Datasets:

Osam-2025
/

uk-maths-curriculum-knowledge-graph

id int64 1 818	name stringlengths 4 90	canonical_name stringlengths 4 90	stage stringclasses 4 values	subject stringclasses 1 value	exam_boards stringclasses 4 values	spec_ref stringlengths 1 6 ⌀	difficulty int64 2 8	tier stringclasses 2 values
1	Number	Number	KS4	maths	AQA	3.1	6	both
2	Structure and calculation	Structure and calculation	KS4	maths	AQA	3.1.1	6	both
3	Order positive and negative integers, decimals and fractions	Order positive and negative integers, decimals and fractions	KS4	maths	AQA,Edexcel	N1	6	both
4	Apply the four operations, including formal written methods, to integers	Apply the four operations, including formal written methods, to integers	KS4	maths	AQA,Edexcel	N2	6	both
5	Recognise and use relationships between operations, including inverse operations	Recognise and use relationships between operations, including inverse operations	KS4	maths	AQA,Edexcel	N3	6	both
6	Use the concepts and vocabulary of prime numbers, factors (divisors), multiples	Use the concepts and vocabulary of prime numbers, factors (divisors), multiples	KS4	maths	AQA,Edexcel	N4	6	both
7	Apply systematic listing strategies including use of the product rule for counting	Apply systematic listing strategies including use of the product rule for counting	KS4	maths	AQA,Edexcel	N5	6	both
8	Use positive integer powers and associated real roots (square	Use positive integer powers and associated real roots (square	KS4	maths	AQA,Edexcel	N6	6	both
9	Calculate with roots, and with integer indices calculate with fractional indices	Calculate with roots, and with integer indices calculate with fractional indices	KS4	maths	AQA,Edexcel	N7	6	both
10	Calculate exactly with fractions calculate exactly with multiples	Calculate exactly with fractions calculate exactly with multiples	KS4	maths	AQA,Edexcel	N8	6	both
11	Calculate with and interpret standard form	Calculate with and interpret standard form	KS4	maths	AQA,Edexcel	N9	6	both
12	Fractions, decimals and percentages	Fractions, decimals and percentages	KS4	maths	AQA	3.1.2	6	both
13	Work interchangeably with terminating decimals and their corresponding fractions (such as	Work interchangeably with terminating decimals and their corresponding fractions (such as	KS4	maths	AQA,Edexcel	N10	6	both
14	Identify and work with fractions in ratio problems	Identify and work with fractions in ratio problems	KS4	maths	AQA,Edexcel	N11	6	both
15	Interpret fractions and percentages as operators	Interpret fractions and percentages as operators	KS4	maths	AQA,Edexcel	N12	6	both
16	Use standard units of mass, length, time, money and other measures	Use standard units of mass, length, time, money and other measures	KS4	maths	AQA,Edexcel	N13	6	both
17	Estimate answers	Estimate answers	KS4	maths	AQA,Edexcel	N14	6	both
18	Round numbers and measures to an appropriate degree of accuracy	Round numbers and measures to an appropriate degree of accuracy	KS4	maths	AQA,Edexcel	N15	6	both
19	Apply and interpret limits of accuracy including upper and lower bounds	Apply and interpret limits of accuracy including upper and lower bounds	KS4	maths	AQA,Edexcel	N16	6	both
20	Algebra	Algebra	KS4	maths	AQA	3.2	6	both
21	Notation, vocabulary and manipulation	Notation, vocabulary and manipulation	KS4	maths	AQA	3.2.1	6	both
22	Use and interpret algebraic notation	Use and interpret algebraic notation	KS4	maths	AQA,Edexcel	A1	6	both
23	Substitute numerical values into formulae and expressions, including scientific formulae	Substitute numerical values into formulae and expressions, including scientific formulae	KS4	maths	AQA,Edexcel	A2	6	both
24	Understand and use the concepts and vocabulary of expressions, equations	Understand and use the concepts and vocabulary of expressions, equations	KS4	maths	AQA,Edexcel	A3	6	both
