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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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Adding money and giving change

Mathematics · Measurement · procedural

Find different combinations of coins that equal the same amount of money

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What mastery looks like

  • Show that 50p can be made with 2×20p + 1×10p, or 5×10p, or 1×50p
  • Systematically find multiple coin combinations for a given total
  • Explain why different coin sets give the same total

Check your understanding

If Adding money and giving change needs to make exactly 30p, can they find two or three different ways to do it using different combinations of coins?

Prerequisites

Required first

Helpful

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