AI Constitution

Resources · Learning tool

Education Concept Tracker

A prerequisite knowledge graph of 1590 learning concepts across 8subjects. Track what you've mastered and see exactly what you're ready to learn next — the topics whose prerequisites you've already met. Built on the Marble Open Skill Taxonomy.

Sign in to track your progress and get personalized recommendations. You can browse freely below.

Knowledge-graph map

History
Mastered Ready to learn LockedHover a node for its description · click to open
Discovering Tutankhamun…Discovering Tutankhamun's Tomb — locked Understand that we know about ancient Egypt because archaeologists have dug up and studied objects buried in the sand for thousands of years — and that one of the most exciting discoveries ever was when Howard Carter found the hidden tomb of Tutankhamun in 1922, filled with golden treasuresEgypt, the Nile, and th…Egypt, the Nile, and the Desert — frontier Locate Egypt on a map of Africa and understand that it is a country in a very hot, dry desert, but the River Nile — the longest river in the world — flows through it, bringing water and rich soil that allowed people to grow food and build one of the earliest great civilisationsEgyptian Gods and the A…Egyptian Gods and the Afterlife — locked Understand that the ancient Egyptians believed in many gods and goddesses and believed that life continued after death in a wonderful afterlife — which is why they took great care to prepare bodies and fill tombs with food, jewellery, and precious objects for the dead person to useEveryday Life in Ancien…Everyday Life in Ancient Egypt — frontier Describe what everyday life was like for ordinary people in ancient Egypt: farmers grew wheat and barley near the Nile, families lived in mud-brick houses, children played games and had pets, and people ate bread, fish, fruit, and vegetablesHieroglyphs and PapyrusHieroglyphs and Papyrus — locked Know that the ancient Egyptians used a special writing system called hieroglyphs — pictures and symbols that stood for sounds and words — and that they wrote on a paper-like material called papyrus, which was made from a plant that grew along the NilePharaohs and TutankhamunPharaohs and Tutankhamun — locked Know that ancient Egypt was ruled by powerful kings and queens called pharaohs, who lived in grand palaces and made the laws — and that one of the most famous pharaohs is Tutankhamun, a boy who became pharaoh as a child and whose golden tomb was discovered thousands of years laterPyramids and the Great…Pyramids and the Great Sphinx — locked Know that the ancient Egyptians built enormous stone pyramids as tombs for the pharaohs, that the Great Pyramid at Giza was one of the Seven Wonders of the Ancient World and is still standing today, and that the Great Sphinx — a statue with a lion's body and a human head — guards the pyramidsVocabulary: ancient egy…Vocabulary: ancient egypt — frontier Know and use the key vocabulary of ancient Egypt — pharaoh, pyramid, tomb, mummy/mummification, hieroglyphs, papyrus, sarcophagus, canopic jar, natron, archaeologist, artefact, Nile, delta, irrigation, shaduf, scribe, vizier, obelisk, sphinx, cartouche — and apply these terms accurately when describing Egyptian society, religion, and material cultureAncient Egypt on the Ti…Ancient Egypt on the Timeline — locked Place ancient Egypt on a timeline spanning over 3,000 years — from around 3100 BCE (unification under the first pharaoh) to 30 BCE (Roman conquest) — understanding that this civilisation lasted longer than the time between the Romans and today, and was divided into major periods: the Old Kingdom (pyramid age), Middle Kingdom, and New Kingdom (empire age)Building the PyramidsBuilding the Pyramids — locked Understand how the pyramids were built: thousands of workers moved enormous stone blocks using ramps, rollers, and sledges, the work was organised by the pharaoh's officials, and the design evolved from flat-topped mastabas to step pyramids (like Djoser's) to the smooth-sided Great Pyramid — and know that later pharaohs were buried in hidden rock-cut tombs in the Valley of the KingsEgyptian Social Hierarc…Egyptian Social Hierarchy — locked Describe the social structure of ancient Egypt as a pyramid-shaped hierarchy: the pharaoh at the top, then priests and nobles, followed by scribes and soldiers, then craftworkers and merchants, and farmers and labourers at the base — understanding that a person's position was usually inherited and determined their whole way of lifeEgyptian Tomb Paintings…Egyptian Tomb Paintings and Artefacts — locked Use tomb paintings, artefacts, and objects from ancient Egypt as evidence to find out about daily life: Nebamun's tomb paintings show hunting and feasting, jewellery and furniture reveal craftsmanship, and everyday objects like pots and tools tell us what ordinary people used — understanding that these sources are how we piece together information about a civilisation that ended thousands of years agoMummification Step by S…Mummification Step by Step — locked Describe the step-by-step process of mummification: the body was washed, internal organs were removed and placed in canopic jars, the body was dried with natron salt for 40 days, then wrapped in linen bandages with amulets tucked between the layers, and finally placed in a decorated coffin (sarcophagus)Upper and Lower EgyptUpper and Lower Egypt — locked