25	Simplify and manipulate algebraic expressions	Simplify and manipulate algebraic expressions	KS4	maths	AQA,Edexcel	A4	6	both
26	Understand and use standard mathematical formulae	Understand and use standard mathematical formulae	KS4	maths	AQA,Edexcel	A5	6	both
27	Know the difference between an equation and an identity	Know the difference between an equation and an identity	KS4	maths	AQA,Edexcel	A6	6	both
28	Where appropriate, interpret simple expressions as functions with inputs and outputs	Where appropriate, interpret simple expressions as functions with inputs and outputs	KS4	maths	AQA,Edexcel	A7	6	both
29	Graphs	Graphs	KS4	maths	AQA	3.2.2	6	both
30	Work with coordinates in all four quadrants	Work with coordinates in all four quadrants	KS4	maths	AQA,Edexcel	A8	6	both
31	Plot graphs of equations that correspond to straight-line graphs in the coordinate plane	Plot graphs of equations that correspond to straight-line graphs in the coordinate plane	KS4	maths	AQA,Edexcel	A9	6	both
32	Identify and interpret gradients and intercepts of linear functions graphically	Identify and interpret gradients and intercepts of linear functions graphically	KS4	maths	AQA,Edexcel	A10	6	both
33	Identify and interpret roots, intercepts and turning points of quadratic functions	Identify and interpret roots, intercepts and turning points of quadratic functions	KS4	maths	AQA,Edexcel	A11	6	both
34	Recognise, sketch and interpret graphs of linear functions and quadratic functions	Recognise, sketch and interpret graphs of linear functions and quadratic functions	KS4	maths	AQA,Edexcel	A12	6	both
35	Sketch translations and reflections of a given function	Sketch translations and reflections of a given function	KS4	maths	AQA,Edexcel	A13	7	higher
36	Plot and interpret graphs, and graphs of non-standard functions in real contexts	Plot and interpret graphs, and graphs of non-standard functions in real contexts	KS4	maths	AQA,Edexcel	A14	6	both
37	Calculate or estimate gradients of graphs and areas under graphs	Calculate or estimate gradients of graphs and areas under graphs	KS4	maths	AQA,Edexcel	A15	7	higher
38	Recognise and use the equation of a circle with centre at the origin	Recognise and use the equation of a circle with centre at the origin	KS4	maths	AQA,Edexcel	A16	7	higher
39	Solving equations and inequalities	Solving equations and inequalities	KS4	maths	AQA	3.2.3	6	both
40	Solve linear equations in one unknown algebraically	Solve linear equations in one unknown algebraically	KS4	maths	AQA,Edexcel	A17	6	both
41	Solve quadratic equations algebraically by factorising including those that require	Solve quadratic equations algebraically by factorising including those that require	KS4	maths	AQA,Edexcel	A18	6	both
42	Solve two simultaneous equations in two variables (linear/linear) algebraically	Solve two simultaneous equations in two variables (linear/linear) algebraically	KS4	maths	AQA,Edexcel	A19	6	both
43	Find approximate solutions to equations numerically using iteration	Find approximate solutions to equations numerically using iteration	KS4	maths	AQA,Edexcel	A20	7	higher
44	Translate simple situations or procedures into algebraic expressions or formulae	Translate simple situations or procedures into algebraic expressions or formulae	KS4	maths	AQA,Edexcel	A21	6	both
45	Solve linear inequalities in one variable solve linear inequalities in one or two	Solve linear inequalities in one variable solve linear inequalities in one or two	KS4	maths	AQA,Edexcel	A22	6	both
46	Sequences	Sequences	KS4	maths	AQA	3.2.4	6	both
47	Generate terms of a sequence from either a term-to-term or a position-to-term rule	Generate terms of a sequence from either a term-to-term or a position-to-term rule	KS4	maths	AQA,Edexcel	A23	6	both
