Prior Content: Simplifying Basic Expressions, Manipulating Formulae/ Changing the Subject, Completing the Square, Forming Equations, Substitution, Solving Quadratics, 2D Area & Perimeter, Properties of Numbers
Possible Next Steps: Circle Theorems, Recurring Decimals, Surface Area & Volume, Vectors, Fractions, Surds, Similar Shapes
Contents
- 1.1 Verifying
- 1.2 Counter-Examples
- 2.1 Show That/ Proof with Algebraic Steps
- 2.2 Proving Factors & Multiples
- 3.1 Equating Coefficients (AQA FM)
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Verifying
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – How to Prove Algebraic Identities – Proof Part 2 by Cognito
Identity or Equation – What is the difference? : ExamSolutions Maths Revision by ExamSolutions
Online Platforms (with Videos & Exercises)
Activities & Resources
Worksheets
- CIMT MEP (online self-checking)
Dr Frost Resources
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
Extension Materials
1.2 Counter-Examples
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – How to Disprove a Statement by Counter Example – Proof Part 1 by Cognito
Proof by using a Counter-Example by ExamSolutions
Counterexample by Brightstorm
Online Platforms (with Videos & Exercises)
Activities & Resources
- Don Steward
- Transum
- BossMaths
- A6a Arguing Mathematically✦ (Includes counter-examples)
- Ticktock Maths
- Proof and Counterexamples lesson (slides)
Worksheets
Dr Frost Resources
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 453a: Give a counterexample to show that a conjecture is false using properties of numbers.
- 453b: Determine which conjecture is disproved by a given counterexample.
- 453c: Determine a counterexample by substitution into an algebraic expression.
- 453d: Consider the validity of more general algebraic statements, including constraints on the variables or relationships between expressions.
- 453: Exam Practice: Testing conjectures and identifying counterexamples
Extension Materials
2.1 Show That/ Proof with Algebraic Steps
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Algebraic Proof
Corbett Maths Equating Coefficients
Corbett Maths Geometric Proof
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Don Steward
- Two Fraction Proofs
- Some Square Number Patterns
- Proving Last Digit Facts About Squares
- Two Numbers Conjecture
- Grid Relationships
- Takes and Adders Generalisations (i)
- Takes and Adders Generalisations (iii)
- Takes and Adders Generalisations (iv)
- Takes and Adders Generalisations (ii)
- Squares and Their Predecessors
- Quadratic Patterns
- Hundred Number Grid
- Place Value Algebra
- 4 Consecutive Numbers Mixed Questions
- Maths Tricks
- Some Means
- Product of Four Consecutive Integers
- Bethan Copeland's Theorem
- Acute Learning Problem Pairs
- Level 2 FM: Proof as PowerPoint or PDF
- Go Teach Maths
- MathsPad
- MEI
- Proof cards✦ (original by MEI; from the MEI Teaching Advanced Mathematics (TAM) course; copy hosted on Jo Morgan’s Drive)
- BossMaths
- Standards Unit (DfES)
- Standards Unit A9: Performing Number Magic (Standards Unit, DfES; PDF
Worksheets
- Dr Austin Maths
- Corbettmaths
- Algebraic Proof Practice Questions & Solutions
- Algebraic Proof Worksheet & Solutions
- Geometric Proof AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone
- Algebraic Proof GCSE Questions and Solutions (Mainly forming Equations)
- Physics & Maths Tutor
- Dr Frost
- 1st Class Maths
- MadAsMaths (T. Madas)
- Identities Q7 (difficulty 2 of 5)
- AQA
- Algebraic proof worksheet✦ (original by AQA; copy hosted on Jo Morgan’s Drive)
- Mr Morley Maths
- Algebraic Proof: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (M Welch)
- Algebraic Proof (M Welch, docx)
Dr Frost resources
Dr Frost Video
K597: Identify Expressions That Represent Odd/Even Integers.
K599: Use Expressions for Consecutive Integers.
K600: Use Expressions for Consecutive Odd/Even Integers.
K601: Prove That a Given Algebraic Expression is Always Odd/Even.
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 454b: Identify expressions that represent odd/even integers.
- 454c: Prove that a given algebraic expression is always odd/even (no bracket expansion).
- 454d: Prove that a given algebraic expression is always odd/even, requiring bracket expansion.
- 454g: Use expressions for consecutive integers.
- 454h: Prove that a sum of consecutive integers has some given property.
- 454i: Prove that the sum or difference of the squares of consecutive integers has some given property.
- 454j: Use expressions for consecutive odd/even integers.
- 454k: Prove that a sum of consecutive odd or even integers has some given property.
- 454l: Prove that a sum of the squares of consecutive odd or even integers has some given property.
- 454m: Use expressions for different odd/even integers, not necessarily consecutive.
- 454n: Prove a property about some arithmetic combination of two different odd/even numbers, not necessarily consecutive.
- 454o: Form and solve an equation using relationships between consecutive integers/evens/odds.
- 454p: Prove that an algebraic expression is a perfect square.
- 454: Exam Practice: Algebraic proofs involving integers
Further Practice
- Practise Questions
EXTENSION MATERIALS
2.2 Proving Factors & Multiples
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Algebraic Proof | Grade 7-9 Maths Series | GCSE Maths Tutor by The GCSE Maths Tutor
Algebraic Proof – GCSE Higher Maths by 1st Class Maths
Algebraic Proofs (involving integers) by Dr Frost Maths
Algebraic proof GCSE maths – multiple of 3 question by 3minutemaths
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
- Don Steward
- Ticktock Maths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Algebraic Proof AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone
- Algebraic Proof Workbook, Solutions and Questions Only
- Pixi Maths
Dr Frost resources
Dr Frost Video
K598: Identify Expressions That Represent a Multiple of an Integer.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 454a: Identify expressions that represent a multiple of an integer.
- 454e: Prove that a given algebraic expression is always a multiple of a number.
- 454f: Prove that a given algebraic expression is always something less or something more than a multiple of a number. (not yet active)
- 454: Exam Practice: Algebraic proofs involving integers
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.1 Equating Coefficients
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Dr Frost resources
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Algebraic Proof PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic resources
Acute Learning Problem Pairs
- Proof as PowerPoint or PDF
Worksheets
- MathedUp
- Algebraic Proof: Worksheet · Practice · Quiz · Question Gallery
- Identities & Equating Coefficients: Worksheet · Practice · Quiz · Question Gallery
- Algebraic Proof: Worksheet · Practice · Question Gallery
- Maths Genie
- Proof: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- crashMATHS
- MME
Activities
- Don Steward
- Interwoven Maths
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.