Maths
Curriculum
M.Booth
Subject Performance Leader
Introduction
Over 5,000 years ago Mathematics evolved from basic numeracy into a new language to precisely describe the universe around us and as a tool for mankind to make its mark on t he planet. From the Great Pyramids of Giza to the Apollo Space Program, Mathematics has been at the heart of humanities most impressive achievements. In our modern society it plays an essential role in Economics, Engineering, Science & Technology. In the past 500 years, Mathematics has extended past the confines of physical reality and now represents an exciting frontier for the realms of human thought.
Throughout KS3&4, all independent study is managed via the SPARX platform.
Key Skills & Understanding:
numeracy · calculus · data analysis · inference & interpretation · logical thinking · problem solving · knowledge & retention
let's take a look...
Theme/Unit
Class Content
Assisted Study
The number
system
Calculate with negative numbers.
Find factors and multiples of values.
Recognise prime, square, cube
numbers and their roots. Order of
operations.
Number calculations.
Ask what the prime numbers are up to 30. Give your child calculations with up to 3 digit numbers.
Fractions,
decimals and
percentages
Calculate with fractions.
Calculate with percentages
Retrieving data. Wait a few seconds and try to cut or copy again.
Calculating
space
Calculate the area of shapes.
Calculate the volume of shapes. Use co-ordinates in all four quadrants
Retrieving data. Wait a few seconds and try to cut or copy again.
Mathematical
movement
Use transformations to move shapes
.
Presentation of
data
Construct and interpret pie charts.
Construct and interpret a line graph.
Retrieving data. Wait a few seconds and try to cut or copy again.
Measuring
data
Calculate and interpret averages. Use the mean to find a missing value.
.
Maths
Y7 | Key Stage 3
Maths
KS3
7
YEAR
The Number
System
Find the highest common factor and
lowest common multiple.
Use power notation. Order of
operations with brackets.
Ask how your child uses power notation. Give your child calculations with fractions and check on a calculator. Help your child with calculations involving negative values
Calculating
Number calculations with decimals, fractions and negative numbers.
Check students are getting “green” and if not students need to attend h/ w club (see below)
Sequences
Angles
Describe a sequence with a rule.
Generate a sequence from a rule.
Calculate missing angles in shapes.
Explain reasoning using known angle facts.
Ensure your child has a geometry set.
Fractions,
decimals and
percentages
Solve problems involving percentage changes.
Ask your child how to find percentages of a value.
Equations & inequalities
Solve equations using the balance method.
Check solutions using substitution.
Check students are getting “green” and if not students need to attend h/w club (see below)
Calculating
space
Presentation of data.
Calculate the area of shapes.Calculate the perimeter of shapes. Construct and interpret graphs. Select the most appropriate graph.
Ask your child what formulae they know for the area of shapes.
Outsiders
Simplifying expressions.
Expanding brackets.
Substitute values into formulae.
Check students are getting “green” and if not students need to attend h/w club (see below)
Y8 | Key Stage 3
Maths
Theme/Unit
Class Content
Assisted Study
8
YEAR
Y9 | Key Stage 3
Maths
The number
system
Convert between numbers in standard index form.
Work with powers and roots. Round values to a given degree of accuracy.
Ensure your child has a scientific calculator for all maths lessons.
Algebraic
manipulation
Simplify more complex expressions.
Expanding more than one bracket.
Work with basic laws of indices
Check students are getting “green” and if not students need to attend h/w club (see below)
Sequences
Find the nth term of a sequence. Use the nth term to determine values in a sequence
Ask your child to explain why the nth term is used
Equations
Solving equations with unknowns on both sides.
Forming equations from a practical situation.
Check students are getting “green” and if not students need to attend h/w club (see below)
Probability
List combinations systematically.
Understand and calculate
theoretical and experimental probability.
Ask your child to explain different probabilities when rolling 2 dice .
Data
Use and interpret scatter graphs.
Recognise and explain the meaning of scatter graphs.
Ask your child to give you two
variables that would have positive, negative or no correlation. Explain what correlations means.
Theme/Unit
Class Content
Assisted Study
9
YEAR
Maths (Foundation)
GCSE
Options Booklet
Revision Guides
Exam information
Extra Curricular & Trips
KS4
Autumn Term
Calculating:
Working with Standard index form
Rounding numbers and applying limits of accuracy
Visualising and constructing:
Constructions and applications to loci
Plans and elevations
Calculating space:
Knowing and using circle theorems
Arc lengths, area of sectors and segments
Pythagoras’ theorem
Conjecturing:
Congruency criteria for triangles
Algebraic proficiency:
Understand definitions for algebraic expressions, equations, identities and formulae
Manipulate expressions through collecting like term, multiplication, expanding and factorising brackets
Algebraic proficiency 2:
Understand linear graphs (y=mx+c) and how the gradient and y-intercept can be found.