48	Recognise and use sequences of triangular	Recognise and use sequences of triangular	KS4	maths	AQA,Edexcel	A24	6	both
49	Deduce expressions to calculate the nth term of linear sequences including quadratic	Deduce expressions to calculate the nth term of linear sequences including quadratic	KS4	maths	AQA,Edexcel	A25	6	both
50	Ratio, proportion and rates of change	Ratio, proportion and rates of change	KS4	maths	AQA	3.3	6	both
51	Change freely between related standard units	Change freely between related standard units	KS4	maths	AQA,Edexcel	R1	6	both
52	Use scale factors, scale diagrams and maps	Use scale factors, scale diagrams and maps	KS4	maths	AQA,Edexcel	R2	6	both
53	Express one quantity as a fraction of another	Express one quantity as a fraction of another	KS4	maths	AQA,Edexcel	R3	6	both
54	Use ratio notation, including reduction to simplest form	Use ratio notation, including reduction to simplest form	KS4	maths	AQA,Edexcel	R4	6	both
55	Divide a given quantity into two parts in a given part	Divide a given quantity into two parts in a given part	KS4	maths	AQA,Edexcel	R5	6	both
56	Express a multiplicative relationship between two quantities as a ratio or a fraction	Express a multiplicative relationship between two quantities as a ratio or a fraction	KS4	maths	AQA,Edexcel	R6	6	both
57	Understand and use proportion as equality of ratios	Understand and use proportion as equality of ratios	KS4	maths	AQA,Edexcel	R7	6	both
58	Relate ratios to fractions and to linear functions	Relate ratios to fractions and to linear functions	KS4	maths	AQA,Edexcel	R8	6	both
59	Define percentage as ‘number of parts per hundred’	Define percentage as ‘number of parts per hundred’	KS4	maths	AQA,Edexcel	R9	6	both
60	Solve problems involving direct and inverse proportion	Solve problems involving direct and inverse proportion	KS4	maths	AQA,Edexcel	R10	6	both
61	Use compound units such as speed, rates of pay	Use compound units such as speed, rates of pay	KS4	maths	AQA,Edexcel	R11	6	both
62	Compare lengths, areas and volumes using ratio notation	Compare lengths, areas and volumes using ratio notation	KS4	maths	AQA,Edexcel	R12	6	both
63	Understand that X is inversely proportional to Y is equivalent	Understand that X is inversely proportional to Y is equivalent	KS4	maths	AQA,Edexcel	R13	6	both
64	Interpret the gradient of a straight-line graph as a rate of change	Interpret the gradient of a straight-line graph as a rate of change	KS4	maths	AQA,Edexcel	R14	6	both
65	Interpret the gradient at a point on a curve as the instantaneous rate of change	Interpret the gradient at a point on a curve as the instantaneous rate of change	KS4	maths	AQA,Edexcel	R15	7	higher
66	Set up, solve and interpret the answers in growth and decay problems	Set up, solve and interpret the answers in growth and decay problems	KS4	maths	AQA,Edexcel	R16	6	both
67	Geometry and measures	Geometry and measures	KS4	maths	AQA	3.4	6	both
68	Properties and constructions	Properties and constructions	KS4	maths	AQA	3.4.1	6	both
69	Use conventional terms and notations	Use conventional terms and notations	KS4	maths	AQA,Edexcel	G1	6	both
70	Use the standard ruler and compass constructions (perpendicular bisector of a line	Use the standard ruler and compass constructions (perpendicular bisector of a line	KS4	maths	AQA,Edexcel	G2	6	both
71	Apply the properties of angles at a point	Apply the properties of angles at a point	KS4	maths	AQA,Edexcel	G3	6	both
72	Derive and apply the properties and definitions	Derive and apply the properties and definitions	KS4	maths	AQA,Edexcel	G4	6	both
73	Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)	Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)	KS4	maths	AQA,Edexcel	G5	6	both
