Mathematics simulations
79 interactive Mathematics simulations for ages 11β18, grouped by topic.
Numbers & Arithmetic
- Mathematics Β· Numbers & Arithmetic Square Roots and Cube Roots β Side of a Square and a Cube A square with area S has side βS; a cube with volume V has side βV. Drag the square's corner or the cube's vertex to change S and V and... Ages 14β15
- Mathematics Β· Numbers & Arithmetic Square Roots on the Number Line β Construction and Approximation Construct β2 as the diagonal of a unit square, then chain right triangles with leg 1 to build β3, β4, β¦ βn (the Theodorus spiral), and... Ages 12β13
- Mathematics Β· Numbers & Arithmetic Rounding decimals on a number line A decimal number sits on two number lines: the top one is marked off by the rounding place, and the bottom one zooms into the interval... Ages 11β12
- Mathematics Β· Numbers & Arithmetic Fraction models β comparing and adding Two fractions are shaded on a bar or circle model. Tap the parts to change the numerator and use the buttons to change the denominator.... Ages 11β12
- Mathematics Β· Numbers & Arithmetic Sieve of Eratosthenes β finding prime numbers A grid of numbers from 1 to N. Each time you click 'Next step', the smallest unmarked prime is highlighted in blue and its multiples are... Ages 11β12
- Mathematics Β· Numbers & Arithmetic Adding and subtracting integers on a number line A number line with two arrows: the blue arrow goes from 0 to a, and the red arrow continues b steps further (to the right for adding a... Ages 11β12
- Mathematics Β· Numbers & Arithmetic Rational numbers on a number line β comparing and zooming in Two rational numbers a and b (entered as p/q or a decimal) are marked on a number line; the zoomed-in axis below is divided by their... Ages 12β13
Algebra
- Mathematics Β· Algebra Linear inequality in one variable β solution set on a number line Solve the inequality ax + b > c (or <, β₯, β€) step by step: transpose terms, then divide both sides by a and flip the sign when a < 0.... Ages 14β15
- Mathematics Β· Algebra Grade 10 Math Topics β Linear Systems, Induction & Binomial Theorem, Conic Sections Three Grade 10 elective topics in one simulation, chosen with the topic parameter. System of three linear equations: step through... Ages 15β16
- Mathematics Β· Algebra Polynomials in one variable β graphs, values and roots Choose the degree and the coefficients of a polynomial P(x) of degree 1, 2 or 3; the simulation writes the polynomial in standard form,... Ages 12β13
- Mathematics Β· Algebra Sign of a quadratic function Drag a, b and c to change the parabola y = axΒ² + bx + c and read the matching sign table right away. The simulation shades the part of... Ages 15β16
- Mathematics Β· Algebra The fraction (ax + b)/(cx + d): domain and graph Graphs the value of the rational expression y = (ax + b)/(cx + d) as x varies. Students drag the sliders a, b, c, d and drag point P... Ages 13β14
- Mathematics Β· Algebra Algebraic Identities β Cut and Rearrange Illustrates (a + b)Β², (a β b)Β² and aΒ² β bΒ² using the areas of squares and rectangles. Students drag the handles to change a and b, then... Ages 13β14
- Mathematics Β· Algebra Systems of Three Linear Equations β Planes and Gaussian Elimination Each equation ax + by + cz = d is a plane in space. Rotate the 3D frame to see three planes meet at one point (unique solution), meet... Ages 15β16
- Mathematics Β· Algebra Systems of Two Linear Equations β Solving Graphically Two lines aβx + bβy = cβ and aβx + bβy = cβ are drawn on the coordinate plane; their intersection is the solution of the system.... Ages 14β15
- Mathematics Β· Algebra Solution region of a system of linear inequalities in two variables Draws the solution region of a system of up to 3 inequalities of the form ax + by β€ c (or β₯, <, >) on the coordinate plane. Students... Ages 15β16
- Mathematics Β· Algebra Multiplying polynomials with an area model A rectangle with length a + b and width c + d is split into 4 cells. Students drag the handles on the edges to change a, b, c, d and see... Ages 13β14
- Mathematics Β· Algebra Binomial theorem, Pascal's triangle, and proof by induction The expansion of (a + b)βΏ has coefficients equal to row n of Pascal's triangle. Increase n step by step to see how each new row is... Ages 15β16
- Mathematics Β· Algebra Direct and inverse proportion β table and graph A table of values and the graph of y = kx (direct proportion) or y = k/x (inverse proportion). Drag the point on the graph horizontally... Ages 12β13
Functions & Graphs
- Mathematics Β· Functions & Graphs Rational functions β asymptotes of the graph For y = (ax + b)/(cx + d) or y = (axΒ² + bx + c)/(x + d), drag the coefficients to see the vertical, horizontal and oblique asymptotes... Ages 17β18
