Academics
IdentityForge
See why the algebra identities are true (ages 9-14). A square of side a+b is one big square made of four lots - the a-square, the b-square, and the two matching a-by-b strips in the middle - so build the box, meet the two twin strips (that is the 2ab), snip-test a claim to prove it is a real identity, and teach a daydreaming fox not to forget the middle.
▶ Play it nowBuilt for sittings of about 20 minutes on the screen. That is our design budget, not a measurement.
Meet your mentor
Every Spark & Anvil app has a friendly mentor character that demonstrates, asks, and patiently scaffolds learning. On-device AI personalizes the mentor's responses to your kid's progress — never connecting to a server, never collecting data.
#7c3aed Characters who teach
Meet the cast
IdentityForge is the town of Identity, where every algebra identity is a picture you can cut. Mayor Tila the tortoise tends the whole square field, which is made of all its lots; each friend shows ONE idea with their hands - the two twin strips, the honest cut, the four-room box, the corner counted twice - and Dreamer the fox is the novice you teach not to forget the quiet middle.
Tila
The whole square - Mayor Tila the tortoise, whose square field of side (a+b) is made of four lots: the a-square, the b-square, and the two matching a-by-b strips; count every lot and you have counted (a+b) squared
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Miro & Moro
The matching twins - two otters whose two a-by-b strips are congruent; turn one a quarter-turn and it lands exactly on the other, so the two strips together are 2ab, never a lonely single ab
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Kerf
The snip test - a stag beetle who cuts a square anywhere; a claim that still balances after cut after cut, at any value, is not a lucky answer, it is an identity
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Boxer
The box method - a badger who draws (a+b)(c+d) as a grid; each room is one partial product (ac, ad, bc, bd), every pair gets its own room, and the sum of the rooms is the product
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Overlap
The corner counted twice - an octopus who shrinks a square to side (a-b) by removing two strips; the little corner where they cross is removed twice, so add it back once: a-squared minus 2ab plus b-squared
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Dreamer
The protege - a daydreaming fox who keeps only the two corner squares and forgets the two middle strips (the Freshman's Dream); the friend the learner teaches to count all four lots
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Browse all chapters → · What's distributed-narrative methodology? →
What's inside
Learning goal
See why the algebra identities are true (ages 9-14). A square of side a+b is one big square made of four lots - the a-square, the b-square, and the two matching a-by-b strips in the middle - so build the box, meet the two twin strips (that is the 2ab), snip-test a claim to prove it is a real identity, and teach a daydreaming fox not to forget the middle.
Question kits
16 curriculum-aligned question kits, 400 questions in all, mapped to recognized standards.
On-device AI mentor
FoundationModels-powered hints, feedback, and adaptive difficulty — all running locally.
How IdentityForge handles your kid's data
- ✅ All progress, settings, and AI-generated content stays on the device
- ✅ No analytics, no tracking, no third-party SDKs
- ✅ Free — no ads, no in-app purchases
- ✅ No personal information collected from children — in line with COPPA (updated by the 2026 FTC amendments)
- ✅ No chat with strangers — play-together rooms use a short code and preset emotes, never typed messages
IdentityForge runs on ForgeKit — the open-source Swift Package Manager framework that powers every Spark & Anvil app. ForgeKit ensures consistent accessibility, COPPA compliance, and design language across the portfolio, so your kid's progress and preferences feel coherent across every app they touch.
Coming to the App Store
IdentityForge is in active development. Email us to hear when it ships — no marketing, no spam, just a one-shot launch announcement.
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