Mathematics

Our curriculum intent: why we teach what we teach in Maths

  • Students will learn a knowledge of the main mathematical topics and concepts, including the relationships between them, learning how maths underpins the world we live in.

  • Students will be able to work with procedural fluency which is underpinned by deep conceptual understanding.  We want them to have strategies for investigation and problem solving, and an ability to conjecture, explore, reason, explain and justify their mathematical thought.

  • Students will develop into people who face difficulties with resilience and use their knowledge and creativity with logical thinking to make sense of the world around them.

Maths curriculum intent

Curriculum

Year 7

Year 7 Higher

Year 7 Higher

Autumn Term,

Half Term 1

Autumn Term,

Half Term 2

Spring Term,

Half Term 1

Unit Title Arithmetic , Sequences, Perimeter and Area Averages, Fractions and Decimals, Angles and Algebra. Coordinates, Factors, Multiples and Probability
Key Questions?

How do we use whole number arithmetic to solve calculations?

 

What is a numerical sequence?

 

How can we find the perimeter and area of a shape?

What are averages?

 

What are fractions and decimals?

 

What is an angle?

 

What is algebra?

What are coordinates and straight line graphs?

 

What are decimals?

 

What are factors, multiples, squares and cubes?

 

What is probability?

 

Threshold Concepts

Whole number arithmetic describes the process of either adding, subtracting, multiplying or dividing to solve a calculation.

 

Sequences are lists of numbers which follows a pattern.

 

Perimeter is the distance around a shape.

Area is the amount of space inside a two-dimensional shape

 

An average is a value given to best represent a set of data, including the mean, the median and the mode.

 

Fractions are used to describe numbers that are not a whole number and can also be expressed as decimals.

 

An angle is formed when two straight lines cross or meet each other at a point. The size of an angle is measured by the amount one line has been turned in relation to the other.

 

Algebra is the branch of maths where symbols or letters are used to represent numbers

 

Coordinates are a set of values that show an exact position, often on a straight line graph.

 

A factor is a number that divides into another number exactly and a multiple is a number which can be multiplied to find another number, e.g. 35 is a multiple of 5.

 

Probability is the likelihood of an event happening

Link to Prior Learning

 

Whole number addition, subtraction, division and multiplication.

 

 

Knowledge of whole number multiplication enables factors and multiples to be found. Decimals

 

The Mathematics Department – Year 7 Curriculum

 

Year 7 Higher

Spring Term,

Half Term 2

Summer Term,

Half Term 1

Summer Term,      

 Half Term 2

Unit Title Shape, Number and Equations Transformations, Probability, Graph Work, Rounding and Circles Equations, Sequences, Conversions, Constructions and 3-D Shapes.
Key Question(s)?

How can we construct a triangle?

 

What is ratio?

 

What are negative numbers?

 

How do we find a percentage of an amount?

 

How do we solve equations?

What are transformations (rotation, reflection, translation)?

 

How can we use find and use information displayed in graphical form?

 

How can we round a number?

 

How can we find the area and circumference for a circle?

What is a sequence and how can we express it using algebra?

 

What are 3D shapes and how can we draw and understand them?

Threshold Concepts

A triangle can be constructed with ruler, protractor and pair of compasses

 

A ratio says how much of one thing there is compared to another.

 

A negative number Is a number less than zero.

 

An equation can sometimes be solved to find a value for the variable which satisfies the equation.

Transformations’ is the collective name for reflections, rotations, translations and enlargements.

Equally likely outcomes can be used to find a numerical value of a probability

 

Graphs can be used to display information.

 

Non-exact numbers can be rounded to give an approximate answer which is useful to estimate answers.

 

Formulae for the area and circumference of a circle

 

An arithmetic sequence is a sequence which goes up and down in equal steps and so can be described using a rule, e.g. ‘3n + 1.’

 

Conversions between metric and imperial units can be used.

 

Ruler and compasses can be used to construct perpendicular and angle bisectors.

 

2D and 3D objects can have edges and vertices.

Link to Prior Learning

 

Algebraic substitution

 

Fractions, decimals and percentages

Key principles of common shapes.

 

Coordinates

 

Probability

Solving equations

 

Sequence rules

 

Angle facts

Knowledge and sequencing rationale In Year 7 we are strengthening work on Number as the students join from many Primary schools, then working on topics in Algebra, Shape, Data and Probability.

 

 

Year 7 Core

Year 7

Core

Autumn Term,

Half Term 1

Autumn Term,

Half Term 2

Spring Term,

Half Term 1

Unit Title Arithmetic , Sequences, Perimeter and Area Averages, Fractions and Decimals, Angles and Algebra. Coordinates, Factors, Multiples and Probability
Key Questions?

