# Mathematics

Mathematics is a core subject, essential in many walks of life, and further studies. We have a committed team of 13 staff who regularly provide extra-curricular opportunities in order that each pupil reaches their own potential. Students at Ralph Thoresby School follow a 2-year Key Stage 3. The Key Stage 3 Scheme of work is focused on mastery of some of the core areas of mathematics. This enables a smoother transition on to the GCSE content when students reach Key Stage 4. During Year 7 and 8, students will cover topics from across all of the main strands of Mathematics: Number, Algebra, Geometry and Statistics. Students explore the Mathematical concepts with connections to real life problems and are taught in a way that encourages depth of understanding and reasoning skills. Stretch and challenge are a key element of every lesson and problem solving questions are frequently incorporated into both classwork and homework to help build on these skills in preparation for the new GCSE style questions. Students are given half termly assessments in line with the School PINS system. These assessments are based on the content covered during the term and allow staff and students to review individual strengths and build on the areas needed.

### Links to SMSC and British Values

Developing deep thinking and questioning the way in which the world works promotes the spiritual growth of our students.

Within the classroom, we encourage respect, reward good behaviour. We value listening to others views and opinions on problem solving.

We promote discussion about mathematical understanding and challenge assumptions, supporting students to question information and data that they are presented with.

We encourage collaborative learning in the classroom – in the form of listening and learning from each other and paired discussion / working partners.

We investigate and research cross cultural patterns – tessellation, Islamic tiling.

Courses available to take at KS4 and KS5

• KS4 - GCSE Mathematics
• KS5 - A Level Mathematics
• Year 7 Overview
• 01

#### Course Topic(s)

Number – Place value. Number – Addition and subtraction.

#### Content / Learning Outcomes

Understand and use place value. Order and round numbers, including decimals.
Use written methods for addition and subtraction. Use inverse operations and solve problems involving perimeter.

#### Assessment

Half term 1 PINS assessment

• 02

#### Course Topic(s)

Number – multiplication and division.

#### Content / Learning Outcomes

Use written methods for multiplication, including decimals. Use inverse operations and recognise the order of operations. Use integer powers and roots, including finding the prime decomposition of a number. Calculate the mean and solve problems involving area.

#### Assessment

Half term 2 End of term PINS assessment

• 03

#### Course Topic(s)

Number – Fractions 1.

#### Content / Learning Outcomes

Represent fractions using diagrams and a number line. Express a quantity as a fraction of another and identify equivalent fractions. Order and simplify fractions. Convert between mixed numbers and improper fractions and between fractions, decimals and percentages. Use concepts of LCM to add and subtract fractions.

#### Assessment

Half term 3 PINS assessment

• 04

#### Course Topic(s)

Statistics 1. Number – Negative numbers.

#### Content / Learning Outcomes

Understand the data handling cycle and different types of data. Collect, organise and interpret tally charts, two way tables, averages and consider outliers. Draw and interpret bar charts, pictograms and line graphs.
Use the four operations with negative numbers and understand the order of operations.

#### Assessment

Half term 4 End of term PINS assessment

• 05

Algebra 1.

#### Content / Learning Outcomes

Understand that a letter represents a variable. Understand the difference between an expression, equation, formula, term, function and identity and form expressions from worded problems. Use and interpret algebraic notation. Substitute numerical values into formulae and expressions and collect like terms. Use algebraic notation to solve simple linear equations and generate terms of a sequence, including finding the nth term.

#### Assessment

Half term 4 PINS assessment

• 06

#### Course Topic(s)

Geometry – lines and angles.

#### Content / Learning Outcomes

Describe and draw using conventional terms. Derive and illustrate properties of triangles, quadrilaterals and other plane figures. Measure and draw angles and use angles properties, including angles in parallel lines. Use angles in a triangle to deduce angles in polygon facts.

#### Assessment

Half term 6 End of year PINS assessment

#### How can I support my child?

Revision materials/support for any exams: Year 7 homework book, Mathletics, MyMaths.

Equipment required: Pen, pencil, protractor, compass, ruler, scientific calculator.

Regular activities to undertake: One piece of homework each week, extra activities on mathletics and TT Rockstars would be useful.

#### Homework Information

Students will be set one piece of Maths homework a week. In year 7 this will usually take the form of an exercise from the year 7 homework book. Other homework could include mathletics tasks or worksheets to consolidate learning in the lesson.

• Year 8 Overview
• 01

#### Course Topic(s)

Revision of year 7 work. Number – Fractions 2.

