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MATHEMATICS
Scale Descriptors
The following scale descriptors have been written as a guide to give an indication of the
topics/skills that students achieving different grades are likely to be successful with.
Students achieving a particular grade will be expected to know, understand and be
able to apply the majority of topics up to and including those topics listed for a
particular scale descriptor.
These scale descriptors are used to support teachers when making judgements about
the Current Attainment or Predicted Grades to record at each Data Collection Point.
By implication, these are not used to give a mark for a piece of work or a single test.
The process of feedback after individual pieces of work or tests is to give diagnostic
formative feedback. It is not possible to allocate grades to such contained pieces of
work. Scale descriptors are for judgements in the round, and not judgements about
class work, homework or tests.
Additional Guidance
Even though particular skills have been placed in a specific position on the scale, this is
not set in stone.
Questions that have embedded skills that are not straightforward to identify, increase
the demands on the student. This should result in the level allocated to that question
being raised up the scale.
Example 1
A scientist is studying some rabbits. A disease is killing the rabbits.
A population of 240 of these rabbits was reduced to 180 rabbits in two days.
The rabbit population is decreasing exponentially.
Work out how many of the 240 rabbits will still be alive at the end of 7 days
This would come under repeated percentage change which is level 6 on our scale. The
way the question is phrased means this skill is harder to identify. It is therefore
reasonable to assign a level 7 to similar work.
Other types of questions that increase difficulty are;
1. Multi-skilled questions which rely on several skills being used to successfully
complete the question.
○ e.g. solving a bearing questions using the cosine rule
2. Abstract questions where students need to define variables whilst applying a
particular skill.
○ e.g. combined probabilities where the original probabilities are not known.
Conversely, questions that contain some form of scaffolding make the required skill
more obvious, thus reducing the demands on the student. This should result in the
level allocated to that question being lowered down the scale.
Example 2
Vicky counts the number of birds in her garden at 5 pm on each of 20 days. She
records the information in a frequency table.
Number of
birds (x)
Frequency (f) fx
0 3
1 2
2 3
3 4
4 5
5 3
Estimate the mean number of birds per day.
This would come under estimated mean which is level 4 on our scale. The way the
question is phrased means this skill is easier to identify. The fx column is already there
as a reminder. The question has helpful units that a student can use to remind
themselves of the correct calculation. It is therefore reasonable to assign a level 3 to
similar work.
KS4 Scale Descriptors
NUMBER ALGEBRA RATIO AND PROPORTION
GEOMETRY & MEASURE
STATISTICS PROBABILITY
1 • Read, write and order integers, up to
and including 8-digit numbers and up to three decimal places.
• Use mental methods to add and subtract positive and negative integers.
• Use written methods to multiply & divide up to 3-digit numbers by a single-digit number.
• Multiply and divide whole numbers by powers of 10.
• Understand and apply BIDMAS.
• Understand and use inverse operations.
• Identify square numbers, up to 144.
• Know the definition of a prime number and be able to list the first 10 prime numbers.
• Know the definition of multiples and factors and to be able to list them.
• Round whole numbers to the nearest 10, 100 and 1000.
• Use vocabulary associated with fractions such as numerator and denominator.
• Understand and use fraction notion.
• Use diagrams to find equivalent fractions and to make comparisons.
• Convert simple fractions into decimals, such as tenths and hundredths.
• Read from scales and measures.
• Use the ‘less than’ and ‘greater than’ symbols.
• Write and plot coordinates in the positive quadrant.
• Understand the notation of algebra.
• Multiply, divide, add and subtract basic algebraic terms.
• e.g.: a + a, 2 x a, 𝑎
2, 3a – a
• Write expressions using algebraic notation.
• e.g.: I think of a number, multiply it by 2 and add 5.
• Write ratios.
• Write ratios in their simplest form.
• Solve simple problems involving direct proportion.
• Know the definition of regular and irregular polygon.
• Know the names of regular polygons up to decagon.
• Name the different angles, acute, obtuse, right-angle and reflex.
• Estimate angles.
• Understand the definition of parallel and perpendicular lines.
• Understand the definition of line symmetry and rotational symmetry.
• Draw lines of symmetry on basic shapes as well as give order of rotational symmetry.
• Understand the definition of congruency.
• Calculate the perimeter of 2D shapes
• Recall the names of 3D shapes
• Collect discrete data and record results using a frequency table.
• Draw a bar chart for discrete data.
• Calculate the total population from a bar chart or table.
• Find greatest and least values from a bar chart or table.
• Use the mode and range to describe sets of data.
• Read information and work out totals from a pictogram.
• Represent information as a pictogram (where the symbol represents 5 or 10 units).
• Discuss events using words such as likely, unlikely, certain and impossible.
• Place the probability of events on a scale from impossible to certain.
• Find probabilities based on equally likely outcomes in simple contexts.
• List all outcomes for single events systematically.
2 • Order, add and subtract positive and
negative integers within contexts.
• Round decimals to the nearest integer.
• Multiply & divide any integer or decimal by powers of 10.
• Understand and use decimal notation and place value.
• Add and subtract decimals, including those with differing number of decimal places.
• Use written methods to multiply & divide up to three-digit numbers by a two-digit number.