How do we use whole number arithmetic to solve calculations?

 

What is a numerical sequence?

 

How can we find the perimeter and area of a shape?

What are averages?

 

What are fractions and decimals?

 

What is an angle?

 

What is algebra?

What are coordinates and straight line graphs?

 

What are decimals and how can we multiply and divide them?

 

What are factors, multiples, squares and cubes?

 

What is probability?

 

Threshold Concepts

Whole number arithmetic describes the process of either adding, subtracting, multiplying or dividing to solve a calculation.

 

Sequences are lists of numbers which follows a pattern.

 

Perimeter is the distance around a shape.

Area is the amount of space inside a two-dimensional shape

 

An average is a value given to best represent a set of data, including the mean, the median and the mode.

 

Fractions are used to describe numbers that are not a whole number and can also be expressed as decimals.

 

An angle is formed when two straight lines cross or meet each other at a point. The size of an angle is measured by the amount one line has been turned in relation to the other.

 

Algebra is the branch of maths where symbols or letters are used to represent numbers

 

Coordinates are a set of values that show an exact position, often on a straight line graph.

 

A factor is a number that divides into another number exactly and a multiple is a number which can be multiplied to find another number, e.g. 35 is a multiple of 5.

 

Probability is the likelihood of an event happening

Link to Prior Learning

 

Whole number addition, subtraction, division and multiplication.

 

 

Knowledge of whole number multiplication. Decimals

 

 

 

 

Year 7

Core

Spring Term,

Half Term 2

Summer Term,

Half Term 1

Summer Term,

Half Term 2

Unit Title Shape, Number and Equations Transformations, Probability, Graph Work, Rounding and Algebra Equations, Sequences, Conversions, Constructions and 3-D Shapes.
Key Question(s)?

How can we construct a triangle?

 

What is ratio?

 

What are negative numbers?

 

How do we find a percentage of an amount?

 

How do we solve equations?

What are transformations (rotation, translation)?

 

How can we use find and use information displayed in graphical form?

 

How can we round a number?

 

 

What is a sequence and how can we express it using algebra?

 

What are 3D shapes and how can we draw and understand them?

Threshold Concepts

A triangle can be constructed with ruler, protractor and pair of compasses

 

A ratio says how much of one thing there is compared to another.

 

A negative number Is a number less than zero.

 

An equation can sometimes be solved to find a value for the variable which satisfies the equation.

Transformations’ is the collective name for reflections, rotations, translations and enlargements.

Equally likely outcomes can be used to find a numerical value of a probability

 

Graphs can be used to display information.

 

Non-exact numbers can be rounded to give an approximate answer which is useful to estimate answers.

 

 

An arithmetic sequence is a sequence which goes up and down in equal steps and so can be described using a rule, e.g. ‘3n + 1.’

 

Conversions between metric and imperial units can be used.

 

Ruler and compasses can be used to construct perpendicular and angle bisectors.

 

2D and 3D objects can have edges and vertices.

Link to Prior Learning

 

Algebraic substitution

 

Fractions, decimals and percentages

Coordinates

 

Probability

Solving equations

 

Sequence rules

 

Angle facts

Knowledge and sequencing rationale In Year 7 we are strengthening work on Number as the students join from many Primary schools, then working on topics in Algebra, Shape, Data and Probability.

 The Mathematics Department – Year 7 Curriculum

Year 8

Year 8 Higher

Year 8 Higher

Autumn Term,

Half Term 1

Autumn Term,

Half Term 2

Spring Term,

Half Term 2

Unit Title Number Work, Area and Perimeter Witten Calculations, Decimal Division, Estimates, Angles, Algebra, Problem Solving and Circle Work Reflection, Averages, Algebra, Construction and Locus
Key Question(s)?

How can we decompose a number into prime factors?

 

How can we perform calculations with fractions and negatives?

 

How can we find the area and perimeter of parallelograms and trapeziums?

How can we use written calculations to solve complex mathematical problems?

 

How do we divide decimals?

 

How can we solve angle calculations involving algebra?

 

How can I use formulae to calculate the area and circumference of a circle.

How can we reflect in straight lines on coordinate axes?

 

How do we find averages and use them to compare two sets of data?

 

How can we substitute a value in a formula

 

How can we describe the locus of a point?

Threshold Concepts

A prime number is a number which has exactly two factors and a factor is a number that divides into another number exactly.

 

Area is the amount of space inside a two dimensional shape.

 

Perimeter is the measured distance around the edge of a shape.

A decimal is a way of expressing fractions, while estimation is the process of finding a value that is close enough to the right answer to serve our purpose.

