# Stage 4: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 44 concepts ready. In the app: https://ai.page/roadmap/cambridge-stage-4 Part of: [Cambridge: Mathematics](https://ai.page/roadmap/cambridge.md) Goal: Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 4 ## 1. Statistics and Probability · 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 - [Sorting Data into Categories](https://ai.page/c/sorting-data-into-categories/index.md): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity - [Sorting into categories (age 6+)](https://ai.page/c/sorting-into-categories-age-6/index.md): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another ## 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 - [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 - [Describing Movements](https://ai.page/c/describing-movements/index.md): Describe movements between positions as translations of a given unit to the left/right and up/down - [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 ## 4. Geometry and Measure · Geometrical reasoning, shapes and measurements - [Understanding angles](https://ai.page/c/understanding-angles/index.md): Recognise angles as a property of shape or a description of a turn - [Types of angles](https://ai.page/c/types-of-angles/index.md): Identify acute and obtuse angles; compare and order angles up to two right angles by size - [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 - [2-D shapes (age 8+)](https://ai.page/c/2-d-shapes-age-8/index.md): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry - [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 - [Edges, vertices, and faces](https://ai.page/c/edges-vertices-and-faces/index.md): Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes ## 5. Geometry and Measure · Time - [Telling time to the minute (age 7+)](https://ai.page/c/telling-time-to-the-minute-age-7/index.md): Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation - [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 - [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) ## 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 - [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 - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line/index.md): Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line - [Comparing fractions](https://ai.page/c/comparing-fractions/index.md): Compare and order unit fractions, and fractions with the same denominator - [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 - [Adding fractions (different denominators)](https://ai.page/c/adding-fractions-different-denominators/index.md): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator - [Unit fractions](https://ai.page/c/unit-fractions/index.md): Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators - [Fractions of a whole](https://ai.page/c/fractions-of-a-whole/index.md): 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/b - [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% ## 7. Number · Place value, ordering and rounding - [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) - [Rounding to 10, 100, 1000](https://ai.page/c/rounding-to-10-100-1000/index.md): Round any number to the nearest 10, 100, or 1000 - [Ordering Numbers to 1000](https://ai.page/c/ordering-numbers-to-1000/index.md): Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding - [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000 - [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-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [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 ## 8. Number · Integers and powers - [All times tables to 12×12](https://ai.page/c/all-times-tables-to-12-12/index.md): Recall multiplication and division facts for multiplication tables up to 12 × 12 - [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 - [Reading and writing numbers to 1000](https://ai.page/c/reading-and-writing-numbers-to-1000/index.md): Read and write numbers to 1000 in numerals, number names, and expanded form - [Properties of Operations](https://ai.page/c/properties-of-operations/index.md): Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide - [Adding numbers](https://ai.page/c/adding-numbers/index.md): Add up to four two-digit numbers using strategies based on place value and properties of operations ## 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 - [Patterns & Sequences](https://ai.page/c/patterns-and-sequences/index.md): Order and arrange combinations of mathematical objects in patterns and sequences - [Reasoning with Equivalences](https://ai.page/c/reasoning-with-equivalences/index.md): Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms - [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 ## Health: 0 of 100 Of its 44 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): - Likelihood Language has no explanation yet - Sorting Data into Categories has no explanation yet - Sorting into categories (age 6+) has no explanation yet - Transformations on a grid has no explanation yet - First Quadrant Coordinates has no explanation yet - Describing Movements has no explanation yet - Transformations on a Grid has no explanation yet - Understanding angles has no explanation yet - Types of angles has no explanation yet - Estimating Angles has no explanation yet - 2-D shapes (age 8+) has no explanation yet - Nets of 3-D Shapes has no explanation yet - Edges, vertices, and faces has no explanation yet - Measuring Perimeters has no explanation yet - Telling time to the minute (age 7+) has no explanation yet - 12-hour and 24-hour time has no explanation yet - Converting measurement units has no explanation yet - Decimal & Percent Notation has no explanation yet - Fraction Notation has no explanation yet - Fractions on a number line has no explanation yet - Comparing fractions has no explanation yet - Understanding Percentages has no explanation yet - Fraction Addition Concepts has no explanation yet - Adding fractions (different denominators) has no explanation yet - Unit fractions has no explanation yet - Fractions of a whole has no explanation yet - Percentages as Fractions has no explanation yet - Place value of each digit has no explanation yet - Rounding to 10, 100, 1000 has no explanation yet - Ordering Numbers to 1000 has no explanation yet - Comparing Large Numbers has no explanation yet - Place Value Problem-Solving has no explanation yet - Decimal place value has no explanation yet - Multiplying and dividing has no explanation yet - All times tables to 12×12 has no explanation yet - Factors, multiples, and primes has no explanation yet - Reading and writing numbers to 1000 has no explanation yet - Properties of Operations has no explanation yet - Adding numbers has no explanation yet - Square and cube numbers has no explanation yet - Linear number sequences has no explanation yet - Patterns & Sequences has no explanation yet - Reasoning with Equivalences has no explanation yet - Tenths (age 8+) 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.