Year 10

Maths

Introduction and Overview The opportunities that can come from Mathematical study are endless. The Marches Maths department aim to foster a love for the learning of Maths and we are passionate in supporting all students maximise their performance in this most valuable of academic subjects. No matter what a student’s ability or aspirations there is plenty that Maths study can offer to support their future progression. In Year 10 students begin a two year route towards the GCSE Maths exam. The current Year 10 cohort will sit the new GCSE specification and will receive number rather than a lettered Grade at GCSE Maths – ranging from 1 to 9, with 9 being the highest possible result. The content of the new course is increased and both Higher and Foundation routes have a higher expectation of student performance. There will also be a strong focus on building techniques for approaching and solving Mathematical problems; interpreting a problem, identifying the skill required and using a clear method and determined attitude to arrive at a solution. Year 10 consists of 6 different units of study. The skills covered are assessed at the end of every unit and students will be given targets to work on to improve further.

How to support your child Students must be confident with recalling solutions to any of the 1 to 12 multiplication tables. You can help achieve this goal by verbally testing your child at any opportunity – if you identify a gap in their knowledge then you should focus your questioning regularly on plugging this gap. Your child’s response does not need to be instant but they should be arriving at answers reasonably quickly but confidently. The impact this will have on their mathematical progress is invaluable and students who fall short on this skill can find this subject very difficult to grasp. Students will receive a piece of written feedback in their exercise book at least once every six lessons. This will include a target or extension question to support their progress. You can review your child’s Maths book for these targets or questions and encourage/support them to act on them. All students have full access to www.MyMaths.co.uk. This is an interactive learning tool that allows students to learn/revise specific topics through online lessons, complete online consolidation tasks for homework that give instant results and detailed feedback. In addition to completing tasks set by teachers students should use MyMaths to work independently on their own personal learning targets. Equipment required for Maths sessions are a Pen, a Pencil, a Rubber, a Ruler, a Protractor, a Compass and a Scientific Calculator. We recommend buying a Casio FX-83 Scientific Calculator or similar. A good calculator like this one will support your child for as long as they continue to study Maths. They are available from pupil services for £6.

Year 10 Unit 1 – Number 4 (Foundation route)

Ratio and proportion

Identify and work with fractions in ratio problems (N11)

Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 (R3)

Use ratio notation, including reduction to simplest form (R4)

Divide a given quantity into two parts in a given part : part or part : whole ratio

Express the division of a quantity into two parts as a ratio

Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations) (R5)

Including better value or best-buy problems.

Express a multiplicative relationship between two quantities as a ratio or a fraction (R6)

Understand and use proportion as equality of ratios (R7)

Relate ratios to fractions and to linear functions (R8)

Year 10 Unit 2 – Shape 2 (Foundation route)

Angles

Use conventional terms and notations: o points, lines, vertices, edges, planes, parallel lines,

perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries

Use the standard conventions for labelling and referring to the sides and angles of triangles

Draw diagrams from written descriptions (G1)

Apply the properties of: o angles at a point o angles at a point on a straight line o vertically opposite angles

Understand and use alternate and corresponding angles on parallel lines (G3)

colloquial terms such as Z angles are not acceptable and should not be used

Scale diagrams and bearings

Use scale factors, scale diagrams and maps (R2)

including geometrical problems

Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings (G15)

including the eight compass point bearings and three-figure bearings

2D representations of 3D shapes

Construct and interpret plans and elevations of 3D shapes (G13)

Properties of polygons

Derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) (G3)

Derive and apply the properties and definitions of: o special types of quadrilaterals, including square, rectangle,

parallelogram, trapezium, kite and rhombus o and triangles and other plane figures using appropriate

language (G4)

including knowing names and properties of isosceles, equilateral, scalene, right-angled, acute-angled, obtuse-angled triangles

including knowing names and using the polygons: pentagon, hexagon, octagon and decagon

Congruence and similarity

Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) (G5)

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs (G6)

Apply and use the concepts of congruence and similarity, including the relationships between lengths similar figures (G19)

Measures

Apply and interpret limits of accuracy (N16)

Use standard units of measure and related concepts (length, area, volume / capacity, mass, time, money etc) (G14)

Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate (N13)

know and use metric conversion factors for length, area, volume and capacity. Imperial / metric conversions will be given in the question

Change freely between related standard units (e.g. time, length, area, volume / capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts (R1)

Use compound units such as speed, rates of pay, unit pricing, density and pressure (R11)

including making comparisons

Transformations

Identify, describe and construct congruent and similar shapes,

including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors) (G7)

Describe translations as 2D vectors (G24)

Harder volumes

Compare lengths, areas and volumes using ratio notation

scale factors

make links to similarity (R12)

Know and apply formulae to calculate the volume of cuboids and other right prisms (including cylinders) (G16)