- Mathematics Β· Functions & Graphs Limits of Sequences and Functions, Continuity Sequence mode: the points (n, uβ) approach the line y = L; a draggable band L Β± Ξ΅ shows that from some index Nβ onward every term stays... Ages 16β17
- Mathematics Β· Functions & Graphs Exponential function y = aΛ£ and logarithmic function y = logβx The graphs of y = aΛ£ and y = logβx are reflections of each other across the line y = x. Drag point M on the exponential graph and its... Ages 16β17
- Mathematics Β· Functions & Graphs Linear functions β graphs and the equation ax + b = 0 Graph of y = ax + b on the coordinate plane. Drag the point on the y-axis to change b, drag the second point to change the slope a, and... Ages 13β14
- Mathematics Β· Functions & Graphs Continuity of a function at a point A piecewise function joined at xβ, with an adjustable parameter m. The simulation computes the left-hand limit, the right-hand limit and... Ages 16β17
- Mathematics Β· Functions & Graphs Cubic and rational function analysis β derivatives, extrema, asymptotes Plots y = axΒ³ + bxΒ² + cx + d or y = (ax + b)/(cx + d) alongside a variation table built live from the sign of y'. Drag point M along the... Ages 17β18
- Mathematics Β· Functions & Graphs Quadratic function y = axΒ² + bx + c: vertex, axis of symmetry, variation table The parabola y = axΒ² + bx + c is graphed with three sliders for a, b, c right in the simulation; students can also drag the vertex I... Ages 15β16
- Mathematics Β· Functions & Graphs Parabola y = axΒ² and quadratic equations The graph of y = axΒ² together with the line y = bx + c. Drag the point on the parabola to change a (opens up/down, narrow/wide), and... Ages 14β15
Sequences & Financial Math
- Mathematics Β· Sequences & Financial Math Arithmetic and geometric sequences β simple and compound interest Graph of the terms uββ¦uβ of an arithmetic sequence (points in a straight line) or a geometric sequence (points on an exponential curve).... Ages 16β17
- Mathematics Β· Sequences & Financial Math Grade 12 Math Topics β Discrete Random Variables, Financial Math, Optimization Three Grade 12 elective topics in one simulation, chosen with the topic parameter. Discrete random variable: toss n coins thousands of... Ages 17β18
- Mathematics Β· Sequences & Financial Math Amortized loans β declining balance, annuity, and the flat-rate trap Enter the loan amount, annual interest rate, and term in months, then choose a repayment method: equal principal with interest on the... Ages 17β18
Calculus
- Mathematics Β· Calculus Area between two curves Pick a pair of curves and watch the plane region between them get shaded. The simulation splits the region into thin strips to show that... Ages 17β18
- Mathematics Β· Calculus Parabola and the tangent line at a moving point The graph of y = axΒ² + bx + c has a point M that moves along the parabola. Drag M with the mouse or a finger; the tangent line at M is... Ages 16β17
- Mathematics Β· Calculus Integrals as a limit of rectangle areas The area of the curved region below the curve y = f(x) on [a, b] is approximated by n rectangles (left, right, midpoint) or trapezoids.... Ages 17β18
- Mathematics Β· Calculus Real-world optimization with derivatives Pick a real-world problem β designing a can that uses the least material, folding an open-top box with the largest volume, or setting a... Ages 17β18
Plane Geometry
- Mathematics Β· Plane Geometry Triangle inequality β joining three segments Three segments a, b, c form a triangle if and only if each side is shorter than the sum of the other two. Drag the sliders or drag... Ages 12β13
- Mathematics Β· Plane Geometry Law of Cosines, Law of Sines, and triangle area Triangle ABC is built from two sides a, b and the included angle C; drag any of the three vertices freely. Every side and angle updates... Ages 15β16
- Mathematics Β· Plane Geometry Constructing triangles with a compass β congruence criteria Construct triangle ABC step by step as if using a ruler and compass: the SSS case (three sides), the SAS case (two sides and the... Ages 12β13
- Mathematics Β· Plane Geometry Circles β chords and tangents Circle (O; R) with a chord AB and an external point M. Drag the chord's midpoint H to change the distance OH and see that OH β AB and AB... Ages 14β15
- Mathematics Β· Plane Geometry Parallel Lines and a Transversal β Alternate and Corresponding Angles Two lines a and b are cut by a transversal line c at points A and B, forming 8 angles. Drag the end of line b to tilt it or make it... Ages 12β13
