Number recognition and identification
Naming a number you see, hear or read as a numeral.
About Skills
Skills is the LearnIndex lesson library: more than 1,500 short lessons in Math, English, Social Studies and Sciences, each tagged with a grade level from Kindergarten to Grade 12. Use the subject tiles, search, and the subject and grade menus to find what to learn next. Inside each subject, topics and their skills are arranged from the youngest grade level to the oldest.
Every skill opens as a lesson with three parts: Explanation to read (with read-aloud audio and key words you can tap), Explore to look more closely, and Practice questions that show the right answer after each try. Use the dots on each card, or the buttons on the lesson, to mark a skill Working on, Done or Hidden.
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Monday, November 2 · 7:46 AM
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Counting forwards and backwards
Saying numbers in order up or down, starting from any number.
One-to-one correspondence
Matching each object to exactly one number while counting.
Number names and number words
Writing a number as a word, like “forty-two.”
Number representation using objects, pictures, and symbols
Showing a quantity with objects, pictures, tally marks or numerals.
Ten frames and hundred charts
Grids that organize numbers into tens, showing how numbers are built.
Number lines
A line with equally spaced numbers that shows order and distance.
Before, after, and between numbers
Finding the number just before, just after, or in between two numbers.
Comparing and ordering numbers
Deciding which numbers are bigger or smaller and putting them in order.
Greater than, less than, and equal to
Using the symbols > (greater than), < (less than) and = (equal to).
One more, one less, ten more, and ten less
Finding a number that is 1 or 10 more or less than another.
Skip counting
Counting by 2s, 5s, 10s or other steps instead of by ones.
Ordinal numbers
Numbers that tell position: 1st, 2nd, 3rd and so on.
Even and odd numbers
Even numbers split into two equal groups; odd numbers leave one left over.
Place value
The value of a digit depends on its position in the number.
Composing and decomposing numbers
Breaking a number into parts, or putting parts together.
Standard, expanded, and written number forms
Writing a number in standard form, word form, and expanded form.
Rounding whole numbers
Replacing a number with a nearby friendly one, like the nearest ten.
Estimating quantities and numerical values
Finding an answer that is close enough without exact counting or calculating.
Prime and composite numbers
A prime has exactly two factors, 1 and itself; a composite has more.
Factors and multiples
Factors divide a number exactly; multiples are what you get by multiplying it.
Roman numerals
An ancient number system that uses the letters I, V, X, L, C, D and M.
Positive and negative numbers
Numbers above zero are positive; numbers below zero are negative.
Integers and absolute value
Integers are whole numbers and their opposites; absolute value is distance from zero.
Rational and irrational numbers
Rational numbers are fractions of integers; irrational numbers cannot be written that way.
Divisibility rules
Quick tests that show whether a number divides evenly.
Prime factorization
Writing a number as a product of primes.
Greatest common factor
The largest number that divides two numbers exactly.
Least common multiple
The smallest number that is a multiple of both numbers.
Square numbers and perfect squares
A square number is a number multiplied by itself.
Cube numbers and perfect cubes
A cube number is a number multiplied by itself three times.
Square roots and cube roots
The root undoes a power: √ undoes squaring, ∛ undoes cubing.
Real number system
All the numbers on the number line: rational and irrational together.
Number properties and classifications
Sorting numbers into sets such as natural, whole, integer and rational.
Scientific notation
A short way to write very large or very small numbers using powers of 10.
Number bases and binary numbers
Binary uses only 0 and 1; each place is worth double the one before.
Addition
Putting amounts together to find the total.
Subtraction
Taking an amount away to find what is left, or finding the difference.
Addition and subtraction fact families
Addition and subtraction facts that use the same three numbers.
Multiplication
Repeated addition: a number of equal groups.
Division
Sharing a total equally, or finding how many groups fit.
Multiplication and division fact families
Multiplication and division facts that use the same three numbers.
Mental math strategies
Smart ways to calculate in your head, like doubling or adding to make a ten.
Multi-digit arithmetic
Adding and subtracting numbers with many digits by place value.
Regrouping and borrowing
Exchanging tens, hundreds and so on when a digit is too small to subtract.
Long multiplication
Multiplying by each digit and adding the partial products.
Long division
Dividing step by step: divide, multiply, subtract, bring down.
Remainders
What is left over when a number cannot be shared equally.
Missing-number equations
An equation with a box or letter standing for the unknown number.
Multi-step arithmetic problems
Problems that need more than one calculation.
Estimation and reasonableness of answers
Checking that an answer is sensible by comparing it with an estimate.
Properties of arithmetic operations
Rules like commutative, associative and distributive that always hold.
Order of operations
The agreed order for evaluating: brackets, exponents, ×÷, then +−.
Mixed operations
Problems that combine addition, subtraction, multiplication and division.
Numerical expressions
Number sentences that use operations, like 3 × (4 + 2).
Calculator use and computational strategies
Using a calculator wisely and knowing which strategy fits the problem.
Comparing length, height, mass, area, and capacity
Deciding which object is longer, taller, heavier, bigger or holds more.
Non-standard measurement units
Measuring with everyday objects such as paper clips, hands or blocks.
Metric measurement system
The system based on 10s: millimetres, centimetres, metres, kilometres, grams, litres.
Imperial measurement system
Inches, feet, yards, miles, ounces, pounds and gallons.
Measuring length and distance
Using a ruler or tape to find how long or far.
Measuring mass and weight
Mass is the amount of matter in an object; weight is the force of gravity on it.
Measuring liquid volume and capacity
Volume is the space a liquid takes up; capacity is how much a container holds.
Temperature and thermometers
How hot or cold something is, in °C or °F.
Perimeter
The distance around a shape.
Time measurement and elapsed time
Reading time and finding how long something lasts.
Calendars and scheduling
Days, weeks, months and years, and planning events.
Measurement conversions
Changing from one unit to another using a conversion factor.
Circumference
The distance around a circle: C = 2πr = πd.
Area of two-dimensional figures
The space inside a flat shape.
Area of composite figures
Split an irregular shape into simple shapes, then add or subtract.
Surface area of three-dimensional figures
The total area of all the faces of a solid.
Volume of three-dimensional figures
The space inside a solid, measured in cubic units.
Measurement of composite solids
Add or subtract the volumes of simple solids that make up the shape.
Measurement applications in trades and everyday life
Using measurement skills for building, cooking, sewing and repairs.
Precision, accuracy, and significant figures
Accuracy is closeness to the true value; precision is how finely you measure.
Measurement error and tolerances
The allowed amount a measurement can differ from the target.
Positional and directional language
Words such as above, below, beside, between, left and right.
Two-dimensional shapes
Flat shapes such as circles, triangles and squares.
Three-dimensional shapes
Solid shapes such as cubes, spheres, cones and cylinders.
Shape attributes and classification
Grouping shapes by sides, angles and symmetry.
Points, lines, rays, and line segments
A point marks a location; a segment has two ends; a ray starts at a point and goes…
Parallel, perpendicular, and intersecting lines
Parallel lines never meet; perpendicular lines meet at 90°; intersecting lines cross.
Angles and angle measurement
An angle is the turn between two rays, measured in degrees.
Symmetry
When a shape can be folded or turned so it matches itself.
Plotting ordered pairs
Writing a location as (x, y) and marking it on a grid.
Complementary and supplementary angles
Complementary angles add to 90°; supplementary angles add to 180°.
Angle relationships formed by transversals
Angles formed when a line crosses two parallel lines.
Triangles and their properties
Three-sided shapes whose angles add to 180°.
Quadrilaterals and their properties
Four-sided shapes: square, rectangle, parallelogram, rhombus, trapezoid, kite.
Polygons and their properties
Closed shapes with straight sides.
Circles and their properties
Radius, diameter, chord, arc, sector and tangent.
Congruence
Shapes with the same size and shape.
Reflections, rotations, and translations
Slides, flips and turns that move a shape without changing its size.
Coordinate grids and the Cartesian plane
A grid with an x-axis, a y-axis and four quadrants.
Similarity
Shapes with the same shape and proportional sides.
Dilations
Enlarging or shrinking a shape by a scale factor from a centre.
Geometric constructions
Drawing accurate figures with only a compass and straightedge.
Distance and midpoint formulas
Formulas for the distance between two points and the point halfway between them.
Pythagorean theorem
In a right triangle, a² + b² = c² where c is the hypotenuse.
Applications of geometry in design and construction
Using geometry to plan rooms, buildings and objects.
Equations of circles
(x − h)² + (y − k)² = r² is a circle with centre (h, k) and radius…
Geometric proofs and reasoning
Using definitions, properties and logic to show a statement is true.
Optimization of geometric dimensions
Finding the dimensions that give the most area or least material.
Using manipulatives and visual representations
Physical or drawn tools such as blocks, fraction strips and number lines.
Mathematical vocabulary and notation
The words and symbols that mathematicians use, like sum, difference, product and quotient.
Understanding and interpreting word problems
Finding the question, the facts and the operation hidden in a story problem.
Checking the reasonableness of answers
Asking if an answer fits the story and the size of the numbers.
Selecting appropriate problem-solving strategies
Choosing a method, like guess and check, working backwards or making a table.
Drawing diagrams and using mathematical models
Pictures, bar models, tables and equations that represent a problem.
Logical reasoning
Thinking step by step so each conclusion follows from facts.
Identifying and correcting errors
Finding mistakes in work and fixing them.
Making conjectures
A guess based on a pattern that you test.
Justifying mathematical solutions
Explaining why a step or answer is correct.
Connecting mathematical concepts
Seeing how ideas like fractions, decimals and percents are linked.
Communicating mathematical reasoning
Using words, symbols and diagrams to explain your thinking.
Using spreadsheets and graphing technology
Using technology to organize data, calculate and draw graphs.
Mathematical investigations
Open questions where you collect data, look for patterns and explain what you find.
Mathematical proofs
A logical argument showing that a statement is always true.
Real-world mathematical modelling
Building a mathematical description of a real situation.
Mathematical decision-making
Using math to choose the best option.
Reflecting on solutions and alternative strategies
Looking back to check the answer and ask whether another approach would work.
Repeating patterns
A pattern with a unit that repeats again and again.
Growing and shrinking patterns
Patterns where the number of items increases or decreases by the same amount each step.
Number sequences
An ordered list of numbers that follows a rule.
Pattern rules
A statement that tells how to get from one term to the next, or from position to value.
Input-output tables
A table that lists inputs and the outputs a rule produces.
Variables and constants
A variable stands for a number that can change; a constant stays fixed.
Algebraic expressions
Mathematical phrases that use numbers, variables and operations.
Algebraic terms, coefficients, and like terms
Terms are parts of an expression; like terms have the same variable part.
Evaluating algebraic expressions
Replacing the variable with a number and calculating.
Simplifying algebraic expressions
Combining like terms to write an expression more simply.
Distributive property
a(b + c) = ab + ac: multiply every term inside the brackets.
Solving one-step equations
Solving with one inverse operation to get the variable alone.
Solving multi-step equations
Undo addition or subtraction first, then multiplication or division.
Inequalities
Statements that compare using , ≤ or ≥.
Arithmetic sequences and series
A sequence with a constant difference d; the sum of n terms is n/2 (2a + (n−1)d).
Geometric sequences and series
A sequence with a constant ratio r between terms.
Algebraic identities
Equations that are true for every value, such as (a + b)² = a² + 2ab + b².
Equations with variables on both sides
Collect all the variable terms on one side first.
Literal equations and rearranging formulas
Solving an equation for one variable in terms of others.
Compound inequalities
Two inequalities joined by “and” or “or”.
Absolute-value equations and inequalities
Equations and inequalities involving distance from zero.
Systems of linear equations
Two or more equations solved together.
Adding and subtracting polynomials
Combine like terms to add or subtract polynomials.
Multiplying polynomials
Use the distributive property (FOIL for two binomials).
Factoring algebraic expressions
Writing an expression as a product, the reverse of expanding.
Special products and factoring identities
Patterns like a² − b² and (a ± b)² that speed up factoring.
Radicals and radical expressions
Expressions that use roots, such as √12 = 2√3.
Operations with radicals
Adding, subtracting, multiplying and dividing radicals.
Exponent laws
Rules like aᵐ × aⁿ = aᵐ⁺ⁿ.
Systems of inequalities
Graphing two or more inequalities; the answer is where the shading overlaps.
Polynomials
Expressions with sums of terms like axⁿ.
Dividing polynomials
Dividing a polynomial by a monomial or a binomial.
Rational expressions
Fractions with polynomials, like (x + 2)/(x − 1).
