Proof
Proof is a curriculum strand within Mathematical Reasoning — a thread that runs across grades and deepens each year.
Entity profile
Every node stores the same attribute set, which is why the hierarchy can grow without new templates.
Strand
Depth 2 in the graph
math/mathematical-reasoning/proof
6,708
36 topics · 1,080 concepts · 5,400 micro-concepts
Units
Every unit below is a full entity with its own skills, objectives, misconceptions and resource set.
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.
Proof by Exhaustion
Proof by Exhaustion is a unit of teaching within Proof, usually two to four weeks of lessons with one assessment point.
Skills and learning objectives
Skills hang off the entity; objectives hang off the skill; activities and assessment hang off the objective.
Identify proof
RememberIdentify proof accurately in a familiar context.
Activities — Modelled example on the board · Paired talk task · Mini whiteboard check
Assessment — Exit ticket of four short items
Identify proof independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain proof
UnderstandExplain proof 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 proof independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind proof using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Calculate proof
ApplyCalculate proof 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 proof independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Compare proof
AnalyseCompare proof 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 proof independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind proof using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Semantic relationships
Prerequisite and related edges are what make this a graph rather than a menu.
- MatricesDomain
Misconceptions
Stored on the entity so worksheets, quizzes and lesson plans all target the same known errors.
Students treat proof 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.
Learners apply the correct method to proof but ignore the context or units.
Correction — Require an answer sentence with units on every applied question.
Curriculum alignment
Curricula, boards and countries are data — adding one never changes the architecture.
IB-563.1
Mapped statement covering Proof.
EDE-912.2
Mapped statement covering Proof.
What comes next
Curriculum order is an edge in the graph, so every entity knows the step that follows it.
Problem Solving
Problem Solving is a curriculum strand within Mathematical Reasoning — a thread that runs across grades and deepens each year.
Number Sense
How quantity is represented, compared and manipulated before formal algebra.
Algebra
Algebra is a major domain within Math, grouping the strands that share the same underlying ideas and methods.
Geometry
Geometry is a major domain within Math, grouping the strands that share the same underlying ideas and methods.
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
Proof 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 lessonmatrices
- 02Video explanationProof 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 Proof resources
Every format below is a free, standalone page generated from this entity — 53 of them, all interlinked.
- Free Proof lessons
- Free Proof lesson plans
- Free Proof explanations
- Free Proof worked examples
- Free Proof real life examples
- Free Proof common mistakes
- Free Proof video lessons
- Free Proof worksheets
- Free Proof printable worksheets
- Free Proof interactive worksheets
- Free Proof homework worksheets
- Free Proof revision worksheets
- Free Proof word problems
- Free Proof practice tests
- Free Proof flashcards
- Free Proof study notes
- Free Proof revision notes
- Free Proof cheat sheets
- Free Proof formula sheets
- Free Proof mind maps
- Free Proof vocabulary lists
- Free Proof quizzes
- Free Proof timed quizzes
- Free Proof adaptive quizzes
- Free Proof mcqs
- Free Proof true or false questions
- Free Proof fill in the blanks
- Free Proof matching exercises
- Free Proof short questions
- Free Proof long questions
- Free Proof question banks
- Free Proof exam questions
- Free Proof past paper questions
- Free Proof solved past papers
- Free Proof mock exams
- Free Proof activities
- Free Proof stem activities
- Free Proof experiments
- Free Proof games
- Free Proof projects
- Free Proof case studies
- Free Proof homework
- Free Proof assignments
- Free Proof reading comprehension
- Free Proof writing prompts
- Free Proof spelling practice
- Free Proof grammar practice
- Free Proof teacher guides
- Free Proof parent guides
- Free Proof ai tutor sessions
- Free Proof practice sessions
- Free Proof progress trackers
- Free Proof printables
Connected resources
30 resource types are generated for Proof 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 Proof in the knowledge graph?
- 0 domains, 0 strands, 3 units, 9 chapters, 36 topics, 180 subtopics, 1,080 concepts and 5,400 micro-concepts — every one of them carrying its own worksheets, quizzes, flashcards, lesson plans and AI tutoring.
- What should a learner already know before Proof?
- The graph lists Matrices as prerequisites. Each links to its own practice so a gap can be closed before moving on.
- Which grades is Proof taught in?
- Typically Grade 3, Grade 4, Grade 5, though every resource can be regenerated for any grade in the platform.
Related resources
Work through Proof one-to-one with a tutor who can see exactly where the gap is.
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