# Stage 2: 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-2 Part of: [Cambridge: Mathematics](https://ai.page/roadmap/cambridge.md) Goal: Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 2 ## 1. Thinking and Working Mathematically - [Generalising Patterns](https://ai.page/c/generalising-patterns/index.md): Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts ## 2. 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 ## 3. Statistics and Probability · Statistics - [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 - [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 ## 4. Geometry and Measure · Position and transformation - [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 - [Turns & Directions](https://ai.page/c/turns-and-directions/index.md): Describe movement and direction, including whole, half, quarter, and three-quarter turns - [Position, direction, and movement](https://ai.page/c/position-direction-and-movement/index.md): 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) ## 5. 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 Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes - [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 - [Capacity and volume](https://ai.page/c/capacity-and-volume/index.md): Measure and begin to record capacity and volume using non-standard and standard units - [Measurable Attributes of Objects](https://ai.page/c/measurable-attributes-of-objects/index.md): Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less) - [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 & Plotting Lengths](https://ai.page/c/measuring-and-plotting-lengths/index.md): Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot - [Comparing lengths by measuring](https://ai.page/c/comparing-lengths-by-measuring/index.md): Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit - [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 ## 6. Geometry and Measure · Time - [Telling time to the minute](https://ai.page/c/telling-time-to-the-minute/index.md): Measure and begin to record time in hours, minutes, and seconds - [Telling Time: Hours and Half Hours](https://ai.page/c/telling-time-hours-and-half-hours/index.md): Tell the time to the hour and half past the hour, and draw clock hands to show these times - [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 - [Days, Weeks, Months & Years](https://ai.page/c/days-weeks-months-and-years/index.md): Recognise and use language relating to dates, including days of the week, weeks, months, and years - [Number of minutes in an hour](https://ai.page/c/number-of-minutes-in-an-hour/index.md): Know the number of minutes in an hour and the number of hours in a day ## 7. Number · Fractions, decimals, percentages, ratio and proportion - [What Is a Half?](https://ai.page/c/what-is-a-half/index.md): Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity - [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 - [Halves & Quarters of Shapes](https://ai.page/c/halves-and-quarters-of-shapes/index.md): Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters ## 8. Number · Place value, ordering and rounding - [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 - [Comparing and ordering numbers](https://ai.page/c/comparing-and-ordering-numbers/index.md): Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding - [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 - [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 · Money - [Adding money and giving change](https://ai.page/c/adding-money-and-giving-change/index.md): Find different combinations of coins that equal the same amount of money - [Coin Values](https://ai.page/c/coin-values/index.md): Recognise and know the value of different coins and notes ## 10. 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) - [Multiplication as repeated addition](https://ai.page/c/multiplication-as-repeated-addition/index.md): Understand multiplication as repeated addition and grouping equal sets - [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 - [Division as equal sharing](https://ai.page/c/division-as-equal-sharing/index.md): Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made) - [Inverse: addition undoes subtraction](https://ai.page/c/inverse-addition-undoes-subtraction/index.md): Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems - [Reading and writing numbers to 100](https://ai.page/c/reading-and-writing-numbers-to-100/index.md): Read and write numerals from 0 to 100 ## 11. Number · Counting and Sequence - [Odd and even numbers](https://ai.page/c/odd-and-even-numbers/index.md): Recognise odd and even numbers - [Rote counting to 100](https://ai.page/c/rote-counting-to-100/index.md): Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones - [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 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): - Generalising Patterns has no explanation yet - Likelihood Language has no explanation yet - Simple Chance Experiments has no explanation yet - Sorting into categories (age 6+) has no explanation yet - Pictograms and tally charts has no explanation yet - Transformations on a grid has no explanation yet - Turns & Directions has no explanation yet - Position, direction, and movement has no explanation yet - Calculating with measurements has no explanation yet - Measuring Perimeters 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 - Capacity and volume has no explanation yet - Measurable Attributes of Objects has no explanation yet - Edges, vertices, and faces has no explanation yet - Measuring & Plotting Lengths has no explanation yet - Comparing lengths by measuring has no explanation yet - Measuring with different units has no explanation yet - Telling time to the minute has no explanation yet - Telling Time: Hours and Half Hours has no explanation yet - Telling time to the minute (age 7+) has no explanation yet - Days, Weeks, Months & Years has no explanation yet - Number of minutes in an hour has no explanation yet - What Is a Half? comes before Division as equal sharing, which it needs - What Is a Half? 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 - Halves & Quarters of Shapes has no explanation yet - Rounding to 10, 100, 1000 has no explanation yet - Comparing and ordering numbers has no explanation yet - Ordering Numbers to 1000 has no explanation yet - Adding numbers has no explanation yet - Adding money and giving change has no explanation yet - Coin Values has no explanation yet - Counting in 2s comes before Rote counting to 100, which it needs - Counting in 2s has no explanation yet - Multiplication as repeated addition has no explanation yet - Times tables has no explanation yet - Division as equal sharing has no explanation yet - Inverse: addition undoes subtraction has no explanation yet - Reading and writing numbers to 100 comes before Rote counting to 100, which it needs - Reading and writing numbers to 100 has no explanation yet - Odd and even numbers has no explanation yet - Rote counting to 100 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.