Operations with rational expressions
Adding, subtracting, multiplying and dividing rational expressions.
Rational equations
Equations with variables in denominators.
Radical equations
Isolate the root, square both sides, then check.
Negative and fractional exponents
A negative exponent means reciprocal; a fractional exponent means a root.
Exponential equations
Equations where the unknown is in the exponent.
Logarithms
The exponent that a base must be raised to in order to get a number.
Logarithm laws
log(ab) = log a + log b, and similar rules.
Logarithmic equations
Equations that contain logarithms.
Mathematical modelling with algebra
Using equations to describe real situations.
Likelihood and chance
How possible it is that something will happen.
Certain, likely, unlikely, and impossible events
Words that describe how likely an event is.
Experimental probability
Probability found by doing an experiment and counting.
Theoretical probability
Probability found by reasoning about equally likely outcomes.
Sample spaces
The list of all possible outcomes of an experiment.
Probability of simple events
The chance of one event happening.
Probability of compound events
The chance of two or more events happening together or one of them happening.
Independent and dependent events
Independent events do not affect each other; dependent events do.
Tree diagrams
A branching diagram that shows every outcome and its probability.
Fundamental counting principle
If one choice has m options and another n, together there are m × n.
Factorials
n! = n × (n − 1) × … × 1.
Probability simulations
Using random trials to estimate probabilities.
Conditional probability
P(A | B) is the probability of A given that B has happened.
Permutations
Arrangements where order matters.
Combinations
Selections where order does not matter.
Binomial probability
The chance of exactly k successes in n independent trials.
Probability distributions
A table or graph that shows every possible value and its probability.
Expected value
The average outcome over many repeats: sum of value × probability.
Risk and decision-making using probability
Using probability and expected value to make choices.
Sorting and classifying information
Putting things into groups by a rule, such as colour or size.
Collecting and organizing data
Gathering information and putting it in order.
Tally charts
A chart that uses marks, grouped in fives, to count.
Pictographs
A graph that uses pictures or symbols; a key says what each picture means.
Frequency tables
A table that shows how many times each value occurs.
Bar graphs
A graph with bars whose lengths show amounts.
Line graphs
A graph that connects points to show change over time.
Circle graphs
A circle divided into sectors that show parts of a whole.
Reading and interpreting graphs
Reading values, comparing and drawing conclusions from graphs.
Mean, median, and mode
Three ways to describe the centre of a data set.
Range and interquartile range
Range is max − min; IQR = Q3 − Q1 and measures the spread of the middle half.
Histograms
A bar graph of grouped numerical data with no gaps between bars.
Scatter plots
A graph of paired data, one point for each pair.
Stem-and-leaf plots
A display where the stem is the leading digit(s) and the leaf is the last digit.
Box-and-whisker plots
A box-and-whisker plot shows the minimum, Q1, median, Q3 and maximum.
Choosing appropriate data displays
Picking the graph that fits the question and the type of data.
Variance and standard deviation
Measures of how spread out data are around the mean.
Quartiles and percentiles
Quartiles split ordered data into four parts; percentiles split it into 100.
Outliers
A value far from the rest of the data.
Sampling methods
Ways of choosing who to ask, such as random, systematic, stratified.
Populations and samples
A population is everyone of interest; a sample is the part you actually measure.
Bias in data collection
A systematic error that makes results unrepresentative.
Experimental design
Planning an investigation with control groups, variables and random assignment.
Correlation
How strongly two variables move together, measured by r from −1 to 1.
Regression analysis
Finding an equation that best fits paired data.
Lines of best fit
A straight line drawn close to most of the points on a scatter plot.
Two-variable data analysis
Looking at how two measured quantities relate.
Normal distribution
A bell-shaped, symmetric distribution centred on the mean.
Statistical inference
Using sample data to draw conclusions about a population.
Confidence intervals
A range of plausible values for a population value, with a stated confidence level.
Hypothesis testing
Using sample evidence to test a claim about a population.
Interpreting statistical claims
Checking whether a claim from data is supported or misleading.
Data investigations and reports
Collecting, displaying, analyzing and reporting on data.
Equal parts and fractional units
Parts of a whole that are exactly the same size.
Fractions of shapes, sets, and quantities
Finding a fraction of a shape, of a group, or of an amount.
Numerators and denominators
The numerator counts the parts you have; the denominator says how many equal parts make a whole.
Unit, proper, and improper fractions
Unit fractions have numerator 1; proper are less than 1; improper are 1 or more.
Mixed numbers
A whole number and a fraction together.
Equivalent fractions
Fractions that look different but have the same value.
Comparing and ordering fractions
Deciding which fraction is bigger and sorting from least to greatest.
Fractions on number lines
Placing fractions at exact points between whole numbers.
Adding and subtracting fractions
Combining fractions by using a common denominator.
Decimal place value
The digits after the decimal point are tenths, hundredths, thousandths.
Reading and writing decimals
Saying and writing decimals correctly.
Comparing and ordering decimals
Putting decimals in order by comparing place by place.
Simplifying fractions
Writing a fraction with the smallest possible numerator and denominator.
Multiplying fractions
Multiplying numerators together and denominators together.
Dividing fractions
Dividing by a fraction means multiplying by its reciprocal.
Fraction word problems
Real-life problems that use fractions.
Rounding decimals
Replacing a decimal with a nearby decimal with fewer places.
Adding and subtracting decimals
Line up decimal points, then add or subtract.
Multiplying decimals
Multiply as whole numbers, then place the decimal.
Dividing decimals
Dividing by a decimal by making the divisor a whole number.
Converting fractions and decimals
Divide the numerator by the denominator.
Percentages
A number out of 100.
Converting fractions, decimals, and percentages
Moving between the three forms of the same number.
Finding percentages of quantities
Finding a portion of a quantity.
Percentage increase and decrease
Adding or subtracting a percent of the original amount.
Discounts, sales tax, and tips
Using percents to find sale prices, tax amounts and tips.
Repeating and terminating decimals
Decimals that end or repeat forever.
Percentage change
The change divided by the original amount, written as a percent.
Percent error
How far a measurement is from the true value, as a percent of the true value.
Real-world percentage problems
Using percents in situations like sales, surveys and growth.
Canadian coins and banknotes
Coins and banknotes used in Canada, such as the loonie, toonie and $5 bill.
Counting and exchanging money
Putting coins and bills together, or swapping them for equal value.
Making purchases and calculating change
Finding what you owe and the change you get back.
Comparing prices and unit costs
Finding the best value by comparing price per unit.
Income, wages, and salaries
Income is money received; a wage is paid by the hour, a salary by the year.
Hourly pay and overtime
Extra pay for hours beyond the regular limit, often at 1.5 times the rate.
Gross pay and net pay
Gross pay is before deductions; net pay is what you take home.
Income taxes and deductions
Money taken from pay for government and benefits.
Personal budgeting
A plan for how to spend and save your income.
Tracking income and expenses
Recording what comes in and what goes out.
Saving money
Setting aside money now for later.
Simple interest
Interest earned only on the original amount: I = Prt.
Banking and financial accounts
Chequing accounts hold money for spending; savings accounts earn interest.
Credit and debt
Borrowing money you repay later, usually with interest.
Currency exchange
Changing one country’s money into another’s using a rate.
Compound interest
Interest earned on both the principal and previous interest.
Loans and repayment schedules
Equal payments that cover interest and principal until the loan is repaid.
Credit cards and interest charges
Interest on unpaid balances, often at high annual rates.
Mortgages
A loan used to buy a home, repaid over many years.
Annuities
A series of equal payments made at regular times.
Investing and investment returns
Putting money into assets hoping they grow.
Inflation and purchasing power
A general rise in prices that lowers what money can buy.
Renting versus buying a home
Comparing the costs of renting and of buying.
Vehicle ownership and transportation costs
The costs of buying, fuelling, insuring and repairing a vehicle.
Insurance and risk management
Paying a small premium to protect against a large loss.
Depreciation and appreciation
Depreciation lowers an asset’s value; appreciation raises it.
Profit, loss, and break-even analysis
Profit = revenue − costs; break-even is where they are equal.
Business revenue, costs, and pricing
Money earned, money spent, and the price needed to make a profit.
Financial planning and goal setting
Setting a money target, then planning steps and dates to reach it.
Ratios
A comparison of two quantities, written a : b.
Equivalent ratios
Ratios that describe the same relationship, like 1 : 2 and 3 : 6.
Simplifying ratios
Dividing both parts by their GCF so the ratio uses the smallest whole numbers.
Part-to-part and part-to-whole relationships
Part-to-part compares two parts; part-to-whole compares one part with the total.
Rates
A comparison of quantities with different units, like km per hour.
Unit rates
A rate with 1 in the denominator, like $2 per apple.
Proportional relationships
Two quantities that change at a constant ratio.
Solving proportions
Finding the missing value in equal ratios by cross-multiplying.
Scale factors
The number you multiply by to enlarge or reduce a figure.
Scale drawings and maps
A drawing or map where lengths are in a fixed ratio to real lengths.
Unit pricing and comparison shopping
Comparing prices by finding the cost per unit.
Speed, distance, and time
speed = distance ÷ time.
Direct variation
y = kx: when x doubles, y doubles.
Inverse variation
y = k/x: when x doubles, y halves.
Dimensional analysis
Converting units by multiplying by fractions equal to one.
Proportional reasoning in real-world situations
Using ratios and proportions to solve everyday problems.
Right-triangle trigonometry
Trigonometry connects the angles of a right triangle to the ratios of its sides.
Sine, cosine, and tangent ratios
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Inverse trigonometric ratios
sin⁻¹, cos⁻¹ and tan⁻¹ turn a ratio back into an angle.
Solving for unknown sides and angles
Use trig ratios and the Pythagorean theorem to find missing parts.
Angles of elevation and depression
The angle looking up from the horizontal (elevation) or down (depression).
Sine law
a/sin A = b/sin B = c/sin C; use it when you know an angle and its opposite…
Cosine law
c² = a² + b² − 2ab cos C; use it for SAS and SSS triangles.
Solving non-right triangles
Finding all unknown sides and angles of any triangle.
Radians and degree conversions
Radians measure angles by arc length: 180° = π radians.
Unit circle
A circle of radius 1 centred at the origin, where (cos θ, sin θ) is the point at…
Trigonometric graphs
The graphs of sine, cosine and tangent are waves that repeat.
Amplitude, period, phase shift, and vertical shift
Amplitude is the height, period the length of a cycle, phase shift the horizontal shift, vertical shift the…
Trigonometric identities
Equations true for all angles, such as sin²θ + cos²θ = 1.
Trigonometric equations
Solving for the angles that make a trigonometric statement true.
Sinusoidal modelling
Using sine or cosine waves to model tides, sound and seasons.
Applications of trigonometry in navigation and physics
Using trigonometry for bearings, forces and projectile problems.
Relations and functions
A relation pairs inputs with outputs; a function gives exactly one output for each input.
Function notation
f(x) means “the output of function f when the input is x.”
Domain and range
The domain is the set of inputs; the range is the set of outputs.
Independent and dependent variables
The independent variable is the input; the dependent variable is the output that depends on it.
Tables, graphs, equations, and verbal representations
Showing the same function as a table, graph, equation or words.
Linear relations
Relations whose graphs are straight lines.
Slope and rate of change
Rise over run: how steeply a line rises.
Slope-intercept form
y = mx + b where m is the slope and b is the y-intercept.
Graphing linear equations
Plot two points and join them, or use the slope and y-intercept.
Parallel and perpendicular lines
Parallel lines have equal slopes; perpendicular slopes are negative reciprocals.
Point-slope and standard forms
Other ways to write a line: y − y₁ = m(x − x₁) and Ax + By =…
Piecewise-defined functions
A function with different rules on different parts of its domain.
Quadratic relations and functions
Functions of the form y = ax² + bx + c; their graphs are parabolas.
Factoring quadratic expressions
Writing ax² + bx + c as a product of two brackets.
Solving quadratic equations
Finding x where ax² + bx + c = 0 by factoring or other methods.
Completing the square
Rewriting a quadratic as a(x − h)² + k.
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a solves any quadratic.
Discriminant
b² − 4ac tells how many real roots a quadratic has.
Vertex form and standard form
Vertex form y = a(x − h)² + k shows the vertex; standard form shows the y-intercept.
Parabolas and their characteristics
Vertex, axis of symmetry, intercepts and direction of opening.
Polynomial functions
Functions like f(x) = x³ − 3x² + 2 made of powers of x.
Rational functions
f(x) = P(x)/Q(x) has asymptotes where Q(x) = 0.