Calculate the volume of spheres, pyramids, cones and composite solids (G17)

Including frustums

Calculate exactly with multiples of π (N8)

Year 10 Unit 3 – Algebra 2 (Foundation route)

Coordinates and linear graphs

Work with co-ordinates in all four quadrants (A8)

Solve geometrical problems on co-ordinate axes (G11)

Plot graphs of equations that correspond to straight line graphs in the co-ordinate plane (A9)

Real life graphs

Plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration (A14)

including problems requiring a graphical solution

Interpret the gradient of a straight-line graph as a rate of change (R14)

Quadratic Graphs

Recognise, sketch and interpret graphs of quadratic functions (A12)

Identify and interpret roots, intercepts and turning points of quadratic functions graphically

Deduce roots algebraically (A11)

Including the symmetrical property of a quadratic

Algebra and Graphs

Solve linear equations in one unknown algebraically

Including those with the unknown on both sides of the equation

Find approximate solutions using a graph (A17)

including use of brackets

Translate simple situations or procedures into algebraic expressions or formulae

derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution (A21)

including the solution of geometrical problems and problems set in context

Sketching Graphs

Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions

and the reciprocal function, y = x

1 with x ≠ 0 (A12)

Year 10 Unit 4 – Number 5 (Foundation route)

Indices

Use positive integer powers and associated real roots (square, cube and higher)

Recognise powers of 2, 3, 4, 5 (N6)

Including square numbers up to 15 x 15

Know that 1000 = 10 3 and 1 million = 10 6

Calculate with roots and with integer indices (N7)

Standard Form

Understand and use place value (e.g. when working with very large or very small numbers) (N2)

Calculate with and interpret standard form A 10 n

, where 1 ⩽ A < 10 and n is an integer (N9)

With and without a calculator. Interpret calculator displays.

Year 10 Unit 5 – Data 2 (Foundation route)

Basic Probability

Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees (P1)

probabilities should be written as fractions, decimals or percentages

Apply the property that the probabilities of an exhaustive set of outcomes sum to one

Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one (P4)

Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities (P7)

Probability

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future experiments (P2)

Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale (P3)

Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing sample size (P5)

Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams (P6)

Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions (P8)

know when to add and when to multiply two or more probabilities

Year 10 Unit 6 – Algebra 3 (Foundation route)

Inequalities

Solve linear inequalities in variable

Represent the solution set on a number line (A22)

Know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary.

Graphs recap and extension

Solve geometrical problems on co-ordinate axes (G11)

Use the form to identify parallel lines

Find the equation of the line through two given points, or through one point with a given gradient (A9)

Identify and interpret gradients and intercepts of linear functions graphically and algebraically (A10)

Algebra recap and extension

Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

this will be implicitly and explicitly assessed

Simplify and manipulate algebraic expressions (including those involving surds) by: o collecting like terms o multiplying a single term over a bracket o taking out common factors

Deduce expressions to calculate the nth term of a linear sequence

Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation

including use of brackets

Year 10 Unit 1 – Number 3 (Higher route)

Factors and multiples

Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique factorisation theorem (N4)

prime factor decomposition including product of prime factors written in index form

Apply systematic listing strategies and the use of the product rule for counting (N5)

including using lists, tables and diagrams

Basic Fractions

Order positive and negative fractions (N1)

Apply the four operations, including formal written methods, to simple fractions (proper and improper) and mixed numbers - both positive and negative (N2)

Calculate exactly with fractions (N8)

Year 10 Unit 2 – Shape 2 (Higher route)

Perimeter and area

Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres (G12)

Calculate the perimeter of a 2D shape and composite shapes

Find the surface area of pyramids composite shapes (G17)

Know and apply formulae to calculate area of: o triangles o parallelograms o trapezia (G16)

Circumference and area

Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment (G9)

Know and use the formulae: o Circumference of a circle =2πr=πd o Area of a circle =πr 2

Calculate the perimeters of 2D shapes including circles and composite shapes

Calculate areas of circles and composite shapes

Calculate surface area of spheres, cones and composite solids (G17)

solutions in terms of π may be asked for

Calculate arc lengths, angles and areas of sectors of circles (G18)

Volume

Compare lengths, areas and volumes using ratio notation

Scale factors

Make links to similarity (R12)

Know and apply the formulae to calculate the volume of cuboids and other right prisms (including cylinders) (G16)

Calculate the volume of spheres, pyramids, cones and composite solids (G17)

including frustums

Calculate exactly with multiples of π (N8)

Congruence and similarity

Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) (G5)

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides including the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs (G6)

Apply and use the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures (G19)

Pythagoras theorem and basic trigonometry

Know the formula for Pythagoras' Theorem a 2 +b 2 =c 2

Apply it to find angles and lengths in right angled triangles and, where possible, general triangles in two and three dimensional figures