• Multiply & divide decimals with up to two places by single-digit whole numbers.
• Use a calculator to calculate square and cube roots, and pi button.
• Order of operations.
• Plot coordinates in all four quadrants.
• Identify, expressions, terms, equations and formulae.
• Write an Expression / Formula.
• Simplify linear expressions.
• Solving Equations with two or more steps.
• Multiply terms including single brackets by a positive integer.
• Substituting into formulae with one or more variable (including squares and cubes)
• Calculate a term-to-term rule and continue a sequence.
• Generate sequences from patterns, including pictures.
• Show inequalities on a number line and give numbers that satisfy inequalities.
• Convert between metric units. (lengths, weights and volumes).
• Write and interpret a ratio given a diagram or context.
• Draw scale plans and read measurements from scale plans.
• Solve proportion problems using the unitary method. e.g. Best buys
• Solve ratio problems involving two or more quantities e.g. recipe.
• Identify and calculate angles on a straight line, around a point and vertically opposite.
• Measure and draw angles to nearest degree.
• Construct a triangle given sides and angles.
• Calculate missing angles in triangles and quadrilaterals.
• Identify properties of 3D shapes.
• Identify and construct nets of common 3D shapes.
• Draw plans and elevations of 3D shapes.
• Draw a 3D shape from plans and elevations.
• Reflect, translate and rotate a shape.
• Classify quadrilaterals and triangles given their properties.
• Draw and interpret frequency diagrams for discrete and continuous data.
• Plot scatter graph
• Stem and Leaf
• Calculate the mode, median, mean and range from sets of data.
• Draw and interpret line-bar graphs.
• Understand and use the probability scale from 0 to 1.
• Write probabilities in words or fractions, decimals and percentages.
• Calculate the probability of an event happening using theoretical probability.
• Systematic Listing (e.g. all outcomes using dice, spinners and coins.)
• To input information into sample space diagrams and interpret them to find probabilities.
• You can sort information into Venn diagrams.
• Calculate the probability of an event happening using relative frequency.
• Identify and calculate highest common factors and lowest common multiples using lists.
• Calculation problems.
• List and simplify equivalent fractions and express one number as a fraction of another and simplify.
• Comparing fractions.
• Convert between basic fractions, decimals and percentages.
• Calculate percentages and fractions of amounts.
• Finding percentage increase and decrease
• Writing one number as a percentage of another, and working out the change as a percentage.
• Understand and use simple interest.
• Add, subtract, multiply and divide fractions.
• Use simple tests of divisibility.
• Use the bracket, square, square root and sign change keys of a calculator.
• Use the memory of a calculator and interpret the display in different contexts.
• Solving a simple linear inequality.
• Calculate the input and output of function machines (positive integers only).
• Calculate the area and perimeter of rectangles/squares/triangles.
• Calculate area and perimeter of compound shapes involving rectangles.
3 • Multiply and divide decimals by
decimals.
• Convert integers into standard form and vice versa.
• Use positive and negative square roots, cube and cube roots.
• Use index notation for small positive integer powers.
• Write an integer as a product of its prime factors.
• Use the order of operations, including brackets, with more complex calculations
• Explore links between fractions, decimals and percentages.
• Calculate with fractions, excluding mixed numbers.
• Find the prime factorisation of a number
• Round numbers to a given number of decimal places.
• Manipulate algebraic expressions including collecting like terms; multiplying a number and single term over a bracket; factorise simple terms outside a single bracket).
• Substitute numbers into linear algebraic expressions.
• Solve linear equations and inequalities with the unknown on one side.
• Explore connections between graphs and equations.
• Plot and interpret linear graphs and quadratic graphs.
• Generate linear sequences from nth term.
• Multiply terms including single bracket by a variable.
• Investigate the connection between ratio and proportion.
• Convert fractions to a
ratio, e.g. 1
3 and
2
3 shown
in the ratio 1:2.
• Solve problems involving proportional reasoning, including best buy with simple proportions.
• Calculate speed, distance and time given situations.
• Identify congruent shapes.
• Calculate the area of a trapezium.
• Calculate area and circumference of a circle.
• Calculate angles in isosceles and equilateral triangles.
• Explore all four transformations.
• Use and interpret scale drawings and interpret bearings.
• Know and apply standard mathematical constructions.
• Know Pythagoras’ theorem.
• Distinguish between types of data.
• Construct &interpret graphs and select appropriate graphs & charts.
• Investigate averages and summarise data.
• Analyse and compare sets of data.
• Criticise misleading graphs.
• Understand that the sum of probabilities of all mutually exclusive outcomes is 1.
• Explore experiments and outcomes.
• Develop understanding of probability.
• Use probability to make predictions.
4 • Calculate with powers and roots.
• Convert numbers between 0 and 1 into standard form and vice versa.
• Round numbers to given significant figures.
• Explore the effects of rounding.
• Know and use the laws of indices
e.g.: am x an, am
𝑎𝑛, (am) n, a0 , a1.
• Calculate the Lowest Common Multiple (LCM) & Highest Common Factor (HCF) using Venn diagrams.
• Understand the term reciprocal and calculate reciprocals of any integer, decimal and fraction.