74	Apply angle facts, triangle congruence	Apply angle facts, triangle congruence	KS4	maths	AQA,Edexcel	G6	6	both
75	Identify, describe and construct congruent and similar shapes	Identify, describe and construct congruent and similar shapes	KS4	maths	AQA,Edexcel	G7	6	both
76	Describe the changes and invariance achieved by combinations of rotations	Describe the changes and invariance achieved by combinations of rotations	KS4	maths	AQA,Edexcel	G8	7	higher
77	Identify and apply circle definitions and properties	Identify and apply circle definitions and properties	KS4	maths	AQA,Edexcel	G9	6	both
78	Apply and prove the standard circle theorems concerning angles, radii	Apply and prove the standard circle theorems concerning angles, radii	KS4	maths	AQA,Edexcel	G10	7	higher
79	Solve geometrical problems on coordinate axes	Solve geometrical problems on coordinate axes	KS4	maths	AQA,Edexcel	G11	6	both
80	Identify properties of the faces, surfaces, edges and vertices	Identify properties of the faces, surfaces, edges and vertices	KS4	maths	AQA,Edexcel	G12	6	both
81	Interpret plans and elevations of 3D shapes construct and interpret plans and elevations	Interpret plans and elevations of 3D shapes construct and interpret plans and elevations	KS4	maths	AQA,Edexcel	G13	6	both
82	Mensuration and calculation	Mensuration and calculation	KS4	maths	AQA	3.4.2	6	both
83	Use standard units of measure and related concepts (length, area, volume/capacity	Use standard units of measure and related concepts (length, area, volume/capacity	KS4	maths	AQA,Edexcel	G14	6	both
84	Measure line segments and angles in geometric figures	Measure line segments and angles in geometric figures	KS4	maths	AQA,Edexcel	G15	6	both
85	Know and apply formulae to calculate	Know and apply formulae to calculate	KS4	maths	AQA,Edexcel	G16	6	both
86	Know the formulae: circumference of a circle	Know the formulae: circumference of a circle	KS4	maths	AQA,Edexcel	G17	6	both
87	Calculate arc lengths, angles and areas of sectors of circles	Calculate arc lengths, angles and areas of sectors of circles	KS4	maths	AQA,Edexcel	G18	6	both
88	Apply the concepts of congruence and similarity	Apply the concepts of congruence and similarity	KS4	maths	AQA,Edexcel	G19	6	both
89	Know the formulae	Know the formulae	KS4	maths	AQA,Edexcel	G20	6	both
90	Know the exact values of sin and cos	Know the exact values of sin and cos	KS4	maths	AQA,Edexcel	G21	6	both
91	Know and apply the sine rule	Know and apply the sine rule	KS4	maths	AQA,Edexcel	G22	6	both
92	Know and apply	Know and apply	KS4	maths	AQA,Edexcel	G23	7	higher
93	Vectors	Vectors	KS4	maths	AQA	3.4.3	6	both
94	Describe translations as 2D vectors	Describe translations as 2D vectors	KS4	maths	AQA,Edexcel	G24	6	both
95	Apply addition and subtraction of vectors, multiplication of vectors by a scalar	Apply addition and subtraction of vectors, multiplication of vectors by a scalar	KS4	maths	AQA,Edexcel	G25	6	both
96	Probability	Probability	KS4	maths	AQA	3.5	6	both
97	Record, describe and analyse the frequency of outcomes of probability experiments using	Record, describe and analyse the frequency of outcomes of probability experiments using	KS4	maths	AQA,Edexcel	P1	6	both
98	Apply ideas of randomness, fairness and equally likely events to calculate expected	Apply ideas of randomness, fairness and equally likely events to calculate expected	KS4	maths	AQA,Edexcel	P2	6	both
99	Relate relative expected frequencies to theoretical probability	Relate relative expected frequencies to theoretical probability	KS4	maths	AQA,Edexcel	P3	6	both
100	Apply the property that the probabilities of an exhaustive set of outcomes sum to 1	Apply the property that the probabilities of an exhaustive set of outcomes sum to 1	KS4	maths	AQA,Edexcel	P4	6	both

