Study guides with worked examples

Study guides

Each guide explains one topic with the key idea, worked examples, practice questions and answers, and can be printed as a PDF.

Early learning

• Count up to ten
• Sorting, positions and simple patterns
• Position words and following directions
• Counting, groups and number stories
• Shapes, attributes and sorting explanations
• Describe and extend a pattern
• Position, order and small numbers
• Number patterns, grouping and explaining a choice

Life skills

• Percentage discounts
• A simple budget balance
• Scale a recipe
• Budgets and comparing options
• Timetables, durations and buffer time
• Unit prices and practical comparisons
• Timetables and realistic planning
• Budget arithmetic and opportunity cost
• Instructions, checklists and clear communication
• Plan a budget with stated assumptions
• Timetables, constraints and practical decisions

Mathematics

• Pythagorean theorem
• Area of a circle
• Area of a trapezoid
• Volume of a cylinder
• The discriminant
• Roots from factors
• Axis of symmetry
• Simultaneous equations
• Arithmetic sequences
• Sum of an arithmetic sequence
• Sine in a right triangle
• Tangent in a right triangle
• Combinations
• Weighted mean
• Successive percentage changes
• Volume of a cone
• Scale factors and area
• Finite geometric sums
• Repeated percentage growth
• Integrate a linear function
• Two draws with replacement
• Conditional probability from counts
• Population variance
• Interquartile range
• Find the mistake: number sense
• Find the mistake: fractions and percentages
• Find the mistake: algebra
• Functions: domains and transformations
• Calculus: meaning, conditions and checks
• Probability: what a result does and does not show

Science

• Newton’s second law
• Gravitational potential energy
• Linear momentum
• Mechanical work
• Resistors in series
• Molar concentration
• Atomic number and mass number
• Thermal energy changes
• Spring force magnitudes
• Energy efficiency
• Two parallel resistors
• Solution dilution
• Gas volume and temperature
• Model isotope averages
• Living things and their needs
• Cells and cell structures
• Ecosystems and interactions
• Genetics and inheritance
• Matter and changes
• Atomic structure and chemical language
• Earth systems
• Space and the solar system
• Motion, forces and energy
• Waves and electric circuits
• Materials and everyday changes
• Growing plants: questions and evidence
• Food webs and ecosystem reasoning
• Particle models of matter
• Chemical equations: atom bookkeeping
• Concentration and dilution: avoid common errors

Geography

• Distance on a square grid
• Map area and scale
• Maps and geographical features
• People and places
• Maps, keys and route choices
• Population data and settlement models
• Grid maps, directions and symbols
• Landforms and physical processes
• Weather records and climate comparisons
• Population, settlement and fair comparisons
• Resources, trade-offs and geographic decisions
• Map scale, direction and distance
• Population density and spatial evidence
• Map projections, scale and spatial evidence
• Population density with explicit area
• Position words
• Land or water?
• Reading a map
• Compass turns
• Places in a community

Computer science

• Nested loops
• Uncompressed storage models
• Compare compressed sizes
• Computing foundations
• Advanced computing concepts
• Algorithms without a computer
• Python-style code tracing
• Digital information and responsible use
• Python lists and sequence tracing
• Algorithm tracing and useful tests
• Digital information and source checks
• Designing digital work for more users
• Trace algorithms step by step
• Data quality and privacy-aware design
• Relational data, SQL and safe queries
• Algorithms, invariants and asymptotic costs
• Worst-case comparisons in a perfect binary search
• Ideal payload transfer time
• Robot on a number path
• What comes next?
• Put the steps in order
• Robot moves on a grid
• Repeat loops
• Find the bug
• IF, THEN, ELSE
• Staying safe online
• Clear instructions

Art & music

• Beats in musical bars
• Art and visual language
• Music vocabulary
• Art and design: observation and choices
• Rhythm, metre and musical symbols
• Visual composition and looking carefully
• Rhythm, pulse and note values
• Design briefs, prototypes and constructive critique
• Visual composition and constructive feedback
• Visual composition and explaining design choices
• Counting semitones
• Naming intervals
• Key signatures and relative minors
• Tempo and duration
• Colour theory basics
• Elements of art and principles of design
• Artists and art movements
• Reading dynamics and tempo markings