- Mathematics Β· Plane Geometry Angles β protractor and midpoint Two rays Ox and Oy pivot around vertex O to form angle xOy; a semicircular protractor lines up with ray Ox so you can read the measure.... Ages 11β12
- Mathematics Β· Plane Geometry Lines of symmetry and point symmetry Choose a square, rectangle, rhombus, regular hexagon, or any quadrilateral, and the simulation finds and draws every line of symmetry... Ages 11β12
- Mathematics Β· Plane Geometry Circumscribed and inscribed circles of triangles and regular polygons Drag the three vertices of a triangle: the circumcenter O is the intersection of the three perpendicular bisectors, the incenter I is... Ages 14β15
- Mathematics Β· Plane Geometry Similar triangles β measuring height with shadows Two similar triangles ABC and A'B'C' with ratio k: drag the vertices of ABC to reshape it, or drag B' or C' to change the ratio and... Ages 13β14
- Mathematics Β· Plane Geometry Thales' theorem β parallel lines in a triangle Triangle ABC with a line DE crossing sides AB and AC. Drag D along AB (E follows so that DE β₯ BC) to see the ratios AD/DB = AE/EC and... Ages 13β14
- Mathematics Β· Plane Geometry Quadrilaterals β identifying special shapes Drag the four vertices A, B, C, D on the grid; the simulation measures the sides, angles, and diagonals to identify a trapezoid,... Ages 13β14
3D Geometry
- Mathematics Β· 3D Geometry Orthographic projection β three views of a solid Build a solid from unit cubes (click the grid to raise or lower each column) or pick a preset shape, rotate it to look around, and see... Ages 16β17
- Mathematics Β· 3D Geometry Angle Between a Line and a Plane, Distance in a Regular Pyramid A regular pyramid S.ABCD (or S.ABC) can be rotated with the mouse or a finger. The simulation constructs the projection of the lateral... Ages 16β17
- Mathematics Β· 3D Geometry Regular pyramids β triangular and square base A regular pyramid is drawn in 3D; drag it to rotate in any direction, or switch on auto-rotate. Change the base edge, the height, and... Ages 13β14
- Mathematics Β· 3D Geometry Cuboids and triangular prisms in 3D A cuboid (a Γ b Γ h) or a right prism whose base is a right triangle (legs a, b and height h) is drawn in space; drag to rotate it and... Ages 12β13
- Mathematics Β· 3D Geometry Cross-section of a cuboid through three points The cuboid ABCD.A'B'C'D' can be rotated by mouse or touch. Three points M on AB, N on AD, and P on CC' can be dragged along their edges;... Ages 16β17
- Mathematics Β· 3D Geometry Cylinder, cone, and sphere β surface area and volume A 3D model of a cylinder, cone, or sphere that can be rotated by dragging with the mouse or a finger. Drag the radius R and height h... Ages 14β15
Trigonometry
- Mathematics Β· Trigonometry Unit circle and the sine, cosine, tangent graphs Drag point M on the unit circle and the matching point moves in sync on the graph of y = sin x, cos x or tan x. The line y = m crossing... Ages 16β17
- Mathematics Β· Trigonometry Basic Trigonometric Equations on the Unit Circle Solve sin x = m, cos x = m, or tan x = m using the unit circle: the simulation marks the terminal points that satisfy the equation,... Ages 16β17
- Mathematics Β· Trigonometry Trig ratios of an acute angle β measuring height with elevation angle Right triangle ABC, right-angled at A: drag vertex C to change the acute angle B = Ξ±, drag B to change the adjacent side; sin, cos, tan... Ages 14β15
Vectors & Coordinate Geometry
- Mathematics Β· Vectors & Coordinate Geometry Conic sections by eccentricity With the same focus and directrix, only the eccentricity e changes: e < 1 gives an ellipse, e = 1 a parabola, e > 1 a hyperbola. The... Ages 15β16
- Mathematics Β· Vectors & Coordinate Geometry Conic sections β the reflective property (satellite dish, whispering gallery, telescope) Rays of light hit a mirror shaped like a conic section and you watch where they go after reflecting: rays parallel to the axis of a... Ages 15β16
- Mathematics Β· Vectors & Coordinate Geometry Lines and circles in the coordinate plane Line Ξ: ax + by + c = 0 has normal vector n = (a; b) and direction vector u = (βb; a) drawn right on the figure; circle (C) has center I... Ages 15β16
- Mathematics Β· Vectors & Coordinate Geometry Planes and spheres in 3D space β distance from center to plane In a rotatable Oxyz coordinate system, the plane (P): Ax + By + Cz + D = 0 and a sphere with center I and radius R are drawn together... Ages 17β18
- Mathematics Β· Vectors & Coordinate Geometry Geometric Transformations and Composition Drag the F-shape and the elements of each transformation (translation vector, center of rotation, line of reflection, center of... Ages 16β17