Find the equation of a line from 2 points
Interpret gradient
Recognise, sketch and interpret key graphs
Check that students have watched the video prior to attempting the quiz. If they need further support there are 'Building blocks' on prerequisite skills at the bottom of the page. Students will be assessed each half term on cumulative topics in the style of a GCSE exam. Cheat sheets can be produced and used in these assessments and should be no more than one side of A4. Students can aid their revision by completing weekly Memri or Fix up 5 tasks on SPARX maths.
Spring Term
Solving equations and inequalities 1:
Understand concepts and vocabulary of inequalities
Solve linear inequalities
Represent the solution set to an inequality on a number line
Use a number line to find a set of values that are true for 2 inequalities
Pattern sniffing:
Recognise arithmetic, quadratic, geometric and Fibonacci sequences
Identify term to term rules and find missing terms in a sequence
Establish and use the nth term for linear sequences
Proportional reasoning:
Direct and inverse proportion
Understand and use concepts of congruency and similarity
Understand and use compound units
.
Summer Term
Understanding risk:
Probability of independent and dependant events
Interpret and use Relative frequency and Theoretical probabilities
Solving equations and inequalities 2 :
Solve linear simultaneous equations
Find solutions using a graph
Analysing Statistics:
Interpret Scatter graphs, using a line of best fit to make estimations
Calculate averages from a frequency table including grouped data
Angles:
Calculate angles in polygons
Calculate angles in parallel lines
Investigating properties of shapes:
Use trigonometric ratios to find missing sides and angles in 2D right-angled triangles
Know some exact values for sin, cos and tan ratios for the angles
Transformations:
Describe and construct reflections, rotations and translations
Describe and construct Enlargements including with fractional scale factors
Transformations 2:
Use and interpret visual representations of vectors
Apply addition, subtraction and multiplication by scalar to column vectors.
Solving Algebraically 3:
Approximate solutions of a quadratic equation using its graph
Solve quadratic equations through factorisation where a =1
Calculating space:
calculate the surface area and volume of 3D shapes including spheres, cones and pyramids
Exploring fractions, decimals and percentages:
Calculated repeated percentage change
Recognise when simple interest and compound interest calculations are needed
Set up, solve and interpret growth and decay problems
.
Maths
Y10 | Key Stage 4
Theme/Unit
Class Content
Assisted Study
10
YEAR
Maths
Y11 | Key Stage 4
Theme/Unit
Class Content
Assisted Study
All Terms
Over the course of year 11 each group will follow a bespoke scheme of work which is planned through analysis of the class mock examinations, this will involve revision or extension as appropriate and key skills to access exam level questions.
Studentys will be assessed each half term on non calculator skills.
At December and Easter they will sit full sets of exam papers as mock exams.
Cheat sheets will not be allowed to be used in any year 11 assessment.
All students will be set a weekly examination style booklet.
Class teachers will also set SPARX tasks on specific topics.
Extra parental support: Spelling tests of key words Test times tables and mental arithmetic.
Ask students to explain HOW they have worked something out.
Make posters of important formulae and facts and test recall of these.
All students should have the latest Casio calculator (available in most supermarkets and stationers) and will ideally have a maths equipment set including a protractor and a pair of compasses.
11
YEAR
Maths (Higher)
GCSE
KS4
Options Booklet
Revision Guides
Exam information
Extra Curricular & Trips
Autumn Term
Calculating.
Calculate with roots and integer, negative and fractional indices. Calculate with surds.
Limits of accuracy.
Check that students have watched the video prior to attempting the quiz. If they need further support there are 'Building blocks' on prerequisite skills at the bottom of the page. Students will be assessed each half term on cumulative topics in the style of a GCSE exam. Cheat sheets can be produced and used in these assessments and should be no more than one side of A4. Students can aid their revision by completing weekly Memri or Fix up 5 tasks on SPARX maths.
Sept/Oct
Solving equations and inequalities 1
.
Oct
Find approximate solutions to equations using iteration.
Solve 2 linear simultaneous equations.
.
Dec
Mathematical movement 1
Identify, describe and construct similar shapes.
