# 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.