Problem Solving
Problem Solving 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/problem-solving
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.
Multi-step Problems
Multi-step Problems is a unit of teaching within Problem Solving, usually two to four weeks of lessons with one assessment point.
Modelling
Modelling is a unit of teaching within Problem Solving, usually two to four weeks of lessons with one assessment point.
Checking Reasonableness
Checking Reasonableness is a unit of teaching within Problem Solving, 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 problem solving
RememberIdentify problem solving 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 problem solving independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain problem solving
UnderstandExplain problem solving 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 problem solving independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind problem solving using correct vocabulary.
Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session
Assessment — Extended written response, levelled
Calculate problem solving
ApplyCalculate problem solving 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 problem solving independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Compare problem solving
AnalyseCompare problem solving 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 problem solving independently in an unfamiliar context.
Activities — Independent worksheet · Card sort · Concept-check quiz
Assessment — Marked worksheet with a marking scheme
Explain the reasoning behind problem solving 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.
Misconceptions
Stored on the entity so worksheets, quizzes and lesson plans all target the same known errors.
Students treat problem solving 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 problem solving 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.
CAM-958.1
Mapped statement covering Problem Solving.
NAT-174.2
Mapped statement covering Problem Solving.
What comes next
Curriculum order is an edge in the graph, so every entity knows the step that follows it.
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.
Measurement
Measurement 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
Problem Solving 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 lessonproof
- 02Video explanationProblem Solving 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 Problem Solving resources
Every format below is a free, standalone page generated from this entity — 53 of them, all interlinked.
- Free Problem Solving lessons
- Free Problem Solving lesson plans
- Free Problem Solving explanations
- Free Problem Solving worked examples
- Free Problem Solving real life examples
- Free Problem Solving common mistakes
- Free Problem Solving video lessons
- Free Problem Solving worksheets
- Free Problem Solving printable worksheets
- Free Problem Solving interactive worksheets
- Free Problem Solving homework worksheets
- Free Problem Solving revision worksheets
- Free Problem Solving word problems
- Free Problem Solving practice tests
- Free Problem Solving flashcards
- Free Problem Solving study notes
- Free Problem Solving revision notes
- Free Problem Solving cheat sheets
- Free Problem Solving formula sheets
- Free Problem Solving mind maps
- Free Problem Solving vocabulary lists
- Free Problem Solving quizzes
- Free Problem Solving timed quizzes
- Free Problem Solving adaptive quizzes
- Free Problem Solving mcqs
- Free Problem Solving true or false questions
- Free Problem Solving fill in the blanks
- Free Problem Solving matching exercises
- Free Problem Solving short questions
- Free Problem Solving long questions
- Free Problem Solving question banks
- Free Problem Solving exam questions
- Free Problem Solving past paper questions
- Free Problem Solving solved past papers
- Free Problem Solving mock exams
- Free Problem Solving activities
- Free Problem Solving stem activities
- Free Problem Solving experiments
- Free Problem Solving games
- Free Problem Solving projects
- Free Problem Solving case studies
- Free Problem Solving homework
- Free Problem Solving assignments
- Free Problem Solving reading comprehension
- Free Problem Solving writing prompts
- Free Problem Solving spelling practice
- Free Problem Solving grammar practice
- Free Problem Solving teacher guides
- Free Problem Solving parent guides
- Free Problem Solving ai tutor sessions
- Free Problem Solving practice sessions
- Free Problem Solving progress trackers
- Free Problem Solving printables
Connected resources
30 resource types are generated for Problem Solving 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 Problem Solving 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 Problem Solving?
- The graph lists Proof, Matrices as prerequisites. Each links to its own practice so a gap can be closed before moving on.
- Which grades is Problem Solving 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 Problem Solving one-to-one with a tutor who can see exactly where the gap is.
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