HCF
HCF is a unit of teaching within Factors and Multiples, usually two to four weeks of lessons with one assessment point.
Entity profile
Every node stores the same attribute set, which is why the hierarchy can grow without new templates.
Unit
Depth 3 in the graph
math/number-sense/factors-and-multiples/hcf
2,235
12 topics · 360 concepts · 1,800 micro-concepts
Chapters
Every chapter below is a full entity with its own skills, objectives, misconceptions and resource set.
Introducing HCF
Introducing HCF is a chapter within HCF: a coherent run of lessons that can be taught in one go.
Working with HCF
Working with HCF is a chapter within HCF: a coherent run of lessons that can be taught in one go.
HCF in Context
HCF in Context is a chapter within HCF: a coherent run of lessons that can be taught in one go.
Skills and learning objectives
Skills hang off the entity; objectives hang off the skill; activities and assessment hang off the objective.
Explain hcf
UnderstandExplain hcf 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 hcf independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind hcf using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Calculate hcf
ApplyCalculate hcf 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 hcf independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Compare hcf
AnalyseCompare hcf 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 hcf independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind hcf using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Justify hcf
EvaluateJustify hcf 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 hcf 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.
- Prime FactorisationUnit
- Prime NumbersUnit
- ProportionStrand
Misconceptions
Stored on the entity so worksheets, quizzes and lesson plans all target the same known errors.
Learners over-generalise a special case of hcf to every situation.
Correction — Present a deliberate non-example and ask why the rule fails.
Students treat hcf 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-691.1
Mapped statement covering HCF.
CAM-185.2
Mapped statement covering HCF.
What comes next
Curriculum order is an edge in the graph, so every entity knows the step that follows it.
LCM
LCM is a unit of teaching within Factors and Multiples, usually two to four weeks of lessons with one assessment point.
Whole Numbers
Whole Numbers is a curriculum strand within Number Sense — a thread that runs across grades and deepens each year.
Counting
Counting is a curriculum strand within Number Sense — a thread that runs across grades and deepens each year.
Number Recognition
Number Recognition is a curriculum strand within Number Sense — a thread that runs across grades and deepens each year.
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
HCF 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 lessonprime factorisation
- 02Video explanationHCF 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 HCF resources
Every format below is a free, standalone page generated from this entity — 53 of them, all interlinked.
- Free HCF lessons
- Free HCF lesson plans
- Free HCF explanations
- Free HCF worked examples
- Free HCF real life examples
- Free HCF common mistakes
- Free HCF video lessons
- Free HCF worksheets
- Free HCF printable worksheets
- Free HCF interactive worksheets
- Free HCF homework worksheets
- Free HCF revision worksheets
- Free HCF word problems
- Free HCF practice tests
- Free HCF flashcards
- Free HCF study notes
- Free HCF revision notes
- Free HCF cheat sheets
- Free HCF formula sheets
- Free HCF mind maps
- Free HCF vocabulary lists
- Free HCF quizzes
- Free HCF timed quizzes
- Free HCF adaptive quizzes
- Free HCF mcqs
- Free HCF true or false questions
- Free HCF fill in the blanks
- Free HCF matching exercises
- Free HCF short questions
- Free HCF long questions
- Free HCF question banks
- Free HCF exam questions
- Free HCF past paper questions
- Free HCF solved past papers
- Free HCF mock exams
- Free HCF activities
- Free HCF stem activities
- Free HCF experiments
- Free HCF games
- Free HCF projects
- Free HCF case studies
- Free HCF homework
- Free HCF assignments
- Free HCF reading comprehension
- Free HCF writing prompts
- Free HCF spelling practice
- Free HCF grammar practice
- Free HCF teacher guides
- Free HCF parent guides
- Free HCF ai tutor sessions
- Free HCF practice sessions
- Free HCF progress trackers
- Free HCF printables
Connected resources
30 resource types are generated for HCF 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 HCF in the knowledge graph?
- 0 domains, 0 strands, 0 units, 3 chapters, 12 topics, 60 subtopics, 360 concepts and 1,800 micro-concepts — every one of them carrying its own worksheets, quizzes, flashcards, lesson plans and AI tutoring.
- What should a learner already know before HCF?
- The graph lists Prime Factorisation, Prime Numbers, Proportion as prerequisites. Each links to its own practice so a gap can be closed before moving on.
- Which grades is HCF 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 HCF one-to-one with a tutor who can see exactly where the gap is.
Book a tutor