## Grade U

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

U/2 | 2 | Begin to understand the place value of each digit; use this to order numbers up to 100: know relative size of numbers to 100, use 0 as a place holder |

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

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

U/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 |

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

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

U/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 |

U/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 |

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

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

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

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

U/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 |

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

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

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

U/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 |

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

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

U/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” |

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

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

## Grade E

E/1 | 1 | Use understanding of place value to multiply & divide by 10, 100 and 1000 |

E/2 | 2 | Use equivalence between fractions and decimals and use to order fractions and decimals |

E/3 | 3 | Understand order of operations to find the value of a numerical expression |

E/4 | 4 | Understand and use index notation and roots with and without a calculator |

E/5 | 5 | Reduce a fraction or ratio to its simplest form by cancelling common factors |

E/6 | 6 | Add & subtract fractions with the same denominator and multiply fractions |

E/7 | 7 | Calculate fractions/percentages of quantities/measurements: 3/8 of 400g or 60% of £300 |

E/8 | 8 | Add and subtract including decimals Multiply & divide including decimals |

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

E/10 | 10 | Recognise and use number patterns and relationships: say whether much larger numbers will be in the sequence or not |

E/11 | 11 | Manipulate expressions by collecting like terms Substitute into simple formulae/expressions including negative numbers |

E/12 | 12 | Set up and solve simple equations |

E/13 | 13 | Identify all the symmetries of 2-D shapes: reflective, rotational etc |

E/14 | 14 | Use language associated with angle and know and use the angle sum of a triangle and quadrilateral |

E/15 | 15 | Describe & transform shapes; reflect ion in axes, enlargement (no centre), tessellation |

E/16 | 16 | 2D representations of 3D shapes: nets and isometric drawings |

E/17 | 17 | Read & interpret graphs and timetables |

E/18 | 18 | Solve problems involving the conversion of units and make sensible estimates of a range of measures in relation to everyday situations |

E/19 | 19 | Understand and use the formula for the area of a rectangle and distinguish area from perimeter. Calculate volume in simple cases |

E/20 | 20 | Calculate probability as a number including simple probability of event not happening |

E/21 | 21 | Calculate median mode mean and range |

E/22 | 22 | List outcomes for single events and for two successive events, in a systematic way |

E/23 | 23 | Draw & interpret graphs and diagrams, including pie charts and line graphs |

## Grade B

B/1 | 1 | Understand the equivalence between recurring decimals and fractions |

B/2 | 2 | Use fractions or percentages to solve problems involving repeated proportional changes or the calculation the original quantity given the result of a proportional change |

B/3 | 3 | Solve problems involving calculating with powers, roots and numbers expressed in standard form, checking for correct order of magnitude and using a calculator as appropriate |

B/4 | 4 | Factorise quadratic expressions including the difference of two squares |

B/5 | 5 | Manipulate algebraic formulae, equations and expressions, finding and multiplying two linear expressions |

B/6 | 6 | Derive & use more complex formulae and change the subject of the formula |

B/7 | 7 | Evaluate algebraic formulae, substituting decimals, fractions and negative numbers |

B/8 | 8 | Solve simultaneous equations algebraically and graphically |

B/9 | 9 | Solve more complex inequalities. Solve inequalities in two variables and represent the solution as a region |

B/10 | 10 | Sketch, interpret and identify graphs of linear, quadratic, cubes & reciprocal functions and graphs that model real life situations |

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

B/12 | 12 | Identify and specify coordinates in 3D |

B/13 | 13 | Understand and use congruence and mathematical similarity |

B/14 | 14 | Understand and use trigonometrical relationships in right angled triangles, and use them to solve problems, including those involving bearings |

B/15 | 15 | Find the upper & lower bounds of simple calculations (addition & subtraction) involving quantities given to a particular degree of accuracy |

B/16 | 16 | Estimate and find the median, quartiles and inter-quartile range for large data sets, including using a cumulative frequency diagram |

B/17 | 17 | Compare two or more distributions and make inferences, using the shape of the distributions and measures of average and spread including median and quartiles |

B/18 | 18 | Know when to add and when to multiply two probabilities |

B/19 | 19 | Use tree diagrams to calculate probabilities of combinations of independent events |

## Grade G

G/1 | 1 | Understand place value in numbers to 1000:inc multiply/divide whole numbers by 10 and rounding to nearest 10 etc |

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

G/3 | 3 | Recognise percentage and simple equivalence of fractions and decimals |

G/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) |

G/5 | 5 | Understand place value in decimals: order decimals with one or two decimal points, know that £3.06 = 306p |

G/6 | 6 | Derive associated division facts from known multiplication facts: if 14 x 5 = 70 then 70 ÷ 5 = 14 and 70 ÷ 14 = 5 |

G/7 | 7 | Add and subtract two-digit numbers mentally: 36 + 19, 63 - 26 |

G/8 | 8 | Add and subtract up to three digit numbers using written method: 132 + 239 : 327 – 119 using carrying and decomposition methods |

