## Level 1

L1/1 | 1 | Count reliably up to 10 everyday objects: first to 5, then 10 |

L1/2 | 2 | Read, write numbers to 10: perhaps with some reversals |

L1/3 | 3 | Order numbers to 10: one more/less, ascending/descending order, point to first, second object etc |

L1/4 | 4 | Begin to use the fraction one-half: half shapes by folding, fill containers half full, halve an even number of objects etc |

L1/5 | 5 | Understand addition as finding the total of two or more sets of objects |

L1/6 | 6 | Understand subtraction as ‘taking away’ objects from a set and finding how many are left |

L1/7 | 7 | Add and subtract numbers of objects to 10 |

L1/8 | 8 | Begin to use some addition facts: doubles of numbers to double 5 |

L1/9 | 9 | Solve addition/subtraction problem involving up to 10 objects: how many more to make..., how many balance with..., coin values to 10p, solve money problems etc |

L1/10 | 10 | Record work with objects, pictures, diagrams |

L1/11 | 11 | Begin to use symbols ‘+’ and ‘=’ to record additions |

L1/12 | 12 | Use everyday language to describe properties of 2D and 3D shapes: sort shapes, refer to features- sides, corners, use properties-large, small, roll, stack etc |

L1/13 | 13 | Use everyday language to describe positions of 2D and 3D shapes: positional language-‘behind, under, on top of, next to, in between etc |

L1/14 | 14 | Use everyday language to describe positions of 2D and 3D shapes: directional language-forwards, backwards, turn etc |

L1/15 | 15 | Measure & order objects using direct comparison: order objects by length (longer/shorter), weight (heavier/lighter), capacity (holds more/less than 1 litre etc) |

L1/16 | 16 | Order events: describe the sequence of everyday events- breakfast, morning play, lunch etc |

L1/17 | 17 | Order events: Use the vocabulary of time including days of the week- today, tomorrow, yesterday etc |

L1/18 | 18 | Order events: read the time on an analogue clock at the hour and begin to know the half hour |

L1/19 | 19 | Sort objects using one criterion or into disjoint sets using two criteria: boy/girl, thick/thin etc |

L1/20 | 20 | Sort objects into a given large scale Venn or Carroll diagram |

L1/21 | 21 | Use objects/pictures to create simple block graphs |

L1/22 | 22 | Demonstrate the criterion used: talk about how they have sorted objects and why each belongs in a set |

L1/23 | 23 | Talk about which set has most: most children stayed for lunch etc |

## Level 2

L2/1 | 1 | Count sets of objects reliably: group objects in tens, twos or fives to count them |

L2/2 | 2 | Understand and use place value for integers to order numbers up to 100: know relative size of numbers to 100, use 0 as a place holder. |

L2/3 | 3 | Recognise and continue sequences of numbers, including odd and even numbers: increasing/decreasing in regular steps, counting in tens or twos |

L2/4 | 4 | Know by heart the two, five and ten times tables |

L2/5 | 5 | Begin to use halves and quarters: sharing sweets between 2 or 4,work out halves of numbers to 20, shade half/quarter of a shape etc |

L2/6 | 6 | Use the knowledge that subtraction is the inverse of addition: 6+8 = 14, 14–8 = 6, 8+6 = 14, 14-8 = 8 |

L2/7 | 7 | Understand halving as a way of ‘undoing’ doubling and vice versa: double 4 is 8, half of 8 is 4 |

L2/8 | 8 | Use mental recall of addition and subtraction facts to 10: know 3+7 = 10 and use place value to derive 30+70 = 100 |

L2/9 | 9 | Use mental calculation strategies to solve number problems including those involving money and measures: recall doubles to 10+10, double 50p is £1 etc |

L2/10 | 10 | Choose the appropriate operation when solving addition and subtraction problems: repeated addition to solve multiplication problems, repeated subtraction for sharing |

L2/11 | 11 | Solve number problems involving money and measures: add/subtract two-digit and one-digit numbers, using units such as pence, pounds, centimetres |

L2/12 | 12 | Record work in writing: record mental calculations as number sentences |

L2/13 | 13 | Use mathematical names for common 3-D and 2-D shapes: square, triangle, hexagon, pentagon, octagon, cube, cylinder, sphere, cuboid, pyramid |

L2/14 | 14 | Describe their properties, including numbers of sides and corners: edge, face, corner; sort shapes to a single criterion i.e. pentagons, shapes with a right angle etc |

L2/15 | 15 | Describe the position of objects: first, second, third, upside down |