Enlargement of shapes inc. fractional SF.
Investigating properties of shapes.
Make links to similarity inc. trig. ratios and SF.
Know exact values of Sin∂ and Cos∂ for 30°, 45°, 60° and 90°.
Find angles and lengths in R.A triangles using trigonometry.
.
Feb
Algebraic proficiency.
Simplify and manipulate further algebraic expressions
Factorise quadratic expressions.
Proportional reasoning.
Direct and inverse proportion.
Interpret graphs that illustrate proportion.
.
Spring Term
Calculating space.
Calculate surface area and volume of spheres, pyramids, cones and composite solids.
Apply concepts of congruence and similarity including relationships between length, area and volumes in similar figures.
Sequences:
Deduce expressions to calculate the nth term of quadratic sequences. Geometric progressions.
.
Apr
Algebraic proficiency – visualising.
Plot and interpret graphs inc. exponential and Reciprocal.
Calculate gradient and areas under graphs.
Fractions, decimals and percentages:
.
Jun
Exploring FDP.
Convert between recurring decimals and fractions.
Set up, solve and interpret answers to growth and decay problems, including with compound interest.
.
Jun/July
Solving equations and inequalities 2
Solve quadratic equations algebraically by factorising.
Deduce and sketch key features of quadratic graphs through Completing the Square, Quadratic formula and factorisation.
.
Summer Term
Understanding risk.
Apply systematic listing strategies inc. use of product rule.
Calculate and interpret conditional probabilities.
Analysing statistics.
Understanding and analyse various sampling techniques
Cumulative frequency graphs.
Mathematical movement 2
Add, subtract and multiply vectors.
Proof if vectors are parallel
Angles
Apply the circle theorems concerning angles, radii, tangents and chords.
Investigating properties of shapes
Use trigonometry in 3D.
Apply sine rule, cosine rule and find the area of a non-right angled triangle.
Algebraic Manipulation
Rearrange expressions where the subject appears twice.
Use function machines and notation to write and interpret composite and inverse functions.
Solving Algebraically 2
Solve simultaneous equations including 1 quadratic.
Solve quadratic inequalities.
Communication and reasoning
Perform algebraic and geometrical proof.
.
Maths
Y10 | Key Stage 4
Theme/Unit
Class Content
Assisted Study
10
YEAR
Maths
Y11 | Key Stage 4
Theme/Unit
Class Content
Assisted Study
All Terms
Over the course of year 11 each group will follow a bespoke scheme of work which is planned through use of the analysis of the class mock examinations, this will involve revision or extension as appropriate and key skills to access exam level questions.
Students will be assessed each half term on non calculator skills. At December and Easter they will sit full sets of exam papers as mock exams. Cheat sheets will not be allowed to be used in any year 11 assessments.
Check students are organised on what day to bring their exam paper homeworks.
Are they using revision guides to help if they do not know a topic?
Students can aid their revision through completing regular Memri or Fix up 5 tasks on SPARX.
11
YEAR
Maths
A LEVEL
KS5
Step Up to Sixth Form
Revision Guides
Exam information
Extra Curricular & Trips
What is KS5 Maths?
Mathematics at A-Level is both challenging and interesting as it builds on thetopics you have met at GCSE and develops the ideas further. It is a highly sought after qualification in the workplace and in Higher Education.
12&13
YEARS
Who is it for?
A-level Mathematics is for anyone who has a proven track record in the subject at GCSE. Minimum entry is GCSE grade 6, though ideally you would have gained a grade 7, 8 or 9. It is particularly suited to people who enjoy problem solving, computation and logical reasoning including proof. Importantly, anyone taking the course must have a comprehensive understanding of GCSE Algebra topics and
be willing to spend considerable time independently improving their mathematical fluency and reasoning.
What will i study?
As of 2017 the specification of content and methods of assessment have changed for all exam boards across England. Consequently, all exam boards have identical content (excluding the large data set) and similar methods of assessment. The Kimberley Mathematics Department enters students for the AQA A-Level Mathematics (7357) course, please see AQA.org.uk for more information updates.
Course Content:
Unit 1
Section A: Poetry One question from a choice of two based on an anthology of Pre-1914 poetry plus an unseen text published after 1914. Section B: Prose One question from a choice of two, presented in two parts, based on the reading of a prose fiction text.
Assessment: Exam Paper [30%]
Unit 3: Non-Literary Texts
Section A: Analysis of unseen non-literary texts Comparative analysis of three unseen non-literary texts, one of which will be spoken language. Section B: Non-literary text study One two part question based on the reading of a non-literary text.