Radical functions
Functions that contain a root, such as y = √x.
Exponential functions
Functions of the form y = a·bˣ for growth and decay.
Logarithmic functions
The inverse of an exponential function.
Trigonometric functions
Functions based on angles, such as sine, cosine and tangent.
Function transformations
Shifts, stretches and reflections of a graph.
Composite functions
Applying one function after another: (f ∘ g)(x) = f(g(x)).
Inverse functions
A function that reverses another; swap x and y and solve.
Operations on functions
Adding, subtracting, multiplying and dividing functions.
Zeros, intercepts, and asymptotes
Where a graph meets the axes, or approaches a line it never touches.
Average and instantaneous rates of change
Average rate of change is over an interval; instantaneous rate is at a single point.
Function modelling and applications
Using functions to describe real situations.
Introduction to limits
A limit is the value a function approaches as x gets close to a number.
Evaluating limits
Substitute, factor or simplify to find a limit.
Continuity
A function is continuous if you can draw it without lifting your pencil.
Derivatives and differentiation
The derivative gives the slope of a curve at each point.
Derivatives from first principles
f′(x) = lim (h→0) (f(x + h) − f(x)) / h.
Power, product, quotient, and chain rules
Rules for differentiating powers, products, quotients and compositions.
Derivatives of polynomial, exponential, and trigonometric functions
d/dx (eˣ) = eˣ, d/dx (sin x) = cos x, d/dx (cos x) = −sin x.
Tangent lines and instantaneous rates of change
The slope of the tangent at a point is the instantaneous rate of change.
First and second derivatives
f′ gives slope; f″ tells how the slope is changing.
Increasing and decreasing functions
f is increasing where f′ > 0 and decreasing where f′ < 0.
Critical points and extrema
Where f′ = 0 or is undefined; these may be maxima or minima.
Concavity and points of inflection
Concave up means f″ > 0; an inflection point is where concavity changes.
Curve sketching
Using intercepts, critical points and concavity to sketch a graph.
Optimization problems
Finding the maximum or minimum value in a real situation.
Related rates
Rates that are connected because the quantities are connected.
Motion applications involving position, velocity, and acceleration
Velocity is the derivative of position; acceleration is the derivative of velocity.
Introduction to antiderivatives and integration
The antiderivative reverses differentiation; integration finds the area.
Definite and indefinite integrals
Definite integrals have limits and give a number; indefinite integrals give a family of functions.
Area under curves
The area between a curve and the x-axis is found by integrating.
Applications of integration
Using integrals to find distance, accumulation and total change.
Scalar and vector quantities
A scalar has size only; a vector has size and direction.
Vector representation
Drawn as arrows or written as components like (3, 4).
Vector magnitude and direction
|v| = √(x² + y²), and direction is the angle from the +x axis.
Vector addition and subtraction
Add or subtract matching components.
Scalar multiplication of vectors
Multiplying a vector by a number changes its length (and flips it if negative).
Cartesian vector components
Writing a vector as xi + yj.
Position vectors
A vector from the origin to a point.
Dot product
u · v = u₁v₁ + u₂v₂ = |u||v| cos θ.
Cross product
u × v gives a vector perpendicular to both u and v (in 3D).
Vector projections
The component of one vector in the direction of another.
Equations of lines in two and three dimensions
A line is r = r₀ + t d where d is the direction vector.
Equations of planes
A plane is ax + by + cz = d where (a, b, c) is a normal vector.
Intersections of lines and planes
Where lines and planes cross, are parallel, or coincide.
Distances and angles in three-dimensional space
Using vectors to find lengths and angles in 3D.
Applications of vectors in force and motion
Forces and velocities are vectors that add.
Uppercase and lowercase letters
Every letter has a capital (uppercase) form and a small (lowercase) form.
Connecting letters with sounds
Each letter stands for one or more sounds, and you blend those sounds to read words.
Rhyming words
Rhyming words have the same ending sound, like cat and hat.
Syllables
A syllable is one beat in a word, and each syllable has one vowel sound.
Beginning and ending sounds
Words begin and end with sounds that you can hear, such as /k/ at the start and /t/…
Blending and segmenting words
Blending pushes separate sounds together to say a word; segmenting pulls a word apart into its sounds.
Phonics and decoding
Phonics connects letters and letter teams to the sounds they make, so you can read new words.
Spelling patterns and word families
Words that share the same ending pattern, like cat, hat and mat, make a word family.
Decoding with syllables and word parts
Breaking a long word into syllables or word parts, like un and happy, helps you read and understand…
Sight words
Sight words are common words, like the, and and is, that you learn to read at a glance.
Building vocabulary
Vocabulary is the set of words you know and can use.
Sight-word recognition and fluency
Reading common words instantly and smoothly so that you can think about the meaning.
Word meaning from context
You can work out what a new word means by using the words and sentences around it.
Context clues
Definitions, synonyms, opposites and examples in a sentence can reveal the meaning of an unfamiliar word.
Prefixes and suffixes
A prefix goes at the front of a word and a suffix goes at the end; both change…
Root words
A root word is the main part of a word that can stand alone, like play in replay.
Synonyms and antonyms
Synonyms are words with almost the same meaning; antonyms are words with opposite meanings.
Spelling patterns and vocabulary strategies
Spelling rules, patterns and memory tricks help you spell words correctly and learn new vocabulary.
Greek and Latin roots and affixes
Many English words are built from Greek and Latin roots, prefixes and suffixes whose meanings you can learn.
Word relationships
Words connect in patterns such as synonyms, antonyms, categories and parts, and connotation adds feeling.
Simple stories and informational texts
Listening to or reading short stories and fact texts and telling who or what they are about.
Characters, setting and events
Characters are who a story is about, the setting is where it happens, and events are what happens.
Fiction and nonfiction
Fiction is a made-up story; nonfiction gives true facts about real people, places and things.
Main idea and key details
The main idea is what a text is mostly about; key details are facts that tell more about…
Sequence, and cause and effect
Sequence is the order events happen; a cause is why something happens and the effect is what happens.
Basic inference
An inference is a smart guess that uses clues in the text plus what you already know.
Comparing characters, events and texts
Comparing means telling how two characters, events or texts are alike and how they are different.
Reading fluency and expression
Reading fluently means reading smoothly and accurately, with the right pauses and expression.
Main idea, theme and supporting details
The main idea is what a text is mostly about, the theme is the lesson, and details support…
Making inferences with text evidence
Readers use clues in the text plus what they know to work out ideas, and back them up…
Summarizing texts
A summary retells the most important ideas of a text briefly, in your own words.
Comparing viewpoints and text structures
Texts are organized in patterns, and different authors can have different viewpoints on the same topic.
Citing evidence from a text
Citing evidence means using exact words or details from a text to support a claim or answer.
Reading complex texts
Complex texts need active reading: preview, read, mark, question, reread and summarize.
Making and supporting inferences
A strong inference combines clues from the text with background knowledge and is backed by specific evidence.
Comparing multiple texts and perspectives
Comparing texts means finding where authors agree, where they disagree and why their viewpoints differ.
Capital letters and punctuation basics
A sentence begins with a capital letter and ends with a period, question mark or exclamation mark.
Nouns
A noun names a person, place, thing or idea.
Verbs
A verb is a word that shows an action or a state of being, like run, think or…
Adjectives
An adjective describes a noun by telling what kind, how many or which one.
Pronouns
A pronoun takes the place of a noun, like he, she, it, we and they.
Adverbs
An adverb tells how, when or where something happens, and many end in -ly.
Capitalization, punctuation and basic grammar
Correct sentences use capital letters, ending punctuation, apostrophes, commas in lists and verbs that match.
Conjunctions and prepositions
Conjunctions join words or ideas; prepositions show how a noun relates to another word, such as where it…
Sentence structure and agreement
A sentence needs a subject and a verb that agree, plus correct capital letters and punctuation.
Fragments, run-ons and sentence types
A complete sentence has a subject, a verb and a full thought; fragments and run-ons break these rules.
Commas, apostrophes and quotation marks
Commas, apostrophes and quotation marks show lists, pauses, ownership, contractions and speech.
Varying sentence structure
Writers mix short and long sentences, and simple, compound and complex ones, so their writing flows.
Misplaced modifiers and agreement errors
A modifier must sit next to what it describes, and a verb must agree with the true subject.
Parallel structure and concision
Parallel structure uses matching grammatical forms in a series, and concise writing cuts words that do no work.
Advanced punctuation: semicolons, colons and dashes
Semicolons join related sentences, colons introduce lists or explanations, and dashes add emphasis or interruptions.
Active and passive voice, and verb mood
Active voice shows who does the action, passive voice stresses the receiver, and the subjunctive expresses wishes and…
Writing letters, words and sentences
Young writers write letters, words, labels and simple sentences to share their ideas.
Complete sentences and paragraphs
A paragraph is a group of complete sentences about one idea, with a topic sentence, details and a…
Narrative and descriptive writing
Narrative writing tells a story with a beginning, middle and end; descriptive writing uses details that appeal to…
Opinion and informational writing
Opinion writing says what you think and gives reasons; informational writing teaches true facts about a topic.
Revising and editing basic writing
Revising improves ideas and words; editing fixes spelling, capital letters, punctuation and grammar.
Organized paragraphs and multi-paragraph compositions
A composition has an introduction, body paragraphs that each develop one idea, and a conclusion.
Narrative, informational and opinion pieces
Different purposes call for different forms: narrative tells a story, informational explains and opinion persuades.
The writing process
The writing process moves through planning, drafting, revising, editing and publishing.
Writing clear multi-paragraph essays
A clear essay has an introduction with a thesis, body paragraphs with topic sentences and evidence, and a…
Narrative, explanatory and argumentative writing
Writers choose narrative, explanatory or argumentative forms depending on whether they want to tell, explain or convince.
Claims, evidence, reasoning, introductions and conclusions
Strong writing makes a claim, backs it with evidence, explains the reasoning and frames it with an engaging…
Revising for clarity, organization, style and audience
Revising improves clarity, organization, style and tone so the writing fits its purpose and audience.
Editing for grammar, spelling, punctuation and usage
Editing fixes grammar, spelling, punctuation and usage so the writing is correct and easy to read.
Thesis statements and argumentative essays
An argumentative essay makes a debatable thesis and defends it with reasons, evidence and a response to opposing…
Writing literary analysis essays
A literary analysis essay argues a claim about a text, supports it with quotations and explains how the…
Synthesis and research papers
A research paper asks a question, gathers reliable sources and synthesizes them into a clear, cited argument.
Personal narrative and the college essay
A personal essay uses a specific story, vivid details and honest reflection to show who you are.
Revising for voice and precision
Precise word choice, strong verbs and an authentic voice make writing vivid, direct and memorable.
Speaking in complete thoughts
Kindergarteners speak in complete thoughts, take turns, listen and ask questions.
Alphabetical order and simple reference tools
Alphabetical order, dictionaries, glossaries and tables of contents help readers find information fast.
Reference sources and basic research
Students ask a question, use books, websites and other sources, take notes in their own words and list…
Conducting research and evaluating sources
Researchers pose a focused question, search effectively and judge sources for credibility, accuracy, bias and currency.
Paraphrasing, summarizing, quoting and citing
Writers use paraphrase, summary and quotation to use others’ ideas, and they cite the source each time.
Media literacy
Media literacy means analyzing who made a message, why, for whom and how it shapes what people think.
Citations and academic integrity
Academic integrity means doing your own work and crediting every source with a consistent citation style.
Oral presentations and debate
Strong speakers organize ideas, use eye contact, pacing and evidence, and listen to respond to opposing arguments in…
Figurative language and literary devices
Figurative language, such as similes, metaphors and personification, uses comparisons and word play to paint pictures in the…
Analyzing theme and central idea
A theme is the message about life that a story shares; the central idea is the main point…
Analyzing character, plot and point of view
Stories follow a plot of connected events, feature characters in conflict and are told from a point of…
Analyzing text structure
Authors organize ideas using structures such as sequence, compare and contrast, cause and effect, and problem and solution.
Analyzing tone, mood and word choice
Word choice shapes tone, which is the author’s attitude, and mood, which is the feeling the reader gets.
Analyzing arguments, claims and evidence
An argument states a claim and supports it with reasons and evidence while answering opposing views.
Reading poetry and drama
Poetry uses lines, sound and imagery to say much in few words, and drama is written to be…
Irony, symbolism, allegory and satire
Writers use irony, symbols, allegory and satire to suggest meanings beyond what is said on the surface.
Rhetoric: ethos, pathos and logos
Ethos, pathos and logos are three appeals that persuade through credibility, emotion and logic.
Logical fallacies and evaluating arguments
A logical fallacy is a flaw in reasoning that makes an argument seem stronger than it really is.
Rhetorical analysis of speeches and essays
Rhetorical analysis examines how a speaker or writer uses purpose, audience and devices to persuade.
Literary periods and historical context
Literature reflects the ideas and events of its time, so knowing the period helps explain what a text…
Analyzing style, voice and syntax
Style is how a writer uses diction, syntax and tone to create a distinct voice and effect on…
Abbreviations
What is an abbreviation? An abbreviation is a shortened form of a word or phrase. Abbreviations save time…
Adjectives
What is an adjective? An adjective is a word that describes a noun or a pronoun. Adjectives add…
Adverb
What is an adverb? An adverb is a describing word, but instead of describing nouns it describes verbs,…
Alliteration
What is alliteration? Alliteration is the repetition of the same beginning consonant sound in words that are close…
Alphabet
What is the alphabet? The alphabet is the set of letters we use to write words. The English…
Apostrophe rules
The apostrophe's two jobs The apostrophe (') looks small, but it causes more mistakes than almost any other…
Articles
What are articles? Articles are the tiny words a, an and the. They come before nouns and tell…
Cause and Effect
What is cause and effect? Everything that happens has a reason. Cause and effect describes how one thing…
Clause and Phrase
Clauses and phrases: the building blocks Sentences are built from groups of words. Two of the most important…
Common Mistakes in Language Arts
Why learn common mistakes? Every writer makes mistakes, even professional authors. The difference is that good writers know…
Comparatives and Superlatives
Comparing with adjectives An adjective describes a noun: a tall tree, a fast car, a funny joke. When…
Compound Words
What is a compound word? A compound word is made by joining two or more smaller words to…
Conditionals
What is a conditional? A conditional sentence tells us that one thing depends on another. It usually has…
Conjunctions
What is a conjunction? A conjunction is a joining word. It connects words, phrases or whole ideas so…
Contractions
What is a contraction? A contraction is a short way of writing two words as one. Some letters…
Count and Noncount Nouns
Two kinds of nouns A noun names a person, place, thing, animal or idea. In English, nouns come…
Demonstratives
What are demonstratives? Demonstratives are pointing words. They show exactly which person or thing we mean. There are…
Descriptive Writing
What is descriptive writing? Descriptive writing paints a picture with words. It helps readers see, hear, smell, taste…
Determiners
What is a determiner? A determiner is a small word that comes before a noun. It tells us…
Fiction and Nonfiction
Two big families of books Every book, article and story belongs to one of two big families: Fiction:…
Grammar
What is grammar? Grammar is the set of rules for how words fit together to make meaning. Grammar…
Homonyms
Words that look or sound alike English has many words that look alike, sound alike, or both, but…
Homophones
What are homophones? Homophones are words that sound the same but have different meanings and usually different spellings.…
Interjections
What is an interjection? An interjection is a word or short phrase that shows a sudden feeling or…
Language Arts
What is language arts? Language arts is the school subject about using language well. It teaches you how…
Learning to Read
How children learn to read Learning to read is one of the biggest achievements of childhood. It does…
Literary Devices
What are literary devices? Writers are like chefs. They have special ingredients that make their writing tasty and…
Metaphor
What is a metaphor? A metaphor is a comparison that says one thing is another thing. It does…
Nouns
What is a noun? A noun is a word that names something. Every noun answers the question who?…
Parts Of A Story
Every story has building blocks Every story you have ever read, from fairy tales to novels to movies,…
Passive Voice and Active Voice
Who did it? Every action has a doer, the person or thing doing the action. English lets us…
Personal Titles
What is a personal title? A personal title is a word placed before someone's name to show respect…
Phrasal Verbs
What is a phrasal verb? A phrasal verb is a verb plus one or two small words that…
Plural Spelling Rules
Singular and plural A singular noun names one thing: cat, box, baby. A plural noun names more than…
Point of View
What is point of view? Point of view is the angle from which a story is told. It…
Prefixes
What is a prefix? A prefix is a group of letters added to the beginning of a word.…
Pronouns
What is a pronoun? A pronoun is a word that takes the place of a noun. Pronouns stop…
Pronunciation
What is pronunciation? Pronunciation is how a word is said out loud. Clear pronunciation helps people understand you,…
Punctuation
Why punctuation matters Punctuation marks are the traffic signals of writing. They tell readers when to stop, when…
Quantifiers
What is a quantifier? A quantifier is a word or phrase that tells how much or how many…
Rhyming Words
What are rhyming words? Rhyming words are words that end with the same sound. cat, hat, bat, sat…
Self-Introduction
What is a self-introduction? A self-introduction is how you tell someone who you are. You might introduce yourself…
Sentence Structures
Building sentences Sentences are like buildings. Some are small and simple, like a single room. Others are big…
Silent Letters
What are silent letters? A silent letter is written in a word but not pronounced. Look at knee:…
Similes
What is a simile? A simile is a comparison between two different things using the word like or…
Subject and Object
Who did what? Most sentences tell us who did something and what they did it to. Two important…
Suffixes
What is a suffix? A suffix is a group of letters added to the end of a word.…
Syllables
What is a syllable? A syllable is a part of a word that contains one vowel sound. When…
Tenses
What is verb tense? Verbs tell us what happens. Verb tense tells us when it happens. I walk…
The Power of Nouns
Why nouns are powerful Nouns are more than naming words. They are the words that make pictures appear…
Verbs
What is a verb? A verb is the engine of a sentence. It tells what the subject does…
Vocabulary
What is vocabulary? Your vocabulary is all the words you know. You have different vocabularies for different skills:…
Who, What, Where, When, Why and How
Six powerful questions Reporters, detectives, scientists and readers all use the same six question words to understand events…
Dolch Words
What are Dolch words? Dolch words are a list of very common English words put together by Dr.…
Diphthongs
What is a diphthong? A diphthong (say DIF-thong) is a vowel sound that glides. Your mouth starts in…
Adages
What is an adage? An adage is a short, well-known saying that shares a piece of wisdom about…
Analogies
What is an analogy? An analogy is a comparison between two pairs of words. It says that the…
Antonyms / Opposites
What is an antonym? An antonym is a word that means the opposite of another word. big and…
Commonly Misused Words
Why some words get mixed up Commonly misused words are words that people confuse because they look alike,…
Consonant Blends
What is a consonant blend? A consonant blend is two or three consonants that sit side by side…
Consonant Digraphs
What is a consonant digraph? A digraph is two letters that spell one sound. A consonant digraph is…
Essays
What is an essay? An essay is a short piece of writing about one topic. It shares information,…
Nursery Rhymes
What is a nursery rhyme? A nursery rhyme is a short, traditional poem or song for young children.…
Parts of Speech
What are the parts of speech? Every word in English has a job. The parts of speech are…
Phonics
What is phonics? Phonics is the link between the sounds we hear in words and the letters we…
Prepositions
What is a preposition? A preposition is a small word that shows how one thing is connected to…
Silent E
What is silent e? Silent e is an e at the end of a word that you do…
Synonyms
What is a synonym? A synonym is a word that means the same or nearly the same as…
Word Families
What is a word family? A word family is a group of words that share the same ending…
Living and nonliving things
Living things grow, need food, water and air, and make more of their own kind; nonliving things do…
Basic needs of plants and animals
Plants need sunlight, water, air and space; animals need food, water, air and shelter.
Plant and animal structures
Plants and animals have body parts, called structures, that help them live, grow and meet their needs.
Life cycles and offspring
Plants and animals go through stages in their lives, and parents have offspring that look like them.
The five senses and body functions
We use our eyes, ears, nose, tongue and skin to sense the world, and our body parts help…
Classifying organisms
Scientists sort living things into groups by shared features, such as vertebrates with a backbone and invertebrates without…
Adaptations
An adaptation is a body part or behaviour that helps a living thing survive in its environment.
Inherited traits and life cycles
Inherited traits come from parents, such as eye colour; learned behaviours come from experience, such as riding a…
Basic body systems
The body is made of systems, such as the digestive, respiratory, circulatory and skeletal systems, that work together.
Cells, tissues, organs and organ systems
Living things are organized in levels: cells make tissues, tissues make organs and organs work together in organ…
Human body systems and how they work together
The immune, endocrine, excretory and other systems work with the circulatory and nervous systems to keep the body…
Reproduction
Asexual reproduction uses one parent and makes identical offspring; sexual reproduction uses two parents and makes offspring that…
Cell structure and function
Cells contain organelles that each do a job: the nucleus controls the cell, mitochondria release energy and ribosomes…
Photosynthesis and cellular respiration
Photosynthesis stores light energy in glucose; cellular respiration releases that energy as ATP.
DNA and protein synthesis
DNA is copied into mRNA in transcription, and ribosomes read the mRNA in translation to build a protein.
Homeostasis and feedback
Homeostasis keeps the body’s internal conditions steady using negative feedback loops with a receptor, a control centre and…
Measuring, comparing and classifying
Scientists measure with tools, compare what they find, sort things into groups and record their observations.
Asking questions, predicting and sharing findings
Scientists ask a question, make a prediction, test it, record what happens and share what they learned.
Using measurement and scientific tools
Scientists choose the right tool for each measurement and read it carefully using standard units.
Planning fair tests
In a fair test you change one thing, measure one thing and keep everything else the same.
Collecting, graphing and communicating data
Scientists collect data in tables, show it in graphs and use the pattern to explain what they found.
Engineering design: define, build, test and improve
Engineers define a problem, build a design, test it and improve it again and again.
Metric measurement and unit conversions
The metric system uses prefixes such as kilo, centi and milli, so units convert by multiplying or dividing…
Designing controlled investigations
A controlled investigation changes one variable, measures another and controls every other factor so the result can be…
Variables and evaluating evidence
The independent variable is what you change, the dependent variable is what you measure and controlled variables are…
Interpreting tables, graphs, models and data
Scientists look for patterns in tables and graphs and use models to explain how things work.
Engineering constraints and optimization
Engineers design within criteria and constraints, weigh trade-offs and optimize a design to meet the goal.
Experimental design, uncertainty and error
Every measurement has uncertainty; good experiments reduce random error, identify systematic error and report results honestly.
Scientific models, theories and laws
A scientific theory is a well-tested explanation; a law describes a pattern; models represent ideas so they can…
Data analysis, significant figures and percent error
Scientists report data with the right precision and compare results using percent error.
Scientific argument and peer review
A scientific argument links a claim to evidence with reasoning, and peer review checks it before it is…
Weather, seasons and the sky
Weather changes from day to day, the four seasons repeat each year, and we can watch the Sun,…
Land and water features
Earth has land features such as mountains and valleys and water features such as rivers, lakes and oceans.
Rocks, minerals, fossils, soil and landforms
Rocks are made of minerals and are igneous, sedimentary or metamorphic; fossils are remains of ancient life, and…
Weather, climate and the water cycle
Weather is the daily condition of the air; climate is the pattern over many years; the water cycle…
Earth, the Moon, the Sun and the solar system
Earth and seven other planets orbit the Sun, and Earth’s spin causes day and night while its tilt…
Earth’s layers and plate tectonics
Earth has a crust, mantle and core, and the crust is broken into plates that move slowly and…
Rocks, erosion and geologic processes
Weathering breaks rock down, erosion moves the pieces, deposition drops them, and the rock cycle changes rocks from…
Weather, climate, oceans, atmosphere and human impacts
The atmosphere, oceans and land shape weather and climate, and human activities such as burning fossil fuels are…
Astronomy: gravity, stars and galaxies
Gravity holds planets in orbit and stars in galaxies; stars are huge balls of hot gas that make…
Climate change and the carbon cycle
Carbon moves between air, oceans, living things and rocks; burning fossil fuels adds extra carbon dioxide that traps…
Evidence for plate tectonics and geologic time
Matching coastlines, fossils, rock layers and seafloor spreading support plate tectonics, and rock layers and radioactive dating tell…
Stellar life cycles and the Big Bang
Stars form in nebulae, shine by fusion for billions of years and end as white dwarfs or in…
Earth systems, resources and sustainability
Earth’s spheres interact, and resources can be renewable or nonrenewable, so sustainability means meeting needs without using up…
Properties of materials
We can describe materials by how they look and feel, such as hard, soft, rough, smooth, bendy or…
Solids, liquids and gases; heating and cooling
Solids keep their shape, liquids take the shape of their container, and heating or cooling can change one…
Properties and changes of matter
Matter has mass and takes up space; heating and cooling cause changes of state such as melting, freezing,…
Mixtures, solutions and simple chemical changes
A mixture combines substances that keep their properties, a solution is a mixture that dissolves evenly, and a…
Atoms, elements, compounds and the periodic table
Atoms are the building blocks of matter; elements have one kind of atom, compounds have different atoms bonded,…
Physical and chemical changes
A physical change alters the form of a substance but not what it is made of; a chemical…
Chemical reactions and conservation of matter
In a chemical reaction atoms are rearranged, and the total mass stays the same because matter is conserved.
Acids and bases
Acids have a pH below 7, bases have a pH above 7, and a pH of 7 is…
Atomic structure and periodic trends
Atoms have protons and neutrons in a nucleus and electrons in shells; the number of protons is the…
Chemical bonding
Atoms bond to reach stable outer shells: ionic bonds transfer electrons, covalent bonds share them and metallic bonds…
Balancing equations and reaction types
A balanced equation has the same number of each kind of atom on both sides, and reactions can…
The mole and stoichiometry
The mole counts particles, and amounts of substances in a reaction are related by the coefficients in the…
Gas laws and kinetic theory
Gas particles move randomly, and at constant temperature the pressure of a gas goes up when its volume…
Heat, energy changes and reaction rates
Heat q = m × c × ΔT, exothermic reactions release energy, endothermic reactions absorb energy, and reaction…
Habitats
A habitat is the place where a plant or animal lives and finds what it needs.
Ecosystems and interactions
An ecosystem is the living and nonliving things in a place; producers make food, consumers eat other living…
Food chains and food webs
A food chain shows how energy passes from the Sun to producers and then to the consumers that…
Heredity and genetics
Genes are passed from parents to offspring; dominant alleles show when present and recessive alleles show only when…
Adaptation and evolution
Over many generations, helpful traits become more common because organisms with them survive and reproduce more.
Populations, food webs and environmental change
A population is one kind of organism in an area; its size depends on limiting factors, and changes…
Mendelian genetics and Punnett squares
A Punnett square predicts the possible genotypes and phenotypes of offspring from the alleles each parent can pass…
Natural selection and evidence for evolution
Fossils, similar body structures, DNA comparisons and observed changes in populations all support the theory of evolution by…
Population dynamics and carrying capacity
Populations grow quickly when resources are plentiful, then level off at the carrying capacity the environment can support.
Energy flow and biogeochemical cycles
Energy flows one way through ecosystems, with only about 10% passed to the next trophic level, while matter…
Light, sound and simple energy
Light lets us see, sound is made by vibrations that we hear, and the Sun gives us light…
Light and sound
Light travels in straight lines and can be reflected, bent or absorbed, while sound is a vibration that…
Electricity and magnetism
Electric current flows in a complete circuit through conductors; magnets push and pull on certain metals, and opposite…
Waves and sound
A wave carries energy without carrying matter; its speed equals frequency times wavelength.
Light: reflection, refraction and colour
Light reflects at equal angles, bends when it changes materials, and white light is made of colours that…
Electric circuits and magnets
In a series circuit current has one path, in a parallel circuit it has several, and a moving…
Wave properties and the electromagnetic spectrum
Electromagnetic waves travel at the speed of light and range from radio waves to gamma rays; higher frequency…
Electric circuits and Ohm’s law
Ohm’s law says voltage equals current times resistance, V = I × R.
Optics: mirrors and lenses
Concave mirrors and convex lenses can focus light to form real images, while convex mirrors and concave lenses…
Electromagnetism and induction
A changing magnetic field through a coil induces a voltage, which is how generators make electricity and transformers…
Modern physics: photons and radioactivity
Light comes in packets of energy called photons, and unstable nuclei decay with a half-life, the time for…
Pushes, pulls and motion
A push moves something away from you, a pull moves it toward you, and pushes and pulls can…
Force, motion and gravity
A force is a push or a pull; balanced forces do not change motion, unbalanced forces do, and…
Energy and its forms
Energy is the ability to cause change; it takes forms such as heat, light, sound, motion and stored…
Force, speed and acceleration
Speed is distance divided by time, and acceleration is how fast velocity changes, which happens when an unbalanced…
Energy, work and power
Work is force times distance moved, measured in joules, and power is work divided by time, measured in…
Simple machines
Simple machines such as levers, pulleys and inclined planes make work easier by changing the size or direction…
Newton’s laws of motion
An object keeps its motion unless a net force acts, force equals mass times acceleration, and every action…
Kinematics: velocity, acceleration and graphs
Acceleration is the change in velocity divided by time, and a velocity–time graph shows acceleration as its slope.
Work, energy and conservation of energy
Kinetic energy is ½mv², gravitational potential energy is mgh, and energy is conserved when it changes form.
Momentum and impulse
Momentum is mass times velocity, and in a closed system total momentum is conserved in collisions.
Gravity, weight and circular motion
Weight is the force of gravity on a mass, W = mg with g ≈ 9.8 N/kg, and…
Heat transfer and the laws of thermodynamics
Heat moves by conduction, convection and radiation, and the laws of thermodynamics say energy is conserved and heat…
Amphibians
"Double life" The word amphibian comes from Greek words meaning "double life." Most amphibians start life in water…
Animal Classification
Animal classification is the process of categorizing animals into different groups based on their characteristics. There are several…
Birds
What makes a bird a bird? There are about 11 000 species of birds, from the tiny bee…
Fish
Fish are aquatic animals that have a wide variety of species and can be found in oceans, rivers,…
Insects and Arachnids
The most successful animals Insects and arachnids belong to a huge group called arthropods, which means "jointed feet."…
Mammals
What is a mammal? You are a mammal! So are dogs, whales, bats, mice and elephants. There are…
Reptiles
Meet the reptiles Reptiles have lived on Earth for over 300 million years. Dinosaurs were reptiles, and so…
Asteroids
Asteroids, the small yet fascinating rocky objects that orbit the Sun, are remnants from the formation of the…
Astronomy
Astronomy, the study of celestial objects such as planets, stars, galaxies, and other phenomena beyond Earth's atmosphere, captivates…
Black Holes
Black holes stand as some of the most enigmatic and captivating entities in the vast expanse of our…
Comets
Comets are celestial bodies that capture our imagination with their breathtaking tails and brilliant comas. These icy travelers…
Constellations
A constellation is a group of stars that appear to form a pattern in the night sky. These…
Earth
Earth, our home planet, is the third celestial body orbiting the Sun and the only known place in…
Galaxies
Galaxies are massive systems of stars, gas, dust, and dark matter held together by gravity. Found throughout the…
Jupiter
Jupiter, the largest planet in our Solar System and the fifth planet from the Sun, stands as a…
Lunar Eclipses
A lunar eclipse is a captivating celestial event that occurs when the Earth passes directly between the Sun…
Mars
Mars, the fourth planet from the Sun, often captivates the human imagination with its striking reddish hue visible…
Mercury
Mercury, the innermost planet in our Solar System, captivates scientists and astronomers alike with its unique characteristics and…
Meteors
Meteors, often colloquially referred to as "shooting stars," are cosmic entities that captivate observers as they streak across…
Moon
The Moon, Earth's only natural satellite, has captivated human curiosity for millennia. As one of the most recognizable…
Neptune
Neptune, the eighth planet from the Sun and the fourth largest in our Solar System, is a celestial…
Nuclear Fusion
Nuclear fusion stands at the forefront of scientific innovation, promising a future of clean and nearly limitless energy.…
Pluto
Pluto, once hailed as the ninth planet of our Solar System, now resides in a distinguished category known…
Saturn
Saturn is a captivating planet in our Solar System, renowned for its distinct appearance and extraordinary characteristics. Situated…
Solar Eclipses
A solar eclipse occurs when the Moon passes between the Sun and the Earth, blocking the light of…
Solar System
The Solar System, a captivating array of celestial objects orbiting around the Sun, forms an essential part of…
Solar Wind
Solar wind, a stream of charged particles constantly emanating from the Sun, plays a critical role in shaping…
Stars
Stars are massive, luminous objects held together by their own gravity, serving as the fundamental building blocks of…
Sun
The Sun is the brilliant centerpiece of our Solar System, a colossal and luminous object that provides the…
Sunspot
Sunspots are dark, cooler regions on the Sun's surface, known as the photosphere. These intriguing phenomena are crucial…
Telescopes
Telescopes are indispensable instruments used to observe and study celestial objects such as stars, planets, and galaxies. Their…
Universe
At the heart of humanity's profound fascination with the cosmos lies the compelling narrative of its origin: the…
Uranus
Uranus, the seventh planet from the Sun and the third-largest in our Solar System, remains a celestial enigma…
Venus
Venus, the second planet from the Sun, captivates scientists and space enthusiasts alike due to its remarkable similarities…
Adaptations
Adaptation is a fundamental concept in biology, referring to the process by which organisms become better suited to…
Animal and Plant Cells
All living organisms are made up of cells. Animal and plant cells are the basic unit of life…
Animal Groups
Animals come in all shapes and sizes, exhibiting a vast array of behaviors, habitats, and survival strategies. First,…
Animal Life Cycle
All animals go through a life cycle, which is a series of changes that an organism goes through…
Animals
Animals are a diverse group of living organisms that inhabit our planet. In this lesson, we will explore…
Bacteria
The tiniest living things Bacteria (singular: bacterium) are tiny single-celled living things. They are so small that about…
Biotic and Abiotic
In ecology, the concepts of biotic and abiotic factors play pivotal roles in shaping and maintaining ecosystems. These…
Blood and Heart
Blood is a vital component of human life and has been the focus of medical and scientific research…
Blood Components
Blood is a vital fluid that circulates throughout the body, providing oxygen and nutrients to cells while removing…
Blood Types
Blood is an essential fluid that circulates throughout the human body, delivering oxygen and nutrients to various organs…
Blood Vessels
Blood vessels are vital elements of the circulatory system, responsible for transporting blood throughout the body. This intricate…
Bones
Bones are a vital component of the human body, providing structural support, protecting organs, and enabling movement. The…
Brain
The human brain is unparalleled in its complexity and significance, serving as the central hub for controlling all…
Breathing
Why do we breathe? You breathe about 20 000 times a day without thinking about it. Every breath…
Cancer
Cancer is a complex and devastating disease that affects millions of people worldwide. What is Cancer? Cancer is…
Chloroplasts
Chloroplasts are vital organelles found in the cells of plants and certain other eukaryotic organisms. They have distinctive…
Concussions
Concussions are a form of mild traumatic brain injury (TBI) that occur due to a sudden blow to…
Diabetes
Diabetes is a chronic condition that affects millions of people globally, exerting significant impacts on both individuals and…
Digestive System
The digestive system is a crucial biological system responsible for the breakdown of food into nutrients that can…
Disease
Disease is a phenomenon that has impacted human history in significant ways. In this lesson, we will explore…
DNA
The instruction book of life Every living thing, from a bacterium to a blue whale, carries instructions for…
Enzymes
Enzymes are indispensable biological molecules that perform critical functions in living organisms. These proteins, composed of amino acid…
Epidemics and Pandemics
When diseases spread Most of the time, diseases spread at a steady, low level. But sometimes cases suddenly…
Eukaryotic and Prokaryotic Cells
All living things are composed of cells, the basic units of life that form the structure and function…
Evolution
Evolution is the process by which populations of living organisms change over time through the inheritance of changes…
Food Groups
Food provides our body with the energy and nutrients it needs to function properly. A balanced diet is…
Fossils
Fossils are the remains of plants and animals that lived millions of years ago. They are significant to…
Fungi
Not plants, not animals Mushrooms grow in the ground like plants, but they are not plants. Fungi (singular:…
Genetics
The basic concepts of genetics, its history, and its profound impact on the world. Genetics is a cornerstone…
Hearing
Hearing is one of the five senses that humans possess, and the ear is the primary organ responsible…
Herbivores, Carnivores and Omnivores
There are three primary types of diets among animals: herbivores, carnivores, and omnivores. Each of these dietary categories…
Hereditary Patterns
Hereditary patterns refer to the transmission of genetic traits from one generation to the next, forming the foundation…
Historic Epidemic and Pandemic Diseases
Diseases that changed history Epidemics and pandemics have shaped human history as much as wars and empires. They…
Immune System
The immune system is a remarkable and intricate network of cells, tissues, and organs designed to defend the…
