Simulators

Set the initial value and rate of change in a real context and watch the story, table, graph and equation change together, then compare two options and see where and why they cross.

Drag values on a dot plot to watch the mean, median, quartiles and box plot respond, then fit lines and curves to scatter plots and judge correlation and predictions.

Step through short math programs one line at a time, watching each variable's value and type and the output, then change the marked numbers to model a new situation.

Drag points to see why inscribed and central angles, the angle in a semicircle, chord bisectors, parallel-line angle pairs and triangle properties work, with every measure taken from the diagram.

Edit standard, vertex or factored form, or drag the vertex and zeros, and watch the other two forms, the graph, the table of differences and the completing-the-square steps update together.

Enter or drag two lines and see graphing, substitution and elimination worked out step by step for the current coefficients, including what parallel and identical lines look like in the algebra.

Label opposite, adjacent and hypotenuse, then solve any right or acute triangle step by step with the right tool: SOH CAH TOA, the Pythagorean theorem, or the sine or cosine law.

Drag points to get exact midpoints, lengths, slopes and equations, then use them to verify properties of triangles and quadrilaterals.

Drag a, k, d and c and watch any parent function stretch, flip and slide.

Drag the terminal arm to see exact ratios, reference angles and CAST signs.

Build a sine or cosine curve, then play match-the-graph against a random target.

Terms, series sums, compound interest and annuities with the formulas filled in.

Slide a point along a function to watch its tangent slope, trace the graph of f′ point by point, and see where f′ and f″ reveal maxima, minima and inflection points.

Build a box, fence a field, design a can or price a ticket, then use the derivative to find the size or price that gives the best result.

Drag two vectors to see their components, magnitude, angle and bearings, add and subtract them tip-to-tail or by parallelogram, and watch the dot product and projections change.

Rotate a 3-D view of up to three planes and a line from their equations to see where they meet (a point, a line, or nowhere) and solve the system step by step.

Build a polynomial from its zeros, change each multiplicity, and watch the curve cross, bounce or flatten while the end behaviour follows the degree.

Choose numerator and denominator factors and see which ones become vertical asymptotes, which cancel into holes, and what the degrees do to the ends.

Shrink the interval h and watch the average rate of change converge on the instantaneous rate, with the difference quotient updating as you go.

Pick each parent's genotype for simple dominance, incomplete dominance, codominance, sex-linked or dihybrid crosses, then compare the Punnett square's ratios with a random sample of offspring.

Run a population with a heritable colour trait against a background, set how strongly predators select, and watch the trait's frequency change generation by generation.

Change temperature, pH and substrate concentration, add a competitive or non-competitive inhibitor, and watch the reaction rate curve respond.

Step a DNA template through transcription and translation, then introduce point mutations and see whether they are silent, missense, nonsense or frameshift.

Stimulate a neuron above and below threshold, fire during the refractory period, and follow the Na+ and K+ channels behind each phase of the spike.

Compare exponential and logistic growth with your own r and K, then switch to predator and prey and watch their populations cycle out of phase.

Shade the periodic table by radius, ionization energy, affinity or electronegativity.

Pick a molecule to see its shape, bond angles and whether the dipoles cancel.

Drag temperature and mass to classify a solution as unsaturated, saturated or supersaturated.

A piston obeying PV = nRT, with particles that speed up as you heat them.

Titrate a strong or weak acid and watch the curve, the indicator and the equivalence point.

Build an ICE table, compare the reaction quotient with K, and disturb the system with concentration, pressure or temperature changes to see which way it shifts.

Pick two half-cells, find the anode and cathode, follow the electrons and ions, and calculate the standard cell potential.

Set the energies of the reactants, products and transition state, add a catalyst, and read the enthalpy change and activation energy straight off the diagram.

Release a cart down a ramp and watch kinetic, potential and thermal energy trade places while the total holds steady.

Three tabs: the wave equation, interference and beats, and standing waves in strings and pipes.

Set an initial velocity and acceleration, then watch position, velocity and acceleration graphs draw in step.

Set launch speed, angle and height and watch the path split into independent horizontal and vertical motion, with range, maximum height and flight time.

Collide two carts or pucks in one or two dimensions, elastic or perfectly inelastic, and check that momentum is conserved while kinetic energy may not be.

Change the wavelength, slit separation and screen distance and watch the bright fringes spread out or bunch together, with the fringe spacing calculated as you go.

Shine light of any frequency and intensity on a metal and see why frequency, not brightness, decides whether electrons escape and how fast they leave.

Add and remove protons, neutrons and electrons to build any atom or ion from hydrogen to calcium, and watch its Bohr-Rutherford diagram, mass number, charge and isotope stability update.