Study & wellbeing

• Plan a reading schedule
• Plan several practice sessions
• Study strategies and clear thinking
• Study plans and checking understanding
• Self-checks, feedback and revision plans
• Planning projects and monitoring progress
• Notes, summaries and confidence checks
• Study with recall, feedback and review
• Retrieval practice, spacing and an error log
• Writing SMART goals
• Using “I” statements
• Six study strategies
• Planning time in an exam
• Weighted decision matrix
• Prioritizing by deadline

History

• Historical thinking and evidence
• Societies and historical change
• Historical sources: purpose and corroboration
• Continuity, change and historical explanations
• Timelines, order and duration
• Objects as historical evidence
• Comparing historical accounts
• Continuity, change and multiple causes
• Building a defensible historical argument
• Historical sources and their context
• Change, continuity and historical causation
• Historical causation and comparing sources
• Counting days forward and back
• Months of the year
• Long ago and today
• Who was born first?
• How many years apart?
• Order years on a timeline
• Canadian history: which came first?
• World history: which came first?
• Events and centuries
• Years between historical events
• Primary or secondary source?
• Causes and consequences in history
• Confederation and the growth of Canada
• Questioning a primary source
• The Cold War: key ideas
• Long ago, yesterday and today

Reading & writing

• English grammar essentials
• Reading and literary analysis
• Writing and argument
• The shared garden · reading guide
• Two model bridges · reading guide
• The bus survey · reading guide
• The museum label · reading guide
• The river notebook · reading guide
• The quiet room · reading guide
• The lighting comparison · reading guide
• The tree proposal · reading guide
• Voices in an archive · reading guide
• A relationship in the data · reading guide
• The unreliable clock · reading guide
• Assumptions in a model · reading guide
• Public memory · reading guide
• The revised conclusion · reading guide
• The shared path · reading guide
• Punctuation and sentence editing
• Figurative language and precise interpretation
• Claims, evidence and counterarguments
• Reading numerical claims critically
• Nouns, verbs and adjectives in sentences
• Text structure and main ideas
• The paper boat
• The missing labels
• The changed shopping list
• Two ways to count
• A second life for a lamp
• The strongest bridge?

Social studies

• Community and civic reasoning
• Shared spaces and fair decisions
• Making group decisions fairly
• Shared places and community services
• Perspective, stereotypes and respectful inquiry
• Surveys, public choices and accountability
• Community decisions and representation
• Public decisions, surveys and representation
• Needs and wants
• Goods and services
• Rules, voting and leaders
• Levels of government in Canada
• The Canadian Charter of Rights and Freedoms
• How a federal bill becomes law
• Persuasion techniques in advertising
• Fact or opinion?
• Spot the opinion
• Government budgets: surplus or deficit
• Reading election results
• Supply, demand and prices
• Opportunity cost
• Elections and Parliament in Canada
• Checking claims online

Language learning

• Spanish classroom phrases for English speakers
• French classroom phrases for English speakers
• Brazilian Portuguese classroom phrases for English speakers
• Compare words without assuming exact equivalence
• Meaning, register and careful translation
• Spanish preterite: regular verbs
• French present tense: -er verbs
• Spanish false friends

Physics

• Pushes, pulls and changes in motion
• Light, seeing and shadows
• Sound starts with vibration
• Magnets: test rather than guess
• Measurements, units and sensible precision
• Distance is not displacement
• Average speed and average velocity
• Reading position–time information
• Velocity–time graphs: slope and area
• Balanced forces and inertia
• Force, mass and acceleration
• Interaction pairs act on different objects
• Friction, resistance and terminal motion
• Mass, weight and gravitational field
• Work, transfer and energy accounting
• Kinetic and gravitational potential energy
• Power and efficiency without unit confusion
• Momentum in one-dimensional collisions
• Impulse and stopping time
• Moments, pivots and equilibrium
• Springs and the linear elastic limit
• Pressure, area and depth
• Displacement, density and buoyancy
• Temperature is not total thermal energy
• Conduction, convection and radiation
• Heating versus changing state
• Wave vocabulary and energy transfer
• Sound, echoes and travel time
• Reflection and the normal
• Refraction and critical conditions

