FoF
FoF

Knowledge graph

The knowledge graph shows every idea in the education spine and which ideas each one depends on. Search or filter by topic, then select an idea to see its prerequisites, what builds on it, and the resources that teach, practice, or assess it.

Each box is an idea; an arrow points from what comes first to what builds on it. Drag to move, pinch or scroll to zoom, and select an idea for details. The same ideas in reading order are on the learning path.

One-to-one countingNumber-word sequenceAlphabet as a universalsystemNeuronsTally marksCardinalityPractice strengthenspathsCounting onNumber as abstractionBundlingZeroTwo statesAdditionTens and onesNumber lineWhy two statesRoman numeralsAdd 1 factsSubtractionAdd 0 factsTurnaround factsPositional notationMake tenDoublesMultiplicationSwitch circuitsMinus 1 factsMinus 0 factsPositional numerals areuniversalAdd 2 factsCarryingHalvesWhat a base isEasy 52 addition factsNegative resultsLaws of arithmeticHardest six (SneakySix)TransistorsTimes 0 factsTimes 1 factsPowersDivisionTruth tablesTimes 2 factsMinus 2 factsEasy 52 subtractionfactsBinary is base twoTough 21Digits of a baseSneaky 12Powers of twoRemaindersEasy 52 multiplicationfactsDivision undoesmultiplicationOR gateEqual partsAND gateNOT gateEach place is basetimes the nextSquaresTough rest subtractionBinary place valuesRead another base inbase tenAddition fluencyInverse operationsXOR gateUnit fractionsPerceptronNAND gateSubtraction fluencyColumn additionBits count valuesRead binaryMake binaryWrite a number inanother baseLogarithmsNumerator anddenominatorNeural netsTough rest productsNAND builds every gateEncodingAlgorithmsCount up in binarySymbols versus lengthWeightsMultiplication fluencyFractions as divisionSpecial-purpose versusuniversal machinesAdd two bitsEquivalent fractionsTraining by correctionExtending the numbersDivision factsBinary column additionHalf adderNext-word modelsLogs from successiverootsFull adderRipple-carry adderHow a computer addsOverflowUniversal computerWhat AI isThe jump touniversalityAI helps, people decidePeople as universalexplainersYou are the boss of theagentCommitsRepos and gitBranchesGitHubWorktreesLocal versus liveSecrets and keysThe builder loop
Number and place valueArithmeticBinary and logicUniversalityAlgebraAIAgentic codingneeds firsthelps first