Set fossil-fuel burning, deforestation, tree planting and how strongly oceans and land absorb CO₂, then watch atmospheric CO₂ change from 2025 to 2100 in a simple model of the carbon cycle.

Move the Moon around its orbit to see its phase from Earth, the tidal bulges that make spring and neap tides, and why eclipses happen only when a new or full moon is near a node.

Drag an object in front of a curved mirror or lens to trace the principal rays and see where the image forms, with its size, attitude, location and type checked by the mirror and lens equation.

Pick two materials and an angle to watch light bend, with Snell's law, the speed of light in each, the critical angle and total internal reflection worked out.

Change the coefficients of 24 real reactions and watch a live atom inventory (and the molecules themselves) until every element balances in lowest terms.

Change CO₂ and albedo in a one-layer energy-balance model and see sunlight, reflection and infrared flows and the temperature Earth's surface settles at, compared with no greenhouse effect.

Step through a short Java program one line at a time and watch every variable change.

Flip individual bits and watch decimal, hexadecimal and the ASCII character follow.

Toggle inputs through any of seven gates and see the truth-table row light up.

Build a resistor network, then read total resistance, branch currents and power.

Slide the prefix and watch the mask cut an IP address into network and host bits.

Drive an LED, a motor or a servo and see the waveform behind analogWrite.

Mix in RGB or CMYK, read the hex, and build harmonious schemes off the colour wheel.

Shift demand and supply with real-world factors and events, find the new equilibrium price and quantity, and set your own price to see the surplus or shortage it creates.

Apply real transactions and watch A = L + OE refuse to break.

Read a transaction, pick the accounts and sides, get marked instantly.

Enter statement figures and get every ratio with its formula and interpretation.

Plan six months of receipts and payments for a small venture and watch closing cash carry into the next month, to see how a business that earns money overall can still run out of cash in one month.

Weight the criteria, rate three venture ideas from 1 to 5 and rank them by weighted score, then see how changing what matters most can change which idea wins.

Set price, variable cost and fixed costs and watch the revenue and cost lines cross at the break-even volume, with profit or loss at any sales level.

One cost, one price, two percentages. See why markup divides profit by cost and margin divides the same profit by the selling price.

Edit the cost layers and the sale, then compare cost of goods sold, ending inventory and gross profit under FIFO, weighted average and specific identification.

Build straight-line, declining-balance and units-of-output schedules, compare book value over time, and dispose of the asset to see the gain or loss.

Divide net income or a net loss among two or three partners with salary allowances, interest on capital and a ratio, and watch a negative remainder get shared out.

Draw real climate graphs for ten Canadian cities, work out the range, mean and total precipitation, and use LOWERN to explain why Vancouver and Winnipeg are so different.

Change fertility, life expectancy and immigration, then watch a population pyramid age five years at a time as the median age and dependency ratio change.

Practise latitude and longitude, map scale and compass bearings with instant feedback and a worked solution for every question.

Zoom through Canadian history since 1914 by theme and period, read why each event matters, then test yourself by putting events in order.

Sort the long- and short-term causes, triggers and consequences of turning points from 1914 to 1995, and see where historians disagree.

Explore the treaties, laws, court decisions and movements that contemporary First Nations, Métis and Inuit texts refer to, then test yourself by putting events in order.

Keep the facts of a fictional news story fixed and change only the words, the first voice and the background, to see how each choice shapes what readers conclude.

Pick a verb, a subject and a tense and watch the form get built from its stem, ending and auxiliary, then test yourself on the forms that trip people up.

Change a noun's gender and number and watch every article, adjective and past participle around it change to agree, with the rule for each ending shown.

Tell a story in the past by choosing imparfait, passé composé or plus-que-parfait for each verb, and see where each one sits on the timeline.

Replace the objects in a sentence with pronouns and watch them slot into the right order in statements, negatives, compound tenses and commands.

Build a sentence from a trigger, two subjects and a verb, and watch the second verb switch between subjonctif, indicatif and infinitive with the reason for each decision, then practise choosing the mood and typing the form.

Pick a real, imagined or mixed hypothesis and watch the si-clause and the result take matching tenses on a real-versus-imagined timeline, then fill in clauses and fix the classic si + futur mistake.

Switch a quote between “Elle dit que…” and “Elle a dit que…” and watch every tense, pronoun, possessive and time word shift, each with its rule, then rebuild reported sentences blank by blank.

Work out what the shared noun does in the second sentence, follow the decision chart to qui, que, dont, où or a form of lequel, and watch lequel agree and contract after any preposition.