 

In algebra, a term is a number, variable or a combination of both. Like terms are terms whose variables are the same.

 

The circumference of a circle is the same as its perimeter.

Knowledge of how to draw vertical, horizontal and diagonal straight lines.

 

frequency table is a method of organizing raw data in a compact form by displaying a series of scores in ascending or descending order, together with their frequencies—the number of times each score occurs in the data set.

 

In a stem and leaf diagram, each data value is split into a “leaf” (usually the last digit) and a “stem” (the other digits). For example “32” is split into “3” (stem) and “2” (leaf).

 

Substitution into a formula describes the process of giving a specific letter a value that is used on every occasion it occurs.

 

locus is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

 

 

Link to Prior Learning

 

Review prior learning on factors and multiples

Build on prior work with fractions.

Build on prior skills of area and perimeter of rectangles and triangles.

Consolidate learning on negative numbers and sequences

 

Key principles around the use and manipulation of decimals and place value.

Build on existing angle facts through inclusion of algebra in calculations.

Algebra

Build on prior skills of area and perimeter of shapes.

Key principles of averages (mean, mode and median) are developed.

Build on knowledge of reflection.

Prior constructions skills are used to draw loci accurately

 

 

 

Year 8 Higher

Spring Term,

Half Term 2

Summer Term,

Half Term 1

Summer Term, 

Half Term 2

Unit Title Bearings, Handling Data, Transformations and Equations Enlargement, Sequences, Pythagoras, Graphs,  Ratio, Congruence and Tessellation Algebra, 3D Shapes, Percentages and Probability
Key Question(s)?

What are the key principles of bearings?

 

How can we draw a scatter graph and use it to describe correlation?

 

What are the different types of transformation?

 

How can we solve equations with brackets or variables on both sides?

 How can we enlarge a shape with a given centre of enlargement?

 

How can we express sequences in algebra?

 

How do we use Pythagoras’ theorem?

 

What is a ratio and how do we use them?

How can we solve equations with fractions?

 

How can we describe 3D shapes in maths and find their volume?

 

How can we increase or decrease quantities by a percentage?

 

How can we find the probability of an event not occurring?

Threshold Concepts

A bearing is an angle, measured clockwise from ‘North’. It must have three digits.

 

We can use a range of graphs to represent and handle data. These include bar charts, pie charts and scatter graphs (a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present).

 

A shape is ‘transformed’ when it is manipulated; for example it can be rotated through a given angle. A shape can undergo more than on transformation.

An enlargement is exactly the same shape as the original and has a centre of enlargement and a scale factor

 

The nth term is a general expression used when exploring sequences.

 

Pythagoras’ theorem is used to find the lengths of each side of a right angled triangle. It is expressed as a2 + b2 = c2.

 

A ratio says how much of one thing there is compared to another. For example two adults and three children could be expressed as 2:3.

A prism is a 3D shape that is consistent and has identical ends.

 

The probability of an event not occurring is one minus the probability of event occurring.

 

A percentage multiplier which is (100 +/- % change) / 100) can be used to increase or decrease a quantity.

Link to Prior Learning

 

Knowledge of single transformations is now developed with more than one transformation.

Bar charts, line graphs and simple pie charts are

The algebra in this unit builds on knowledge of expanding brackets and solving simple equations.

 

 

 

Sequences and term to term rules are developed here to give formulae for nth terms.

Coordinates and the algebra needed to plot straight lines are developed more formally and extended to plotting curves

Prior knowledge of angle facts is needed to find angles to prove congruence.

Knowledge of solving of equations is revisited and extended.

Percentage multipliers builds on knowledge of percentages and is an efficient way to solve more complex problems.

Knowledge and sequencing rationale Each year we aim to revisit key topics, deepening understanding and developing knowledge. Number work is strengthened and used to develop work in Shape and Data handling. Algebra is developed across this year.

 

 

 

 

Year 8 Core

Year 8

Core

Autumn Term,

Half Term 1

Autumn Term,

Half Term 2

Spring Term,

Half Term 2

Unit Title Sequences, Number Work, Area and Perimeter Estimation, Algebra, Fractions, Decimals, Percentages, Angles and Circle Work Written calculations, Formulae and expressions, Drawing Graphs and  Reflection
Key Question(s)?

How can we decompose a number into prime factors?

 

How can we perform calculations with fractions and negatives?

 

How can we find the area and perimeter of parallelograms and trapeziums?

How can we use estimates to find an approximate answer to an calculation?

 

How can we collect like terms and form expressions in algebra?

 

How can we convert between decimals, fractions and percentages?

 

How can I find angles with parallel lines?

