Introducing Proof by Exhaustion
Introducing Proof by Exhaustion is a chapter within Proof by Exhaustion: a coherent run of lessons that can be taught in one go.
Entity profile
Every node stores the same attribute set, which is why the hierarchy can grow without new templates.
Chapter
Depth 4 in the graph
math/mathematical-reasoning/proof/proof-by-exhaustion/introducing-proof-by-exhaustion
744
4 topics · 120 concepts · 600 micro-concepts
Topics
Every topic below is a full entity with its own skills, objectives, misconceptions and resource set.
Introducing Proof by Exhaustion Essentials
Introducing Proof by Exhaustion Essentials is a teachable topic within Introducing Proof by Exhaustion, broken into subtopics that each take roughly one lesson.
Introducing Proof by Exhaustion Techniques
Introducing Proof by Exhaustion Techniques is a teachable topic within Introducing Proof by Exhaustion, broken into subtopics that each take roughly one lesson.
Introducing Proof by Exhaustion Word Problems
Introducing Proof by Exhaustion Word Problems is a teachable topic within Introducing Proof by Exhaustion, broken into subtopics that each take roughly one lesson.
Introducing Proof by Exhaustion Common Errors
Introducing Proof by Exhaustion Common Errors is a teachable topic within Introducing Proof by Exhaustion, broken into subtopics that each take roughly one lesson.
Skills and learning objectives
Skills hang off the entity; objectives hang off the skill; activities and assessment hang off the objective.
Explain introducing proof by exhaustion
UnderstandExplain introducing proof by exhaustion accurately in a familiar context.
Activities — Modelled example on the board · Paired talk task · Mini whiteboard check
Assessment — Exit ticket of four short items
Explain introducing proof by exhaustion independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind introducing proof by exhaustion using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Calculate introducing proof by exhaustion
ApplyCalculate introducing proof by exhaustion accurately in a familiar context.
Activities — Modelled example on the board · Paired talk task · Mini whiteboard check
Assessment — Exit ticket of four short items
Calculate introducing proof by exhaustion independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Compare introducing proof by exhaustion
AnalyseCompare introducing proof by exhaustion accurately in a familiar context.
Activities — Modelled example on the board · Paired talk task · Mini whiteboard check
Assessment — Exit ticket of four short items
Compare introducing proof by exhaustion independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind introducing proof by exhaustion using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Justify introducing proof by exhaustion
EvaluateJustify introducing proof by exhaustion accurately in a familiar context.
Activities — Modelled example on the board · Paired talk task · Mini whiteboard check
Assessment — Exit ticket of four short items
Justify introducing proof by exhaustion independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Semantic relationships
Prerequisite and related edges are what make this a graph rather than a menu.
- Algebraic ProofUnit
Misconceptions
Stored on the entity so worksheets, quizzes and lesson plans all target the same known errors.
Learners over-generalise a special case of introducing proof by exhaustion to every situation.
Correction — Present a deliberate non-example and ask why the rule fails.
Students treat introducing proof by exhaustion as a rule to memorise rather than a relationship to understand.
Correction — Anchor the rule in a visual model first, then abstract it — the model is the explanation.
Curriculum alignment
Curricula, boards and countries are data — adding one never changes the architecture.
OCR-385.1
Mapped statement covering Introducing Proof by Exhaustion.
CAM-405.2
Mapped statement covering Introducing Proof by Exhaustion.
What comes next
Curriculum order is an edge in the graph, so every entity knows the step that follows it.
Working with Proof by Exhaustion
Working with Proof by Exhaustion is a chapter within Proof by Exhaustion: a coherent run of lessons that can be taught in one go.
Proof by Exhaustion in Context
Proof by Exhaustion in Context is a chapter within Proof by Exhaustion: a coherent run of lessons that can be taught in one go.
Counterexamples
Counterexamples is a unit of teaching within Proof, usually two to four weeks of lessons with one assessment point.
Algebraic Proof
Algebraic Proof is a unit of teaching within Proof, usually two to four weeks of lessons with one assessment point.
Difficulty ladder
The same entity, six levels of demand — easy through to olympiad and exam level.
Scaffolded first attempt with worked support.
Standard curriculum demand, unscaffolded.
Multi-step questions and unfamiliar contexts.
Stretch tasks that need reasoning, not recall.
Competition-style problems built on the same idea.
Board-styled questions with mark schemes.
Learning intent
Not every visitor wants the same thing. Each intent routes to the resource that actually does that job.
Audience views
Introducing Proof by Exhaustion in Grade 3, surfaced differently for each reader.
AI Tutor context chain
Open the tutor from here and it already knows where you are — this is the sequence it recommends.
- 01Prerequisite lessonalgebraic proof
- 02Video explanationIntroducing Proof by Exhaustion modelled end to end
- 03Interactive practiceAnswer on screen with instant checking
- 04QuizTen graded items with hints
- 05FlashcardsRetrieval on a 14-day schedule
- 06Common mistakesThe misconceptions stored on this node
- 07Harder worksheetSame concept, exam-level demand
- 08Past paper questionsBoard questions on this concept
- 09Mock testTimed, marked, with feedback
- 10Book a tutorOne-to-one on exactly this gap
Free Introducing Proof by Exhaustion resources
Every format below is a free, standalone page generated from this entity — 53 of them, all interlinked.
- Free Introducing Proof by Exhaustion lessons
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Connected resources
30 resource types are generated for Introducing Proof by Exhaustion automatically — the graph never produces an entity without them.
Concept Explanation
The idea itself, explained from first principles.
Lesson
A taught sequence with modelling and checks for understanding.
Real Life Examples
Where the idea shows up outside school.
Common Mistakes
The misconceptions and how to correct them.
AI Tutor
Socratic one-to-one practice on this exact idea.
Quiz
Graded retrieval with hints and explanations.
Question Bank
Every question filtered to this entity.
MCQs
Multiple choice items with distractor analysis.
True or False
Fast misconception checks.
Fill in the Blanks
Cloze items for vocabulary and method.
Matching
Pair terms, models and definitions.
Short Questions
One to three mark responses.
Long Questions
Extended responses with method marks.
Exam Questions
Board-styled questions and command words.
Past Papers
Authentic papers filtered to this entity.
Solved Papers
Full worked solutions and examiner notes.
Frequently asked
- What sits underneath Introducing Proof by Exhaustion in the knowledge graph?
- 0 domains, 0 strands, 0 units, 0 chapters, 4 topics, 20 subtopics, 120 concepts and 600 micro-concepts — every one of them carrying its own worksheets, quizzes, flashcards, lesson plans and AI tutoring.
- What should a learner already know before Introducing Proof by Exhaustion?
- The graph lists Algebraic Proof as prerequisites. Each links to its own practice so a gap can be closed before moving on.
- Which grades is Introducing Proof by Exhaustion taught in?
- Typically Grade 3, Grade 4, Grade 5, though every resource can be regenerated for any grade in the platform.
Related resources
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