Mathematics

 

MATHEMATICS

The mathematics department at Lacon Childe School is committed to providing our students with the tools they need to make sense of a universe which can only be understood by the language of maths. Of course we want them to have the good mental arithmetic and basic functional skills that are needed for their everyday lives, but we also want them to ask: ‘why is that true?’; ‘is there a pattern there?’; ‘how can I explain that?’ and ‘does that answer make sense?’.

In short, we want them to be independent problem solvers; as will their future employers.

Key Stage 3

As soon as students start mathematics at Lacon Childe, they should view each year as a progressive step towards building the skills and knowledge they need to succeed in the GCSE course at the end of Year 11.

In the first two years, students are timetabled for three hours of maths lessons per week. They are placed in banded groups at the start of Year 7 which allows us to focus on reinforcing, developing and using key concepts that are already partially familiar to them from the excellent grounding they receive at their primary schools.

Year 8 is when students will really start to utilise their problem solving skills, as they become more competent at linking ideas from different areas of mathematics and developing resilience in their ability to work through more open ended or challenging problems. Students are taught in sets from Year 8 onwards to ensure that they are accessing the right level of foundation or higher tier material. These are carefully monitored using regular assessments, performance data and discussions with the students themselves.

A detailed breakdown of the content delivered and skills developed across both Key Stages can be found in the document below: ‘Maths Learning Ladder Descriptors’.

maths learning ladder descriptors

 

Key Stage 4

From Year 9 onwards, we start the actual GCSE content and students receive seven hours of timetabled lessons per fortnight to allow for the significant amount of new content which must be delivered. We follow the Pearson Edexcel 9-1 Mathematics GCSE specification which is assessed at the end of Year 11 via three, ninety minute examinations. All three exams must be entered at either foundation tier (grades 1 – 5) or higher tier (grades 4 – 9).

The topics taught within each tier are summarised below:

 

topics taught within each tier at keystage 4

Foundation Tier Unit

Foundation Tier Topics

 

Higher Tier Unit

Higher Tier Topics

1. Number

BIDMAS, Decimals, Place value, Factors & multiples, Squares, Cubes & roots, Index notation, Prime factors

 

1. Number

Place value & estimating, HCF & LCM, Calculating with indices, Zero, negative & fractional indices, Powers of 10 & Standard form, Surds

2. Algebra

Algebraic expressions, Simplifying, Substitution, Formulae, Expanding, Factorising,

 

2. Algebra

Algebraic indices, Expanding & factorising, Equations, Formulae, Linear sequences, Non-linear sequences

3. Graphs, Tables & Charts

Frequency tables, 2 way tables, Representing data, Time series, Stem & leaf diagrams, Pie charts, Scatter graphs, Lines of best fit

 

3. Interpreting & Representing Data

Statistical diagrams, Time series, Scatter graphs, Lines of best fit, Averages & range,

4. Fractions & Percentages

Operations with fractions, Multiplying & dividing, Fractions & decimals, Fractions & percentages, Calculating percentages

 

4. Fractions, Ratios & Percentages

Fractions, Ratios, Ratios & (direct) proportion, Percentages, Fractions, decimals & percentages

5. Equations, inequalities & sequences

Solving equations, Solving with brackets, Inequalities, Using formulae, Generating sequences, nth term

 

5. Angles & Trigonometry

Angle properties of triangles & quadrilaterals, Interior & exterior angles of polygons, Pythagoras' theorem, Trigonometry

6. Angles

Properties of shapes, Angles in parallel lines, Angles in triangles, Exterior & interior angles, Geometrical Problems

 

6. Graphs

Linear graphs, Graphing rates of change, Real-life graphs, Line segments, Quadratic graphs, Cubic & reciprocal graphs, More graphs

7. Averages & Range

Mean & range, Mode, median & range, Types of average, Estimating the mean, Sampling

 

7. Area & Volume

Perimeter & area, Units & accuracy, Prisms, Circles, Sectors of circles, Cylinders & spheres, Pyramids & cones

8. Perimeter, Area & Volume 1

Rectangles, parallelograms & triangles, Trapezia & changing units, Area of compound shapes, Surface area of 3D solids, Volume of prisms

 

8. Transformations & Constructions

3D solids, Reflection & rotation, Enlargement, Transformations & combinations of transformations, Bearings & scale drawings, Constructions, Loci

9. Graphs

Coordinates, Linear graphs, Gradient, y = mx + c, Real life graphs, Distance-time graphs

 

9. Equations & Inequalities

Solving quadratic equations, Completing the square, Solving simultaneous equations, Solving linear and quadratic simultaneous equations, Solving linear inequalities

10. Transformations

Translation, Reflection, Rotation, Enlargement, Describing enlargements, Combining transformations