 

How can I use formulae to calculate the area and circumference of a circle.

How can we solve mathematical problems with and  without a calculator?

 

How can we substitute a  value into a formula?

 

How can we draw straight lines on coordinate axes and understand the equation of a line?

 

How can we interpret information shown graphically?

 

How can we reflect shapes in a given line?

Threshold Concepts

A prime number is a number which has exactly two factors and a factor is a number that divides into another number exactly.

 

Area is the amount of space inside a two dimensional shape.

 

Perimeter is the measured distance around the edge of a shape.

Estimation is the process of using a value that is close enough to the original to get an approximate answer to a calculation.

 

In algebra, a term is a number, variable or a combination of both. Like terms are terms whose variables are the same.

 

The circumference of a circle is the same as its perimeter.

Substitution into a formula describes the process of giving a specific letter a value that is used on every occasion it occurs.

 

Knowledge of how to draw vertical, horizontal and diagonal straight lines.

 

 

 

Link to Prior Learning

 

Review prior learning on factors and multiples

Build on prior work with fractions.

Build on and extend knowledge of area and perimeter.

Consolidate and extend learning on negative numbers and sequences

 

Key principles around the use and manipulation of decimals and place value.

Build on existing angle facts through inclusion of algebra in calculations.

Algebra

Build on prior skills of area and perimeter of shapes.

Build on knowledge of coordinates and reflection.

Build and extend knowledge of what “3x” means in algebra

 

Year 8

Core

Spring Term,

Half Term 2

Summer Term,

Half Term 1

Summer Term, 

Half Term 2

Unit Title Data, Transformations, Graphs, Fractions. Brackets and Equations Ratio, Sequences, Enlargement, Congruent Shapes, Drawing Graphs Percentages, Probability, Algebra, 3-D objects
Key Question(s)?

How can we find the mean, median, mode and range and use them to compare two sets of data?

 

How can we rotate a shape?

 

How can we interpret real-life graphs?

 

How can we solve equations with brackets?

What is a ratio and how do we use them?

 

How can we express sequences in algebra?

 

How can we enlarge a shape with a given centre of enlargement?

 

How can I draw a graph given its’ equation?

 

How do I know 2 shapes are congruent?

 

How can we express on number as a percentage of another?

 

How can we find the probability of an event not occurring?

 

How can we confidently work with algebra?

 

How can we describe 3D shapes in maths and find their volume?

 

Threshold Concepts

Data can be compared by looking at both the general behaviour (through use of an average) and the variability (using the range)

 

 

When a shape is rotated, it has a centre of rotation, and angle turned through and direction of rotation.

 

When an equation includes a bracket, this must be expanded as the first step of solving

 

An enlargement is exactly the same shape as the original and has a centre of enlargement and a scale factor

 

The nth term is a general expression used when exploring sequences.

 

A ratio says how much of one thing there is compared to another. For example two adults and three children could be expressed as 2:3.

A prism is a 3D shape that is consistent and has identical ends.

 

The probability of an event not occurring is one minus the probability of event occurring.

 

 

Link to Prior Learning

 

Knowledge of averages is developed in this unit.

Knowledge of single transformations is now developed with more than one transformation.

The algebra in this unit builds on knowledge of expanding brackets and solving simple equations.

 

Sequences and term to term rules are developed here to give formulae for nth terms.

Coordinates and the algebra needed to plot straight lines are developed more formally and extended to plotting curves

Knnowledge of like terms, brackets and solving of equations is consollidated.

 

Percentages

 

Knowledge of probability is extended in this unit.

Knowledge and sequencing rationale Each year we aim to revisit key topics, deepening understanding and developing knowledge. Number work is strengthened and used to develop work in Shape and Data handling. Algebra is developed across this year.

The Mathematics Department – Year 8 Curriculum

Year 9
Year 9 Higher Autumn Term, Half Term 1 Autumn Term, Half Term 2 Spring Term,  Half Term 1
Unit Title Fractions, Algebra, Angles and Data Fractions, Indices and Standard form. Transformations, sequences, rounding and percentage change.
Key Question(s)?

What are the key principles of fractions?

What are the key principles of algebra?

What is an average?

 

How do we multiply fractions and use standard form to describe extremely large numbers?

How do we accurately transform a shape?

How do we find the nth term?

How do we find percentage change?

 

Threshold Concepts

To add and subtract terms in algebra they must be like terms.

 

An equation can sometimes be solved to find a value for the variable which satisfies the equation.

 

An average is a value to best represent a set of data.

 

 

 

 

 

To multiply fractions, multiply the numerators and denominators. To divide fractions, multiply the first fraction by the reciprocal of the second.

