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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

Mathematics
Mastered Ready to learn LockedHover a node for its description · click to open
Numbers on a number lineNumbers on a number line — frontier Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagramSystematic ListingSystematic Listing — frontier Enumerate possibilities of combinations of two variables systematically (e.g. all ways to choose from a set of options)Comparing groups: more…Comparing groups: more or fewer — frontier Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategiesHow Many in Total?How Many in Total? — locked Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order countedOne-to-one countingOne-to-one counting — frontier One-to-one correspondence when counting objects: each object is paired with exactly one number nameCounting objects to 20Counting objects to 20 — locked Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)Rote counting to 100Rote counting to 100 — locked Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by onesTwo written numerals be…Two written numerals between 1 and 10 — frontier Compare two written numerals between 1 and 10 to determine which is greater or lessSorting into categoriesSorting into categories — locked Classify objects into given categories, count the number in each category, and sort the categories by countPictograms and tally ch…Pictograms and tally charts — locked Interpret and construct simple pictograms, tally charts, block diagrams, and simple tablesPictograms and tally ch…Pictograms and tally charts (age 6+) — frontier Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting dataSorting Data into Categ…Sorting Data into Categories — locked Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantityStatistical Analysis Vo…Statistical Analysis Vocabulary — frontier Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describesCalculating the MeanCalculating the Mean — locked Calculate and interpret the mean as an average of a data setLine graphs (age 10+)Line graphs (age 10+) — locked Interpret and construct pie charts and line graphs; use these to solve problemsComparing measurementsComparing measurements — locked Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliersPictograms and tally ch…Pictograms and tally charts (age 11+) — locked Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data typeScatter Graphs & Correl…Scatter Graphs & Correlation — locked Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictionsFraction NotationFraction Notation — frontier Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a wholeFractions of amountsFractions of amounts — locked Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantityUnderstanding fractionsUnderstanding fractions — locked Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2Equivalent fractionsEquivalent fractions — locked Recognise and show, using diagrams, equivalent fractions with small denominatorsDecimal & Percent Notat…Decimal & Percent Notation — frontier Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same valueDecimal equivalents of…Decimal equivalents of tenths and hundredths — locked Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)Fractions of a wholeFractions of a whole — locked Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/bDecimals for Tenths & H…Decimals for Tenths & Hundredths — locked Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)Decimals and fractions…Decimals and fractions (age 10+) — locked Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts2-D shapes2-D shapes — frontier Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)3-D shapes3-D shapes — frontier Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)Positional LanguagePositional Language — frontier Describe the position of objects using terms such as above, below, beside, in front of, behind, next to3-D shapes (age 5+)3-D shapes (age 5+) — locked Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributesTurns & DirectionsTurns & Directions — locked Describe movement and direction, including whole, half, quarter, and three-quarter turns2-D shapes (age 6+)2-D shapes (age 6+) — locked Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical lineAngles in triangles (ag…Angles in triangles (age 6+) — locked Distinguish defining attributes of shapes (e.g. triangles are closed and three-sided) from non-defining attributes (e.g. colour, orientation, overall size)Patterns & SequencesPatterns & Sequences — frontier Order and arrange combinations of mathematical objects in patterns and sequencesPosition, direction, an…Position, direction, and movement — locked Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)Right Angles & TurnsRight Angles & Turns — locked Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turnFirst Quadrant Coordina…First Quadrant Coordinates — frontier Describe positions on a 2-D grid as coordinates in the first quadrantNets of 3-D ShapesNets of 3-D Shapes — frontier Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the netTransformations on a gr…Transformations on a grid — frontier Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and sizeTypes of angles (age 8+)Types of angles (age 8+) — frontier Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown valuesParts of a circleParts of a circle — frontier Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radiusCircles: Circumference…Circles: Circumference & Area — locked Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular partsEarly Maths VocabularyEarly Maths Vocabulary — frontier Use mathematical words carefully when counting, comparing, and describing shapes and positionsFinding efficient metho…Finding efficient methods — frontier Notice when a calculation or pattern repeats and use this to count more efficiently or predict resultsHands-On Problem SolvingHands-On Problem Solving — frontier Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problemMaking Sense of ProblemsMaking Sense of Problems — frontier Make sense of a problem by identifying what is being asked, choosing concrete objects or pictures to represent the situation, and explaining a pathway to the solutionReal-World to Maths Con…Real-World to Maths Connections — frontier Move between a real-world situation and a mathematical representation using concrete objects, drawings, diagrams, tables, number sentences, or bar modelsShowing Your WorkingShowing Your Working — frontier Show and tell how a mathematical answer was found using objects, drawings, and spoken wordsSpotting mathematical p…Spotting mathematical patterns — frontier Notice simple patterns and structures: spot that changing order doesn't change the total, and recognise how numbers relate to each otherUsing objects to model…Using objects to model real problems — frontier Use objects, drawings, or simple number sentences to represent a real-world situation (early mathematical modelling)Explaining Mathematical…Explaining Mathematical Reasoning — locked With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or wordsAdvanced Maths Vocabula…Advanced Maths Vocabulary — locked Communicate with mathematical precision: use correct vocabulary for ratio, proportion, algebra, volume, coordinate geometry, and circle parts; specify units including cm³, m³, and miles/km; use notation for algebraic expressions and order of operations accuratelyComparing CapacityComparing Capacity — locked Compare and describe capacity and volume using language such as full, empty, more than, less than, half fullComparing durationsComparing durations — frontier Use comparative language for time: quicker, slower, earlier, laterComparing Lengths & Hei…Comparing Lengths & Heights — locked Compare two objects directly by length or height and describe the difference using language such as long, short, tall, longer, shorter, taller, double, halfMeasurable Attributes o…Measurable Attributes of Objects — frontier Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)Measuring mass and weig…Measuring mass and weight (age 4+) — locked Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter thanOrdering Events in TimeOrdering Events in Time — frontier Sequence events in chronological order using language such as before, after, next, first, today, yesterday, tomorrow, morning, afternoon, eveningDays, Weeks, Months & Y…Days, Weeks, Months & Years — locked Recognise and use language relating to dates, including days of the week, weeks, months, and yearsArea (age 8+)Area (age 8+) — locked Measure areas by counting unit squares (square cm, square m, square in, square ft)Understanding AreaUnderstanding Area — frontier Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlapsComparing and ordering…Comparing and ordering numbers — locked Compare and order two-digit numbers using the symbols >, =, and <, based on place value understandingRoman numerals to 100Roman numerals to 100 — frontier Read Roman numerals to 100 (I to C) and understand that the numeral system changed over time to include zero and place valueLikelihood LanguageLikelihood Language — frontier Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossibleBar Models for RatiosBar Models for Ratios — frontier Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answerPercentages (age 9+)Percentages (age 9+) — frontier Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)Calculating PercentagesCalculating Percentages — locked Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparisonScale and similar shapesScale and similar shapes — locked Solve problems involving similar shapes where the scale factor is known or can be foundCompound UnitsCompound Units — locked Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound unitsOne Quantity as a Fract…One Quantity as a Fraction — locked Express one quantity as a fraction of another where the result may be less than 1 or greater than 1, and interpret the meaning in contextProportion GraphsProportion Graphs — frontier Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphedProportional Reasoning…Proportional Reasoning Vocabulary — frontier Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contextsScale and similar shape…Scale and similar shapes (age 11+) — locked Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versaProportionProportion — locked Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representationsRatio Notation and Rela…Ratio Notation and Relationships — locked Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
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Expanding Single Brackets

Mathematics · Algebra · procedural

Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers

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What mastery looks like

  • Multiply a single positive term over a bracket to expand the expression
  • Multiply a negative term over a bracket, correctly handling signs
  • Combine expanding brackets with collecting like terms to simplify fully

Check your understanding

Can Expanding Single Brackets expand a bracket like 3(2x + 5) by multiplying everything inside, to get 6x + 15?

Prerequisites

Required first

Unlocks (2 directly)