#### Content / Learning Outcomes

Multiply and divide proper and improper fractions and mixed numbers, including negatives. Find a fraction of an amount and inversely find the whole amount when given a fraction. Find a fractional increase and decrease.

#### Assessment

Half term 1 PINS assessment

• 02

#### Course Topic(s)

Number – Percentages.

#### Content / Learning Outcomes

Define percentage and interpret them as a fraction and a decimal. Express one quantity as a percentage of another. Compare two quantities using percentages, and work with percentages greater than 100%. Solve problems involving percentage change.

#### Assessment

Half term 2 End of term PINS assessment

• 03

Algebra 2.

#### Content / Learning Outcomes

Substitute numerical values into formulae and expressions, including scientific formulae. Simplify and manipulate algebraic terms to maintain equivalence. Use algebraic methods to solve linear equations. Understand and use the concepts of inequalities. Rearrange formulae to change the subject.

#### Assessment

Half term 3 PINS assessment

• 04

#### Course Topic(s)

Geometry – Circles and area.

#### Content / Learning Outcomes

Convert between cm2 and m2. Derive and apply formulae to calculate and solve problems involving area of circles, composite shapes and trapeziums. Calculate and solve problems involving perimeters of 2-D shapes (including circles).

#### Assessment

Half term 4 End of term PINS assessment

• 05

#### Course Topic(s)

Ratio, proportion and rates of change.

#### Content / Learning Outcomes

Convert freely between related standard units.
Use ratio notation, write ratio in its simplest form. Divide a given quantity into two or more parts. Given information about one part, find the whole or other part(s). Use compound units such as speed, unit pricing and density to solve problems. Solve problems involving direct and inverse proportion. Draw and interpret pie charts.

#### Assessment

Half term 5 PINS assessment

• 06

#### Course Topic(s)

Statistics. Geometry – 3D shapes.

#### Content / Learning Outcomes

Construct and analyse stem and leaf diagrams, including back to back. For non-grouped data in a table, find the mean, median, mode, range.
Use the properties of faces, surfaces, edges and vertices to solve problems in 3D. Convert between cm3 and m3. Derive and apply formulae to solve problems involving volume and surface area of cuboids (including cubes) and other prisms (including cylinders). Construct and interpret plans and elevations of 3-D shapes.

#### Assessment

Half term 6 End of year PINS assessment

#### How can I support my child?

Revision materials/support for any exams: Mathletics, MyMaths.

Equipment required: Pen, pencil, protractor, compass, ruler, scientific calculator.

Regular activities to undertake: One piece of homework each week, extra activities on mathletics and TT Rockstars would be useful.

#### Homework Information

Students will be given one piece of homework per week. This will take the form of consolidation of classwork in order to identify areas of weakness.

• Year 9 Overview
• 01

#### Course Topic(s)

Foundations: Unit 1 – Number. Higher: Unit 1 – Number

#### Content / Learning Outcomes

Foundation:
Unit 1: Calculations, Decimal numbers, Place value, Factors and multiples, Squares, cubes and roots, Index notation, Prime factors.

Higher:
Unit 1: Number problems and reasoning, Place value and estimating, HCF and LCM, Calculating with powers, Zero, negative and fractional indices, Powers of 10 and standard form, Surds.

#### Assessment

PINS assessments completed after each unit.

• 02

#### Course Topic(s)

Foundation: Unit 2 – Algebra. Higher: Unit 2 – Algebra

#### Content / Learning Outcomes

Foundation:
Unit 2: Algebraic expressions, Simplifying expressions, Substitution, Formulae, Expanding brackets, Factorising, Using expressions and formulae.

Higher:
Unit 2: Algebraic indices, Expanding and factorising, Equations, Formulae, Linear sequences, Non-linear sequences.

#### Assessment

PINS assessments completed after each unit.

• 03

#### Course Topic(s)

Foundation: Unit 3 – Graphics, tables and charts. Unit 4 – Fractions and percentages. Higher: Unit 3 – Interpreting and representing data. UNit 4 – Fractions, ratio and percentages.

#### Content / Learning Outcomes

Foundation:
Unit 3: Frequency tables, Two way tables, Representing data, Time series, Stem and Leaf diagrams, Pie charts, Scatter graphs, Line of best fit.
Unit 4: Working with fractions, Operations with fractions, Multiplying fractions, Dividing fractions, Fractions and decimals, Fractions and percentages, Calculating percentages.

Higher:
Unit 3: Statistical diagrams 1, Time series, Scatter graphs, Line of best fit, Averages and range, Statistical diagrams 2.
Unit 4: Fractions, Ratios, Ratio and proportion, Percentages, Fractions, decimals and percentages.