Understand that ancient Egypt was divided into Upper Egypt (the narrow river valley in the south) and Lower Egypt (the wide delta in the north), that the two lands were united under one pharaoh, and that Egyptians managed the Nile's water through irrigation canals and shadufs to grow crops year-roundEgyptian Timelines and…Egyptian Timelines and Maps — frontier Read and construct historical timelines — place Ancient Egyptian periods, pharaohs, and key events on a timeline relative to each other and to the present day; interpret maps showing the Nile delta, trade routes, and the location of key sitesAncient Greece and Rome…Ancient Greece and Rome on the Map — frontier Locate Greece and Italy on a map and know they are countries around the Mediterranean Sea where two great ancient civilisations — Ancient Greece and Ancient Rome — grew up thousands of years ago, long after the ancient Egyptians but long before our timeAncient life vs todayAncient life vs today — locked Compare how children in ancient Greece or Rome lived with how children live today — including differences in school (writing on wax tablets, learning to fight in Sparta), food (olives, bread, grapes), games, and clothing (tunics and sandals) — and understand these civilisations existed thousands of years agoGreek gods & Mount Olym…Greek gods & Mount Olympus — locked Know that the ancient Greeks believed in many gods and goddesses who lived on Mount Olympus — including Zeus (king of the gods, thunder), Athena (wisdom), Poseidon (the sea), Hermes (messages), and Aphrodite (love) — and that each god had special powers and a role in the worldRoman soldiers & builde…Roman soldiers & builders — locked Know that Roman soldiers marched across a huge empire building straight roads and strong walls, and that some Roman roads, walls, and buildings can still be seen today — showing that the Romans were powerful builders whose work has lasted thousands of yearsRomulus & RemusRomulus & Remus — locked Know the Roman founding myth of Romulus and Remus — twin brothers abandoned as babies, raised by a she-wolf, who grew up to found the city of Rome — and understand that this is a legend the Romans told about how their city beganThe first OlympicsThe first Olympics — locked Know that the Olympic Games began in ancient Greece at a place called Olympia as athletic competitions held in honour of Zeus, and that the modern Olympic Games we watch today were inspired by those ancient gamesAthens Versus SpartaAthens Versus Sparta — locked Compare Athens and Sparta as two very different Greek city-states: Athens focused on learning, arts, debate, and democracy, while Sparta focused on military training, discipline, and obedience — and understand that a city-state was a city that ruled itself like a small countryGladiators & PompeiiGladiators & Pompeii — frontier Know that Romans watched gladiators fight in huge arenas like the Colosseum in Rome, that gladiators were usually enslaved people or prisoners trained to fight, and that the city of Pompeii was buried by the eruption of Mount Vesuvius in AD 79, preserving an extraordinary snapshot of Roman daily lifeGreek theatreGreek theatre — frontier Know that the ancient Greeks invented theatre, performing tragedies and comedies in large open-air amphitheatres with actors wearing masks — and that plays were performed as part of religious festivals honouring the god Dionysus, with audiences of thousandsEvidence for Greek and…Evidence for Greek and Roman Life — frontier Understand that historians and archaeologists piece together ancient Greek and Roman life from evidence — pottery paintings, coins, inscriptions, ruins like Pompeii, and written texts by authors such as Homer and Pliny — and that the same evidence can be interpreted in different ways by different historiansHidden Voices of Greece…Hidden Voices of Greece and Rome — locked Examine the lives of people usually left out of the Greek and Roman story — enslaved people who made up roughly 30% of Athens and powered Rome's economy, women whose lives varied dramatically between Athens (largely confined to the home) and Sparta (physical training, property ownership), and conquered peoples across both empires — and evaluate whose voices are missing from the historical record and whyTroy: Myth or History?Troy: Myth or History? — locked Explore how Heinrich Schliemann's excavation at Hisarlik in modern Turkey raised questions about whether the Trojan War described in Homer's Iliad was historical, partly historical, or entirely mythical — understanding that archaeology and literary sources can support or contradict each other, and that the line between myth and history in the ancient world is often blurredFall of the Roman Repub…Fall of the Roman Republic — locked Trace how Roman political violence — the murder of the Gracchi brothers, civil wars between Marius and Sulla, Caesar's crossing of the Rubicon and assassination on the Ides of March, and the final war between Octavian and Antony — destroyed the Republic and led to one-man rule under Augustus, and debate whether the fall of the Republic was inevitable or a series of choicesDifferent Accounts of t…Different Accounts of the Same Event — locked Recognise that different people can give different accounts of the same event — and that both can be genuine while still disagreeingEvidence from the PastEvidence from the Past — locked Understand that everything