Know and use the trigonometric ratios

(G20)

Know the exact values of

0°, 30° 45°, 60° and 90°

Know the exact value of

0°, 30°, 45° and 60° (G21)

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides including Pythagoras’ Theorem and use known results to obtain simple proofs (G6)

Compare lengths using ratio notation; make links to trigonometric ratios (R12)

Year 10 Unit 3 – Algebra 3 (Higher route)

Algebra: introduction to quadratics and rearranging formulae

Simplify and manipulate algebraic expressions by: o expanding products of two binomials o factorising quadratic expressions of the form x

2 + bx + c

including the difference of two squares o simplifying expressions involving sums, products and

powers, including the laws of indices (A4)

Understand and use standard mathematical formulae

Rearrange formulae to change the subject (A5)

including use of formulae from other subjects in words and using symbols

Algebra: quadratics, rearranging formulae and identities

Simplify and manipulate algebraic expressions (including those involving surds) by:

o expanding products of two or more binomials

o factorising quadratic expressions of the form including the difference of two squares

o factorising quadratic expressions of the form

o simplifying expressions involving sums, products and

powers, including the laws of indices (A4)

Understand and use standard mathematical formulae

Rearrange formulae to change the subject (A5)

including use of formulae from other subjects in words and using symbols

Where appropriate, interpret simple expressions as functions with inputs and outputs

Interpret the reverse process as the ‘inverse function’

Interpret the succession of two functions as a ‘composite function’ (A7)

understand and use function notation: f(x) , fg(x) , f −1 (x) is expected at higher tier

Algebraic fractions

Simplify and manipulate algebraic expressions involving algebraic fractions (A4)

Year 10 Unit 4 – Number 4 (Higher route)

Ratio and proportion

Identify and work with fractions in ratio problems (N11)

Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 (R3)

Use ratio notation, including reduction to simplest form (R4)

Divide a given quantity into two parts in a given part:part or part:whole ratio

Express the division of a quantity into two parts as a ratio

Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing and concentrations) (R5)

including better value or best buy problems

Express a multiplicative relationship between two quantities as a ratio or fraction (R6)

Understand and use proportion as equality of ratios (R7)

Relate ratios to fractions and to linear functions (R8)

Standard Form

Understand and use place value (e.g. when working with very large or very small numbers) (N2)

including questions set in context

Calculate with and interpret standard form

where and n is an integer

with and without a calculator

interpret calculator displays

Indices

Use positive integer powers and associated real roots (square, cube and higher)

Recognise powers of 2, 3, 4, 5

Estimate powers and roots of any given positive number (N6)

Including square numbers up to 15 x 15

Know that 1000 = 10 3 and 1 million = 10 6

Calculate with roots and with integer and fractional indices (N7)

Year 10 Unit 5 – Algebra 4 (Higher route)

Sketching Graphs

Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions

and the reciprocal function, y = x

1 with x ≠ 0 (A12)

including using the symmetry of functions

Further equations and graphs

Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation

Find approximate solutions using a graph (A17)

including use of brackets

Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula

Find approximate solutions using a graph (A18)

Recognise, sketch and interpret graphs of linear and quadratic functions (A12)

Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square (A11)

including the symmetrical property of a quadratic

Translate simple situations or procedures into algebraic expressions or formulae

derive an equation, solve the equation and interpret the solution (A21)

including solution of geometrical problems and problems set in context

Further sketching graphs

Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions

and the reciprocal function with ,

exponential functions for positive values of , and the trigonometric functions (with arguments in degrees)

for angles of any size (A12)

Simultaneous equations

Solve two simultaneous equations in two variables (linear / linear or linear/quadratic) algebraically

Find approximate solutions using a graph (A19)

Translate simple situations or procedures into algebraic expressions or formulae

Derive two simultaneous equations

Solve the equations and interpret the solution (A21)

including the solution of geometrical problems and problems set in context

Linear and quadratic equations and their graphs

Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation

Find approximate solutions using a graph (A17)

including use of brackets

Solve quadratic equations algebraically by factorising

Find approximate solutions using a graph (A18)

Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and the solve the equation and interpret the solution (A21)

including solution of geometrical problems and problems set in context

Real life graphs

Plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration (A14)

including problems requiring a graphical solution

Interpret the gradient of a straight-line graph as a rate of change

(R14)

Year 10 Unit 6 – Data 2 (Higher route)

Basic Probability

Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees (P1)

probabilities should be written as fractions, decimals or percentages

Apply the property that the probabilities of an exhaustive set of outcomes sum to 1

Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1 (P4)

Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities (P7)

Probability

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future experiments (P2)

Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale (P3)

Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing sample size (P5)

Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams (P6)

Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions (P8)

know when to add and when to multiply two or more probabilities

Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams