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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.

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Knowledge-graph map

English
Mastered Ready to learn LockedHover a node for its description · click to open
Reading for MeaningReading for Meaning — frontier Understand that reading is about making meaning, not just saying words correctly — a text that can be decoded but not understood has not been readMonitoring ComprehensionMonitoring Comprehension — locked Notice the difference between decoding words and actually understanding them — recognise when you've read the words but not grasped the meaning, and do something about itKnowing What You Don't…Knowing What You Don't Know — frontier Monitor your own vocabulary gaps — notice words you half-know, distinguish confident from uncertain knowledge, and develop strategies to resolve the uncertaintyBuilding sentencesBuilding sentences — frontier Understand that words combine to make sentences — a sentence expresses a complete thought; produce and expand complete sentences in speech and writingBasic Nouns & VerbsBasic Nouns & Verbs — frontier Use frequently occurring nouns (people, places, things) and verbs (action words) appropriately in speech and writingCapitals for Names, Day…Capitals for Names, Days and I — frontier Use capital letters for proper nouns (names of people, places) the days of the week, and the personal pronoun 'I'Joining Words with 'And'Joining Words with 'And' — locked Join words and clauses using the conjunction 'and' to create longer sentencesPrepositionsPrepositions — frontier Understand and use the most frequently occurring prepositions of location and direction (e.g. to, from, in, out, on, off, for, by, with)Question WordsQuestion Words — frontier Understand and use question words (who, what, where, when, why, how) to form and answer questionsRegular Plural NounsRegular Plural Nouns — frontier Form and use regular plural nouns orally and in writing by adding -s or -es; understand that plural means more than oneStarting and Ending Sen…Starting and Ending Sentences — locked Begin sentences with a capital letter and end them with the appropriate mark (full stop, question mark, or exclamation mark); recognise and name end punctuationCommas in listsCommas in lists — locked Use commas to separate items in a list within a sentence (e.g., 'I bought apples, bananas, and oranges')Expanded noun phrasesExpanded noun phrases — locked Use expanded noun phrases to describe and specify, adding adjectives and other modifiers before a noun (e.g., 'the blue butterfly', 'the old, creaky door')Four Types of SentencesFour Types of Sentences — locked Understand and use the four sentence types — statement, question, exclamation, and command — recognising how grammatical patterns indicate sentence functionPast, Present and Progr…Past, Present and Progressive Tense — locked Use verbs to convey past and present tense correctly and consistently, including the progressive form (e.g., she is drumming, he was shouting), understanding how tense indicates timeSubordinate clausesSubordinate clauses — locked Use subordination (when, if, that, because) and co-ordination (or, and, but) to join clauses and create compound and complex sentencesPunctuating Titles of W…Punctuating Titles of Works — frontier Use underlining, quotation marks, or italics to indicate titles of works, applying conventions for different types of works such as books, stories, poems, songs, and articlesSitting and holding a p…Sitting and holding a pencil — frontier Sit correctly at a table holding a pencil comfortably and correctly; form lower-case letters in the correct direction starting and finishing in the right placeForming Capital LettersForming Capital Letters — locked Form capital letters correctly; print many upper- and lowercase letters legiblyWriting digits 0-9Writing digits 0-9 — frontier Form digits 0-9 correctly and legiblyJoining LettersJoining Letters — locked Begin to join letters using diagonal and horizontal strokes, understanding which letter pairs are best left unjoined, forming letters of correct size relative to one anotherBlending Sounds to Read…Blending Sounds to Read Words — locked Apply phonic knowledge to blend sounds in unfamiliar words containing taught grapheme-phoneme correspondences; respond speedily to graphemes for all 40+ phonemesKnowing all lettersKnowing all letters — locked Recognise and name all uppercase and lowercase letters of the alphabet; name the letters in order and use letter names to distinguish between alternative spellingsOnsets & RimesOnsets & Rimes — frontier Blend and segment onsets and rimes in single-syllable words; isolate and pronounce individual phonemes (initial, medial, final) in CVC words; add or substitute phonemes to make new wordsRhyming wordsRhyming words — frontier Recognise and produce rhyming words; join in with predictable phrases and rhymes in stories and poems; learn to appreciate and recite poems by heartUnderstanding printUnderstanding print — frontier Demonstrate understanding that print carries meaning, follows left-to-right top-to-bottom directionality, and is organised page by page in booksCompound WordsCompound Words — frontier Recognise and spell compound words by identifying the two component words that combine to form a single wordDiphthongs and complex…Diphthongs and complex vowels — frontier Read and spell words containing diphthongs and complex vowel patterns (ow, ou, ew, ue, ie, aw, au) and words ending in -y as a vowel soundSyllablesSyllables — frontier Count, blend, and segment syllables in spoken words; divide written words into syllables as an aid to reading and spellingTrigraphsTrigraphs — frontier Read and spell words containing trigraphs — three-letter graphemes representing a single sound (igh, air, ear, are)Reading with Expression…Reading with Expression and Accuracy — locked Read aloud with accuracy, appropriate rate, and expression (prosody), re-reading familiar texts to build fluency and confidence, and using context to self-correctPredicting what happens…Predicting what happens next — frontier Predict what might happen next in a story based on what has been read so far; discuss the significance of titles and eventsBook Features and Autho…Book Features and Author's Reasons — locked Identify front cover, back cover, and