#### Assessment

PINS assessments completed after each unit.

• 04

#### Course Topic(s)

Foundation: Unit 5 – Equations, inequalities and sequences. Higher: Unit 5 – Angles and trigonometry.

#### Content / Learning Outcomes

Foundation:
Unit 5: Solving equations, Introducing inequalities, Formulae, Generating sequences, Using the nth term of a sequence.

Higher:
Unit 5: Angle properties of triangles and quadrilaterals, Interior angles of a polygon, Exterior angles of a polygon, Pythagoras’ theorem, Trigonometry.

#### Assessment

PINS assessments completed after each unit.

• 05

#### Course Topic(s)

Foundation: Unit 6 – Angles. Unit 7 – Averages and range. Higher: Unit 6 – Graphs. Unit 7 – Area and Volume

#### Content / Learning Outcomes

Foundation:
Unit 6: Properties of shapes, Angles in parallel lines, Angles in triangles, Exterior and interior angles, Geometrical patterns.
Unit 7: Mean, mode, median and range, Types of average, Estimating the mean, Sampling.

Higher:
Unit 6: Linear graphs, Graphing rates of change, Real life graphs, Line segments, Quadratic graphs, Cubic and reciprocal graphs, More graphs.
Unit 7: Perimeter and area, Units and accuracy, Prisms, Circles, Sectors of circles, Cylinders and spheres, Pyramids and cones.

#### Assessment

PINS assessments completed after each unit.

• 06

#### Course Topic(s)

Foundation: Unit 8 – Perimeter, area and volume. Higher: Unit 8 – Transformations and constructions.

#### Content / Learning Outcomes

Foundation:
Unit 8: Rectangles, parallelograms and triangles, Trapezia and changing units, Area of compound shapes, Surface area of 3D solids, Volume of prisms.

Higher:
Unit 8: 3D Solids, Reflection, rotation, translation and enlargement, Combinations of transformations, Bearings and scale drawings, Constructions, Loci.

#### Assessment

PINS assessments completed after each unit.

#### How can I support my child?

Revision materials/support for any exams: MyMaths, Corbett maths, Kesh maths, PiXL maths app, GCSE revision guides (available to buy from school).

Equipment required: Pen, pencil, protractor, compass, ruler, scientific calculator.

Regular activities to undertake: One piece of homework each week, extra activities on Mymaths, Corbett maths, Kesh maths, PiXL maths app would be useful.

#### Homework Information

Students will be given one piece of homework per week. This will take the form of consolidation of classwork in order to identify areas of weakness.

• Year 10 Overview
• 01

#### Course Topic(s)

Foundation: Unit 9 – Graphs Unit 10 – Transformations. Higher: Unit 9 – Equations and inequalities Unit 10 – Probability

#### Content / Learning Outcomes

Foundation:
Unit 9: Coordinates, Linear graphs, Gradient, y=mx + c, Real-life graphs, Distance-time graphs.
Unit 10: Translation, reflection, rotation and enlargement, Combining transformations.

Higher:
Unit 9: Solving quadratic equations, Completing the square, Solving simple simultaneous equations, Solving linear and quadratic simultaneous equations, Solving linear inequalities.
Unit 10: Combined events, Mutually exclusive events, Experimental probability, Independent events and tree diagrams, Conditional probability, Venn diagrams and set notation.

#### Assessment

PINS assessments completed after each unit.

• 02

#### Course Topic(s)

Foundation: Unit 11 – Ratio and proportion. Higher: Unit 11 – Multiplicative reasoning

#### Content / Learning Outcomes

Foundation:
Unit 11: Writing ratios, Using ratios, Ratios and measures, Comparing using ratios, Using proportion, Proportion and graphs, Proportion problems.

Higher:
Unit 11: Growth and decay, Compound measures, Ratio and proportion.

#### Assessment

PINS assessments completed after each unit.

• 03

#### Course Topic(s)

Foundation: Unit 12 – Right angled triangles Unit 13 – Probability. Higher: Unit 12 – Similarity and congruence Unit 13 – More trigonometry

#### Content / Learning Outcomes

Foundation:
Unit 12: Pythagoras’ theorem, Trigonometry, Finding lengths and angles using trigonometry.
Unit 13: Calculating probability, Two events, Experimental probability, Venn diagrams, Tree diagrams.

Higher:
Unit 12: Congruence, Geometric proof and congruence, Similarity, Similarity in 3D solids.
Unit 13: Accuracy, Graph of the sine, cosine and tangent functions, Calculating areas and the sine rule, The cosine rule and trigonometric problems, Solving problems in 3D, Transforming trigonometric graphs.