L2/16 | 16 | Distinguish between straight and turning movements: left/right, clockwise/anti clockwise |

L2/17 | 17 | Recognise right angles in turns and understand angle as a measurement of turn: whole turns/half turns/quarter turns |

L2/18 | 18 | Begin to use everyday non-standard and standard units to measure length and mass: hand widths, cm/m/g, read scales to the nearest labelled division |

L2/19 | 19 | Sort objects and classify them using more than one criterion: sort shapes into triangle/not triangle and blue/not blue |

L2/20 | 20 | Understand vocabulary relating to handling data: sort, group, set, list, table, most common, most popular |

L2/21 | 21 | Collect and sort data to test a simple hypothesis: count a show of hands to test “Most children in our class are in bed by 7.30pm” |

L2/22 | 22 | Enter data into a simple computer database |

L2/23 | 23 | Record and communicate findings, using the simple lists, tables, pictograms and block graphs |

## Level 3

L3/1 | 1 | Understand and use place value for integers to order numbers up to 1000: represent numbers using number lines, 100 squares etc, multiply/divide whole numbers by 10 |

L3/2 | 2 | Recognise negative numbers in contexts such as temperature |

L3/3 | 3 | Recognise a wider range of sequences: multiples of 2, 5, 10 |

L3/4 | 4 | Understand and use simple fractions; ½, ¼, ⅟₃, ⅟₅, ⅟₁₀ ; those that are several parts of a whole; ¾, ⅖ and recognise some fractions equivalent to ½ (⁵⁄₁₀ etc) |

L3/5 | 5 | Begin to use decimal notation in contexts such as money: order decimals with one or two dp, know that £3.06 = 306p |

L3/6 | 6 | Know by heart the three, four and six times tables |

L3/7 | 7 | Derive associated division facts from known multiplication facts: if 14 x 5 = 70 then 70 ÷ 5 = 14 and 70 ÷ 14 = 5 |

L3/8 | 8 | Begin to understand the role of ‘=’ when solving ‘balancing’ problems: 7 x 10 = 82 - □ |

L3/9 | 9 | Add and subtract two-digit numbers mentally: 36 + 19, 63 - 26 |

L3/10 | 10 | Use mental recall of addition/subtraction facts to 20 in solving problems involving larger numbers |

L3/11 | 11 | Solve whole number word problems including those involving multiplication or division that may give rise to remainders: identify appropriate operations/ round up or down |

L3/12 | 12 | Add and subtract three digit numbers using written method: 132 + 239 : 327 – 119 using carrying and decomposition methods |

L3/13 | 13 | Multiply and divide two digit numbers by 2, 3, 4 or 5 as well as 10 with whole number answers and remainders: 22÷5 = 4 r 2 |

L3/14 | 14 | Classify 3-D and 2-D shapes in various ways using mathematical properties such as reflective symmetry for 2-D shapes |

L3/15 | 15 | Begin to recognise nets of familiar 3-D shapes: cube, cuboid, triangular prism, square-based pyramid |

L3/16 | 16 | Recognise shapes in different orientations and reflect shapes, presented on a grid, in a vertical or horizontal mirror line or at 45 degrees to the mirror line |

L3/17 | 17 | Describe position and movement: left/right, clockwise/anticlockwise/quarter turns /90degrees to give directions along a route |

L3/18 | 18 | Use standard units in a range of contexts (length, capacity and mass): measure length to nearest ½ cm, read simple scales, read a 12 hour clock |

L3/19 | 19 | Use a wider range of measures: find areas of shapes by counting squares, angles as measure of turn, perimeter as a measure of length |

L3/20 | 20 | Gather information: decide what data to collect, make appropriate choice of tally chart, frequency table etc |

L3/21 | 21 | Construct bar charts and pictograms, where the symbol represents a group of units |

L3/22 | 22 | Use Venn and Carroll diagrams to record their sorting and classifying of information: shapes sorted using properties such as right angles and equal sides. |

L3/23 | 23 | Extract and interpret information presented in simple tables, lists, bar charts and pictograms: use keys, read scales, compare data etc |

## Level 4

L4/1 | 1 | Recall multiplication facts up to 10 × 10 and quickly derive corresponding division facts: Gold Standard |

L4/2 | 2 | Recognise and describe number relationships including multiple, factor and square: 5 is factor of 20, 20 is multiple of 5 |

L4/3 | 3 | Use place value to multiply and divide whole numbers by 10 or 100: 342 x 10 = 3420 2456 ÷ 100 = 24.56 |

