Practice and Teaching Tools
Use these resources at home for extra practice or in-center for teaching moments.
Show a regular hexagon with three unit circles removed to visualize a target area.
Inputs: Hexagon radius n controlled by a slider; tangent highlight updates automatically.
Outputs: Hexagon area, center distance, target area, and tangent/non-tangent visual status.
Used for: Use for geometry lessons on composite area and tangent-circle constraints.
Break a regular hexagon into six equilateral triangles and track area values.
Inputs: Hexagon side/radius n selected by slider.
Outputs: Triangle height, one-triangle area, and full hexagon area with live diagram updates.
Used for: Use for geometry instruction on decomposition and area formulas.
Build and animate grid paths to compare Manhattan distance, Euclidean distance, and path counts.
Inputs: Square size n, optional general grid values m and n, and manual/auto path controls.
Outputs: Live path visualizations plus combinatorial counts shown with binomial expressions.
Used for: Use for counting, combinatorics, coordinate geometry, and strategy discussions.
Animate Lissajous curves to connect frequency ratios with visible symmetry.
Inputs: Frequency A, frequency B, phase, speed, and play/pause state.
Outputs: A continuously drawn curve that changes shape as trigonometric parameters change.
Used for: Use for algebra and trigonometry discussions on periodic functions and parameter effects.
Plot Pascal triangle entries modulo k to reveal repeating and fractal-like structure.
Inputs: Row count, modulo base, and dot size.
Outputs: Canvas plot of nonzero modulo entries colored by remainder value.
Used for: Use for number patterns, modular arithmetic, and pattern recognition activities.
Draw diagonals from one vertex to show why a polygon splits into n - 2 triangles.
Inputs: Number of polygon sides n.
Outputs: Triangulated polygon view plus triangle-count and interior-sum formulas.
Used for: Use for geometric proofs and interior-angle sum reasoning.
Show how each interior angle changes as the number of regular-polygon sides changes.
Inputs: Number of sides n.
Outputs: Total interior-angle sum and one interior angle with highlighted angle arc.
Used for: Use for polygon-angle lessons and formula-to-figure connections.
Enter algebraic and trigonometric expressions with live math rendering, instant evaluation, and history.
Inputs: Keyboard or keypad expressions with operators, parentheses, trig/log functions, roots, constants, and Ans.
Outputs: Live rendered math expression, right-aligned running result, and a short recent-results history.
Used for: Use for arithmetic fluency, function practice, and quick verification during instruction or homework.
Connect angle measure to area by shading a circle sector and scaling equal sectors.
Inputs: Central angle theta in degrees and number of equal sectors.
Outputs: Single-sector area and scaled total area with a live sector diagram.
Used for: Use for circle geometry, fraction reasoning, and area proportionality.