Chemistry

• Particles, states and changes
• Elements, compounds and mixtures
• Atoms, isotopes and ions
• Balance equations without changing formulas
• Moles, mass and particle counts
• Ionic formulas and charge balance
• Periodic patterns and their limits
• Bonding, shape and polarity
• Oxidation states and redox bookkeeping
• Coordination chemistry: an introduction
• Carbon frameworks and structural formulas
• Straight-chain alkanes and names
• Branched alkanes and locants
• Alkenes, alkynes and unsaturation
• Recognize common functional groups
• Alcohols and ethers: structure and properties
• Carboxylic acids and esters
• Amines, amides and basicity
• Constitutional isomers and stereoisomers
• Chirality and geometric isomerism
• Monomers, repeat units and polymer properties
• Spectroscopy: combine clues carefully
• Reaction energetics and system boundaries
• Reaction rates and catalysts
• Dynamic chemical equilibrium
• Acids, bases and logarithmic pH
• Buffers and acid–base ratios
• Gas laws and consistent units
• Electrochemistry: electrodes and potentials
• Concentration and dilution

Biology

• Living things and careful observations
• Roots, stems, leaves and flowers
• Cells and their components
• Microscope scales and magnification
• Diffusion, osmosis and active transport
• Cell cycle and mitosis
• Meiosis and chromosome sets
• DNA structure and complementary sequences
• From genes to proteins
• Single-gene inheritance models
• Variation beyond simple dominance
• Photosynthesis and matter sources
• Transport in plants
• Pollination, seeds and reproduction
• Cellular respiration and breathing
• Gas exchange and surface design
• Circulation, vessels and blood components
• Digestion, absorption and nutrients
• Homeostasis and negative feedback
• Nervous and hormonal communication
• Microorganisms and classification
• Immune defense and biological memory
• Food chains, food webs and energy
• Ecological sampling and population estimates
• Population change and carrying capacity
• Natural selection and population change
• Classification, biodiversity and relatedness
• Biological investigations and causal claims
• Actual size from an image
• Quadrat density estimate

Earth & space science

• Rocks, minerals and geological processes
• Earth, seasons and observation geometry
• Rocks, plate boundaries and geological timescales

Environmental science

• Environmental systems and trade-offs
• Environmental stocks, flows and system boundaries
• Runoff in a simplified catchment

Business & economics

• Opportunity cost and constrained choices
• Revenue, break-even and evidence
• Costs, contribution and opportunity cost
• Break-even sales volume
• Point price elasticity of linear demand

Engineering & design

• Design briefs, criteria and constraints
• Statics, free-body diagrams and design margins
• Support reaction for a simply supported beam

Media literacy

• Headlines, advertising and source checks
• Digital evidence, provenance and misleading charts

Music

• Rhythm, meter and note values
• Rhythm, metre and note-value arithmetic

Drama & speaking

• Speaking, character and audience
• Objectives, subtext and speaking choices

Physical education

• Movement games and fair participation
• Movement observation, rules and inclusive participation

Philosophy & ethics

• Reasons, values and ethical disagreements
• Valid arguments, assumptions and ethical tradeoffs

Astronomy & space

• Parallax distance in parsecs
• Magnitude difference from a flux ratio
• Distance from an unextinguished distance modulus
• Relative luminosity of a blackbody star
• Blackbody peak wavelength
• Kepler period with a central mass ratio
• Radius ratio from an idealized transit depth
• One-way signal delay
• Redshift from a spectral line
• Scale factor from cosmological redshift
• Enclosed mass from an idealized rotation speed
• Poisson photon-count signal-to-noise
• Order of the planets
• Rocky planets and giant planets
• Planet facts
• Earth, Moon and sky
• The Moon’s phases in order
• Mass and weight on other worlds

Artificial intelligence

• Prediction from a linear model
• Mean squared error on three cases
• One gradient-descent parameter update
• Precision from true and false positives
• Recall from true positives and false negatives
• Parameter count in a dense layer
• Output of a scalar ReLU unit
• A two-score softmax probability
• Explained variance of the first principal component
• Retrieval recall on a labeled evidence set
• Sequential workflow latency