• Identify equations and identities.
• Expand and simplify brackets including with negatives e.g.: 3 (𝑥 + 4) – (𝑥 +5)
• Construct and solve linear equations.
• Substitute numbers into algebraic expressions involving powers.
• Factorise expressions into a single bracket.
• Solving equations and inequalities with the unknown on both sides.
• Calculate the nth term of a linear sequence.
• Use proportional reasoning to compare proportions.
• Investigate ways of representing proportion.
• Identify congruent shapes.
• Write, simplify and divide into a ratio.
• Know and use compound units in a range of situations.
• Calculate volumes of cuboids and other prisms.
• Know angle facts involving parallel lines.
• Know the properties of special quadrilateral.
• Apply an enlargement with a centre (not fractional or negative scale factors).
• Use and apply Pythagoras’ theorem.
• Constructions – including construction of triangles (SSS, SAS, ASA).
• Construct and interpret graphs of time series.
• Interpret and plot scatter diagrams.
• Describe correlation.
• Calculate averages from frequency tables.
• Understand and use tree diagrams.
• Develop understanding of probability in situations involving combined events.
• Convert simple fractions into recurring decimals using bus-stop method.
• Calculate percentage increase and decrease.
• Calculate simple interest.
• Solve simultaneous equations algebraically and graphically.
• Identify and continue the Fibonacci sequence and explore quadratic sequences.
• Add and subtract simple
algebraic fractions e.g.: 2
𝑥 +
2
3𝑥
• Plot quadratic functions with and without a calculator.
• Investigate features of straight-line graphs.
• Explore graphs of other standard non-linear functions.
• Create and use graphs of non-standard functions.
• Solve kinematic problems.
5 • Use index notation, including the use
of negative integer powers.
• Estimate the answer to square roots
& cube roots e.g.: √70 must lie between 8 and 9.
• Calculate with standard form.
• Calculate the upper and lower bounds of a number to a given degree of accuracy.
• Use upper and lower bounds for addition and subtraction calculations.
• Estimate answers to calculations with the use of rounding numbers.
• Multiply & divide integers and decimals by a number between 0-1.
• Add, subtract, multiply and divide mixed numbers.
• Construct and solve linear equations that involve fractions and fractional answers.
• Construct and solve linear inequalities.
• Expand and factorise double brackets.
• Substitute fractional and negative values into expressions.
• Rearrange formulae with variable on one side and use to solve problems.
• Calculate the equation of a line in the form y = mx + c.
• Plot cubic graphs.
• Calculate missing dimensions in similar shapes.
• Calculate compound interest and depreciation after 2-5 years.
• Write, simplify and divide a ratio given situations.
• Convert between currencies.
• Interpret and solve best buy deals.
• Identify when shapes are congruent and similar.
• Calculate the number of sides on a regular polygon given the interior and exterior angles
• Understand and use the formulae for sum of interior and exterior angles
• Explore trigonometry in right-angled triangles.
• Calculate the area and arc length of a sector.
• Calculate the length of a line given two coordinates.
• Define a geometric progression and continue a sequence.
• Use and apply trigonometry to right-angled triangle, including worded problems.
• Identify roots and turning points on a quadratic graph.
• Calculate volumes of 3D shapes.
• Transform shapes by reflecting, rotating, enlarging (integer scale factor) and translating (using column vectors).
• Describe fully a single transformation.
• Use constructions to solve loci problems.
• Vector notation.
• Adding and subtracting vectors.
• Find multiples of vectors.
• Construct and interpret pie charts.
• Construct and interpret composite bar charts.
• Display data with an appropriate graph.
• Construct and interpret real-life graphs (including speed/distance/velocity graphs).
• Calculate averages from a grouped frequency table.
• Write probabilities using fractions, percentages or decimals.
• Use tree diagrams to calculate the probabilities of two dependent events.
• Understand and use experimental and theoretical probability to calculate estimated outcomes.
• Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values.
6 • Practice index laws such as n0 = 1
and involving fractional powers (9 ½ and 8 ⅓)
• Understand the definition of a surd and perform calculations involving roots e.g. √16 x √4 = 8
• Simplify surds e.g. √12 = 2√3
• Convert a fraction to a recurring decimal and vice versa.
• Solve problems involving standard form.
• Use iterative processes to generate sequences.
• Use iterative methods to calculate solutions.
• Multiply three binomials.
• Identify linear, quadratic, cubic, reciprocal and exponential graphs.
• Solve quadratics by factorizing and graphically.
• Solve and simplify simple algebraic fractions.
• Construct and solve simultaneous linear equations.
• Calculate reverse and compound percentage.
• Construct and solve equations involving direct and inverse proportion.
• Use kinematics formulae to calculate speed and acceleration from worded and graphical situations.
• Enlarge a shape given a negative scale factor.
• Describe the changes and invariance achieved by transformations.
• Recall and use the formulae for volume and surface area for pyramids, frustums and cones.
• Calculate the dimensions given the volume or surface area.
• Plot and interpret cumulative frequency graphs.
• Plot and interpret boxplots.
• Calculate the outcomes of two or more events by using the product rule.
• Calculate a missing probability from a list or two-way table, including algebraic terms.
