Practice and Teaching Tools

Show a regular hexagon with three unit circles removed to visualize a target area.

Decompose a regular polygon into center triangles to compute area by summing triangle areas.

Build and animate grid paths to compare Manhattan distance, Euclidean distance, and path counts.

Compare permutation and combination formulas with slot visuals and overcount corrections.

Animate Lissajous curves to connect frequency ratios with visible symmetry.

Identify the correct parent function from a transformed graph using shifts, reflections, and stretches.

Enter a radicand to build a factor tree, group prime pairs, and simplify the radical step by step.

Build factor trees to classify numbers as prime or composite and decompose composites into prime factors.

Drag parent-function graphs to match target transformations in the form y = f(x+h) + k.

Solve percent-mixture problems by balancing total solute and total amount across inputs and output.

Plot $A = P(1 + rt)$ over time with adjustable principal, rate, and years.

Plot $A = P(1 + r/n)^{nt}$ with adjustable compounding frequency $n$.

Plot $A = Pe^{rt}$ with interactive principal, rate, and time controls.

Plot $A_n = (1 + 1/n)^n$ to see how increasing $n$ converges toward Euler's number $e$.

Explore Pascal triangle coefficients modulo k with a live plot and a selectable coefficient inspector.

Draw diagonals from one vertex to show why a polygon splits into $n - 2$ triangles.

Show how each interior angle changes as the number of regular-polygon sides changes.

Drag a point around the unit circle to connect coordinates with trig values and verify $\sin^2\theta + \cos^2\theta = 1$

Explore the key unit-circle angles with exact coordinate pairs to connect x = cos θ and y = sin θ.

Move a horizontal line and a point to see the reflected point update on a coordinate grid.

Move a vertical line and a point to see the reflected point update on a coordinate grid.

Walk through translate, rotate, reflect, rotate-back, and translate-back for $y = mx + b$.

Move a point and reflect it across the diagonal line $y = x$ on a coordinate grid.

Move a shifted diagonal mirror line and point to see reflection updates in real time for $y = x + b$.

Walk through the shortcut for $y = x + b$: subtract $b$, flip across $y = x$, then add $b$ back.

Plot the parabolic arc of a projectile with adjustable launch speed and angle.

Decompose an initial velocity vector into horizontal and vertical components using trigonometry.

Plot horizontal range as a function of launch angle and find the 45° optimum.

Explore multiple 3D solids, compare each face with its net, and build total surface area as a sum.

Enter algebraic and trigonometric expressions with live math rendering, instant evaluation, and history.

Connect angle measure to area by shading a circle sector and scaling equal sectors.

Compare a stick figure and tree shadow to solve unknown height with equivalent fractions.