#### Assessment

PINS assessments completed after each unit.

• 04

#### Course Topic(s)

Foundation: Unit 14 – Multiplicative reasoning. Higher: Unit 14 – Further statistics

#### Content / Learning Outcomes

Foundation:
Unit 14: Percentages, Growth and decay, Compound measures, Distance, speed and time, Direct and inverse proportion.

Higher:
Unit 14: Sampling, Cumulative frequency, Box plots, Drawing histograms, Interpreting histograms, Comparing and describing populations.

#### Assessment

PINS assessments completed after each unit.

• 05

#### Course Topic(s)

Foundation: Unit 15 – Constructions, loci and bearings Unit 16 – Quadratic equations and graphs. Higher: Unit 15 – Equations and graphs Unit 16 – Circle theorems

#### Content / Learning Outcomes

Foundation:
Unit 15: 3D Solids, Plans and elevations, Accurate drawings, Scale drawings and maps, Constructions, Loci and regions, Bearings.

Higher:
Unit 15: Solving simultaneous equations graphically, Representing inequalities graphically, Graphs of quadratic functions, Solving quadratic functions graphically, Graphs of cubic functions.
Unit 16: Radii and chords, Tangent, Angles in circles, Applying circle theorems.

#### Assessment

PINS assessments completed after each unit.

• 06

#### Course Topic(s)

Foundation: Unit 17 – Perimeter, area and volume Higher: Unit 17 – More algebra

#### Content / Learning Outcomes

Foundation:
Unit 17: Circumference of a circle, Area of a circle, Semicircles and sectors, Composite 2D shapes and cylinders, Pyramids and cones, Spheres and composite solids.

Higher:
Unit 17: Rearranging formulae, Algebraic functions, Simplifying algebraic functions, Surds, Solving algebraic fraction equations.

#### Assessment

PINS assessments completed after each unit.

#### How can I support my child?

Revision materials/support for any exams: MyMaths, Corbett maths, Kesh maths, PiXL maths app, GCSE revision guides (available to buy from school).

Equipment required: Pen, pencil, protractor, compass, ruler, scientific calculator.

Regular activities to undertake: One piece of homework each week, extra activities on Mymaths, Corbett maths, Kesh maths, PiXL maths app would be useful.

#### Homework Information / Coursework Information

Students will receive one piece of homework each week. This will take the form of essential skills revision where students will practice core skills to help prepare them for their GCSEs.

• Year 11 Overview
• 01

#### Course Topic(s)

Foundation: Unit 18 – Fractions, indices and standard form Unit 19 – Congruence, similarity and vectors. Higher: Unit 18 – Vectors and geometric proof

#### Content / Learning Outcomes

Foundation:
Unit 18: Multiplying and dividing fractions, The laws of indices, Writing numbers in standard form, Calculating with standard form.
Unit 19: Similarity and enlargement, Using similarity, Congruence, Vectors.

Higher:
Unit 18: Vectors and vector notation, Vector arithmetic, Parallel vectors and collinear points, solving geometric problems.

#### Assessment

PINS assessments completed after each unit.

• 02

#### Course Topic(s)

Foundation: Unit 20 – More algebra. Higher: Unit 19 – Proportion and graphs

#### Content / Learning Outcomes

Foundation:
Unit 20: Graphs of cubic and reciprocal functions, Non-linear graphs, Solving simultaneous equations graphically, Solving simultaneous equations algebraically, Rearranging formulae, Proof.

Higher:
Unit 19: Direct proportion, Inverse proportion, Exponential functions, Non-linear graphs, Translating graphs of functions, Reflecting and stretching graphs of functions.

#### Assessment

PINS assessments completed after each unit.

• 03

#### Course Topic(s)

GCSE revision

#### Content / Learning Outcomes

GCSE revision

#### Assessment

PINS assessments completed after each unit.

• 04

#### Course Topic(s)

GCSE revision

#### Content / Learning Outcomes

GCSE revision

#### Assessment

PINS assessments completed after each unit.

• 05

#### Course Topic(s)

GCSE revision

#### Content / Learning Outcomes

GCSE revision

#### Assessment

PINS assessments completed after each unit.

• 06

#### Course Topic(s)

GCSE revision

#### Content / Learning Outcomes

GCSE revision

#### Assessment

PINS assessments completed after each unit.

#### How can I support my child?

Revision materials/support for any exams: MyMaths, Corbett maths, Kesh maths, PiXL maths app, GCSE revision guides (available to buy from school).

