Compares two groups of objects, saying when they have the same number. Shows an interest in number problems. Separates a group of three or four objects in different ways, beginning to recognise that the total is still the same. Shows an interest in numerals in the environment. Shows an interest in representing numbers. Realises not only objects, but anything can be counted, including steps, claps or jumps. | |

40 - 60 Months | Recognise some numerals of personal significance. Recognises numerals 1 to 5. Counts up to three or four objects by saying one number name for each item. Counts actions or objects which cannot be moved. Counts objects to 10, and beginning to count beyond 10. Counts out up to six objects from a larger group. Selects the correct numeral to represent 1 to 5, then 1 to 10 objects. Counts an irregular arrangement of up to ten objects. Estimates how many objects they can see and checks by counting them. Uses the language of ‘more’ and ‘fewer’ to compare two sets of objects. Records, using marks that they can interpret and explain. Begins to identify own mathematical problems based on own interests and fascinations | |

Early Learning Goal | Children count reliably with numbers from one to 20. | |

Age 5-6 | 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 | There isn't anything in the New Primary Curriculum for this area of learning in year one, so consolidation and progression of skills in previous 5 areas need to be revisited. |

Age 6-7 | Order and arrange combinations of mathematical objects in patterns and sequences Show that multiplication of two numbers can be done in any order(commutative) and division of one number by another cannot Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication, division, and equals signs Show that addition of two numbers can be done in any order(commutative)and that subtraction from one number from another cannot | Ask and answer questions about totalling and comparing categorical data Interpret and construct simple pictograms, tally charts, block diagrams and simple tables |

Age 7-8 | 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 Estimate the answer to a calculation and use inverse operations to check answers Solve problems including missing number problems using number facts, place value, and more complex addition and subtraction | Solve one-step and 2-step questions (ie How many more? How many fewer?)using information presented in scales, bar charts and pictograms and tables Interpret and present data using bar charts, pictograms and tables |

Age 8-9 | Estimate and use inverse operations to check answers to a calculation Recognise and use factor pairs and commutativity in mental calculations Round decimals with one decimal place to the nearest whole number Solve problems involving multiplying and adding, including 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 Solve number and practical problems with increasingly large positive numbers Find the effect of dividing a one-digit or two-digit number by 10 and 100, identifying the value of the digit in the answer as ones, tenths and hundredths. Read Roman numerals to 100 and know that over time, the numeral system changed to include the concept of zero and place value Round any number to the nearest 10, 100 or 1000 Recognise the place value of each digit in a four-digit number(thousands, hundreds, tens and ones) | Interpret and present discrete and continuous data using appropriate mathematical and graphical methods including bar charts and time graphs Solve comparison, sum and difference problems using information presented in bar charts, pictograms and other graphs |

Age 9-10 | Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes Know and use the vocabulary of prime numbers, prime factors and composite(non-prime) numbers Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why Read Roman numerals to 1000 and recognise years written in Roman Numerals Establish whether a number up to 100 is prime and recall prime numbers to 19 Solve problems, involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign | Solve comparison, sum and difference problems using information presented in a line graph |

Age 10-11 | Identify the value of each digit in numbers given to 3 decimal places and multiply and divide by 10, 100, 1000 giving answers up to three decimal places Use simple formulae Generalisations of number patterns Equivalent expressions(for example a + b = b + a) Enumerate possibilities of combinations of two variables Identify common factors, common multiples and common primes Express missing number problems algebraically Number puzzles( for example what two numbers can add up to) Use their knowledge of the order of operations to carry out calculations involving the four operations Generate and describe linear number sequences Find pairs of numbers that satisfy an equation with two numbers | Interpret and construct pie charts and line graphs and use these to solve problems Calculate and interpret the mean as an average |

KS3 | Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property Recognise and use relationships between operations including inverse operations Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations Use and interpret algebraic notation, including: ab in place of a × b 3y in place of y + y + y and 3 × y a2 in place of a × a, a3 in place of a × a × a; a2 b in place of a × a × b ba in place of a ÷ b coefficients written as fractions rather than as decimals brackets Substitute numerical values into formulae and expressions, including scientific formulae Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors Simplify and manipulate algebraic expressions to maintain equivalence by: collecting like terms multiplying a single term over a bracket taking out common factors expanding products of two or more binomials Understand and use standard mathematical formulae; rearrange formulae to change the subject Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement) | Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities. Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data Describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs |