# Stage 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 43 concepts ready. In the app: https://ai.page/roadmap/cambridge-stage-5 Part of: [Cambridge: Mathematics](https://ai.page/roadmap/cambridge.md) Goal: Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 5 ## 1. Statistics and Probability · Probability - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability - [Likelihood Language](https://ai.page/c/likelihood-language/index.md): Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible ## 2. Statistics and Probability · Statistics - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): 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 describes - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): 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 outliers ## 3. Geometry and Measure · Position and transformations - [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): 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 size - [Transformations on a Grid](https://ai.page/c/transformations-on-a-grid-maths/index.md): Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed - [First Quadrant Coordinates](https://ai.page/c/first-quadrant-coordinates/index.md): Describe positions on a 2-D grid as coordinates in the first quadrant ## 4. Geometry and Measure · Geometrical reasoning, shapes and measurements - [Angle Sum Rules](https://ai.page/c/angle-sum-rules/index.md): Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles - [Estimating Angles](https://ai.page/c/estimating-angles/index.md): Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size - [Translating and reflecting shapes](https://ai.page/c/translating-and-reflecting-shapes/index.md): Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes - [Nets of 3-D Shapes](https://ai.page/c/nets-of-3-d-shapes/index.md): 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 net - [Understanding angles](https://ai.page/c/understanding-angles/index.md): Recognise angles as a property of shape or a description of a turn - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes - [Perimeters of polygons](https://ai.page/c/perimeters-of-polygons/index.md): Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa) - [Perimeter of Compound Shapes](https://ai.page/c/perimeter-of-compound-shapes/index.md): Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres - [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties ## 5. Geometry and Measure · Time - [Converting measurement units](https://ai.page/c/converting-measurement-units/index.md): Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day) - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-4/index.md): Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line - [Telling time to the minute (age 9+)](https://ai.page/c/telling-time-to-the-minute-age-9/index.md): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days) - [12-hour and 24-hour time](https://ai.page/c/12-hour-and-24-hour-time/index.md): Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks ## 6. Number · Fractions, decimals, percentages, ratio and proportion - [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): 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 value - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% - [Understanding Percentages](https://ai.page/c/understanding-percentages/index.md): Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal - [Fraction Addition Concepts](https://ai.page/c/fraction-addition-concepts/index.md): Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way - [Fraction Notation](https://ai.page/c/fraction-notation/index.md): 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 whole - [Mixed numbers and improper fractions](https://ai.page/c/mixed-numbers-and-improper-fractions/index.md): Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5) - [Multiplying fractions (age 11+)](https://ai.page/c/multiplying-fractions-age-11/index.md): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150) ## 7. Number · Place value, ordering and rounding - [Decimal place value](https://ai.page/c/decimal-place-value/index.md): Round decimals with one decimal place to the nearest whole number - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Place value of each digit](https://ai.page/c/place-value-of-each-digit/index.md): Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) - [Place Value Problem-Solving](https://ai.page/c/place-value-problem-solving/index.md): Solve number and practical problems involving place value with increasingly large positive numbers - [Decimal place value](https://ai.page/c/decimal-place-value-2/index.md): Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6) - [Reading Decimal Places](https://ai.page/c/reading-decimal-places/index.md): Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths) ## 8. Number · Integers and powers - [Tenths (age 8+)](https://ai.page/c/tenths-age-8/index.md): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10 - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems - [Prime numbers](https://ai.page/c/prime-numbers/index.md): Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19 - [Multiplying and dividing](https://ai.page/c/multiplying-and-dividing/index.md): Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000 - [Order of operations](https://ai.page/c/order-of-operations/index.md): Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances ## 9. Number · Counting and sequences - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers/index.md): Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) - [Linear number sequences](https://ai.page/c/linear-number-sequences/index.md): Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule - [What Multiplication Means](https://ai.page/c/what-multiplication-means/index.md): Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7) - [Negative Numbers](https://ai.page/c/negative-numbers/index.md): Count backwards through zero to include negative numbers ## Health: 0 of 100 Of its 43 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Experimental probability has no explanation yet - Likelihood Language has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Comparing measurements has no explanation yet - Transformations on a grid has no explanation yet - Transformations on a Grid has no explanation yet - First Quadrant Coordinates has no explanation yet - Angle Sum Rules has no explanation yet - Estimating Angles has no explanation yet - Translating and reflecting shapes has no explanation yet - Nets of 3-D Shapes has no explanation yet - Understanding angles has no explanation yet - Measuring Perimeters has no explanation yet - Perimeters of polygons has no explanation yet - Perimeter of Compound Shapes has no explanation yet - Classifying shapes by properties has no explanation yet - Converting measurement units has no explanation yet - Numbers on a number line has no explanation yet - Telling time to the minute (age 9+) has no explanation yet - 12-hour and 24-hour time has no explanation yet - Decimal & Percent Notation has no explanation yet - Percentages as Fractions has no explanation yet - Understanding Percentages has no explanation yet - Fraction Addition Concepts has no explanation yet - Fraction Notation has no explanation yet - Mixed numbers and improper fractions has no explanation yet - Multiplying fractions (age 11+) has no explanation yet - Decimal place value has no explanation yet - Decimal place value has no explanation yet - Place value of each digit has no explanation yet - Place Value Problem-Solving has no explanation yet - Decimal place value has no explanation yet - Reading Decimal Places has no explanation yet - Tenths (age 8+) has no explanation yet - Factors, multiples, and primes has no explanation yet - Prime numbers has no explanation yet - Multiplying and dividing has no explanation yet - Order of operations has no explanation yet - Positive and Negative Numbers has no explanation yet - Square and cube numbers has no explanation yet - Linear number sequences has no explanation yet - What Multiplication Means has no explanation yet - Negative Numbers has no explanation yet Credit: The structure of Cambridge Primary, Lower Secondary and IGCSE: Mathematics (https://www.cambridgeinternational.org/programmes-and-qualifications/cambridge-primary-and-lower-secondary/); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.