• Use a two-way table to calculate conditional probability.
• Compare relative frequency and theoretical probabilities including from different sample sizes.
• Generate quadratic sequences from nth term.
• Calculate the equation of a linear function given two coordinates.
• Plot reciprocal graphs.
7 • Solve complex problems involving
index laws.
• Evaluate numbers with positive, fractional and negative indices.
• Rationalise simple fractions with a surd as the denominator.
• Write the denominator in terms of its prime factors, determine whether a fraction can be expressed as a recurring or terminating decimal.
• Use upper and lowers bounds for calculations involving multiplication and addition.
• Rearrange formulae with the same variable on both sides and use to solve problems.
• Recognise the difference of two squares, and factorise into double brackets.
• Solve quadratics using the formula, factorizing and including completing the square.
• Calculate with algebraic fractions.
• Algebraic proof.
• Plot and find the equation of a circle.
• Calculate the equation of a line given two points and the equations of a perpendicular line.
• Solve inequalities algebraically and graphically.
• Solve problems involving inverse and direct proportion including squares and square roots.
• Plot and interpret exponential functions (y = kx) for positive values of k.
• Use similarity in length, area and volume to calculate scale factors and vice versa.
• Identify trigonometric graphs.
• Use and apply Pythagoras in 3D situations.
• Calculate the area of any given triangle using ½absinC.
• Use and apply both sine and cosine rule to triangles and bearings questions.
• Enlarge a shape given a negative fractional scale factor.
• Calculate and solve vector problems involving ratio.
• Use and apply all circle theorems.
• Use graphs to solve problems involving distance, speed and acceleration.
• Construct and interpret histograms.
• Use moving averages to identify seasonality and trends in time series data and use them to make predictions.
• Understand the structure of a stratified sample and calculate the proportion.
• Use a tree diagram to calculate conditional probability.
8 • Solve and calculate the value of
complex indices including surds.
• Rationalise more complex
denominators e.g. 1
2+√3
• Understand and use rational and irrational numbers.
• Calculate the nth term of a quadratic sequence.
• Solve simultaneous equations with one linear and one quadratic function.
• Use the equation of a circle to find points of intersection with a line.
• Calculate the equation of a circle given the centre and a point of the circumference.
• Estimate area under a quadratic or other graph by dividing it into trapezia.
• Calculate the acceleration and distance from velocity-time graphs.
• Simplify and solve complex algebraic fractions.
• Construct and use composite functions.
• Calculate the inverse function.
• Transform trigonometric and other functions (only reflections and translations).
• Sketch quadratic functions; identifying x and y-axis intercepts and turning points.
• Set up, solve and interpret the answers to growth and decay problems.
• Use the sine and cosine rule in 3 dimensions.
• Prove all circle theorems algebraically.
• Use and apply vectors to prove lines are co-linear or parallel.
• • Use a Venn diagram to calculate conditional probability.
Please note: 9 is an exceptional performance award for (approximately) the top 2-5% of students who achieve a Grade 8. Therefore, there are no such Grade 9 topics / skills.
Foundation Scale Descriptors
The Foundation scale descriptors are the same as the KS4 scale descriptors but have had KS4 content removed for a more focussed and refined assessment tool.
NUMBER ALGEBRA RATIO AND PROPORTION
GEOMETRY & MEASURE
STATISTICS PROBABILITY
1 • Read, write and order integers, up to and
including 8-digit numbers and up to three decimal places.
• Use mental methods to add and subtract positive and negative integers.
• Use written methods to multiply & divide up to 3-digit numbers by a single-digit number.
• Multiply and divide whole numbers by powers of 10.
• Understand and apply BIDMAS.
• Understand and use inverse operations.
• Identify square numbers, up to 144.
• Know the definition of a prime number and be able to list the first 10 prime numbers.
• Know the definition of multiples and factors and to be able to list them.
• Round whole numbers to the nearest 10, 100 and 1000.
• Use vocabulary associated with fractions such as numerator and denominator.
• Understand and use fraction notion.
• Use diagrams to find equivalent fractions and to make comparisons.
• Convert simple fractions into decimals, such as tenths and hundredths.
• Read from scales and measures.
• Use the ‘less than’ and ‘greater than’ symbols.
• Write and plot coordinates in the positive quadrant.
• Understand the notation of algebra.
• Multiply, divide, add and subtract basic algebraic terms.
• e.g.: a + a, 2 x a, 𝑎
2, 3a
– a
• Write expressions using algebraic notation.
• e.g.: I think of a number, multiply it by 2 and add 5.
• Write ratios.
• Write ratios in their simplest form.
• Solve simple problems involving direct proportion.
• Know the definition of regular and irregular polygon.
• Know the names of polygons up to decagon.
• Name the different angles, acute, obtuse, right-angle and reflex.
• Estimate angles.
• Understand the definition of parallel and perpendicular lines.
• Understand the definition of line symmetry and rotational symmetry.
• Draw lines of symmetry on basic shapes as well as give order of rotational symmetry.
• Understand the definition of congruency.
• Calculate the perimeter of 2D Shapes.
• Recall the names of 3D Shapes.
• Collect discrete data and record results using a frequency table.
• Draw a bar chart for discrete data.