G/9 | 9 | Multiply and divide two digit numbers by a single digit with whole number answers and remainders: 22÷5 = 4 r 2 |

G/10 | 10 | Solve whole number word problems including those involving multiplication or division that may give rise to remainders: identify appropriate operations/ round up or down |

G/11 | 11 | Recognise special numbers & sequences: multiples, factors, odds, evens |

G/12 | 12 | Begin to understand the role of ‘=’ when solving ‘balancing’ problems: 7 x 10 = 82 – |

G/13 | 13 | Use coordinates to describe position in the first quadrant |

G/14 | 14 | Recognise & name types of angles, lines and parts of a circle |

G/15 | 15 | Name 2D shapes & identify their properties |

G/16 | 16 | Name 3D shapes & identify their properties |

G/17 | 17 | Reflect a shape in a vertical or horizontal line and visualise in different orientations |

G/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 |

G/19 | 19 | Find area, perimeter & volume by counting |

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

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

G/22 | 22 | Extract and interpret information presented in simple tables, lists, bar charts and pictograms: use keys, read scales, compare data etc |

G/23 | 23 | Understand & use a probability scale |

## Grade D

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

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

D/3 | 3 | Write ratio notation and solve problems involving ratio and proportion |

D/4 | 4 | Use a given calculation to work out another; estimate and use a calculator efficiently to perform complex calculations |

D/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 |

D/6 | 6 | Manipulate algebraic expressions by multiplying a single term over a single bracket and by taking out a common factor |

D/7 | 7 | Construct and solve linear equations with integer coefficients, using an appropriate method |

D/8 | 8 | Generate terms of a sequence using term-to-term rule and from a given nth term |

D/9 | 9 | Plot the graphs of linear functions; recognise that equations of the form y = mx + c correspond to straight-line graphs |

D/10 | 10 | Use the convention of coordinates in a plane to describe the midpoint of a line segment |

D/11 | 11 | Derive and substitute numbers into a formula |

D/12 | 12 | Know and use bearings to solve problems by calculation and drawing |

D/13 | 13 | Solve geometric problems using angle facts associated with parallel and intersecting lines |

D/14 | 14 | Solve geometric problems using angle facts about interior and exterior angles of polygons |

D/15 | 15 | Construct triangles accurately |

D/16 | 16 | Visualise and use 2D representations of 3D objects inc nets |

D/17 | 17 | Enlarge 2D shapes, given a centre of enlargement and a positive whole-number scale factor |

D/18 | 18 | Know that translations (no vector), rotations and reflections preserve length and angle and map objects onto congruent images |

D/19 | 19 | Know and use formulae for areas involving triangle, rectangle. parallelogram, trapezium |

D/20 | 20 | Calculate volumes and surface areas of simple solids |

D/21 | 21 | Know and use the formulae for the circumference and area of a circle |

D/22 | 22 | 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 |

D/23 | 23 | Construct and interpret data; stem & leaf diagrams; scatter graphs, and identify which is the most useful in the context of the problem |

D/24 | 24 | Interpret a table of discrete data using mean, median, mode & range |

D/25 | 25 | Communicate interpretations and results of a statistical survey by comparing distributions using mean and range |

D/26 | 26 | Know that the sum of all mutually exclusive outcomes is 1 and use this when solving problems |

## Grade A

A/1 | 1 | Use fractional and negative indices |

A/2 | 2 | Manipulate simple surds |

A/3 | 3 | Determine the bounds of intervals |

A/4 | 4 | Understand and use direct and inverse proportion |

A/5 | 5 | Solve quadratic equations by factorising |

A/6 | 6 | Solve quadratic equations by using the quadratic formula(a =1 ) |

A/7 | 7 | Combine algebraic fractions (all 4 operations) |

A/8 | 8 | Solve equations involving fractions |

A/9 | 9 | Solve a pair of simultaneous equations, one linear and one quadratic Solve graphically simultaneous equations, one linear and one quadratic |

A/10 | 10 | Draw the graph of the exponential function |

A/11 | 11 | Draw the graph of the circle |

A/12 | 12 | Draw the graphs of trigonometric functions |

A/13 | 13 | Derive & use more complex formulae; change the subject (inc .subject occurs twice) |

A/14 | 14 | Enlarge a shape by a fractional & negative scale factor |

A/15 | 15 | Understand and use SSS, SAS, ASA, RHS conditions to prove triangles congruent |

A/16 | 16 | Find the volume & area of similar solids. |

A/17 | 17 | Understand & use Pythagoras Theorem to solve 3D problems Use trig ratios in 3D shapes |

A/18 | 18 | Solve problems involving SA & volume of cylinders, pyramids, cones & spheres |

A/19 | 19 | Understand & use the formulae for length of arcs and area & perimeter of sectors Area of segment |

A/20 | 20 | Know & use circle theorems |

A/21 | 21 | Select and justify a sampling scheme |

A/22 | 22 | Use, interpret & compare histograms including those with unequal class intervals |

A/23 | 23 | Recognise when & how to work with probabilities associated with independent & mutually exclusive events |