we know about the past comes from evidence — objects, buildings, pictures, documents, and stories that have survivedVocabulary: historical…Vocabulary: historical thinking — frontier Know and use the vocabulary of historical thinking — source, evidence, primary source, secondary source, artefact, chronology, chronological order, BC/BCE, AD/CE, century, decade, era, period, timeline, excavation, archaeologist, interpretation, corroborate, bias, perspective — and apply these terms when discussing how we know about the past and how reliable our knowledge isChecking Sources Agains…Checking Sources Against Each Other — locked Corroborate: check whether multiple sources agree on the same facts — and investigate why they might notQuestioning Historical…Questioning Historical Sources — locked Before trusting a historical source, ask: who made this, when, and why? — the answers shape how much weight the source should carryUnderstanding People in…Understanding People in Their Own Time — locked Understand that people in the past saw the world very differently from us — judge their actions by the context they lived in, not only by today's valuesEvidence Versus Interpr…Evidence Versus Interpretation — locked Distinguish between historical evidence and historical interpretation — evidence is what survived, interpretation is the argument a historian builds from it, and the same evidence can support different argumentsKings & QueensKings & Queens — locked What medieval kings and queens did: ruling the land, making laws, collecting taxes; the crown and throne as symbols of power; the Tower of LondonKnights & ArmourKnights & Armour — locked What knights were: trained warriors who served a lord; armour, shields, swords, and lances; the code of chivalry as rules for how knights should behaveMedieval ClothingMedieval Clothing — locked What people wore in medieval times: peasant clothes (wool, linen) vs noble clothes (silk, fur, bright colours); no zippers or buttons; how clothes showed your place in societyMedieval Food & FeastsMedieval Food & Feasts — locked What people ate in medieval times: bread and pottage for ordinary people, grand feasts for the rich; no forks, eating with hands; the great hall as the centre of castle lifeRobin Hood & King ArthurRobin Hood & King Arthur — frontier The legends of Robin Hood (Sherwood Forest, stealing from the rich, Merry Men) and King Arthur (Round Table, Excalibur, Camelot); that these are stories, not proven history, but reflect medieval valuesThe VikingsThe Vikings — frontier Who the Vikings were: seafaring warriors and traders from Scandinavia; longships; Viking raids on Britain; that Vikings also settled and farmedVillage LifeVillage Life — frontier Daily life for ordinary people in a medieval village: thatched houses, farming, baking bread, fetching water; how different life was from todayWhat Is a Castle?What Is a Castle? — frontier What a castle is: a fortified building used as both a home and a defence; key parts including towers, moat, drawbridge, and thick walls; why castles were builtAnglo-Saxon BritainAnglo-Saxon Britain — frontier Who the Anglo-Saxons were: Germanic peoples who settled in Britain after the Romans left; their kingdoms, villages, place names, art, and eventual conversion to ChristianityCastle Design Through t…Castle Design Through the Ages — locked How castles were built and evolved: from wooden motte-and-bailey to stone keeps to concentric castles; rooms and their uses; how castle design responded to new attack methodsMedieval Pyramid of Pow…Medieval Pyramid of Power — locked How medieval society was organised: king at the top, then lords, then knights, then peasants/serfs; who owed what to whom; the pyramid of power and mutual obligationsThe Black DeathThe Black Death — locked The Black Death of 1348-49: what the plague was, how it spread, its devastating death toll; how it changed society by giving surviving workers more power and higher wagesThe Medieval ChurchThe Medieval Church — locked The enormous power of the medieval Church: monasteries and the daily life of monks and nuns; building great cathedrals; pilgrimage as a religious journey; the Church's influence over everyday lifeVikings vs Anglo-SaxonsVikings vs Anglo-Saxons — locked The conflict between Vikings and Anglo-Saxons for control of England: Viking raids, Alfred the Great's resistance, the Danelaw, Athelstan as first king of all England, Edward the ConfessorMedieval Legacy in Mode…Medieval Legacy in Modern Life — locked What the Middle Ages gave us: Parliament, universities, common law, Gothic architecture, the English language (Anglo-Saxon + Norman French), place names, surnames; why we are still fascinated by the medieval world
← Back

Nth-Term Rules

Mathematics · Algebra · procedural

Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence

Sign in to track this

What mastery looks like

  • Derive the nth-term rule for an arithmetic sequence such as 3, 7, 11, 15, … as 4n − 1
  • Use an nth-term formula to find the 50th or 100th term without listing all preceding terms
  • Determine whether a given number (e.g., 99) is a term in a specified arithmetic sequence

Check your understanding

If Nth-Term Rules is given the sequence 4, 7, 10, 13…, can they find a formula for the nth term — and use it to check whether, say, 100 is in the sequence?

Prerequisites

Required first

Helpful

Unlocks (0 directly)

None.