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GeometryForge — a geometry construction workshop: kids drawing shapes with a compass and stretching a rubber band on a geoboard, geometric solids and tangrams, no numbers

GeometryForge

Geometry is something you build. Make angles, raise polygons, slide and flip shapes across a grid, and stretch a band to an exact area — then meet the guides who each embody one geometric idea.

Construction Lab Geoboard
Level 1

Start here

Construction Lab Compass and straightedge, exactly — an engine checks your construction and scores your move economy. Transformation Lab Slide, flip, turn, and scale shapes on a coordinate grid — name the move, predict where a vertex lands. Geoboard Stretch a rubber band around the pegs to enclose an exact area — and watch Pick’s Theorem balance. Geometry Duel A head-to-head kit round for 2–4 players — one device or an online room by code. Highest first-try score wins.
Brain Break Take a quiet moment between builds — a fun teaser or a short breather. Brain breaks help you remember what you learn.

All activities

Build & reason

Property-Chain Reasoning Build a proof yourself — pick the deduction that follows next until you reach the conclusion. Fill the Point Which shapes tile? Place polygon corners into a vertex and fill toward exactly 360° — no gap, no overlap. Geometry Studio Make an angle to a target with a live protractor, build a polygon to an angle-sum, set complementary pairs. Roll the Block Tip a tall block across a grid until it stands upright on the goal — a rigid-motion rotation of a solid; picture how it tumbles standing ↔ lying. Calm, no-fail.

Practice & play

Mixed Practice Shuffles questions from the kits you’ve played, brought back when they’re ready to review — great for making it stick.

Practice the concepts

17 kits from an intro to points & angles up to advanced synthesis — a short round with a hint whenever you get stuck.

All 17 kits
Kit 1: Points, Lines, and Angles Angles & lines · grades 4-5 · 25 questions Kit 2: Classifying 2D Shapes Shapes · grades 4-5 · 25 questions Kit 3: Area and Perimeter Measurement · grades 5-6 · 25 questions Kit 4: 3D Shapes and Volume Measurement · grades 5-6 · 25 questions Kit 5: Symmetry and Transformations Transformations · grades 5-6 · 25 questions Kit 6: Coordinate Geometry Coordinate geometry · grades 6-7 · 25 questions Kit 7: Pythagorean Theorem Measurement · grades 7-8 · 25 questions Kit 8: Geometric Proofs and Reasoning Reasoning & proof · grades 7-8 · 25 questions Kit 9: Circles & Arc Measures Circles · grades 6-8 · 25 questions Kit 10: Similarity & Scale Similarity & congruence · grades 6-8 · 25 questions Kit 11: Intro to Trigonometry Measurement · grades 7-8 · 25 questions Kit 12: Geometric Constructions Constructions · grades 6-8 · 25 questions Kit 13: Cross-Topic Connections Reasoning & proof · grades 5-6 · 25 questions Kit 14: Real-World Applications Reasoning & proof · grades 6-7 · 25 questions Kit 15: Misconceptions & Reasoning Reasoning & proof · grades 6-7 · 25 questions Kit 16: Advanced Synthesis Reasoning & proof · grades 7-8 · 25 questions Kit 17: Congruence and Triangles Similarity & congruence · grades 6-8 · 25 questions

For grown-ups — progress report →A private, on-device snapshot mapped to the skill areas practiced. Export a CSV or print — nothing that names you leaves this device.

More ways in

More ways to play

What the shooter sees Pentagons and hexagons Water in the pool Quiz Arena Geometry Run Estimate π Coordinate Hunt Waypoints One fold trisects Count the units
Where this idea comes from

Plimpton 322

A clay tablet written in Babylonia (now Iraq) around 1800 BCE, in cuneiform with base-60 numbers. The publisher George Plimpton bought it in the 1920s; it has been at Columbia University in New York since 1936.

One thing to hold: A broken clay tablet about the size of a postcard, with fifteen rows of numbers.

Why it matters: Its rows are linked to right-angled triangles whose sides are whole numbers. The first row has 119 and 169, the short side and the long slanted side of a triangle whose other side is 120 — more than a thousand years before Pythagoras.

What we don’t know: Nobody knows what it was for. Scholars still argue whether it was a teacher’s table, a list of practice problems, or something else.

Sources: Columbia University Rare Book & Manuscript Library, Plimpton Cuneiform 322 · Eleanor Robson, “Words and Pictures: New Light on Plimpton 322”, American Mathematical Monthly 109 (2002)

Kolam

Patterns drawn each morning with rice flour at the threshold of homes in Tamil Nadu and other parts of South India, mostly by women.

One thing to hold: A grid of dots (pulli) with a line looping around them, often drawn without lifting the hand.

Why it matters: Many kolams are one closed curve around a dot grid; mathematicians have studied them as rules for drawing curves.

Sources: Gift Siromoney, Rani Siromoney and Kamala Krithivasan, “Array grammars and kolam”, Computer Graphics and Image Processing 3 (1974) · Vijaya Rettakudi Nagarajan, Feeding a Thousand Souls: Women, Ritual, and Ecology in India — An Exploration of the Kōlam (Oxford University Press, 2018)

Sangaku

Wooden tablets of geometry problems hung in Shinto shrines and Buddhist temples in Japan during the Edo period (1603–1867).

One thing to hold: A painted wooden board with circles inside triangles and a problem written beside it.

Why it matters: People offered a hard geometry problem, sometimes with its answer, as a gift and a challenge to visitors.

What we don’t know: Many tablets were lost; who wrote some problems is not known.

Sources: Fukagawa Hidetoshi and Tony Rothman, Sacred Mathematics: Japanese Temple Geometry (Princeton University Press, 2008)

Same idea, another world

Something you practice here shows up somewhere else too — that's real learning that travels.

Enlarging a shape by a scale factor multiplies every side by the same number — that fixed multiplier is a ratio. The shared idea: a fixed scale factor (y = kx) — a dilation multiplies every length by the SAME number, exactly the fixed ratio you scale a proportion by Try RatioRealm → Flipping a shape across its mirror line is exactly how light reflects off a mirror — the angle in equals the angle out. The shared idea: reflection — flipping a shape across its line of symmetry is the same mirror reflection as a light ray bouncing so the angle in equals the angle out Try PrismForge →
GeometryForge mascot

Meet the cast — the characters who teach this

Each one stands for an idea you’ll practice. Tap a character to read their illustrated story and hear their audio drama.

Ensemble stories — the cast together

Explore all the stories →

What next? Pick a door

Chosen from what this app is about. What you open is remembered on this device only.

📚 Books for GeometryForge

Read the story, print a workbook, or color the cast — free PDFs to read offline or print at home.

Browse all books →

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