## Grade F

F/1 | 1 | Recognise and describe number relationships including multiple, factor, prime and square and cube |

F/2 | 2 | Multiply & divide a 3 digit number by a 2 digit number |

F/3 | 3 | Use rounding to estimate answers |

F/4 | 4 | Order simple fractions, decimals and percentages using equivalence |

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

F/6 | 6 | Begin to understand simple ratio: girls to boys ratio = 2 to 3 so 20 girls means 30 boys |

F/7 | 7 | Solve problems with or without a calculator: solve two step problems choosing appropriate operations, interpret calculator display of 4.5 as £4.50 |

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

F/9 | 9 | Write a simple algebraic expression |

F/10 | 10 | Simplify an expression by collecting like terms |

F/11 | 11 | Simple substitution into an expression or word formula |

F/12 | 12 | Recognise the rule for a sequence; find the missing number or pattern in a sequence |

F/13 | 13 | Use rules in number machines |

F/14 | 14 | Solve simple equations using a letter for the unknown |

F/15 | 15 | Plot and read coordinates in four quadrants |

F/16 | 16 | Understand angle properties on straight line and about a point |

F/17 | 17 | Use the properties of 2-D and 3-D shapes: recognise most quadrilaterals, all triangles, Including faces, edges, vertices |

F/18 | 18 | Reflect simple shapes in a mirror line at 45 degrees Translate shapes & begin to rotate a simple shape about its centre or a vertex |

F/19 | 19 | Interpret a range of measuring instruments Estimate and measure angles and use the 3 letter notation for angle |

F/20 | 20 | Find perimeters and area of simple shapes; begin to find areas of shapes that need dividing into rectangles |

F/21 | 21 | Use Venn and Carroll diagrams to sort and classify information: |

F/22 | 22 | Understand and use the mode and range to describe sets of data: |

F/23 | 23 | Calculate probability of outcome of an event |

## Grade C

C/1 | 1 | Use a multiplier to work out a percentage increase or decrease Write one quantity as a percentage of another |

C/2 | 2 | Divide an amount into a given ratio |

C/3 | 3 | Add, subtract, multiply and divide fractions involving mixed numbers |

C/4 | 4 | Estimate calculations by rounding numbers to one significant figure and multiplying and dividing mentally including numbers between 0 and 1 |

C/5 | 5 | Find HCF and LCM; Express a number as the product of prime factors |

C/6 | 6 | Expand brackets and simplify expressions; more complex factorisation |

C/7 | 7 | Apply the laws of indices |

C/8 | 8 | Solve inequalities in one variable and represent the solution set on a number line Use systematic trial and improvement to find approximate solutions of equations |

C/9 | 9 | Substitute numbers into more complex expressions/ formulae; derive a formulae and, in simple cases, change its subject |

C/10 | 10 | Find and use the nth term of linear sequences |

C/11 | 11 | Use ‘m’ and ‘c’ to write down the equation of a straight line graph Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions |

C/12 | 12 | Understand and apply Pythagoras’ theorem when solving problems in 2D |

C/13 | 13 | Calculate lengths, areas and volumes in plane shapes and right prisms including volume of cylinder/surface area of cylinder Convert units of area and volume |

C/14 | 14 | Describe and transform 2-D shapes; distinguish properties that are preserved under particular transformations |

C/15 | 15 | Use constructions and draw loci |

C/16 | 16 | Recognise that measurements given to the nearest whole unit may be accurate by up to one-half of the unit in either direction |

C/17 | 17 | Understand and use compound measures such as speed |

C/18 | 18 | Design and criticise questions in a questionnaire |

C/19 | 19 | Use & draw frequency polygons |

C/20 | 20 | 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 |

C/21 | 21 | Compare two or more distributions and make inferences |

C/22 | 22 | Calculate the relative frequency from experimental evidence and compare with theoretical probability .Use probability to predict outcomes |

C/23 | 23 | Use lines of best fit on scatter graphs to make predictions |

## Grade A*

A*/1 | 1 | Manipulate expressions containing surds Rationalise a denominator |

A*/2 | 2 | Determine the bounds of intervals and use in complex calculations |

A*/3 | 3 | Solve quadratic equations by using the quadratic formula (including a ≠1) |

A*/4 | 4 | Complete the square to solve quadratic equations |

A*/5 | 5 | Simplify algebraic fractions by factorising and cancelling |

A*/6 | 6 | Transform graphs of functions, using y = f(x)+a, y = f(x + a), y = f(ax) and y = af(x) & trigonometric functions |

A*/7 | 7 | Find the volume & surface area of similar solids and use to solve related problems |

A*/8 | 8 | Use the Sine and Cosine Rules in triangles that are not right angled Use the formula A = ½ absinC to find the area of any triangle |

A*/9 | 9 | Solve problems involving surface area and the volume of the frustum of a truncated cone |

A*/10 | 10 | Solve problems in 2D using vectors, including use of commutative & associative properties of vector addition |

A*/11 | 11 | Draw & use tree diagrams to calculate probabilities of successive dependent events |