Reciprocal means 1/ the number.

 

Indices are often called powers. The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.

 

Standard form is a way of writing very large or very small in numbers in the form a x 10n where ‘a’ is a number between 1 and 10.

There are a number of key ways that we can transform a shape, including reflection, rotation and enlargement.

 

The nth term is a general expression which can be used to find any numbered term by substituting in a value for n.

 

Percentage change refers to the difference between an original number and its new value, expressed as a percentage of the original value.

Link to Prior Learning

Higher

Reviewing previous learning on fractions. Building on skills regarding solving equations.

Reviewing previous learning on averages, and deepening understanding.

Reviewing previous learning on fractions. Generalising existing knowledge of indices, then leading into standard form. Reviewing and building on previous learning on transformations. Reviewing and building on existing knowledge of sequences. Reviewing and building on existing knowledge of percentages.
Spring Term, Half Term 2 Summer Term, Half Term 1 Summer Term,  Half Term 2
Unit Title Final Transformation, Charts, Graphs and Simultaneous Equations Trigonometry, Inequalities and Probability GCSE Units 1 & 2 (Number)
Key Question(s)?

How can we use charts to express mathematical information?

 

What are simultaneous equations and how can they be solved?

How can we use trigonometric functions to relate sides and angles?

 

How can we calculate probabilities?

1) Can we become fluent in working with whole numbers, fractions, decimals and surds?

2) How can we use percentages to describe change, including simple and compound interest, and reverse percentages? What is a ratio and how is it used? What are the index laws?

Threshold Concepts

Translation is the process of “Sliding” – moving a shape without rotating or flipping it. The shape still looks exactly the same, just in a different place.

To fully describe a transformation, you must give all the information that would be required to do it from the beginning.

 

A pie chart uses pie ‘slices’ or sectors to show the relative size of each value in a set of data.

 

A bar chart is a chart that uses bars to show comparison between categories of data.

 

Simultaneous equations are a set of two or more equations that contain two or more unknown letters which can often be found.

Trigonometry is the study of triangles and in this unit we learn about:

 

 

An inequality is similar to an equation, but results in a range of possible values rather than a single correct answer. Inequalities are solved in a similar way to equations, by balancing each side.

 

Probability refers to the likelihood of an outcome. Equally likely outcomes are possibilities where each outcome has the same probability, for example rolling a far die.

1) Recurring decimals can be written as fractions. Surds are exact representations of irrational numbers which can be manipulated and sometimes simplified.

2) The full (or ‘original’) amount is 100%, which is equivalent to 1. Ratio can be most easily represented through bar-modelling. Index laws relate to multiplication & division in a similar manner to the way in which multiplication & division relate to addition & subtraction.

Link to Prior Learning

Higher

Translation is the 4th transformation to learn following the last unit.

Reviewing and building on graph/chart work.

Simultaneous graphs build on essential number and algebraic skills already taught.

Trigonometry builds on knowledge of functions and equations.

Inequalities builds on knowledge of solving equations.

Reviewing and building on existing knowledge of probability.

1) Key principles of whole number arithmetic, place value, and manipulating fractions. Surds are a largely new concept.

2) Increasing or decreasing by a % is equivalent to using the appropriate decimal multiplier. Knowledge of indices is strengthened and extended.

Knowledge and sequencing rationale Each year we aim to re-visit key topics, deepening understanding and extending knowledge. This year we are strengthening work on Number after the summer holidays, then working on topics in Shape, Algebra and Probability.

 

Year 9 Core Autumn Term, Half Term 1 Autumn Term, Half Term 2 Spring Term,  Half Term 1
Unit Title Arithmetic, algebra, properties of shapes and data handling Geometry, solving equations, numerical reasoning Graphs, area, shape transformations, 3d shapes
Key Question(s)? What are the key principles of algebra? How do we multiply fractions and use standard form to describe extremely large numbers?

How do we draw a graph given an equation?

 

How do we calculate volume?

 

Threshold Concepts

To add and subtract terms in algebra they must be like terms. Formulae can be rearranged using algebraic manipulation to make a single letter the subject of the equation.

 

Expanding a bracket means to multiply letters or numbers inside the bracket by the letter or number outside the bracket. Factorising means to reverse this process and put an expression into brackets.

 

Only add/subtract fractions once their denominators are equal.

Circumference is the calculation of the distance around the edge of a circle.

Area is the amount of space inside a two-dimensional shape.

 

An equation can sometimes be solved to find a value for the variable which satisfies the equation.

 

Rounding means making a number simpler but keeping its value close to what it was.

An equation can be interpreted using a table of values which then gives coordinates which can be plotted on a graph.