 

10. Probability

Combined events, Mutually exclusive events, Experimental probability, Independent events & tree diagrams, Conditional probability, Venn diagrams and set notation

11. Ratio & Proportion

Writing ratios, Using ratios, Ratios & measures, Comparing using ratios, Using proportion, Proportion & graphs

 

11. Multiplicative Reasoning

Growth & decay, Compound measures, Ratio & proportion

12. Right Angled Triangles

Pythagoras’ theorem, Sine ratio, Cosine ratio, Tangent ratio, Finding lengths & angles using trigonometry

 

12. Similarity & Congruence

Congruence, Geometric proof, Similarity, Similarity in 3D solids

13. Probability

Calculating probability, Two events, Experimental probability, Venn diagrams, Tree diagrams

 

13. Further Trigonometry

Accuracy (bounds), Trigonometric graphs, Sine rule, Cosine rule, Area rule, 3D trigonometry, Transforming trigonometric graphs

14. Multiplicative Reasoning

Percentages, Growth & decay, Compound measures, Distance, Speed & time, Direct & inverse proportion

 

14. Further Statistics

Sampling, Cumulative frequency, Box plots, Drawing & interpreting histograms, Describing populations

15. Constructions, loci & bearings

3D solids, Plans & elevations, Accurate drawings, Scale drawings & maps, Constructions, Loci & regions, Bearings

 

15. Equations & Graphs

Solving simultaneous equations graphically, Quadratic graphs, Solving quadratics graphically, Cubic graphs

16. Quadratic equations & graphs

Expanding double brackets, Plotting quadratic graphs, Using quadratic graphs, Factorising quadratic expressions, Solving quadratic equations algebraically

 

16. Circle Theorems

Radii & chords, Tangents, Angles in circles, Applying circle theorems

17. Perimeter, Area & Volume 2

Circumference of a circle, Area of a circle, Semicircles & sectors, Composite 2D shapes & cylinders, Pyramids & cones, Spheres & composite solids

 

17. Further Algebra

Rearranging formulae, Algebraic fractions, Simplifying algebraic fractions, Surds, Solving algebraic fraction equations, Functions, Proof

18. Fractions, Indices & Standard Form

Multiplying & dividing fractions, Laws of indices, Standard form for large & small numbers, Calculating with standard form

 

18. Vectors & Geometric Proof

Vectors & vector notation, Vector arithmetic, Parallel vectors & collinear points, Solving geometric problems

19. Congruence, similarity & vectors

Similarity & enlargement, Using similarity, Congruence, Vectors

 

19. Proportion & Graphs

Direct proportion, Inverse proportion, Exponential functions, Non-linear graphs, Translating graphs of functions, Reflecting & stretching graphs of functions

20. Further Algebra

Graphs of cubic and reciprocal functions, Non-linear graphs, Solving simultaneous equations graphically & algebraically, Rearranging formulae, Proof

     

Assessment

At Key Stage 3, your child can expect to sit one assessment test per half term within their normal maths lessons. Once per year, this test will take place in the hall instead, as a mock exam.

At Key Stage 4, students complete a topic test at the end of each of the taught units, again within their maths lessons. They will also sit extra mock examinations in the hall which are designed to approximate the real GCSE exam experience as closely as possible, depending on their stage within the course.

Revision materials and past papers can be found on the school network or by using the OneDrive link in the ‘Useful Websites & Links’ section.

Support

Extra support is always available in the form of maths help sessions which are run at lunchtimes by members of the department. We also offer comprehensive revision sessions after school for Year 11 students in preparation for their GCSE exams.

We offer discounted revision guides and workbooks to students and advise that they obtain these early in Year 9 in order to assist them with their studies.

You can help your child even more by:

  • ensuring that they have the necessary equipment: ruler, compass, protractor, scientific calculator;
  • discussing their maths work and checking that they are up to date with homework and revision as relevant;
  • reminding them to use maths help sessions at school if they are having difficulty with a particular topic;
  • encouraging independence in their learning by suggesting that they complete questions from their workbook or past papers to supplement their class and homework;
  • doing puzzles with them or making mental maths questions part of everyday conversations.

For extra information regarding supporting Year 11 students, please click on the link below to refer to the recent presentation to parents: ‘Maths Department Presentation to Y11 Parents’.

maths presentation to yr11 parents

Suggested Reading List

  • Maths for Mums & Dads (Mike Askey & Rob Eastaway)
  • Fermat’s Last Theorem (Simon Singh)
  • Just Six Numbers (Martin Rees)
  • 17 Equations that Changed the World (Ian Stewart)
  • Flatland (Edwin Abbott)

… or any popular maths, puzzle or lateral thinking book!

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