# Maths

### Year 7

**Term 1:** Word Problems – Scholars will learn how to: Understand place value; Add and subtract; Estimate by rounding; Find the perimeter of rectilinear shapes; Represent and solve word problems.

**Term 2:** Explain and Investigate – Scholars will learn how to: Find factors and multiples of numbers; Find the HCF or LCM of pairs of numbers; Multiply and divide; Find the area of a rectangle and triangle; Calculate the mean.

**Term 3:** 2D Geometry – Scholars will learn how to: Draw, measure and name acute and obtuse angles; Find unknown angles using certain rules (straight lines, at a point, vertically opposite); List and use properties of triangles and quadrilaterals.

**Term 4:** Fractions – Scholars will learn how to: Find equivalent fractions; Compare and order fractions and decimals; Change mixed numbers to improper fractions and vice versa; Find a fraction of a quantity.

**Term 5:** Algebra – Scholars will learn how to: Apply the order of operations; Simplify algebraic expressions; Represent word problems with expressions; Substitute values into an expression.

**Term 6:** Percentages and Pie Charts – Scholars will learn how to: Read and interpret pie charts; Convert between percentages, Fractions and decimals; Find a percentage of a quantity; Find the whole given the part and the percentage.

### Year 8

**Term 1: **Number – Scholars will learn how to: Identify prime numbers; Use prime factorisation to find LCM, HCF, squares, cubes; Apply the order of operations including indices; Round to significant figures and use this to estimate; Multiply and divide fractions and mixed numbers; Add and subtract fractions and mixed numbers; Calculate with positive rational and decimal numbers; Use a calculator.

**Term 2:** Algebraic Equations – Scholars will learn how to: Use negative numbers; Create statements using inequality symbols; Calculate and evaluate expressions with rational numbers; Manipulate algebraic expressions; Solve linear equations; Create and solve equations from real-world situations.

**Term 3:** 2D Geometry – Scholars will learn how to: Draw accurate triangles and quadrilaterals (ruler, protractor, compasses); Find unknown angles (including parallel lines); Convert between length units and between area units; Find area and perimeter of composite figures; Find area of parallelograms and trapeziums.

**Term 4:** Proportional Reasoning – Scholars will learn how to: Convert between percentages and fractions and decimals; Calculate percentage increase and decrease; Find the whole given the part and the percentage; Recognise where equivalent ratios and rates are equivalent; Share a quantity into a given ratio; Calculate speed, distance and time.

**Term 5:** 3D Geometry – Scholars will learn how to: Find the circumference and area of a circle; Convert between mass units and between volume units; Visualise and identify 3D shapes and their nets; Find the surface area and volume of: cuboids, prisms, cylinders, composite solids.

**Term 6:** Statistics – Scholars will learn how to: Collect and organise data; Construct and interpret graphs – pictograms, bar charts, pie charts, histograms, line graphs; Interpret and compare statistical representations.

### Year 9

**Term 1: **Scholars will: Plot coordinates in all four quadrants; Find the midpoint of a line segment joining two points; Find an endpoint of a line segment, given the midpoint and one endpoint; Solve problems using coordinate grids; Identify the equations of horizontal and vertical lines; Plot coordinates from a rule to generate a straight line; Identify key features of a linear graph; Make links between the graphical and the algebraic representation; Identify parallel lines from algebraic equations. Recognise when two quantities are directly or inversely proportional to each other; Recognise the graphical representation of a proportional relationship; Solve proportion problems; Interpret and analyse real-life linear graphs; Use standard form to express very large and small numbers; Convert between standard form and ordinary numbers; Order large and small numbers; Use standard form to solve simple problems; Use scales to solve distance and area problems in context.

**Term 2:** Scholars will: Recognise linear sequences and non-linear sequences; Find the rule for the nth term for a linear sequence; Explore simple non-linear sequences; Generate sequences from a given context; Solve problems involving a variety of sequences; Multiply a term over a single bracket; Expand two or more binomials; Make links between area and perimeter and expanding brackets; Factorise expressions into a single bracket; Write expressions, equations and formulae to represent relationships; Use informal substitution to find the value of one variable given other values; Make links between solving linear equations and rearranging formulae; Apply “changing the subject” to equations of straight lines; Manipulate familiar formulae such as known formulae for area and perimeter.