- Mathematics Β· Vectors & Coordinate Geometry Vectors β sum, difference, scalar multiple and dot product Two vectors u, v are drawn from the origin O on a coordinate grid; students drag the tips of u and v (snapped to the grid) and pick an... Ages 15β16
- Mathematics Β· Vectors & Coordinate Geometry Vectors in 3D space β sum, dot product, angle An Oxyz coordinate system rotates with the mouse or a finger, showing two vectors u and v with given coordinates. The simulation draws... Ages 17β18
Statistics
- Mathematics Β· Statistics Grouped frequency table and relative frequency chart A data sample (student height, weight, or daily self-study time) is grouped into classes of a chosen width. The frequency table n_i,... Ages 14β15
- Mathematics Β· Statistics Data charts β bar, line, and pie from the same table A single data table (monthly temperatures, top students per class, quarterly revenueβ¦) is drawn as a bar chart, a line graph, or a pie... Ages 12β13
- Mathematics Β· Statistics Choosing chart types β misleading graphs The same dataset is drawn as a bar chart, grouped bar chart, line graph, and pie chart. Students switch chart types, drag the top of a... Ages 13β14
- Mathematics Β· Statistics Variance, standard deviation, and IQR of grouped data Two samples with the same mean but different spread are grouped and plotted overlapping each other. Drag each sample's Ο slider to watch... Ages 17β18
- Mathematics Β· Statistics Mean, median and mode of grouped data Generate a sample of test scores out of 100 and group them into a frequency chart. Change the class width or the distribution shape, and... Ages 16β17
- Mathematics Β· Statistics Summary statistics of a data set β dragging data points A data sample is shown as a dot plot on a number line. Drag any point (or click 'Random') and watch the mean, median, quartiles Qβ, Qβ,... Ages 15β16
Probability
- Mathematics Β· Probability Discrete random variables β expectation as the long-run average Build the probability distribution table of a discrete random variable in a real-world scenario (a dice game with a prize, the number of... Ages 17β18
- Mathematics Β· Probability Rolling two dice β sample space and probability The sample space for rolling two dice has 36 equally likely outcomes, arranged in a 6Γ6 table. Choose an event (sum equals k, sum at... Ages 14β15
- Mathematics Β· Probability Permutations, arrangements & combinations β choosing k from n items n items labeled A, B, Cβ¦ sit in a row; students tap to pick k of them, either ordered or unordered, and compare against the full list of... Ages 15β16
- Mathematics Β· Probability Addition and Multiplication Rules of Probability with Venn and Tree Diagrams A Venn diagram with areas proportional to probability: drag event B closer to or farther from A to change P(AB), and instantly see P(A βͺ... Ages 16β17
- Mathematics Β· Probability Dice and coin tosses β experimental probability Roll a die or flip a coin many times; each outcome is tallied in a table and a frequency bar chart updates instantly. Students compare... Ages 11β12
- Mathematics Β· Probability Spinning wheel and bag of marbles β events and probability A spinning wheel is divided into colored slices of different widths (or a bag holds a matching number of marbles per color). Spin once... Ages 12β13
- Mathematics Β· Probability Classical probability: sample space and events List out the entire sample space Ξ© when tossing 2β3 coins or rolling 1β2 dice (shown as a 6 Γ 6 grid with dice faces drawn as pips).... Ages 15β16
- Mathematics Β· Probability Conditional probability and Bayes' theorem: disease testing A medical-testing problem: disease prevalence, sensitivity P(+|disease), and specificity P(β|healthy) are given. A tree diagram, a 2Γ2... Ages 17β18
- Mathematics Β· Probability Experimental probability from repeated marble draws A bag holds red, blue, and yellow marbles; draw one at random, record its color, put it back, and repeat N times. Students draw one... Ages 13β14
Sets, Logic & Graph Theory
- Mathematics Β· Sets, Logic & Graph Theory Venn Diagrams β Set Operations Two or three sets A, B, C are drawn as a Venn diagram inside the universal set U = {1; 2; β¦; N}, with every element placed in its exact... Ages 15β16
- Mathematics Β· Sets, Logic & Graph Theory Grade 11 electives β transformations, graphs, and technical drawing Three Grade 11 elective topics in one template, switched with the topic parameter. Transformations: drag the triangle's three vertices... Ages 16β17
- Mathematics Β· Sets, Logic & Graph Theory Weighted graphs and shortest path β Dijkstra's algorithm A map of locations is modeled as a graph: vertices are places, edges are roads, and weights are distances in kilometers. Choose a start... Ages 16β17
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