Assessment: Exam Paper [20%]
Unit 2: Drama
Section A: Shakespeare One extract based task and one essay style question from a choice of two based on the reading of a Shakespeare play. Section B: Post- 1900 Drama One question from a choice of two based on the reading of one play from a prescribed list.
Assessment: Exam Paper [30%]
Unit 4: Coursework
Section A: Genre study A critical and sustained study of a prose genre. Section B: Related creative writing Two writing assignments (one literary and one non-literary).
Assessment: Coursework [20%]
Further Maths
A LEVEL
KS5
Step Up to Sixth Form
Revision Guides
Exam information
Extra Curricular & Trips
YEARS
What is 'Further Maths'?
A-level Further Mathematics is designed to broaden and deepen the mathematical knowledge and skills developed when studying A-level Mathematics. It provides a stimulating experience for those who enjoy the subject as it delves into the complexities of reasoning and logic. Topics such as matrices and complex numbers are introduced for the first time, while others, such as algebra, calculus and trigonometry are studied in greater depth. At the Kimberley 6th Form two additional modules are taken; discrete mathematics, (the theory behind computation), and advanced mechanics (the application of advanced mathematical modelling). Students planning for a degree in areas such as mathematics, physics, engineering or economics will benefit greatly from taking A-level Further Mathematics.
12&13
Who is it for?
To take A-level Further Mathematics you must achieve at least a grade 7 in GCSE mathematics and take A-level Mathematics. Students will be expected to dedicate their time to gaining complete fluency in mathematical manipulation as well as logical reasoning. As outlined above, further mathematics is for those who wish to take mathematics, or a course based in mathematics. It also helps for applications to Oxbridge Universities for these courses.
What will i study?
As of 2017 the specification of content and methods of assessment have changed for all exam boards across England. Consequently, the content covered by each exam board is very similar but the combinations of optional topics can vary. The Kimberley Mathematics Department enters students for the AQA A-Level Further Mathematics (7367) course, having taught the Mechanics and Discrete optional content, please see AQA.org.uk for more information and updates.
Course Content:
First Year
F irst year specifications in Further Mathematics must require students to demonstrate the overarching knowledge and skills contained in sections OT1, OT2 and OT3. These m ust be applied, along with associated mathematical thinking and understanding, across the whole of the detailed content in sections B to DG. • OT1: Mathematical argument, language and proof • OT2: Mathematical problem solving • OT3: Mathematical modelling • A: Proof • B: Complex Numbers • C: Matrices • D: Further algebra and functions • E: Further Calculus • F: Further Vectors • G: Polar coordinates • H: Hyperbolic functions • L: Coordinate geometry • MA: Dimensional analysis • MB: Momentum and collisions • MC: Work, energy and power • MD: Circular Motion • DA: Graphs • DB: Networks • DC: Network flows • DD: Linear programming • DE: Critical path analysis • DF: Game theory for zero-sum games • DG: Binary operations
Assessment: 2 Exam Papers each 1hr30min [50% of first year grade]
Paper 1: Content: Sections B, C, D, E, F, G, H, L.
Paper 2: Content: Sections MA, MB, MC, MD, DA, DB, DC, DD, DE, DF, DG.
Questions: Both have a mix of questions from short, single-mark questions to multistep problems.
A2
A -level specifications in Mathematics require that students meet the first year specifications and content detailed above and to a more advanced level. Additional c ontent for the A-level is the following sections; • I: Differential equations • J: Trigonometry • K: Numerical methods • ME: Centres of mass and moments • DG: Binary operations and group theory
Assessment: 3 Exam Papers each 2hrs [33.3% of A Level grade]
Paper 1: Content: Sections A, B, C, D, E, F, G, H, I, J, K, L.
Paper 2: Content: Sections A, B, C, D, E, F, G, H, I, J, K, L.
Paper 3: Content: MA, MB, MC, MD, ME, DA, DB, DC, DD, DE, DF, DG.
Questions: Both have a mix of questions from short, single-mark questions to multistep problems.
Further Maths at KS5
After each lesson you should:
-
Review your lesson notes and highlight anything that you do not understand so that you can ask about this in the next lesson
-
Locate and read the relevant material in the textbook and add anything extra or interesting to your notes
• complete any outstanding questions or exercises
Each week you should:
-
Review the work you have done over the week and make some active revision resources. Examplesmay include glossaries, mindmaps, flash cards, flow diagrams, quizzes, mood boards, drawings for understanding … be creative!