• Calculate the total population from a bar chart or table.
• Find greatest and least values from a bar chart or table.
• Use the mode and range to describe sets of data.
• Read information and work out totals from a pictogram.
• Represent information as a pictogram (where the symbol represents 2, 5 or 10 units).
• Discuss events using words such as likely, even chance, unlikely, certain and impossible.
• Place the probability of events on a scale from impossible to certain.
• Find probabilities as fractions based on equally likely outcomes in simple contexts.
• List all outcomes for single events systematically.
2 • Order, add and subtract positive and negative
integers within contexts.
• Round decimals to the nearest integer and to any number of decimal places.
• Multiply & divide any integer or decimal by powers of 10.
• Understand and use decimal notation and place value.
• Add and subtract decimals, including those with differing number of decimal places.
• Use written methods to multiply & divide up to three-digit numbers by a two-digit number.
• Multiply & divide decimals with up to two places by single-digit whole numbers.
• Use a calculator to calculate square and cube powers and roots, and pi button.
• Order of operations.
• Identify and calculate highest common factors and lowest common multiples using lists.
• Calculation problems.
• List and simplify equivalent fractions and express one number as a fraction of another and simplify.
• Comparing fractions.
• Converting between fractions, decimals and percentages with harder values.
• Calculate percentages and fractions of amounts.
• Plot coordinates in all four quadrants.
• Identify, expressions, terms, equations and formulae.
• Writing an Expression/Formula
• Simplify linear expressions.
• Solving Equations with two or more steps.
• Multiply terms including single brackets by a positive integer.
• Substituting into formulae with one or more variable (Including squares and cubes).
• Calculate a term-to-term rule and continue a sequence.
• Generate sequences from patterns, including pictures.
• Show inequalities on a number line and give
• Convert between metric units. (lengths, weights and volumes).
• Write and interpret a ratio given a diagram or context.
• Draw scale plans and read measurements from scale plans.
• Solve proportion problems using the unitary method. e.g. Best buys
• Solve ratio problems involving two or more quantities e.g. recipe.
• Identify and calculate angles on a straight line, around a point and vertically opposite.
• Measure and draw angles to nearest degree.
• Construct a triangle given sides and angles.
• Calculate missing angles in triangles and quadrilaterals.
• Identify properties of 3D shapes.
• Identify and construct nets of common 3D shapes.
• Draw plans and elevations of 3D shapes.
• Draw a 3D shape from plans and elevations.
• Reflect, translate and rotate a shape.
• Classify quadrilaterals and triangles given their properties.
• Calculate the area and perimeter of rectangles/squares/triangles.
• Calculate area and perimeter of compound shapes involving rectangles.
• Draw and interpret frequency diagrams for discrete and continuous data.
• Plot scatter graph
• Stem and Leaf
• Calculate the mode, median, mean and range from sets of data.
• Draw and interpret line-bar graphs.
• Understand and use the probability scale from 0 to 1.
• Write probabilities in words or fractions, decimals and percentages.
• Calculate the probability of an event happening using theoretical probability.
• Systematic Listing (e.g. all outcomes using dice, spinners and coins.)
• To input information into sample space diagrams and interpret them to find probabilities.
• You can sort information into Venn diagrams
• Calculate the probability of an event happening using relative frequency.
• Finding percentage increase and decrease
• Writing one number as a percentage of another, and working out the change as a percentage.
• Understand and using simple interest.
• Add, subtract, multiply and divide fractions.
• Use simple tests of divisibility
• Use the bracket, square, square root and sign change keys of a calculator.
• Use the memory of a calculator and interpret the display in different contexts.
numbers that satisfy inequalities.
• Solving a simple linear inequality.
• Calculate the input and output of function machines (positive integers only).
3 • Multiply and divide decimals by decimals.
• Convert integers into standard form and vice versa.
• Use positive and negative square roots, cube and cube roots.
• Use index notation for small positive integer powers.
• Write an integer as a product of its prime factors.
• Use the order of operations, including brackets, with more complex calculations
• Explore links between fractions, decimals and percentages.
• Calculate with fractions, excluding mixed numbers.
• Find the prime factorisation of a number
• Round numbers to a given number of decimal places.
• Manipulate algebraic expressions including collecting like terms; multiplying a number and single term over a bracket; factorise simple terms outside a single bracket)
• Substitute numbers into linear algebraic expressions.
• Solve linear equations and inequalities with the unknown on one side.
• Explore connections between graphs and equations.
• Plot and interpret linear graphs and quadratic graphs.
• Generate linear sequences from nth term.
• Multiply terms including single bracket by a variable.
• Investigate the connection between ratio and proportion.
• Convert fractions to a ratio,
e.g. 1
3 and
2
3 shown in the ratio
1:2.
• Solve problems involving proportional reasoning, including best buy with simple proportions.
• Calculate speed, distance and time given situations.
• Identify congruent shapes.
• Calculate the area of a trapezium.
• Calculate area and circumference of a circle.
• Calculate angles in isosceles and equilateral triangles.
• Explore all four transformations.
• Use and interpret scale drawings and interpret bearings.
• Know and apply standard mathematical constructions.
• Know Pythagoras’ theorem.