Influenza
What is the flu? Influenza, or the flu, is a contagious illness of the nose, throat and lungs…
Level of organization
In biology, living organisms are composed of different levels of organization. From the smallest unit of life to…
Materials
Materials are an essential part of our daily lives, from the clothes we wear to the buildings we…
Medicine and Pharmaceutical Drugs
What is a medicine? A medicine is a substance used to treat illness, prevent disease, or relieve symptoms…
Mitochondria
Mitochondria are organelles found in most eukaryotic cells that are responsible for generating energy in the form of…
Muscles
Muscles are an essential part of the human body, responsible for a multitude of functions that are vital…
Nervous System
The nervous system is a fascinating and intricate network of nerves and cells that serves as the body’s…
Nucleus
The nucleus is a vital component of cells, containing the genetic material that determines the characteristics of an…
Organ Systems
An organ system is a group of organs that work together to perform a specific function or set…
Organisms
Organisms are the fundamental units of life, embodying the intricate and diverse nature of biological existence. This extensive…
Organs
Organs are an essential part of the human body, performing specific functions necessary for life. These complex structures…
Parts of a Plant
Plants are indispensable living organisms that play a crucial role in sustaining life on Earth. They perform a…
Photosynthesis
Photosynthesis is a vital biological process occurring in plants, algae, and some bacteria. In this lesson, we will…
Plant Growth and Reproduction
Plants, as living organisms, possess remarkable capabilities for growth and reproduction, crucial for the continuation of their species.…
Proteins
Proteins are fundamental to the survival and functionality of all living organisms. Their myriad functions in biological processes…
Ribosomes
Ribosomes are tiny, yet vital structures within cells that serve as the sites for protein synthesis. Despite their…
Sight
Sight is one of the most essential senses that humans possess, allowing us to perceive and interact with…
Skeleton
The human skeleton is a marvel of engineering, serving as the structural foundation that supports our bodies, protects…
Skin
The skin is the largest organ in the human body and plays a crucial role in protecting and…
Smelling
Smelling and tasting are two senses that intricately work together, creating a symphony of flavors and aromas that…
States Of Matter
The Fundamental States of Matter: Solid, Liquid, and Gas Everything in the universe is composed of matter, which…
Teeth
Teeth are fundamental to our daily lives, serving crucial roles in chewing, speech articulation, and facial structure maintenance.…
The Cell
The cell is the most fundamental unit of life, serving as the building block of all living organisms.…
The Human Body
The human body is a marvel of biological engineering, an intricate system of organs, tissues, and cells that…
Types of muscles
Muscles are fundamental to human movement and come in various types, each with unique characteristics and functions. In…
Vascular and Non-Vascular Plants
Plants are indispensable to life on Earth, serving as the primary producers that convert solar energy into food…
Vertebrates and Invertebrates
Animals represent an immense and diverse kingdom, encompassing an astonishing variety of life forms. To bring some order…
Viruses
Smaller than small Viruses are tiny particles that cause diseases like colds, flu, chickenpox and COVID-19. They are…
Warm Blooded and Cold Blooded
Animals can be classified into two main groups based on how they regulate their body temperature: warm-blooded and…
Acids and Bases
Acids and bases are two types of chemicals that are important in many areas of chemistry and everyday…
Chemical Bonding
Why do atoms join together? Most atoms aren't stable on their own. They join with other atoms by…
Chemical reactions
Chemical reactions are fundamental to chemistry, and they involve the transformation of one or more substances into new…
Chemistry Lab Equipment
In chemistry, various tools and equipment are used to conduct experiments and perform different types of analyses. These…
Crystals in Chemistry
Order inside solids Look closely at grains of salt and you'll see tiny cubes. Snowflakes have six sides.…
Famous Chemists
Chemistry is a fascinating field of science that has been studied for centuries. Throughout history, many famous chemists…
Isotopes
Isotopes are atoms of the same element with the same number of protons but different number of neutrons…
Melting and boiling
Changing states Matter can change from one state to another when it gains or loses energy. Ice turns…
Metals
The metal elements About three-quarters of all elements are metals. They are found on the left side and…
Mixtures
What is a mixture? A mixture is two or more substances combined physically, not chemically. Each part keeps…
Molecules
Molecules are fundamental components of all matter, created when atoms bond together. They can range from very simple…
Naming Compounds
In the realm of chemistry, compounds are fundamental substances composed of two or more different types of atoms…
Organic Chemistry
Organic Chemistry is a branch of chemistry that focuses on the study of compounds containing carbon, known as…
Periodic Table of Elements
The Periodic Table of Elements is a fundamental tool for understanding chemistry, serving as a tabular arrangement of…
Radioactivity and Radiation
Radioactivity refers to the spontaneous emission of particles or radiation from the nucleus of an atom. The term…
Salts and Soaps
Salts and soaps are two important classes of compounds in chemistry. Exploring their chemical nature, methods of production, and…
Separating Mixtures
Taking mixtures apart Because the parts of a mixture aren't chemically bonded, they can be separated using physical…
Solids, Liquids, and Gases
Solids, liquids, and gases are the three states of matter that we commonly observe in our everyday lives.…
Solutions
In chemistry, a solution is a homogeneous mixture composed of two or more substances. In other words, it's…
The Atom
Building blocks of matter Everything around you is made of tiny particles called atoms. Your body contains about…
Water
Water is a fundamental component of life, indispensable for all forms of existence on Earth. As the most…
Air Pollution
The air we breathe Each day, you breathe about 11 000 litres of air. Air pollution is harmful…
Atmosphere
The atmosphere is the layer of gases that surrounds the Earth and is held in place by gravity.…
Biomass Energy
Biomass is a renewable energy source that is derived from organic materials such as wood, agricultural waste, and…
Carbon Cycle
Carbon is everywhere Carbon is in your body, the air you breathe out, the food you eat, the…
Climate
Climate vs. weather Weather is what's happening in the atmosphere right now: sunny, rainy, cold or windy. Climate…
Clouds
What is a cloud? A cloud is a huge collection of tiny water droplets or ice crystals floating…
Composition of the Earth
The Earth is a complex planet that is made up of a variety of different materials. Scientists have…
Coral Reef
The rainforests of the sea Coral reefs cover less than 1% of the ocean floor, yet they're home…
Dangerous Weather
When weather becomes dangerous Most days, weather is just something we dress for. But sometimes it becomes severe…
Deserts
Deserts are one of the most fascinating and unique biomes in the world. A desert is defined as…
Earthquakes
The ground is moving Earth's outer layer is broken into giant plates that slowly move a few centimetres…
Erosion
Erosion is the process by which the surface of the Earth is worn away by natural forces such…
Food Chain and Web
Food chains and webs are important concepts in ecology that describe the relationships between different organisms in an…
Forest Fires
Fire in the forest A wildfire is an uncontrolled fire that burns through forests, grasslands or other natural…
Freshwater
A precious resource About 71% of Earth's surface is covered in water, but nearly all of it is…
Geology
Geology is the scientific study of the Earth, including its composition, structure, and processes. It is a field…
Geothermal Energy
Heat from below Deep beneath your feet, Earth is very hot. The temperature rises about 25–30 °C for…
Glaciers
Rivers of ice A glacier is a huge mass of ice that moves slowly over land under its…
Grasslands
Grasslands, also known as prairies or savannas, are vast expanses of land characterized by the presence of tall…
Hurricanes
Giant spinning storms A hurricane is one of the most powerful storms on Earth. It's a huge, spinning…
Hydropower
Power from water For thousands of years, people have used flowing water to do work. Ancient Greeks and…
Ice Age
When ice covered Canada Imagine standing where Toronto, Winnipeg or Montreal is today and seeing nothing but ice,…
Land Pollution
When land becomes polluted Land pollution is damage to land and soil caused by waste, chemicals and human…
Marine
The ocean covers over 70% of our planet and is home to an incredible array of marine life.…
Minerals
What is a mineral? A mineral must meet five rules: It forms naturally. It's a solid. It's inorganic…
Mountains
Mountains are majestic landforms that rise prominently above the surrounding terrain, often creating dramatic landscapes and influencing both…
Nitrogen Cycle
Nitrogen: plenty, but hard to use Nitrogen makes up about 78% of the air you breathe. Every living…
Ocean Tides
The breathing ocean If you spend a day at the seashore, you'll notice the water creeping up the…
Ocean Waves and Currents
The restless ocean The ocean is always moving. Waves roll onto beaches, and huge currents carry water around…
Oxygen Cycle
The oxygen cycle is a fundamental ecological process that ensures the production and consumption of oxygen in the…
Phases of the Moon
Exploring the Phases of the Moon The moon is a fascinating object in our sky that has been…
Plate Tectonics
Plate tectonics is the scientific theory that explains the movement of the Earth's lithosphere (the rigid outer layer…
Recycling
What happens to our garbage? Canadians produce a lot of waste: about 700 kg per person each year…
Renewable Energy
Energy that won't run out Renewable energy comes from sources that are naturally replaced in a human lifetime:…
Rocks
The solid ground Earth's crust is made of rock. A rock is a natural solid made of one…
Savanna
A sea of grass A savanna is a tropical grassland dotted with trees and shrubs. Savannas cover about…
Seasons
Seasons are a natural phenomenon that occurs due to the Earth's orbit around the sun. Understanding the science…
Soil Science
More than dirt Soil is one of Earth's most important resources. It grows nearly all our food, filters…
Solar Power
Energy from the Sun The Sun sends Earth more energy in about an hour and a half than…
Taiga Forest
Taiga forest, also known as the boreal forest, is one of the largest terrestrial ecosystems on the planet.…
Temperate Forest
The forest of four seasons A temperate forest grows in the middle latitudes, between the tropics and the…
The Ozone Layer
The ozone layer is a layer of gas in the Earth's stratosphere that plays a critical role in…
Topography
Topography is the study of the Earth's physical features, focusing on both natural and man-made formations. By mapping…
Tornadoes
Nature's most violent winds A tornado is a violently rotating column of air that stretches from a thunderstorm…
Tropical Rainforest
Earth's richest biome Tropical rainforests cover only about 6% of Earth's land, but they're home to more than…
Tsunamis
Harbour waves Tsunami is a Japanese word meaning "harbour wave." Tsunamis are not ordinary waves. They're a series…
Tundra
The cold, treeless land The word tundra comes from the Sami word tūndâr, meaning "treeless plain." The tundra…
Volcanoes
Mountains of fire A volcano is an opening in Earth's crust where melted rock, gases and ash escape.…
Water Cycle
The water cycle, also known as the hydrologic cycle, is the continuous process by which water moves from…
Water Pollution
Our water at risk Clean water is essential for drinking, farming, industry and wildlife. Water pollution happens when…
Wave and Tidal Energy
As the world's demand for energy continues to grow, scientists are looking for alternative sources of energy to…
Weather
What is weather? Weather is the condition of the atmosphere at a certain time and place. Is it…
Weather Forecasting
Predicting the sky Will it rain on the class trip? Should farmers harvest today? Will a snowstorm close…
Wind
What makes the wind blow? Wind is moving air. You can't see it, but you can see what…
Wind Power
Harnessing the wind People have used wind power for thousands of years. Ancient Egyptians sailed the Nile using…
Air Conditioning
Staying cool For thousands of years, people kept cool with shade, fans, thick walls, open windows and water.…
Airplane
The dream of flight For thousands of years, people watched birds and dreamed of flying. Leonardo da Vinci…
Antibiotics
Medicines that fight bacteria Antibiotics are medicines that kill bacteria or stop them from multiplying. They treat bacterial…
Electricity Invention
Was electricity invented? Electricity wasn't invented; it's a natural part of the universe, found in lightning, your nerves…
GPS (Global Positioning System)
Where am I? For thousands of years, travellers found their way using the Sun, stars, landmarks, maps and…
MRI (Magnetic Resonance Imaging)
Detailed pictures without X-rays MRI (magnetic resonance imaging) creates detailed pictures of the inside of the body using…
Pacemaker
The heart's electrical system Your heart beats about 100 000 times a day. Each beat starts with a…