-
Be proactive when using revision sites - locate the pages relevant to the material that you have been covering in lessons. Add any extra or interesting information to your notes
-
Complete the independent work set each week
-
Below are some particularly useful sites for elements of the course Website: Useful for:
The British Library - The British Library (bl.uk) Context (AO3) and Critical Theory (AO5)
Learning tools, flashcards, and textbook solutions | Quizlet
Useful for pre-made Critical Interpretation flashcards for each unit.
CliffsNotes Study Guides | Book Summaries, Test Preparation & Homework Help | Written by Teachers Useful for strengthening your understanding of a text
At least once per half-term you should:
-
Carry out a folder cleanse. Ensure work is in a sensible order (chronological or by theme) and that sections are clearly divided ( e.g. different teachers / different topics / assessments v class work)
-
Identify any missing work and take steps to fill gaps – liaise with a trusted study partner or your teacher.
Throughout the year you should:
-
Complete past paper questions with mark schemes from the Eduqas website: AS and A Level English Literature | Eduqas
You should work through these questions to test your knowledge and critically assess your work using the mark schemes. This will be most useful in the run up to your mock exams and Summer exams.
Keep up with your own personal reading. An English student should be reading a wide variety of texts, improving your knowledge and understanding of genres and the writer’s craft
Y12/13 Guide to Independent Learning
Maths at KS5
After each lesson you should:
-
1. After each lesson you should:
• review your lesson notes and highlight anything that you do not understand so that you can ask about this in the next lesson (remembering that you can access all the lesson materials through the OneDrive links Emailed to you at the start of the year)
• locate and read the relevant material either on the integralmaths.org website of in the Further Mathematics textbook and add anything extra or interesting to your notes
• complete any outstanding questions or exercises using the answers (which may be available through the OneDrive) to self-assess your fundamental understanding and your application of knowledge to more advanced problems.
Each week you should:
-
Review the work you have done over the week and make some active revision resources. Examples may include glossaries, mindmaps, flash cards, flow diagrams, quizzes, mood boards, drawings for understanding … be creative!
-
Be proactive when using revision sites - locate the pages relevant to the material that you have been covering in lessons and repeat revision of previous topics using the Assessment and Revision Schedulein your Folder of Awesomeness. Add any extra or interesting information to your notes
-
Below are some particularly useful sites for elements of the course Website: Useful for: Integralmaths.org This is the most comprehensive website. It has notes, walkthroughs, videos, exercises, online quizzes, interactive learning tools, revision sheets and more.
Physicsandmathstutor.com Additional exercises, revision notes, old specification papers and mark schemes Mathedup.co.uk Old specification exam questions sorted into topic “takeaways” Youtube channel with excellent content coverage
At least once per half-term you should:
-
Carry out a folder cleanse. Ensure work is in a sensible order (chronological or by theme) and that sections are clearly divided ( e.g. different teachers / different topics / assessments v class work)
-
Identify any missing work and take steps to fill gaps – liaise with a trusted study partner or your teacher
-
Review and make full corrections to the formal assessments from the previous half term
-
Review all previous topics and address any areas of difficulty as all assessments are cumulative
Throughout the year you should:
-
Refer to you Folder of Awesomeness to find all the information you need about the A-level course and how it is taught at The Kimberley Sixth Form.
-
Use the OneDrive links provided and the start of the year to access all of the lesson resources.
-
Use the revision materials provided through Satchel:One or as printed booklets to practice applying knowledge to exam-style questions. Exam resources from the AQA Exam Board website (www.aqa.org) are provided at an appropriate time in the year. If you have not been provided with these resources but would like to test your abilities on new specification exam questions, you can use either www.ocr.org.uk/qualifications/past-paper-finder or www.qualifications.pearson.com/en/support/support-topics/exams/past-papers
Where can this subject take me?
*Updates Pending*
Higher Education courses or careers that list A-Level Mathematics as essential or highly desirable include:
Computing
Economics
Architecture
Accountancy
Psychology
Biology
Finance
Medicine
Biology
Engineering
Actuary
Chemistry
Physics
and of course, pure maths itself
Further Education or vocation based training would significantly help towards freelance practices or careers in:
update pending
For more information of post-school progression please check out our dedicated Careers Page for related links and guidance.
For more information on this course throughout all key stages please contact Mrs M. Booth
m.booth@kimberleyschool.co.uk