• Distinguish between types of data.
• Construct &interpret graphs and select appropriate graphs & charts.
• Investigate averages and summarise data.
• Analyse and compare sets of data.
• Criticise misleading graphs.
• Understand that the sum of probabilities of all mutually exclusive outcomes is 1.
• Explore experiments and outcomes.
• Develop understanding of probability.
• Use probability to make predictions.
4 • Calculate with powers and roots.
• Convert numbers between 0 and 1 into standard form and vice versa.
• Round numbers to given significant figures.
• Explore the effects of rounding.
• Know and use the laws of indices e.g.: am x an, am
𝑎𝑛, (am) n, a0 , a1.
• Calculate the Lowest Common Multiple (LCM) & Highest Common Factor (HCF) using Venn diagrams.
• Understand the term reciprocal and calculate reciprocals of any integer, decimal and fraction.
• Convert simple fractions into recurring decimals using bus-stop method.
• Calculate percentage increase and decrease.
• Calculate simple interest.
• Identify equations and identities.
• Expand and simplify brackets including with negatives e.g.: 3 (𝑥 + 4) – (𝑥 +5)
• Construct and solve linear equations.
• Substitute numbers into algebraic expressions involving powers.
• Factorise expressions into a single bracket.
• Solving equations and inequalities with the unknown on both sides.
• Calculate the nth term of a linear sequence.
• Identify and continue the Fibonacci sequence and explore quadratic sequences.
• Investigate features of straight-line graphs.
• Use proportional reasoning to compare proportions.
• Investigate ways of representing proportion.
• Identify congruent shapes.
• Write, simplify and divide into a ratio.
• Know and use basic compound units in a range of situations.
• Calculate volumes of cuboids and other prisms
• Know angle facts involving parallel lines.
• Know the properties of special quadrilaterals.
• Apply a rotation, reflection and translation on a co-ordinate grid
• Apply an enlargement with a centre (not fractional or negative scale factors)
• Use and apply Pythagoras’ theorem.
• Constructions – including construction of triangles (SSS, SAS, ASA).
• Construct and interpret graphs of time series.
• Interpret and plot scatter diagrams
• Describe correlation.
• Calculate averages from frequency tables.
• Understand and use tree diagrams and frequency trees
• Develop understanding of probability in situations involving combined events.
5 • Use index notation, including the use of
negative integer powers.
• Estimate the answer to square roots & cube
roots e.g.: √70 must lie between 8 and 9.
• Estimate answers to calculations with the use of rounding numbers.
• Multiply & divide integers and decimals by a number between 0-1.
• Add, subtract, multiply and divide mixed numbers.
• Construct and solve linear equations that involve fractions and fractional answers.
• Construct and solve linear inequalities.
• Expand and factorise double brackets.
• Substitute fractional and negative values into expressions.
• Rearrange formulae with variable on one side and use to solve problems.
• Calculate the equation of a line in the form y = mx + c.
• Calculate missing dimensions in similar shapes.
• Write, simplify and divide a ratio given situations.
• Convert between currencies.
• Interpret and solve best buy deals.
• Calculate the number of sides on a regular polygon given the interior and exterior angles
• Understand and use the formulae for sum of interior and exterior angles
• Calculate volumes of 3D shapes.
• Transform shapes by reflecting, rotating, enlarging (integer scale factor) and translating (using column vectors).
• Describe fully a single transformation.
• Use constructions to solve loci problems.
• Construct and interpret pie charts.
• Construct and interpret composite bar charts.
• Display data with an appropriate graph.
• Construct and interpret real-life graphs (including speed/distance/velocity graphs)
• Calculate averages from a grouped frequency table.
• Write probabilities using fractions, percentages or decimals.
• Understand and use experimental and theoretical probability to calculate estimated outcomes.
• Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values.
Please note: Should a higher grade be awarded than a 5, please refer to the KS4 scale descriptor table.
B Scale Descriptors
NUMBER & ALGEBRA GEOMETRY & MEASURE STATISTICS & PROBABILITY
B1 • Count to and across 100, forwards and backwards, beginning with 0 or 1, or from
any given number
• Count, read and write numbers to 100 in numerals; Given a number, identify one more and one less
• 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 from 1 to 20 in numerals and words.
• Read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
• Represent and use number bonds and related subtraction facts within 10
• Add and subtract one-digit numbers to 10, including zero
• Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations
• Recognise, find and name a half as one of two equal parts of an object, shape or quantity
• Compare, describe and solve practical problems for: ✓ Lengths and heights [for example, long/short, longer/shorter, tall/short] ✓ Mass/weight [for example, heavy/light, heavier than, lighter than] ✓ Capacity and volume [for example, full/empty, more than, less than] ✓ Time [for example, quicker, slower, earlier, later]
• Sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]
• Recognise and use language relating to dates, including days of the week
• Tell the time to the hour and draw the hands on a clock face to show these times
• Recognise and name common 2-D including: [rectangles (including squares), circles and triangles]
• Describe position, direction and movement, including whole and half
B2 • Count in multiples of twos, fives and tens
• Represent and use number bonds and related subtraction facts within 20
• Add and subtract one-digit and two-digit numbers to 20, including zero
• Solve one-step missing number problems such as 7 = – 9 using concrete objects and pictorial representations
• 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
• Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.
• Compare, describe and solve practical problems for:
• Lengths and heights [for example: double/half]Capacity and volume [for example, half, half full, quarter]
• Measure and begin to record the following: lengths and heights, mass/weight, capacity and volume, time (hours, minutes, seconds)
• Recognise and know the value of different denominations of coins and notes
• Recognise and use language relating to dates, including weeks, months and years
• Tell the time to half past the hour and draw the hands on a clock face to show these times
• Recognise and name common 3-D shapes, including: [cuboids (including cubes), pyramids and spheres]
• Describe position, direction and movement, including whole, half, quarter and three- quarter turns
B3 • Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and
backward
• Recognise the place value of each digit in a two-digit number (tens, ones)
• Identify, represent and estimate numbers using different representations, including
the number lines
• Compare and order numbers from 0 up to 100
• Read and write numbers to at least 100 in numerals and in words
• Use place value and number facts to solve problems
• Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures
• Recall and use addition and subtraction facts to 20 fluently
• Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones, a two-digit number and tens
• Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
• Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
• Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, including problems in contexts. Recognise, find, name and write fractions 1/3, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity
• Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm) to the nearest appropriate unit, using rulers
• Compare and order lengths
• Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
• Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
• Tell and write the time including quarter past/to the hour and draw the hands on a clock face to show these times
• Identify and describe the properties of 2-D shapes, including the number of sides
• Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
• Compare and sort common 2-D and 3-D shapes and everyday objects
• Order and arrange combinations of mathematical objects in patterns and sequences
• Interpret and construct tally charts and simple tables
• Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
• Ask and answer questions about totalling and comparing categorical data
B4 • Compare and order numbers from 0 up to 100; use <, > and = signs
• Read and write numbers to at least 1000 in numerals and in words
• Recall and use addition and subtraction facts to 20 fluently, and derive and use
related facts up to 100
• Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones, a two-digit number and tens, two
• Choose and use appropriate standard units to estimate and measure mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using scales,
thermometers and measuring vessels
• Compare and order mass, volume/capacity and record the results using >, < and =
• Find different combinations of coins that equal the same amounts of money
• Compare and sequence intervals of time
• Interpret and construct simple pictograms and block diagrams
• Ask and answer simple questions by counting the number of objects in each category and sorting the categories by
quantity
two-digit numbers, adding three one-digit numbers
• Show that addition of two numbers can be done in any order (commutative) and
subtraction of one number from another cannot
• Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
• Recall and use multiplication and division facts for the 3-multiplication table
• Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
• Solve problems involving multiplication and division, using multiplication and
division facts, including problems in contexts.
• Write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of 2/4
• and 1/2.
• Tell and write the time to five minutes, including quarter past/to the hour and draw the
hands on a clock face to show these times
• Know the number of minutes in an hour and the number of hours in a day.
• Identify and describe the properties of 2-D shapes, including line symmetry in a vertical
line
• Identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
• Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-
clockwise)
• Ask and answer questions about totalling and comparing categorical data
B5 • Count in multiple of 4 and 8 from 0
• Recognise place value of each digit in a 3-digit number
• Compare and order numbers up to 1000
• Read and write numbers up to 1000 in numerals and in words
• Add and subtract numbers mentally, including: a three-digit number and ones and a three-digit number and tens
• Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
• Write and calculate mathematical statements for multiplication using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
• Recognise and show, using diagrams, equivalent fractions with small denominators
• Add and subtract fractions with the same denominator within one whole
• Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
• Measure the perimeter of simple 2-D shapes
• Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
• Identify horizontal and vertical lines
B6 • Count in multiples of 50 and 100 from 0
• Find 10 or 100 more or less than a number
• Identify, represent and estimate numbers using different representations
• Solve number problems and practical problems involving these ideas.
• Add and subtract numbers mentally – 3-digit number and hundreds
• Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
• 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.
• Write and calculate mathematical statements for division using the multiplication tables that they know, including for two-digit numbers divide by a one-digit numbers, using mental and progressing to formal written methods
• Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
• Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
• Compare and order unit fractions, and fractions with the same denominators
• Add and subtract amounts of money to give change, using both £ and p in practical contexts
• Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
• Know the number of seconds in a minute and the number of days in each month, year and leap year
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Order and compare numbers beyond 1000
• Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
• Recognise angles as a property of shape or a description of a turn
• Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle
• Interpret and present data pictograms, simple bar charts and tables
• Solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.
B7 • 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.
• Identify pairs of perpendicular and parallel lines.
• Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
• Solve problems that involve all previous fraction skills from B5 and B6
• Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, a.m./p.m., morning, afternoon, noon and midnight
• Compare durations of events [for example to calculate the time taken by particular events or tasks].
• Count in multiples of 6, 7, 9, 25 and 1000
• Find 1000 more or less than a given number
• Round any number to the nearest 10, 100 or 1000
• Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
• Recognise and show, using diagrams, families of common equivalent fractions
• Identify acute and obtuse angles and compare and order angles up to two right angles by size
• Complete a simple symmetric figure with respect to a specific line of symmetry.
B8 • Count backwards through zero to include negative numbers
• 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.