 

Translation means moving a shape vertically and/or horizontally.

 

Volume is a measure of how much space a solid object takes up.

Link to Prior Learning

Core

Reviewing and building on previous learning with algebra. Building on skills regarding expanding and factorising.

Reviewing and building on previous learning on fractions.

Reviewing work on perimeter/area and applying this to a circle.

Reviewing work on algebra and extending knowledge of solving equations.

Extending work on rounding to estimation.

Reviewing work on substitution and coordinates leading to drawing graphs.

Translation builds on confidence with coordinates and other transformations.

Knowledge of volume is strengthened and deepened.

Spring Term, Half Term 2

 

Summer Term, Half Term 1 Summer Term,  Half Term 2
Unit Title Percentages, algebra, averages and ratio Consolidation, preparing for GCSE, and Pythagoras’ Theorem GCSE Unit 1 (Number) & 2 (Algebra)
Key Question(s)?

How can you describe a sequence by giving a general term?

 

What is an average?

 

How are the 3 sides of a right-angled triangle linked?

1) Can we become fluent in basic numeracy, negatives, BIDMAS, powers, roots. How do we find factors, multiples, HCFs and LCMs? What is a prime number. How do we write a number as a product of its prime factors? What is standard form?

2) What is algebra, and what are the main types? How does substitution into an expression or formula work?

Threshold Concepts

A sequence can be described using the nth term. This is a general expression which can be used to find any numbered term by substituting in a value for n. Eg. If the

nth term = 3n + 1, the 5th term = 3 x 5 + 1 = 16.

 

An average is a value to best represent a set of data.

Pythagoras’ Theorem is a relationship between the lengths of the sides of a right angled triangle.

Pythagoras’ Theorem is used to find 3rd side of a right-angled triangle using a2 + b2= c2

 

1) Place value is used to describe the value of a digit, depending upon where it appears within the number. Multiplication and division should be understood as inverses, but also as repeated addition and subtraction respectively. Addition and subtraction, in turn, are inverses. The order of operations is summarised by the acronym BIDMAS. Factors multiply to make a larger number. Multiples are the elements of the multiplication tables. Two numbers can have an HCF and an LCM. A prime has only two distinct factors. Every whole number can be written as a product of primes. Standard form is used to write very large and very small numbers efficiently.

2) Algebra consists of (a) Substitution, (b) Simplifying Expressions, and (c) Solving Equations. Substitution is important when using a formula; numbers replace letters before a calculation is performed.

Link to Prior Learning

Core

Nth term work builds on knowledge of sequences and substitution.

Knowledge of averages is strengthened and deepened.

Pythagoras’ builds on knowledge of triangles and substitution and equations.

1) Basic numeracy will have been taught since primary school. Factors, multiples and primes have been considered during each year of KS3. Standard form relies upon understanding that multiplying and dividing by 10 moves a digit across the columns using place value.

2) This has been studied in previous years.

Knowledge and sequencing rationale Each year we aim to re-visit key topics, deepening understanding and extending knowledge. This year we are strengthening work on Number after the summer holidays, then having a particular emphasis on Algebra, in addition to extending knowledge of Shape.

 

The Mathematics Department – Year 9 Curriculum

Year 10
Year 10 Higher Autumn Term, Half Term 1 Autumn Term, Half Term 2 Spring Term,  Half Term 1
Unit Title GCSE Units 3 (Geometry) & 4 (Algebra) GCSE Units 5 (Number) & 6 (Algebra) GCSE Units 6 (Algebra) & 8 (Statistics)*
Key Question(s)?

3) What are the key principles (or ‘angle rules) of geometry?

4) How does one use substitution? How does one expand a bracket, or factorise? What is a quadratic expression? How does one solve a quadratic equation?

5) What are prime factors useful for? How does one use standard form? How can numbers be rounded? What is proportionality?

6) How do you solve a linear equation? How do you change the subject of an equation? What is a function, and what are inverse and composite functions?

6) What is iteration? What are the key features of straight line graphs and curved graphs? How do tangents and areas under curves relate to ‘real-life’ quantities? What are the equations of motion?

8) What is the difference between theoretical probability and relative frequency? What is expectation? What is the best way to list possible outcomes?

Threshold Concepts

3) Interior and exterior angles in polygons can be calculated. Angles in circles satisfy certain special properties called circle theorems.

4) Working with quadratics in a variety of ways must be mastered: factorising, difference of two squares, solving an equation, solving a word problem.

5) Prime factors are useful for finding the HCF and LCM of two numbers. Standard form is an efficient way of writing very large and very small numbers. Measured quantities always contain error – bounds help us quantify that error. Proportion describes the manner in which two quantities relate to each other.

6) Solving a linear equation and changing the subject of a formula use the same skill-set. A function is a set of rules which transform one quantity into another. Specific notation must be learned. Finding an inverse function requires the changing of the subject; finding a composite function involves algebraic substitution.

6) Iteration is a good technique for finding estimated solutions to otherwise unsolvable equations. A straight line is defined by two quantities – the gradient (a.k.a. the rate of change) and the y-intercept. Key points on a quadratic curve are the turning point and the intercepts with each axis. Tangents and chords on distance-time and velocity-time graphs can be used to calculate velocity and acceleration (either instantaneous or average). The area under the curve on a velocity-time graph described the distance travelled. These are related to the equations of motion.

8) It is possible to estimate how often something will probably happen if one know the probability of it happening combined with how many trials there will be. Outcomes should be listed in a logical, ordered manner to avoid error.

Link to Prior Learning

Higher

3) An angle is formed when two straight lines cross or meet each other at a point. The size of an angle is measured by the amount one line has been turned in relation to the other. Angle rules relating to straight lines and triangles will be strengthened and extended.

4) Substitution and working with brackets was studied last year and will be strengthened and extended.

5) HCFs, LCMs and standard form have been studied at a lower level in previous years. Bounds and (algebraic) proportion are largely new areas of study, although numerical proportion has been studied previously.

6) Solving a simple linear equation has been studied in some depth previously. Functions are a completely new area of study.

6) In previous years students have learned how to plot straight lines and curves from equations, but understanding the underlying concepts is a new area of study. Using tangents, areas and the equations of motion relates to work in Physics.

8) Probability was studied last year and will be strengthened and extended.

Knowledge and Knowledge and sequencing rationale Each year we aim to re-visit key topics, deepening understanding and extending knowledge. This year we are strengthening work on Number, then working on topics in Shape, Algebra and Probability.

 

*Unit 7 is not on the specification.

Year 10 Higher Spring Term, Half Term 2 Summer Term, Half Term 1 Summer Term,  Half Term 2
Unit Title GCSE Units 8 (Statistics) & 9 (Geometry) GCSE Units 9 (Geometry) & 10 (Geometry) GCSE Units 10 (Geometry), 11 (Statistics), 12 (Algebra)
Key Question(s)?

8) What is the product rule for counting? What is set notation and how is a Venn diagram used? What are independent and mutually exclusive events? What are the ‘and’ & ‘or’ rules for probability trees? What is conditional probability?

9) What are symmetry, translation and reflection?

9) What are rotation and enlargement? How do you prove that two triangles are congruent?

10) How are compound measures worked with? How does understanding their units of measurement help? What is Pythagoras’s Theorem?

10) What is trigonometry and how can it be applied to right-angled triangles? What is a vector? How are they used?

11) What are two-way tables, pie charts and scatter graphs useful for? What is a trend? How should sampling be done?

12) How are straight-line graphs to be considered? What are simultaneous equations and how are they solved? How does one find the rule for a sequence?

Threshold Concepts

8) New symbolism for set notation must be learned and used.

9) Translation & reflection are two of the four types of transformation which can be applied to shapes.

9) Rotation & enlargement are two of the four types of transformation which can be applied to shapes. Proving congruence using SSS, ASA, SAS and RHS.

10) How to apply techniques for solving linear equations to working with speed, density, pressure and other compound measures. Being able to recognise when (and how) to use Pythagoras’s Theorem, which expresses the relationship between the side lengths of a right angled triangle and is expressed as a2 + b2 = c2, if the hypotenuse is labelled ‘c’.

10) Trigonometry provides a means of finding the missing side lengths or angles within a right angled triangle. Vectors are translations and can be used to prove geometric relationships.

11) Statisticians use pie charts, scatter diagrams and sampling to show information regarding a set of data. Two-way tables are useful in probability.

12) Straight line graphs take the form of y=mx+c, where ‘m’ is the gradient and ‘c’ the y-intercept. Linear simultaneous equations describe the intersection between two straight lines. The mathematics of a straight line is identical to that for a linear sequence, except that the input for the latter is limited to integers.

Link to Prior Learning

Higher

8) Set notation is a new area of study. Probability has been studied in previous years; this work builds upon that.

9) Transformations have been studied in previous years; this work builds upon that.

9) Transformations have been studied in previous years; this work builds upon that. Congruence is a new area of study.

10) Being able to solve an equation which has a unknown in the denominator.

10) This has been studied in previous years; this work builds upon that.

11) This has been studied in previous years; this work builds upon that.

12) This has been studied in previous years; this work builds upon that.