L4/4 | 4 | Recognise approximate proportions of a whole and use simple fractions/percentages to describe these: simple equivalence between fractions, decimals and percentages |

L4/5 | 5 | Convert mixed numbers to improper fractions and vice versa: 1¾ = 7/4 etc |

L4/6 | 6 | Solve problems with or without a calculator: solve two step problems choosing appropriate operations, interpret calculator display of 4.5 as £4.50 |

L4/7 | 7 | Use efficient written methods of addition and subtraction: column addition, subtraction and of short multiplication and division: TU x U, HTU x U, HTU ÷ U |

L4/8 | 8 | Add and subtract decimals to two places and multiply a simple decimal by a single digit: 36.2 x 8 |

L4/9 | 9 | Simplify ratio |

L4/10 | 10 | Begin to understand simple ratio: girls to boys ratio = 2 to 3 so 20 girls means 30 boys |

L4/11 | 11 | Recognise and describe number patterns: continue sequences involving decimals 1.3, 1.6, 1.9, 2.2, etc |

L4/12 | 12 | Use inverse operations: ‘undo’ two step operations, understand ‘balancing’ sums 20 + □ = 100 ÷ 4 |

L4/13 | 13 | Understand the use of brackets in simple calculations: brackets take priority in calculation (3 x 4) + 14 12 + 14 = 26 |

L4/14 | 14 | Use and interpret coordinates in the first quadrant |

L4/15 | 15 | Use the properties of 2-D and 3-D shapes: recognise most quadrilaterals, all triangles, oblique lines of symmetry, use terms horizontal, vertical, congruent |

L4/16 | 16 | Reflect simple shapes in a mirror line: at 45 degrees to the mirror line, begin to use the distance of vertices from mirror line to reflect more accurately |

L4/17 | 17 | Translate shapes horizontally or vertically and begin to rotate a simple shape or object about its centre or a vertex |

L4/18 | 18 | Interpret, with appropriate accuracy, numbers on a range of measuring instruments: measure to within 2mm, measure acute and obtuse angles to nearest 5 degrees |

L4/19 | 19 | Find perimeters of simple shapes and find areas by counting squares and part squares: begin to find areas shapes that need dividing into rectangles |

L4/20 | 20 | Collect, record and group discrete data: test a hypothesis about the frequency of an event (how many 6s in 50 throws of a die), record using frequency table |

L4/21 | 21 | Continue to use Venn and Carroll diagrams to record their sorting and classifying of information: sorting numbers ‘multiples of 8’ and ‘multiples of 6’ |

L4/22 | 22 | Construct and interpret frequency diagrams and simple line graphs: interpret simple pie charts, scale on bar graphs reading between the labelled divisions etc |

L4/23 | 23 | Understand and use the mode and range to describe sets of data:mode = most common, range = highest – lowest |

L4/24 | 24 | Understand the language of probability: more likely, equally likely, fair, unfair, certain, impossible etc |

## Level 5

L5/1 | 1 | Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 and 1000 and explain the effect: 2.6 x 1000 : 2.6 ÷ 100 |

L5/2 | 2 | Round decimals to the nearest decimal place and order negative numbers in context: 38.47 = 38.5 to 1 d.p. |

L5/3 | 3 | Recognise and use number patterns and relationships: say whether much larger numbers will be in the sequence or not |

L5/4 | 4 | Use equivalence between fractions and order fractions and decimals: convert fractions such as 2/5 into tenths or hundredths/express as decimals or percentages |

L5/5 | 5 | Reduce a fraction to its simplest form by cancelling common factors: 16/20 = 8/10 = 4/5 |

L5/6 | 6 | Use known facts, place value, knowledge of operations and brackets to calculate including using all four operations with decimals to two places |

L5/7 | 7 | Use a calculator where appropriate to calculate fractions/percentages of quantities/measurements: 3/8 of 400g or 60% of £300 |

L5/8 | 8 | Understand and use an appropriate non-calculator method for solving problems that involve multiplying and dividing any three digit number by any two-digit number |

L5/9 | 9 | Solve simple problems involving ordering, adding, subtracting negative numbers in context |

L5/10 | 10 | Solve simple problems involving ratio and direct proportion: use multiplication rather than trial and error |

L5/11 | 11 | Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1 |

L5/12 | 12 | Solve problems involving the conversion of units and make sensible estimates of a range of measures in relation to everyday situations |

L5/13 | 13 | Apply inverse operations and approximate to check answers to problems are of the correct magnitude |