Equipment required: Pen, pencil, protractor, compass, ruler, scientific calculator.

Regular activities to undertake: One piece of homework each week, extra activities on Mymaths, Corbett maths, Kesh maths, PiXL maths app would be useful.

#### Homework Information / Coursework Information

Students will receive one piece of homework each week. This will take the form of essential skills revision where students will practice core skills to help prepare them for their GCSEs.

• Year 12 Overview
• 01

#### Course Topic(s)

Algebra and Functions Statistics Mechanics

#### Content / Learning Outcomes

Sampling, data presentation and interpretation
Quantities and units in mechanics, kinematics, equations with constant acceleration

#### Assessment

Topic test at end of each unit

• 02

#### Course Topic(s)

Co-ordinate geometry Further Algebra Statistics Mechanics

#### Content / Learning Outcomes

Straight line graphs, parallel and perpendicular lines, length and area problems, circles
Algebraic division, polynomials, factor theorem, binomial expansion
Scatter diagrams, regression lines, outliers
SUVAT formulae, motion under gravity

#### Assessment

Topic test at end of each unit

• 03

#### Course Topic(s)

Trigonometry Vectors Statistics Mechanics

#### Content / Learning Outcomes

Trig ratios, graphs, identities and equations.
Vector definitions, scalars and multiples, geometric problems
Probability, using the binomial distribution to calculate probabilities
Forces and Newton’s Laws

#### Assessment

Topic test at end of each unit

• 04

#### Course Topic(s)

Calculus Statistics Mechanics

#### Content / Learning Outcomes

Differentiation, Integration
Hypothesis testing
Forces and Newton’s Laws

#### Assessment

Topic test at end of each unit

• 05

#### Course Topic(s)

Exponentials and logarithms Statistics Mechanics Revision

#### Content / Learning Outcomes

Exponential functions and natural logarithms
Hypothesis tests involving the binomial distribution
Kinematics 2 – variable acceleration

#### Assessment

Topic test at end of each unit

• 06

#### Course Topic(s)

Revision Proof Algebra

#### Content / Learning Outcomes

Revision to prepare for exam
Proof by deduction, proof by exhaustion, counter examples
Algebraic fractions and partial fractions.

#### Assessment

End of year exam – covers all topics taught this year

#### How can I support my child?

Revision materials/support for any exams: A level revision guides – teachers will advise on these

Equipment required: Scientific Calculator – your teacher will advise which model is best

Regular activities to undertake: Complete additional questions on every topic you are taught

#### Homework Information

Students should repeat exercises they have struggled with.  They will regularly be given exam style questions and they should complete these.

• Year 13 Overview
• 01

#### Course Topic(s)

Algebra Statistics Mechanics

#### Content / Learning Outcomes

Functions and modelling
Sequences and series
Binomial theorem
Regression and correlation
Moments

#### Assessment

Topic test at end of each unit

• 02

#### Course Topic(s)

Trigonometry Statistics Mechanics

#### Content / Learning Outcomes

Radians, arcs and sectors, trig identities
Parametric equations
Conditional probability
Set notation
Resolving forces
Friction

Mock exams

• 03

#### Course Topic(s)

Differentiation Numerical methods Statistics Mechanics

#### Content / Learning Outcomes

Differentiating trig functions, products, quotients
Chain rule
Implicit and Parametric differentiation
Iteration, Newton-Raphson method
The Normal Distribution
Applications of kinematics

#### Assessment

Topic test at end of each unit

• 04

#### Course Topic(s)

Integration Statistics Mechanics

#### Content / Learning Outcomes

Integration by parts, integration by substitution
Trapezium rule
Differential equations
Using the Normal distribution
Applications of forces

#### Assessment

Topic test at end of each unit

• 05

#### Course Topic(s)

Vectors Statistics Mechanics

#### Content / Learning Outcomes

3D vectors
Hypothesis testing for the mean of the Normal distribution
Further kinematics
Revision

Mock exams

• 06

#### Course Topic(s)

A level exam

#### Content / Learning Outcomes

Revision and preparation for exams

#### Assessment

A level exams

#### How can I support my child?

Revision materials/support for any exams: A level revision guides – teachers will advise on these

Equipment required: Scientific Calculator – your teacher will advise which model is best

Regular activities to undertake: Complete additional questions on every topic you are taught

#### Homework Information

The best preparation for maths exams is completing exam questions on every topic.  These will be provided for you.

Ensure you show complete working out for any question you attempt.  Always ensure your work is checked.

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