Knowledge and Knowledge and sequencing rationale Each year we aim to re-visit key topics, deepening understanding and extending knowledge. This year we are strengthening work on Number, then working on topics in Shape, Algebra and Probability.

The Mathematics Department – Year 10 Curriculum

Year 11
Year 11 Higher Autumn Term, Half Term 1 Autumn Term, Half Term 2 Spring Term,  Half Term 1
Unit Title GCSE Units 12 (Algebra) & 13 (Geometry) GCSE Units 13 (Geometry) & 14 (Statistics) GCSE Units 16 (Algebra) & 17 (Geometry)*
Key Question(s)?

12) What is ‘completing the square’, and why is it useful? When and how is the quadratic formula used? How are simultaneous equations solved when one of them represents a curve? What is the equation of a circle? How do you find the equation of a tangent to a circle? What is an exponential equation? How can equations be interpreted graphically?

13) How does one calculate the arc length or area of the sector of a circle? How does one calculate the volume of a prism, sphere, pyramid or cone?

13) What do similar (2D) shapes have in common? What do similar (3D) objects have in common?

14) How can averages and ranges be used? How can they be calculated from tabulated data? What is a cumulative frequency graph and what does it show? What is a box-plot? What is a histogram? How are two sets of data best compared?

16) How does one solve an inequality, and how can the solution be represented graphically? How does one solve an equation with algebraic fractions, and how is this different from simplifying algebraic fractions? How can algebra be used to prove claims about numerical relationships and angle rules?

17) How does one use a map scale? What is construction, and what are the basic types? What are loci? What are the three trigonometric curves? How does one solve a trigonometric equation? How can algebra be used to define the transformation of a function?

Threshold Concepts

12) All quadratic expressions can be written in the form (x+a)2+b; this is useful for determining turning points and solving quadratic equations. The quadratic formula is a method for solving quadratic equations, particularly those which cannot be factorised. Simultaneous equations which involve a curve must be solved by substitution rather than by elimination. The general equation of a circle is x2  y2 = r2, where ‘r’ is the radius. Finding the equation of a tangent to a circle relies upon the fact that the tangent and radius are perpendicular. Exponential equations describe growth and decay curves, and have practical uses in finance and science. The roots of equations can be interpreted graphically; understanding this equivalence is crucial to further progress.

13) The formulae are new but previous techniques are sufficient.

13) The length scale factor is different from, but related to, area and volume scale factors.

14) Different types of diagrams and charts help us to extract different types of useful information. It is important to know which tool to use to achieve which result. Data is best compared by considering both the average and the spread of the data.

16) Multiplying or dividing by a negative when solving an inequality results in the sign being reversed. Two (or more) algebraic fractions can be simplified by finding a common denominator; cancelling can only be done after factorising both numerator and denominator. Solving equations which include algebraic fractions is best achieved by multiplying through by the LCM of the denominators. Algebraic proof normally requires a sentence to be re-interpreted algebraically before expanding, simplifying and factorising; it is then possible to analyse the result.

17) Map scales can be used to find distances on a map or outside by converting from one to another. A scale of 1:50 000 means that 1 cm on a map represents 50 000cm. Most constructions depend upon the properties of the equilateral triangle and rhombus. A locus is a variable point which obeys a rule – the path it traces out is the result. Trigonometric graphs are a graphical representation of the relationship between the angle produced as a radius rotates around a circle and the lengths of two of the sides of the triangle thus produced. Graphical transformations can be described algebraically.

Link to Prior Learning

Higher

12) Finding the equation of a tangent to a circle relies upon a Circle Theorem, studied in Y10. Everything else is new, although relies on basic skill sets in algebra which have been studied since Y7.

13) The concept of proportion is very helpful for understanding arcs and areas of sectors. Everything relies on basic skill sets in algebra which have been studied since Y7.

13) Proportion and ratio are critical for understanding the different scale factors; these have been studied since Y7.

14) Averages and ranges have been studied since Y7; cumulative frequency graphs, box plots and histograms are largely new material. Comparing data has been studied since Y7.

16) Prior algebraic skills (studied since Y7) need to be well-grounded if this work is to be grasped.

17) Proportion and ratio (studied since Y7) are critical to understanding map scales. Construction and loci have been considered in previous years and are developed here. The trigonometry is largely new, but builds upon Y9 work. The transformation of functions is a new area of study.

Knowledge and Knowledge and sequencing rationale Each year we aim to re-visit key topics, deepening understanding and extending knowledge. This year we are strengthening work on Number, then working on topics in Shape, Algebra and Probability.

 

*Unit 15 is not on the specification.

The Mathematics Department – Year 11 Curriculum