title page of a book; identify the reasons an author gives to support points in informational textCharacters, settings, a…Characters, settings, and events — locked Identify characters, settings, and major events in stories; become familiar with key stories, fairy tales, and traditional tales and retell them with key details in sequenceConnecting reading to e…Connecting reading to experience — frontier Link what is read or heard to own experiences; draw on background knowledge and vocabulary to support understanding of textsDifferent Types of TextsDifferent Types of Texts — frontier Recognise common types of texts (storybooks, poems, non-fiction); name the author and illustrator and define the role of each in telling or presenting a textDiscussing Texts as a G…Discussing Texts as a Group — frontier Participate in discussions about what is read, taking turns and listening to others; explain understanding clearly; actively engage in group reading activitiesListening to Texts Read…Listening to Texts Read Aloud — frontier Listen to and discuss poems, stories, and non-fiction at a level beyond independent reading; confirm understanding of texts read aloud by asking and answering questions about key detailsMain Topic of Informati…Main Topic of Informational Texts — locked Identify the main topic and retell key details of informational texts; describe connections between individuals, events, ideas, or pieces of informationPictures and Text Worki…Pictures and Text Working Together — frontier Describe the relationship between illustrations and the text in which they appear; use pictures to support and extend comprehensionSelf-Correcting While R…Self-Correcting While Reading — locked Check that text makes sense while reading and self-correct inaccurate reading by re-reading or using contextCharacters' Viewpoints…Characters' Viewpoints and Responses — locked Identify and compare characters' points of view, recognise who is narrating a story, describe how characters respond to events and challenges, and compare characters' experiences across different stories or versions of the same storyStory Sequence and Cent…Story Sequence and Central Message — locked Discuss the sequence of events in narrative texts and how items of information are related in non-fiction, retelling stories including key details and demonstrating understanding of central message or lessonInferring Characters' F…Inferring Characters' Feelings and Motives — locked Draw inferences from independently-read texts, such as inferring characters' feelings, thoughts and motives from their actions, and justifying inferences with evidence from the textRecommending BooksRecommending Books — locked Recommend books to peers, giving reasons for choices based on knowledge of a wide range of genres, authors, and themes, and making comparisons within and across booksUsing Multiple SourcesUsing Multiple Sources — frontier Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or solve a problem efficientlyAsking QuestionsAsking Questions — locked Ask relevant questions to extend understanding; ask and answer questions to seek help, get information, or clarify something not understoodDescribing AloudDescribing Aloud — frontier Describe familiar people, places, things, and events with detail; speak audibly and express thoughts, feelings, and ideas clearly; give well-structured descriptions and explanationsExploring Ideas Through…Exploring Ideas Through Talk — frontier Use spoken language to develop understanding through speculating, hypothesising, imagining, and exploring ideas; use strategies to build vocabulary through talkExpressing & Justifying…Expressing & Justifying Opinions — frontier Articulate and justify answers, arguments, and opinions; participate in discussions, presentations, performances, role play, and debatesGroup discussionsGroup discussions — locked Participate actively in collaborative conversations staying on topic; continue a conversation through multiple exchanges; maintain attention in discussionsListening and respondingListening and responding — frontier Listen and respond appropriately to adults and peers; follow agreed-upon rules for discussion such as listening to others and taking turns speakingEngaging Listeners and…Engaging Listeners and Valuing Viewpoints — locked Gain, maintain and monitor the interest of listeners when speaking; consider and evaluate different viewpoints, attending to and building on others' contributions; begin to select appropriate language for different situationsMultimedia PresentationsMultimedia Presentations — frontier Include multimedia components and visual displays in presentations when appropriate to enhance the development of main ideas or themesPerforming Scripts & Po…Performing Scripts & Poetry — frontier Improvise, rehearse, and perform play scripts and poetry — using role, intonation, tone, volume, mood, silence, stillness, and action to generate language, explore meaning, and add impact to performancePhonics VocabularyPhonics Vocabulary — frontier Know and use the vocabulary of phonics and word structure — phoneme, grapheme, GPC (grapheme-phoneme correspondence), blend, segment, digraph, CVC, vowel, consonant, syllable, root word, suffix, prefix, and homophone — and understand that these words describe the building blocks that phonics instruction is built onSegmenting words into s…Segmenting words into sounds — locked Segment spoken words into phonemes and spell CVC and simple phonetically regular words by writing a letter or letters for each soundApostrophes for possess…Apostrophes for possession — locked Use the possessive apostrophe with singular nouns to show ownership (e.g., the girl's book, the dog's bone)Discussing and Question…Discussing and Questioning New Words — frontier Ask and answer questions about unknown words in texts; discuss word meanings and link new vocabulary to words already knownShades of MeaningShades of Meaning — frontier Distinguish shades of meaning among verbs describing similar actions and among adjectives differing in intensity; make real-life connections between words and their useSorting & Categorising…Sorting & Categorising Words — frontier Sort common objects and words into categories to understand how concepts relate; demonstrate understanding of opposites (antonyms) for common verbs and adjectivesUsing New VocabularyUsing New Vocabulary — frontier Use words and phrases acquired through conversations, being read to, and responding to texts in own speech and writingWord Parts as CluesWord Parts as Clues — frontier Use knowledge of common inflections and affixes (-ed, -s, un-, -er) as clues to the meaning of unknown words; understand how the prefix un- changes meaningDefining WordsDefining Words — locked Define words by category and by one or more key attributes (e.g., 'a duck is a bird that swims'), making real-life connections between words and their useFormal and Informal Eng…Formal and Informal English — frontier Recognise and compare formal and informal uses of English, understanding that language choices vary based on audience, purpose and contextDomain Vocabulary Acros…Domain Vocabulary Across Subject Areas — locked Acquire and use accurately academic and domain-specific vocabulary relevant to grade-level topics, including words that signal precise meaning in informational texts across subject areasResponding to Writing F…Responding to Writing Feedback — frontier With teacher guidance, re-read own writing aloud to check it sounds right; listen and respond to questions and suggestions from teacher or peers to add detail, clarify meaning, and strengthen writing — this is the scaffolded beginning of writing self-evaluation, not an independent skillSaying Sentences Before…Saying Sentences Before Writing Them — locked Say out loud what is going to be written; compose sentences orally before writing them down as preparation for independent writingShared Research ProjectsShared Research Projects — frontier Participate in shared research and writing projects; recall information from experiences or gather information from sources to answer a questionSharing and Publishing…Sharing and Publishing Your Writing — frontier Read own writing aloud clearly enough to be heard by peers and the teacher; use digital tools to produce and publish writingSimple Stories with Beg…Simple Stories with Beginning and Ending — locked Write simple narratives by sequencing sentences to describe events in order; narrate a single event or linked events with a beginning, middle, and ending or reactionWriting Process Vocabul…Writing Process Vocabulary — frontier Know and use the vocabulary of the writing process — compose, plan, draft, revise, edit, proofread, genre, audience, purpose, narrative, recount, instruction, paragraph, sequence, and detail — and understand that these words describe distinct steps and decisions that all writers make, not just tasks to tick offWriting to informWriting to inform — locked Compose informative or explanatory texts using drawing, dictating, or writing that name a topic and supply some information about itBuilding Writing StaminaBuilding Writing Stamina — locked Write about real events and for different purposes, developing stamina for sustained writing across genres beyond narrative (e.g., recounts, letters, instructions)Planning Ideas Before W…Planning Ideas Before Writing — locked Plan before writing by saying aloud or noting down what will be written, writing down ideas and key words, and encapsulating ideas sentence by sentence before composingRevising and editingRevising and editing — locked Proof-read own writing to check for errors in spelling, grammar, and punctuation; evaluate and revise writing with teacher/peer support, re-reading to ensure meaning is clear and tense is consistentOrganising Writing into…Organising Writing into Paragraphs — locked Organise writing into paragraphs, grouping related material around a theme, and use simple organisational devices such as headings and sub-headings in non-narrative writingRevising and editing (a…Revising and editing (age 7+) — locked Evaluate and edit writing by assessing effectiveness, proposing changes to grammar and vocabulary for consistency, and proof-reading for spelling, grammar and punctuation errors at Y3-4 levelRevising and editing (a…Revising and editing (age 8+) — locked Read back your own writing critically and independently — notice where meaning is unclear, where a word could be stronger, or where the reader might be confused; make revisions without needing teacher prompts, using your own judgment about what is and isn't workingShort Research ProjectsShort Research Projects — locked Conduct short research projects that build knowledge about a topic, gather information from print and digital sources, and take brief organised notesWriting Craft VocabularyWriting Craft Vocabulary — frontier Know and use the vocabulary of writing craft and effect — form, structure, register, tone, voice, coherence, cohesion, argument, evidence, perspective, rhetoric, technique, formal, informal, and style — and understand that these words describe choices writers make intentionally to achieve a particular effect on the readerChoosing Form and Tone…Choosing Form and Tone for Your Audience — locked Identify the audience for and purpose of writing before beginning, selecting the appropriate form, tone, and register to match the intended reader and communicative goalPlanning NarrativesPlanning Narratives — frontier Plan narrative writing by considering how authors have developed characters and settings, drawing on techniques observed in texts read, heard, or performedWriting Character & Dia…Writing Character & Dialogue — locked Write narratives that develop real or imagined experiences using effective technique — including establishing context and point of view, developing characters through dialogue, pacing, and description, using varied transitions, and providing a reflective conclusion
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Simultaneous Equations

Mathematics · Algebra · conceptual

Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations

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What mastery looks like

  • Explain that the intersection of two lines represents values satisfying both equations
  • Find the approximate solution to a pair of simultaneous equations by reading a graph
  • Verify a proposed solution by substituting into both equations

Check your understanding

Can Simultaneous Equations explain that solving two equations simultaneously means finding the one pair of values that satisfies both at once — and show what that looks like on a graph?

Prerequisites

Required first

Helpful

Unlocks (0 directly)

None.