# Stage 3: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 50 concepts ready. In the app: https://ai.page/roadmap/cambridge-stage-3 Part of: [Cambridge: Mathematics](https://ai.page/roadmap/cambridge.md) Goal: Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 3 ## 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 - [Simple Chance Experiments](https://ai.page/c/simple-chance-experiments/index.md): Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes ## 2. Statistics and Probability · Statistics - [Pictograms and tally charts](https://ai.page/c/pictograms-and-tally-charts/index.md): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables - [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 - [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 ## 4. Geometry and Measure · Geometrical reasoning, shapes and measurements - [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units - [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen - [Understanding angles](https://ai.page/c/understanding-angles/index.md): Recognise angles as a property of shape or a description of a turn - [2-D shapes](https://ai.page/c/2-d-shapes/index.md): Recognise and name common 2-D shapes (circles, triangles, rectangles including squares) - [2-D shapes (age 6+)](https://ai.page/c/2-d-shapes-age-6/index.md): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line - [Sorting 2-D and 3-D shapes](https://ai.page/c/sorting-2-d-and-3-d-shapes/index.md): Compare and sort common 2-D and 3-D shapes and everyday objects by their properties - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes ## 5. Geometry and Measure · Time - [Sequence intervals of time](https://ai.page/c/sequence-intervals-of-time/index.md): Compare and sequence intervals of 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 - [Comparing Time Durations](https://ai.page/c/comparing-time-durations/index.md): Compare durations of events and calculate the time taken by particular events or tasks ## 6. Number · Fractions, decimals, percentages, ratio and proportion - [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 of amounts](https://ai.page/c/fractions-of-amounts/index.md): Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity - [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 - [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 - [Simple Fraction Sums](https://ai.page/c/simple-fraction-sums/index.md): Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7) - [Adding Fractions (Same Denominator)](https://ai.page/c/adding-fractions-same-denominator/index.md): Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8) - [Understanding fractions](https://ai.page/c/understanding-fractions-maths/index.md): Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2 - [Fraction-Decimal Equivalents](https://ai.page/c/fraction-decimal-equivalents/index.md): Recognise and write decimal equivalents of 1/4, 1/2, and 3/4 - [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 - [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 - [Percentages (age 9+)](https://ai.page/c/percentages-age-9/index.md): 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) ## 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 - [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 - [Place value understanding and number facts](https://ai.page/c/place-value-understanding-and-number-facts/index.md): Use place value understanding and number facts to solve problems ## 8. Number · Integers and powers - [Counting in 2s](https://ai.page/c/counting-in-2s/index.md): Count in multiples of 2, 5, and 10 (skip counting) - [Number Words to 100](https://ai.page/c/number-words-to-100/index.md): Read and write numbers to at least 100 in words - [Times tables](https://ai.page/c/times-tables/index.md): Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables - [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) - [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 - [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 ## 9. Number · Money - [Money Addition & Subtraction](https://ai.page/c/money-addition-and-subtraction/index.md): Solve simple money problems involving addition and subtraction, including giving change - [Giving Change](https://ai.page/c/giving-change/index.md): Add and subtract amounts of money to give change, using both £ and p in practical contexts ## 10. Number · Counting and sequences - [Patterns & Sequences](https://ai.page/c/patterns-and-sequences/index.md): Order and arrange combinations of mathematical objects in patterns and sequences - [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 - [Odd and even numbers](https://ai.page/c/odd-and-even-numbers/index.md): Recognise odd and even numbers - [Counting forwards and backwards](https://ai.page/c/counting-forwards-and-backwards/index.md): Count forwards and backwards in steps of 3 from 0 - [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 - [Counting objects to 20](https://ai.page/c/counting-objects-to-20/index.md): Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered) ## Health: 0 of 100 Of its 50 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 - Simple Chance Experiments has no explanation yet - Pictograms and tally charts 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 - Describing Movements has no explanation yet - Calculating with measurements has no explanation yet - Measuring with different units has no explanation yet - Understanding angles has no explanation yet - 2-D shapes has no explanation yet - 2-D shapes (age 6+) has no explanation yet - Sorting 2-D and 3-D shapes has no explanation yet - Measuring Perimeters has no explanation yet - Sequence intervals of time 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 - Comparing Time Durations has no explanation yet - Fraction Notation has no explanation yet - Fractions of amounts has no explanation yet - Fractions on a number line has no explanation yet - Comparing fractions has no explanation yet - Decimal & Percent Notation has no explanation yet - Simple Fraction Sums has no explanation yet - Adding Fractions (Same Denominator) has no explanation yet - Understanding fractions has no explanation yet - Fraction-Decimal Equivalents has no explanation yet - Fractions of a whole has no explanation yet - Unit fractions has no explanation yet - Percentages (age 9+) 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 - Place Value Problem-Solving has no explanation yet - Place value understanding and number facts has no explanation yet - Counting in 2s has no explanation yet - Number Words to 100 has no explanation yet - Times tables has no explanation yet - What Multiplication Means has no explanation yet - Properties of Operations has no explanation yet - Adding numbers has no explanation yet - Reading and writing numbers to 1000 has no explanation yet - Money Addition & Subtraction has no explanation yet - Giving Change has no explanation yet - Patterns & Sequences has no explanation yet - Linear number sequences has no explanation yet - Odd and even numbers has no explanation yet - Counting forwards and backwards has no explanation yet - Tenths (age 8+) has no explanation yet - Counting objects to 20 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.