Penicillin
A world without antibiotics Before the 1940s, a small cut, a sore throat or an ear infection could…
Printing Machine
From presses to printers Gutenberg's printing press of the 1440s could print a few hundred pages a day.…
Solar Panels
Turning light into electricity A solar panel turns sunlight directly into electricity, with no moving parts, no fuel…
Television
Pictures that move through the air Television sends moving pictures and sound from one place to screens everywhere.…
Television
Pictures that move through the air Television sends moving pictures and sound from one place to screens everywhere.…
The Airplane
The dream of flight For thousands of years, people watched birds and dreamed of flying. Leonardo da Vinci…
The Atomic Bomb
A turning point in history The atomic bomb is one of the most powerful and destructive inventions ever…
The Automobile
A horseless carriage Before the automobile, people travelled by foot, horse, carriage, bicycle, boat or train. Cars changed…
The Bicycle
The most efficient machine The bicycle is one of the most efficient ways to travel. A person on…
The Camera
Capturing light A camera captures images by letting light in through a small opening and recording it on…
The Computer
From counting to computing A computer is a machine that takes in data, processes it by following instructions,…
The Internet
A network of networks The internet is a worldwide network that connects billions of computers, phones and devices.…
The Light Bulb
Lighting up the night Before electric light, people lit homes with candles, oil lamps and gas lamps. These…
The Light Bulb
Lighting up the night Before electric light, people lit homes with candles, oil lamps and gas lamps. These…
The Microwave Oven
A melted chocolate bar In 1945, Percy Spencer, an engineer at the Raytheon company in the United States,…
The Printing Press
Copying books by hand Before the printing press, books in Europe were copied by hand, letter by letter.…
The Radio
Sound through the air Radio was the first technology to send voices and music through the air, without…
The Radio
Sound through the air Radio was the first technology to send voices and music through the air, without…
The Refrigerator
Keeping food fresh Bacteria and mould grow quickly at room temperature, spoiling food. Cold slows them down. For…
The Smartphone
A computer in your pocket A smartphone is a mobile phone that's also a powerful computer. It can…
The Steam Engine
Power from boiling water Boil water in a kettle, and steam pushes out with surprising force. The steam…
The Telephone
Talking across distance Before the telephone, the fastest way to send a message far away was the telegraph,…
The Washing Machine
From washboards to machines Washing clothes by hand was once one of the hardest household jobs. People carried…
The Wheel
A simple shape that changed the world It's hard to imagine life without the wheel. Cars, bikes, trains,…
Vaccination
Training the body's defences Vaccination is one of the most important medical inventions in history. It has saved…
Velcro
Inspired by a walk in the woods In 1941, Swiss engineer George de Mestral went hunting in the…
X-ray
Seeing inside the body Before X-rays, doctors could only guess what was happening inside a patient's body, or…
Actinium (Ac)
Actinium, a fascinating element on the periodic table, was independently discovered by two prominent chemists: André-Louis Debierne, a…
Aluminum (Al)
Aluminum was first isolated by Hans Christian Ørsted in 1825 through a chemical process involving aluminum chloride. However,…
Americium (Am)
Americium, a fascinating element with profound implications in both scientific research and everyday applications, was discovered in 1944…
Antimony (Sb)
Antimony was known to ancient civilizations and used in cosmetics and medicines as far back as 3000 BC.…
Argon (Ar)
Argon was discovered in 1894 by Lord Rayleigh and Sir William Ramsay in London. Their discovery came about…
Arsenic (As)
Arsenic has captivated human curiosity and scientific inquiry for centuries. Recognized since antiquity, arsenic's journey from a mysterious…
Astatine (At)
Astatine, symbolized by At and holding the atomic number 85, is an element shrouded in mystery due to…
Barium (Ba)
Barium, a remarkable element with the symbol Ba and atomic number 56, has played a significant role in…
Berkelium (Bk)
Berkelium, symbolized as Bk and holding the atomic number 97, stands as a remarkable element in the periodic…
Beryllium (Be)
Beryllium was discovered by Louis Nicolas Vauquelin in 1798 as he analyzed beryl and emeralds. He found a…
Bismuth (Bi)
Bismuth, a fascinating element known to alchemists since the 15th century, has a rich history of discovery and…
Bohrium (Bh)
Bohrium is a synthetic element with the atomic number 107, and it occupies a unique position in the…
Boron (B)
Boron is a fascinating element with a variety of important applications, both in industry and in scientific research.…
Bromine (Br)
Bromine, symbolized as Br with an atomic number of 35, is a chemical element with profound industrial and…
Cadmium (Cd)
Cadmium was discovered by German chemist Friedrich Stromeyer in 1817 while he was examining zinc carbonate samples. Stromeyer…
Calcium (Ca)
Calcium was isolated by Sir Humphry Davy in 1808, shortly after his discovery of potassium and sodium. Davy…
Californium (Cf)
Quick reference Property Value Symbol Cf Atomic number 98 Atomic weight [251] (most stable isotope) Group Actinide Discovered…
Carbon (C)
Carbon, unlike many other elements, was known to the ancients and does not have a specific discovery date…
Cerium (Ce)
Cerium was discovered in 1803 by Swedish chemists Jöns Jakob Berzelius and Wilhelm Hisinger, and independently by the…
Cesium (Cs)
Cesium was discovered in 1860 by German scientists Robert Bunsen and Gustav Kirchhoff, the inventors of spectroscopy, when…
Chlorine (Cl)
Chlorine was discovered by Carl Wilhelm Scheele in 1774, although he mistakenly believed it to be a compound…
Chromium (Cr)
Chromium was discovered by the French chemist Louis Nicolas Vauquelin in 1797. While analyzing samples of Siberian red…
Cobalt (Co)
Cobalt was discovered by Swedish chemist Georg Brandt in 1735 when he was studying minerals that gave glass…
Copernicium (Cn)
Copernicium, an extraordinary discovery in the world of chemistry and physics, has captivated scientists and researchers since its…
Copper (Cu)
Copper is one of the most ancient metals known to humanity, with a rich history extending back to…
Curium (Cm)
Curium, a synthetic element with the symbol Cm and atomic number 96, represents a significant milestone in the…
Darmstadtium (Ds)
Darmstadtium, an element with the symbol Ds and atomic number 110, is one of the most fascinating and…
Dubnium (Db)
The quest for understanding the building blocks of matter has driven scientists to extraordinary lengths. The discovery of…
Dysprosium (Dy)
Dysprosium was discovered in 1886 by the French chemist Paul-Émile Lecoq de Boisbaudran. He identified its existence through…
Einsteinium (Es)
Einsteinium is a fascinating element with a storied history and a critical role in advancing our understanding of…
Erbium (Er)
Erbium was discovered in 1843 by the Swedish chemist Carl Gustaf Mosander, who separated it from other rare…
Europium (Eu)
Europium, symbolized as Eu and bearing the atomic number 63, is a rare earth element that stands out…
Fermium (Fm)
Fermium, an element with the symbol Fm and atomic number 100, stands as a testament to human ingenuity…
Flerovium (Fl)
Flerovium was discovered in 1998 by a collaboration between scientists at the Joint Institute for Nuclear Research in…
Fluorine (F)
Fluorine was isolated by Henri Moissan in 1886, although its compounds, such as fluorspar, cryolite, and fluorapatite, were…
Francium (Fr)
Francium, with the symbol Fr and atomic number 87, is one of the most enigmatic elements on the…
Gadolinium (Gd)
Gadolinium was discovered by Swiss chemist Jean Charles Galissard de Marignac in 1880. Marignac detected its spectroscopic lines…
Gallium (Ga)
Gallium was discovered by French chemist Lecoq de Boisbaudran in 1875 through spectroscopic analysis of a sample of…
Germanium (Ge)
Germanium is a fascinating element with a rich history and a wide range of applications. Discovered in 1886…
Gold (Au)
Gold, a metal that has captivated humanity for thousands of years, continues to fascinate due to its unmatched…
Hafnium (Hf)
Hafnium was discovered in 1923 by Dutch physicist Dirk Coster and Hungarian chemist George Charles de Hevesy. The…
Hassium (Hs)
Hassium, denoted by the symbol Hs and holding the atomic number 108, is a superheavy element that continues…
Helium (He)
Helium was first detected as a yellow spectral line in sunlight during a solar eclipse in 1868 by…
Holmium (Ho)
Holmium was discovered in 1878 by the Swiss chemists Marc Delafontaine and Jacques-Louis Soret, who spotted its unusual…
Hydrogen (H)
Hydrogen, denoted by the symbol "H" and having the atomic number 1, is the most elementary and widespread…
Indium (In)
Indium was discovered in 1863 by German chemists Ferdinand Reich and Hieronymus Theodor Richter. While analyzing zinc ore…
Iodine (I)
When French chemist Bernard Courtois accidentally stumbled upon iodine in 1811, he could never have guessed how profoundly…
Iridium (Ir)
Iridium, one of the rarest and most remarkable elements on Earth, was discovered in 1803 by the English…
Iron (Fe)
Iron is one of the earliest metals discovered and used by human civilizations, with its use dating back…
Krypton (Kr)
Krypton, a noble gas of fascinating characteristics, was discovered in 1898 by the esteemed scientists Sir William Ramsay…
Lanthanum (La)
Lanthanum was discovered in 1839 by Swedish chemist Carl Gustaf Mosander, who separated it from a sample of…
Lawrencium (Lr)
Lawrencium stands as a remarkable testament to the achievements in nuclear chemistry and physics. Discovered in 1961 by…
Lead (Pb)
Lead, a metal known and utilized by humans for millennia, stands out as one of the earliest metals…
Lithium (Li)
Lithium was discovered by Johan August Arfwedson in 1817 during an analysis of petalite ore, one of the…
Livermorium (Lv)
The synthesis of livermorium stands as a monumental achievement in the field of nuclear chemistry, marking the collaborative…
Lutetium (Lu)
Lutetium was independently discovered in 1907 by French chemist Georges Urbain and Austrian scientist Carl Auer von Welsbach.…
Magnesium (Mg)
Magnesium was first isolated by Sir Humphry Davy in 1808, through the electrolysis of a mixture of magnesia…
Manganese (Mn)
Manganese was recognized as an element by the Swedish chemist Johan Gottlieb Gahn in 1774, though compounds containing…
Meitnerium (Mt)
Meitnerium, symbolized as Mt and with the atomic number 109, stands as a significant milestone in the realm…
Mendelevium (Md)
Mendelevium (symbol: Md, atomic number: 101) is a synthetic element with significant historical and scientific importance. Discovered in…
Mercury (Hg)
Mercury, known since ancient times, has held a significant place in human history. Its usage dates back to…
Molybdenum (Mo)
Molybdenum was discovered in 1778 by Swedish chemist Carl Wilhelm Scheele, who identified it as a distinct element…
Moscovium (Mc)
Moscovium, symbol Mc, with an atomic number of 115, represents a significant achievement in the realm of nuclear…
Neodymium (Nd)
Quick reference Property Value Symbol Nd Atomic number 60 Atomic weight 144.242 Group Lanthanide (rare earth metal) Discovered…
Neon (Ne)
Neon was discovered in 1898 by Sir William Ramsay and Morris Travers in London, shortly after their discoveries…
Neptunium (Np)
In the realm of chemistry and nuclear science, the discovery of neptunium marked a pivotal moment in our…
Nickel (Ni)
Nickel, with the chemical symbol Ni and atomic number 28, is a transition metal that plays a pivotal…
Nihonium (Nh)
Nihonium, with the symbol Nh and atomic number 113, stands as a monumental achievement in the realm of…
Niobium (Nb)
Niobium was discovered by the English chemist Charles Hatchett in 1801 when he analyzed a sample of columbite…
Nitrogen (N)
Nitrogen was discovered by Daniel Rutherford in 1772 when he removed oxygen and carbon dioxide from air, revealing…
Nobelium (No)
The journey to the discovery and recognition of nobelium is a tale of scientific rivalry, groundbreaking research, and…
Oganesson (Og)
Quick reference Property Value Symbol Og Atomic number 118 Atomic weight [294] (mass number of known isotope) Group…
Osmium (Os)
In 1803, the English chemist Smithson Tennant made a groundbreaking discovery that would add a new dimension to…
Oxygen (O)
Oxygen was discovered independently by Carl Wilhelm Scheele in Sweden and Joseph Priestley in England around 1774. Scheele…
Palladium (Pd)
Palladium was discovered by English chemist William Hyde Wollaston in 1803 while he was working on platinum ores.…
Phosphorus (P)
Phosphorus was discovered in 1669 by Hennig Brand, a German alchemist in Hamburg who was searching for the…
Platinum (Pt)
Platinum is a precious metal with a storied history and significant impact on contemporary technology and industry. Known…
Plutonium (Pu)
In the annals of chemistry and nuclear science, few discoveries have had as profound an impact as that…
Polonium (Po)
Polonium, discovered in 1898 by Marie Curie and her husband Pierre Curie, stands as a monumental achievement in…
Potassium (K)
Potassium was first isolated by Sir Humphry Davy in 1807 through the electrolysis of potash (KOH, potassium hydroxide),…
Praseodymium (Pr)
Praseodymium was discovered by Austrian chemist Carl Auer von Welsbach in 1885. Von Welsbach separated praseodymium, along with…
Promethium (Pm)
Promethium was discovered in 1945 by Jacob A. Marinsky, Lawrence E. Glendenin, and Charles D. Coryell during their…