**Term 3:** Scholars will: Use the standard ruler and compass constructions for: perpendicular bisector of a line segment; constructing a perpendicular to a given line from/at a given point; bisecting a given angle; Understand and use the perpendicular distance from a point to a line as the shortest distance to the line; Construct regular polygons within circles; Derive and use the conditions for congruent triangles; Appreciate when any two shapes are congruent; Enlarge shapes from a given centre, with and without coordinate grids; Understand that the corresponding angles of similar shapes are equal; Solve problems involving similar triangles; Derive and use the conditions for congruent triangles; Appreciate when any two shapes are congruent; Enlarge shapes from a given centre, with and without coordinate grids; Understand that the corresponding angles of similar shapes are equal; Solve problems involving similar triangles; Derive the proof of the sum of the angles in a triangle; Find the formula for sum of the angles of any polygon; Understand and use the sum of the exterior angles of a polygon; Solve problems involving the angles/number of sides in a regular polygon

**Term 4:** Scholars will: Form and solve linear equations and inequalities in one unknown, including those where the unknown appears on both sides; Rearrange linear equations and inequalities given in any form, including those involving fractions and brackets; Form simultaneous equations; Appreciate the links between the graphical and algebraic representations of equations; Use graphs to find approximate solutions to linear simultaneous equations; Understand that the accuracy of solutions can be checked through substitution into the original equations; Draw quadratic graphs; Solve problems using given quadratic graphs; Solve problems using given reciprocal graphs; Solve problems using given piece-wise linear graphs; Solve problems using given exponential graphs; Interpret and analyse real-life linear graphs.

**Term 5:** Scholars will: Use Pythagoras’ theorem to find missing sides in right-angled triangles; Solve associated problems in other shapes where right-angled triangles exist; Deduce whether a triangle is right-angled by considering its sides; Investigate the trigonometric ratios in a 90^{0}, 60^{0}, 30^{0} triangle; Solve problems involving the 90^{0}, 60^{0}, 30^{0} triangle; Translate a shape by a given vector; Reflect a shape in a line, including on coordinate axes; Rotate a shape about a centre, including on coordinate axes; Identify the type of transformation carried out by comparing an object and image; Know the difference between a demonstration and a proof; Follow and understand a line of formal reasoning; Use known results to develop simple geometric proofs.

**Term 6:** Scholars will: Understand and use the probability scale from 0 to 1: Understand and use the language associated with probability ; Understand the relationship between relative frequency and theoretical probability; Understand that different trials of an experiment may produce different outcomes; Systematically list outcomes using a variety of representations; Use Venn diagrams and understanding the meaning of union and intersection; Appreciate the difference between discrete and continuous data; Understand why the exact mean cannot be found from grouped data; Find an estimate of the mean from grouped data and continuous data; Interpret and draw stem and leaf diagrams, appreciating the need for a key; Use a wide variety of representations and averages to compare a set of distributions; Plot scatter graphs; Describe the type of correlation observed; Interpret correlation in the context of the data set.

### Year 10

**Term 1: **Scholars will: Understand the meaning of higher powers and know how to find these, and corresponding roots, using a calculator when necessary; Understand the difference between decimal approx and exact values of roots; Derive, understand and use the rules of indices with integer values; Be able to perform calculations involving standard form, with and without a calculator as appropriate; Solve problems involving simple and compound interest; Solve other problems involving repeated change, such as depreciation; Solve problems involving growth and decay; Recognise and describe arithmetic and geometric sequences; Generate terms of a sequence given a rule; Find a formula for the n^{th} term of a linear and geometric sequences; Explain whether a number is a member of a given sequence.

**Term 2: **Scholars will: Enlarge shapes from a given centre (positive integer & fractional scale factors); Find the centre of enlargement given a shape and its image; Understand the meaning of similarity; Find missing sides in pairs of similar shapes, including similar triangles; Solve problems involving bearings; Understand and use the trigonometric ratios sin, cos and tan; Understand the link between similar triangles and trigonometry; Derive and use the exact values of sin θ and cos θ for θ = 0^{0}, 30^{0}, 45^{0}, 60^{0} and 90^{0}; know the exact value of tan θ for θ = 0^{0}, 30^{0}, 45^{0}, 60^{0.}

**Term 3: **Scholars will: Formulate simple formulae from real-world situations; Simplify more complex algebraic expressions; Use reasoning to show whether two expressions are equivalent; Solve problems involving co-ordinates and mid-points of line segments; Find the equation of a straight line given sufficient information; Prove whether two straight lines are parallel; Use angle facts to find missing angles in increasingly complex situations; Use angle facts to justify results in simple proofs; Use the known properties of triangles and quadrilaterals to follow and to derive simple proofs in rectilinear figures, including key angle and area facts; Represent a two-dimensional vector as a column vector; Add and subtract vectors; Multiply a vector by a scalar.

**Term 4: **Scholars will: Recognise the vocabulary associated with 3D solids; Construct and interpret plans and elevations of 3D solids; Calculate the surface area and volume of spheres, cones, pyramids; Compare the surface area and volume of solid shapes; Form and solve equations related to 3D shapes; Give answers in terms of p if appropriate; Understand the limits of accuracy, using inequality notation; Convert between area and volume units; Apply ruler and compass constructions to construct figures; Identify the loci of points and use these to solve real-world problems; Prove pairs of triangles are congruent using SSS, ASA, AAS and RHS.