L5/134 | 14 | Use a wider range of properties of 2-D and 3-D shapes: name quadrilaterals, recognise right angled, equilateral, isosceles etc parallel, perpendicular, no. of faces/vertices |

L5/15 | 15 | Identify all the symmetries of 2-D shapes: reflective, rotational etc |

L5/16 | 16 | Use language associated with angle and know and use the angle sum of a triangle and that of angles at a point: acute, obtuse, reflex: triangle 180˚: point 360˚ |

L5/17 | 17 | Reason about position and movement and transform shapes: visualise 3D shapes from nets; transfer patterns from shapes to nets, draw shapes with given lines of symmetry |

L5/18 | 18 | Measure and draw angles to the nearest degree, when constructing models and drawing or using shapes |

L5/19 | 19 | Read and interpret scales on a range of measuring instruments, explaining what each labelled division represents: thermometer, scales, measuring cylinder, ruler etc |

L5/20 | 20 | Understand and use the formula for the area of a rectangle and distinguish area from perimeter: find length given perimeter and width/find area/perimeter of simple L shapes |

L5/21 | 21 | Understand and use the probability scale from 0 to 1: 0-impossible, 1-certain, 0.5-equally likely, 0.2-unlikely, etc |

L5/22 | 22 | Understand and use the mean of discrete data and compare two simple distributions, using the range and one of mode, median or mean |

L5/23 | 23 | Understand that different outcomes may result from repeating an experiment: rolling a die 36 times may give different no of sixes rolled but probability stays 1 in 6 |

L5/24 | 24 | Interpret graphs and diagrams, including pie charts and line graphs (where the intermediate values have meaning), and draw conclusions |

## Level 6

L6/1 | 1 | Use the equivalence of fractions, decimals and percentages to compare proportions |

L6/2 | 2 | Calculate percentages and find the outcome of a given percentage increase or decrease |

L6/3 | 3 | Divide a quantity into two or more parts in a given ratio and solve problems involving ratio and direct proportion |

L6/4 | 4 | Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole |

L6/5 | 5 | Add and subtract fractions by writing them with a common denominator, calculate fractions of quantities (fraction answers), multiply and divide an integer by a fraction |

L6/6 | 6 | Use scale factors, scale diagrams and maps |

L6/7 | 7 | Use systematic trial and improvement methods and ICT tools to find approximate solutions to equations such as x³ + x = 20 |

L6/8 | 8 | Construct and solve linear equations with integer coefficients, using an appropriate method |

L6/9 | 9 | Generate terms of a sequence using term-to-term and position-to-term definitions, on paper and using ICT; write an expression to describe the nth term of a sequence |

L6/10 | 10 | Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straight-line graphs |

L6/11 | 11 | Construct functions arising from real-life problems and plot their corresponding graphs |

L6/12 | 12 | Interpret graphs arising from real situations |

L6/13 | 13 | Classify quadrilaterals by their geometric properties |

L6/14 | 14 | Solve geometric problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons |

L6/15 | 15 | Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360° |

L6/16 | 16 | Devise instructions for a computer to generate and transform shapes and paths |

L6/17 | 17 | Visualise and use 2D representations of 3D objects |

L6/18 | 18 | Enlarge 2D shapes, given a centre of enlargement and a positive whole-number scale factor |

L6/19 | 19 | Know that translations and reflections preserve length and angle and map objects onto congruent images |

L6/20 | 20 | Use straight edge and compasses to do standard constructions |

L6/21 | 21 | Deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid; calculate volumes and surface areas of cuboids |

L6/22 | 22 | Know and use the formulae for the circumference and area of a circle |

L6/23 | 23 | Draw, measure and calculate three figure bearings |

L6/24 | 24 | Design a survey/experiment to capture the necessary data from one/more sources; trial and refine data collection sheets; construct tables for large discrete and continuous sets of raw data, choosing suitable class intervals; design and use two-way tables |

L6/25 | 25 | Select, construct and modify, on paper/ICT: pie charts for categorical data; bar charts/ frequency diagrams for discreet/continuous data; simple time graphs for time series; scatter graphs, and identify which are the most useful in the context of the problem |

L6/26 | 26 | Find and record all possible mutually exclusive outcomes for single and two successive events in a systematic way |

L6/27 | 27 | Know that the sum of all mutually exclusive outcomes is 1 and use this when solving problems |

L6/28 | 28 | Communicate interpretations and results of a statistical survey using selected tables, graphs and diagrams in support |

## Level 7

L7/1 | 1 | Understand and use proportionality |

L7/2 | 2 | Calculate the result of any proportional change using multiplicative methods |