Protactinium (Pa)
Protactinium, a fascinating yet lesser-known element, was discovered through the concerted efforts of multiple scientists in the early…
Radium (Ra)
In 1898, a groundbreaking discovery was made that would revolutionize our understanding of the natural world and pave…
Radon (Rn)
Radon, a significant and intriguing element, was discovered in 1900 by the German physicist Friedrich Ernst Dorn. Initially…
Rhenium (Re)
German chemists Walter Noddack, Ida Tacke, and Otto Berg discovered rhenium through their meticulous work with platinum ores…
Rhodium (Rh)
Rhodium was discovered in 1803 by English chemist William Hyde Wollaston shortly after his discovery of palladium. Wollaston…
Roentgenium (Rg)
Roentgenium, symbol Rg, atomic number 111, is a superheavy element that was first synthesized in 1994 by a…
Rubidium (Rb)
Rubidium was discovered in 1861 by German chemists Robert Bunsen and Gustav Kirchhoff, who were pioneers in the…
Ruthenium (Ru)
Ruthenium was discovered in 1844 by the Baltic German scientist Karl Ernst Claus at the University of Kazan,…
Rutherfordium (Rf)
Rutherfordium, a synthetic element with the symbol Rf and atomic number 104, represents a pivotal chapter in the…
Samarium (Sm)
Samarium was discovered by French chemist Paul Émile Lecoq de Boisbaudran in 1879. He isolated samarium oxide from…
Scandium (Sc)
Scandium was discovered in 1879 by Swedish chemist Lars Fredrik Nilson. He isolated scandium by analyzing the minerals…
Seaborgium (Sg)
Seaborgium, symbolized as Sg and holding atomic number 106, represents a significant achievement in the field of nuclear…
Selenium (Se)
Selenium was discovered in 1817 by Swedish chemist Jöns Jacob Berzelius. The discovery occurred when Berzelius was working…
Silicon (Si)
The foundational breakthrough in understanding silicon was accomplished in 1824 by Swedish chemist Jöns Jacob Berzelius. Through an…
Silver (Ag)
Silver has been known and valued as a precious metal since ancient times. The exact time of its…
Sodium (Na)
Sodium was first isolated by Humphry Davy in 1807 through the electrolysis of caustic soda (NaOH), shortly after…
Strontium (Sr)
Strontium was discovered in 1790 by Adair Crawford and William Cruickshank, who identified a new mineral (strontianite) in…
Sulfur (S)
Sulfur is one of the few elements known since ancient times, mentioned in the Bible and by early…
Tantalum (Ta)
In 1802, Swedish chemist Anders Gustaf Ekeberg made a groundbreaking discovery that would later revolutionize various industries. By…
Technetium (Tc)
Technetium was the first element to be artificially produced, marking a significant milestone in nuclear chemistry. It was…
Tellurium (Te)
Tellurium was discovered in 1782 by the Austrian mineralogist Franz-Joseph Müller von Reichenstein, who was the chief inspector…
Tennessine (Ts)
In the realm of nuclear chemistry and physics, few discoveries have generated as much excitement and intrigue as…
Terbium (Tb)
Terbium was discovered by Swedish chemist Carl Gustaf Mosander in 1843. Mosander was able to isolate terbium as…
Thallium (Tl)
Thallium was discovered by British chemist Sir William Crookes in 1861 while he was conducting flame spectroscopy experiments…
Thorium (Th)
Thorium, symbol Th, atomic number 90, and atomic weight 232.03806, is a silvery white metal discovered in 1828…
Thulium (Tm)
Thulium was discovered by Swedish chemist Per Teodor Cleve in 1879. While examining the residues left after removing…
Tin (Sn)
Tin is one of the earliest metals discovered by humans, known and used in prehistoric times. The exact…
Titanium (Ti)
Titanium was discovered in 1791 by William Gregor, an English clergyman, and mineralogist, in the mineral ilmenite from…
Tungsten (W)
Tungsten, symbolized as W, is an exceptional element discovered in 1783 by the Spanish chemists and brothers Juan…
Uranium
Uranium, a heavy metal with the atomic number 92, has played a crucial role in the development of…
Vanadium (V)
Vanadium was first discovered by the Spanish-Mexican mineralogist Andrés Manuel del Río in 1801 in the mineral vanadinite.…
Xenon (Xe)
Xenon was discovered in 1898 by Scottish chemist Sir William Ramsay and English chemist Morris M. Travers in…
Ytterbium (Yb)
Quick reference Property Value Symbol Yb Atomic number 70 Atomic weight 173.045 Group Lanthanide (rare earth metal) Discovered…
Yttrium (Y)
Yttrium was discovered by Finnish chemist Johan Gadolin in 1794. The discovery came after analyzing a mineral from…
Zinc (Zn)
Zinc, represented by the symbol Zn and possessing an atomic number of 30, is a transition metal with…
Zirconium (Zr)
Zirconium was discovered by German chemist Martin Heinrich Klaproth in 1789. Klaproth identified a new element in a…
Acceleration
Acceleration is a fundamental concept in physics that describes how quickly an object's velocity changes over time. It…
Basics of Sound
Every sound starts with a vibration Put your fingers on your throat and hum. You'll feel a buzz.…
Conductors and insulators
Letting energy through, or not Why are electrical wires made of copper but covered in plastic? Why do…
Digital Electronics
Digital electronics is a field of electronics that deals with digital circuits and systems. Digital circuits use binary…
Electric circuits
A path for electricity When you flip a light switch, the light turns on almost instantly. That's because…
Electric current
Electric current is the flow of electric charge through a conductor, such as a wire. It is an…
Electric Motors
Turning electricity into motion An electric motor converts electrical energy into motion. Motors are everywhere: in fans, fridges,…
Electricity
Energy that powers our world Electricity lights our homes, runs our devices and charges our phones. It's energy…
Electromagnetic Waves
Waves you can't see Visible light is just a tiny slice of a much larger family of waves…
Electronic Communications
Talking across distances For most of history, messages travelled only as fast as a person, horse or ship.…
Energy
Energy is a fundamental concept in science and refers to the ability of a system to do work…
Force
Force is a fundamental concept in physics that describes the interaction between two objects that can cause a…
Friction
Friction is a force that opposes motion between two surfaces that are in contact with each other. It…
Gravity
The force that holds the universe together Drop a ball and it falls. Jump and you come back…
Heat
What is heat? Everything is made of particles that are always moving. The faster they move, the more…
How Musical Notes Work
Music is organized sound All sounds come from vibrations. Noise is a jumble of random vibrations. A musical…
Intro to Light
What is light? Light is a form of energy that lets us see. It travels from a source,…
Intro to Waves
What is a wave? At a stadium, fans stand up and sit down one after another, creating a…
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion. It is a fundamental concept in…
Laws of Motion
Three rules for motion Why does a soccer ball roll after you kick it? Why do you lurch…
Lenses
Bending light on purpose A lens is a curved piece of clear glass or plastic that bends light…
Light and Optics
Light is a form of electromagnetic radiation that travels in waves. It is a fundamental aspect of our…
Light as a Wave
What is light, really? For centuries, scientists argued about what light is. Isaac Newton thought light was a…
Light Spectrum
The light spectrum, also known as the electromagnetic spectrum, encompasses all types of electromagnetic radiation. Light that is…
Magnetism
Magnetism is a phenomenon that occurs when certain materials, such as iron and nickel, are attracted to magnets.…
Mass and Weight
Two words often mixed up In everyday life, people say "I weigh 40 kilograms." But in science, that's…
Momentum and Collisions
Mass in motion Which is harder to stop: a bowling ball rolling slowly or a ping-pong ball rolling…
Motion
Motion is the act of changing position or location over time. It is a fundamental concept in physics…
Nuclear Energy and Fission
Nuclear energy is the energy that is released when the nucleus of an atom is split (fission) or…
Nuclear Physics and Relativity
Nuclear Physics is the study of the atomic nucleus, the heart of the atom. It is a field…
Ohm’s Law
One simple equation In 1827, German physicist Georg Ohm discovered a simple rule connecting the three most important…
Photons
Photons are elementary particles that make up light and other forms of electromagnetic radiation. They were first proposed…
Physics
Physics is the study of matter, energy, and the interactions between them. It is a fundamental branch of…
Pitch and Acoustics
High and low sounds A tiny bird chirps with a high, squeaky sound. A big dog growls with…
Potential Energy
Potential energy is a form of energy that is stored in an object due to its position, shape,…
Power
Same job, different speed Two students carry identical boxes up the same flight of stairs. One walks; the…
Pressure
Force spread over an area Why can you walk on snow in snowshoes but sink in boots? Why…
Properties of Waves
Describing waves Every wave, whether it's sound, light or a ripple on water, can be described using a…
Quarks
Smaller than small Everything is made of atoms. Atoms are made of protons, neutrons and electrons. But are…
Relativity – Light and Time
Relativity is a branch of physics that explores the behavior of objects in motion, particularly in relation to…
Resistors in Series and Parallel
Combining resistors Real circuits often contain several resistors. To understand them, we need to know how resistors behave…
Resistors, capacitors, and inductors
Three building blocks of electronics Open up almost any electronic device, from a radio to a phone charger,…
Simple machines
Simple machines are basic mechanical devices that are used to make work easier. There are six types of…
Speed and velocity
How fast? Which way? A cheetah sprints at about 100 km/h. A garden snail creeps at about 0.05…
Static Electricity
Static electricity is the build-up of electric charge on the surface of a material. It occurs when there…
Temperature
What does temperature measure? All matter is made of tiny particles in constant motion. In a hot cup…
The Ear and Hearing
The ear is the organ responsible for hearing and maintaining balance. It is divided into three parts: the…
The Eye and Seeing
How do we see? Seeing seems effortless, but it's a remarkable partnership between your eyes and brain. Light…
The Sound Wave
Picturing a sound wave We can't see sound, but scientists can picture it. A sound wave is a…
Theory of Relativity
A new way to think about space and time In the early 1900s, a young patent clerk in…
Uses of Electricity
Electricity is everywhere Think about your morning: an alarm wakes you, lights turn on, the fridge keeps milk…
Vector Math
Vector Math is the branch of mathematics that deals with the mathematical operations on vectors, which are mathematical…
Wave Behavior
How waves act when they meet things Waves don't just travel in straight lines forever. When they hit…
Waves and Sound
Waves carry energy A wave is a disturbance that carries energy from one place to another. When you…
Work and Energy
Work and energy are two important concepts in physics that are closely related. Work is defined as the…
Biology
Biology is the scientific study of life and living organisms. This vast and diverse field encompasses everything from…
Chemistry
Chemistry is the scientific study of matter, its properties, and the changes it undergoes. Matter, defined as anything…
Earth Science
Earth Science is a branch of science that delves into the physical and chemical processes shaping our planet.…
Environment
The environment, encompassing the natural world and its surroundings, includes both living and non-living components. It plays a…
Physics
Physics is the natural science that studies matter, motion, and energy. As one of the most fundamental scientific…
Science
Science is a systematic approach to understanding the natural world through observation, experimentation, and analysis. This comprehensive method…
Airplanes
Airplanes are fixed-wing flying machines designed to navigate the air through various mechanisms like lift, thrust, drag, and…
Amateur Radio
Amateur radio, also known as ham radio, is a non-commercial radio service for two-way communication using designated frequencies.…
Artificial Intelligence (AI)
Artificial intelligence (AI) is the branch of computer science that deals with creating intelligent systems capable of learning…
Astronomy
Astronomy is the study of celestial objects and phenomena beyond Earth's atmosphere. This activity focuses on learning about…
Aviation
Aviation is the study and practice of flight. It encompasses various aspects like the design, development, operation, and…
Biology
Biology is the study of living organisms and their life processes. This activity focuses on learning about different…
Chemistry
Chemistry is the study of the composition, structure, properties, and reactions of matter. This activity focuses on understanding…
Coding with Scratch
Coding with blocks Scratch is a free programming language where you snap together colourful blocks instead of typing…
Computers
Learning about computers involves gaining knowledge and understanding of how computers work, their various components, their applications in…
Criminal Forensics
Criminal forensics is the scientific application of various methods and procedures to gather, analyze, and interpret evidence left…
Electricity
Electricity is a fundamental form of energy related to the movement of charged particles. It powers various devices…
Lunar Science
Lunar Science involves the study of the Moon's origins, geology, surface properties, and its effects on Earth. It…
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