• Solve number and practical problems that involve all previous number skills and with increasingly large positive numbers
• Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.
• Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
• Recognise and use factor pairs and commutativity in mental calculations
• 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.
• Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• Recognise and write decimal equivalents to ¼, ½ ¾
• Round decimals with one decimal place to the nearest whole number
• Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
• Find the area of rectilinear shapes by counting squares
• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. (if whole amounts e.g. 3 hours)
• Identify lines of symmetry in 2-D shapes presented in different orientations
• Describe positions on a 2-D grid as coordinates in the first quadrant
• Describe movements between positions as translations of a given unit to the left/right and up/down
B9 • Read, write and order integers up to and including 6-digit numbers and up to 2
decimal places.
• Appreciate the symmetry of the number line including negatives, be able to count forwards and backwards with positive and negative whole numbers including through 0.
• Be able to divide a 3-digit number by a single-digit number when there is no remainder
• Be able to multiply 2-digit numbers by 2-digit numbers by using the grid method
• Multiply and divide whole numbers by 10
• Use their knowledge of the order of operations to carry out calculations involving the four operations
• Understand and use inverse operations
• Being able to find factor pairs of a number. Appreciate that some numbers only have 2 factors.
• Be able to list the first few multiples of any number under 20
• Can round numbers to the nearest 10 and 100 for numbers up to 1000
• Convert between different units of measure [for example, kilometre to metre; hour to minute]
• Estimate, compare and calculate different measures, including money in pounds and pence
• Read, write and convert time between analogue and digital 12- and 24-hour clocks
• Plot specified points and draw sides to complete a given polygon.
Sample Assessment Material
Grade B7 Sample Questions
1. Write in words:
o 234
o 62
o 8723
o 98123
2. Which picture shows a line of symmetry?
3. What’s the time?
Grade B8 Sample Questions
1. Can you spot the pattern? Draw the next shape.
2) Write out the expressions that represent each of the following:
a) e plus 2
b) p take away 4
c) 6 more than a
3) Draw a rectangle. Draw a triangle. What is the difference?
Grade B9 Sample Questions
1) There are 90 cards in a box. Harold takes 43 cards. How many are left?
2) Nathan starts with 7 Skittles. He gets 67 more from Larry. How many Skittles does Nathan end with?
3) Measure the length of your desk in cm
4) What different sandwiches could you make?
Bread Filling
White Ham
Brown Cheese
Grade 1 Sample Questions
Grade 1 Learning Objective Grade 1 Example Questions
L.O: multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000: The product is 400. At least one of the numbers is a multiple of 10. What two numbers could have been multiplied together? Are there any other possibilities?
L.O: Know angles are measured in degrees: estimate and
compare acute, obtuse and reflex angles
Look at these angles.
Label each angle acute, obtuse or reflex. List the 5 angles in order from smallest to largest.
L.O: Divide numbers up to 3 digits by a one-digit number
• They increase the efficiency
of the methods that they are
using. For example:
196 ÷ 6 is approximately 200 ÷
5 = 40
3 2 r4 or 4/6 or 2/3
6 196
L.O: identify lines of symmetry in 2-D shapes
L.O: Know definition of multiples and factors and be able to list them. My age is a multiple of 8. Next year my age will be a multiple of 7. How old am I? Find some numbers that have a factor of 4 and a factor of 5. What do you notice?
L.O Write and plot coordinate in positive quadrants
L.O: Convert fractions to
decimals
Write the total as a decimal:
4 + 6⁄10 + 2⁄100 =
L.O: Write expression using algebraic notation Simplify a + a+ a +a = 3 x 1 16 a /4= 5 a – 2a
Grade 2 Sample Questions
Grade 2 Learning Objectives
Grade 2 Example Questions
Convert between fractions, decimals and percentages.
Plot coordinates in all four quadrants.
Construct a triangle given sides and angles.
Ratio problems involving recipe.
Grade 3 Sample Questions
Grade 3 Learning Objectives
Grade 3 Example Questions
Calculate angles in isosceles and equilateral triangles.
Understand that the sum of probabilities of all mutually exclusive outcomes is 1.
Calculate the area of a trapezium.
Share an amount in a given ratio.
Generate a sequence from the nth term.
Grade 4 Sample Questions
Grade 4 Learning Objectives Grade 4 Example Questions
Know and use the laws of
indices e.g.: am x an, am
𝑎𝑛, (am) n,
a0 , a1.
Calculate simple interest.
Expand and simplify brackets including with negatives e.g.: 3 (𝑥 + 4) – (𝑥 +5)
Identify and continue the Fibonacci sequence.
Use proportional reasoning to compare proportions.
Describe a rotation, reflection and translation on a co-ordinate grid.
Complete Venn diagrams and use union and intersection notation.
Grade 5 Sample Questions
Grade 5 Learning Objectives
Grade 5 Example Questions
Use upper and lower bounds for addition and subtraction calculations.
Expand and factorise single and double brackets, including difference of two squares.
Calculate compound interest and depreciation after 2-5 years.
Calculate volumes of 3D shapes and prisms.
Construct and interpret pie charts.
Grade 6 Sample Questions
Grade 7 Sample Questions
Grade 8 Sample Questions
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