L7/3 | 3 | Understand the effects of multiplying and dividing by numbers between 0 and 1, add, subtract, multiply and divide fractions |

L7/4 | 4 | Make and justify estimates and approximations of calculations; estimate calculations by rounding numbers to one significant figure and multiplying and dividing mentally |

L7/5 | 5 | Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation |

L7/6 | 6 | Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals |

L7/7 | 7 | Square a linear expression and expand and simplify the product of two linear expressions of the form (x ± n) and simplify the corresponding quadratic equation |

L7/8 | 8 | Use linear graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations. Solve simultaneous equations algebraically. |

L7/9 | 9 | Solve inequalities in one variable and represent the solution set on a number line |

L7/10 | 10 | Use formulae from mathematics and other subjects; substitute numbers into expressions and formulae; derive a formulae and, in simple cases, change its subject |

L7/11 | 11 | Find the next term and nth term of quadratic sequences and functions and explore their properties |

L7/12 | 12 | Understand and use measures of speed (and other compound measures such as density or pressure) to solve problems |

L7/13 | 13 | Plot graphs of simple quadratic and cubic functions, e.g. y = x², y = 3x² + 4, y = x³ |

L7/14 | 14 | Understand and apply Pythagoras’ theorem when solving problems in 2D |

L7/15 | 15 | Calculate lengths, areas and volumes in plane shapes and right prisms |

L7/16 | 16 | Enlarge 2D, given a centre of enlargement and a fractional scale factor, on paper and using ICT; recognise the similarity of the resulting shapes |

L7/17 | 17 | Find the locus of a point that moves according to a given rule, both by reasoning and using ICT |

L7/18 | 18 | Recognise that measurements given to the nearest whole unit may be accurate by up to one-half of the unit in either direction |

L7/19 | 19 | Suggest a problem to explore using statistical methods, frame questions and raise conjectures; identify possible sources of bias and plan how to minimise it |

L7/20 | 20 | Select, construct and modify, on paper/using ICT suitable graphical representation to progress an enquiry including frequency polygons and lines of best fit on scatter graphs |

L7/21 | 21 | Estimate the mean, median and range of a set of grouped data and determine the modal class, selecting the statistic most appropriate to the line of enquiry |

L7/22 | 22 | Compare two or more distributions and make inferences, using the shape of the distributions and measures of average and range |

L7/23 | 23 | Understand relative frequency as an estimate of probability and use this to compare outcomes of an experiment |

L7/24 | 24 | Examine critically the results of a statistical enquiry, and justify the choice of statistical representation in written presentation |

## Level 8

L8/1 | 1 | Understand the equivalence between recurring decimals and fractions. Work interchangably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8). |

L8/2 | 2 | Use integer powers and associated real roots (square, cube and higher), recognise powers of 2,3,4,5 and distringuish between exactly representations of roots and their decimal approximations. Interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero. |

L8/3 | 3 | Solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics. |

L8/4 | 4 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations. |

L8/5 | 5 | Factorise quadratic expressions including the difference of two squares. |

L8/6 | 6 | Manipulate algebraic formulae, equations and expressions, finding and multiplying two linear expressions |

L8/7 | 7 | Understand and use standard mathematical formulae; rearrange formulae to change the subject. |

L8/8 | 8 | Evaluate algebraic formulae, substituting decimals, fractions and negative numbers |

L8/9 | 9 | Solve inequalities in two variables and find the solution set |

L8/10 | 10 | Sketch, interpret and identify graphs of linear, quadratic, cubes & reciprocal functions. Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs. |

L8/11 | 11 | Understand the effect on a graph of addition of (or multiplication by) a constant |

L8/12 | 12 | Use quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations. |

L8/13 | 13 | Simplify and manipulate algebraic expressions to maintain equivalence by expanding products of two or more binomials. |

L8/14 | 14 | Understand and use congruence and mathematical similarity |

L8/15 | 15 | Understand and use trigonometrical relationships in right angled triangles, and use them to solve problems, including those involving bearings |

L8/16 | 16 | Understand the difference between formulae for perimeter, area and volume in simple contexts by considering dimensions |

L8/17 | 17 | Estimate and find the median, quartiles and inter-quartile range for large data sets, including using a cumulative frequency diagram |

L8/18 | 18 | Compare two or more distributions and make inferences, using the shape of the distributions and measures of average and spread including median and quartiles |

L8/19 | 19 | Know when to add and when to multiply two probabilities |

L8/20 | 20 | Use tree diagrams to calculate probabilities of combinations of independent events |