**Term 5: **Scholars will: Know the difference between a sample and a population; Understand different types of sampling; Find the sizes of groups in a stratified sample; Discuss the reliability of different types of sample; Understand what is meant by relative frequency; Understand why relative frequency is sometimes used as an estimate for probability; Compare theoretical probability with result obtained by experiments; Use Venn diagrams and two-way tables to solve probability problems; Construct Venn diagrams and two-way tables to solve probability problems; Use the addition law for probability, understanding when events are mutually exclusive; Systematically list sample spaces; Use the product rule for counting**; **Understand the multiplication rule for independent and dependent events; Use tree diagrams to solve probability problems; Construct tree diagrams to solve probability problems.

**Term 6: **Scholars will: Expand products of two binomials; Factorise quadratic expressions of the form; Solve quadratic equations by factorising; Develop proofs using quadratic expressions; Draw and recognise quadratic graphs; Use quadratic graphs to find the approximate solution to quadratic equations; Identify intercepts and the turning points of graphs of quadratic functions; Use tables of values to plot polynomial graphs; Use tables of values to plot reciprocal graphs; Recognise and sketch graphs of y=x; Set up and solve (algebraically) two linear simultaneous equations in two variables, interpreting the solution in context; Find the approximate solution to two simultaneous equations using a graph.

### Year 11

Year 11 scholars are entered for GCSE at two tiers; Foundation and Higher Tier. Year 11 scholars are entered for the Edexcel GCSE 1MA1 course examination. Scholars will be graded on a 9 - 1 grade scale with 4 being a pass and 5 a strong pass.

At both Higher and Foundation tiers, assessment is 100% by examination and scholars sit three papers:

- Paper 1 (non-calculator) 80 marks - 1 hour 30 minutes
- Paper 2 (calculator) 80 marks - 1 hour 30 minutes
- Paper 3 (calculator) 80 marks - 1 hour 30 minutes

Where appropriate, a smaller group of scholars will also work towards the following qualifications in addition to their GCSE:

- Entry Level Qualification (AQA)
- Level 1 Numeracy and Measure (Edexcel)
- Level 2 Numeracy and Measure (Edexcel)
- Level 2 Algebra skills (Edexcel)

**Term 1:**

**Foundation:** Identify and use the terms centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. Calculate the length of an arc of a circle. Calculate the area of a sector of a circle. Solve formal problems involving direct proportion. Solve formal problems involving inverse proportion. Follow and form logical arguments in both algebra and geometry.

**Higher: **Prove and use: The angled subtended by an arc at the centre of a circle is twice that at the circumference. The angle in a semi-circle is a right angle. Angles in the same segment are equal. Opposite angles of a cyclic quadrilateral sum to 180 degrees. A radius bisects a chord if and only if it is perpendicular to the chord. The angle between a tangent and a radius is a right angle. The alternate segment theorem. Recognise and use the equation of a circle, centre the origin. Find the equation of a tangent to a circle at a given point. Solve problems involving a quantity directly or inversely proportional to a power or a root of another quantity.

**Term 2:**

**Foundation: **Design tables to classify data. Choose the most appropriate pictorial representation for a particular set of data. Recognise when graphs and charts can be misleading. Choose the most appropriate measures for representation of a particular set of data. Interpret and construct line graphs for time series data. Identify trends within time series. Identify outliers. Plot and use scatter graphs to identify correlation. Understand that correlation does not imply causality. Draw (by eye) lines of best fit. Interpolate and extrapolate to make estimates, knowing the limitations of this. Spot outliers on a scatter graph. Use and apply compound units such as density and pressure. Know and apply Density = Mass ÷ Volume. Use and apply compound units in algebraic contexts. Solve increasingly complex number problems, some of which will require the use of compound units.

**Higher: **Construct and interpret histograms with equal and unequal class intervals. Plot and interpret cumulative frequency diagrams. Calculate estimates of statistical measures from graphical representations of grouped data. Draw and interpret box plots. Use the median and interquartile range to compare distributions.

**Term 3:**

**Foundation: **Examination revision and preparation.

**Higher:** Understand and use function notation. Find the inverse of a function. Interpret the succession of two functions as a composite function. Identify and sketch the graphs of translations and reflections of a given graph. Identify and sketch the graphs of translations and reflections of the graph of a given equation.

**Term 4:**

**Foundation: **Examination revision and preparation.

**Higher: **Find approximate solutions to equations by using: Trial and improvement/decimal search. Sign change methods. Calculate estimates of gradients of graphs using gradients of chords. Interpret gradients of real-world graphs. Calculate estimates areas under graphs. Interpret areas under real-world graphs.

**Term 5: Foundation and Higher: **Examination revision and preparation.