End of preview. Expand in Data Studio

UK Maths Curriculum Knowledge Graph

Description

A structured knowledge graph of UK Mathematics curriculum concepts for GCSE, AS-Level and A-Level, covering the AQA, Edexcel and OCR specifications, plus the National Curriculum strands for KS2 and KS3. Stages run from KS2 to KS5.

786 curriculum concepts:
- KS2: 4
- KS3: 5
- KS4 (GCSE): 329
- KS5 (AS and A-Level): 448
1,179 edges:
- part_of: 824 (from the spec section numbering)
- related_to: 252 (an OCR GCSE topic and the DfE subject-content statement it cites)
- progresses_to: 31 (the same concept at the next key stage)
- prerequisite_of: 72 (LLM extracted)
Stages: KS2, KS3, KS4, KS5
Boards: AQA, Edexcel, OCR

Files

concepts.jsonl: all concepts
edges.jsonl: all relationships
concepts.csv: the concepts in CSV format
edges.csv: the edges in CSV format

Concept fields

Field	Meaning
`id`	Concept id, used by `from_id` / `to_id` in the edges
`name`	The concept name as it appears in that spec (a heading, or the first clause of a content statement)
`canonical_name`	Shared by matching concepts on different boards at the same stage
`stage`	`KS2`–`KS5`
`subject`	`maths`
`exam_boards`	Comma separated, e.g. `AQA,Edexcel`. Empty for the National Curriculum
`spec_ref`	The board's reference, e.g. `3.2.1`, `A22`, `1.02a`
`difficulty`	1–10, a heuristic from stage and tier (KS2 2, KS3 4, KS4 6, KS4 Higher only 7, KS5 8)
`tier`	`higher` for GCSE Higher-tier-only content, otherwise `both`

AQA and Edexcel GCSE both use the DfE subject-content codes (N1–N16, A1–A25 and so on) for the same statements, so each of these is one concept with exam_boards = "AQA,Edexcel".

Edge fields

Each edge is from_concept → to_concept, with an edge_type, a confidence from 0 to 1, and a source (spec_numbering or llm_extracted). A part_of edge points from the child to its parent. A prerequisite_of edge points from what must be learned first to what it supports. Names repeat across boards and stages ("Probability" is five concepts), so each end also carries its stage, boards, spec ref and id.

How It Was Built

Section headings and content statements were extracted from the official AQA, Edexcel and OCR specification PDFs, with one parser per board.
The part_of hierarchy comes from the spec section numbering.
progresses_to edges link concepts whose names match at consecutive key stages (difflib ratio ≥ 0.85).
prerequisite_of edges were extracted using an LLM on Groq (Qwen 3.8 27B, with GPT-OSS models as fallback), asked once per KS4/KS5 concept, and matched back to concepts by name.
Prerequisite edges were spot-checked by hand, and 15 pairs judged wrong were removed. Names garbled by PDF text extraction were repaired, and 3 that could not be repaired were dropped.
Validated against the spec PDFs on 28 October 2026: 20 sampled concepts and all 85 prerequisite edges were checked. This added the missing AQA GCSE 3.1.3 section, the Edexcel A-Level topic headings (P1–P10, S1–S5, M6–M9) and 12 missing Edexcel A-Level statements, and removed 13 wrong prerequisite edges. See validation_report.md in the source project.

Limitations

Names are cut from the spec text. Some are long or end mid-phrase, and mathematical notation is lost, e.g. "Integrate xn and related sums".
Prerequisite coverage is sparse. Only about 4% of the LLM's suggestions matched a concept closely enough to keep, and the kept edges were spot-checked, not fully reviewed.
KS2 and KS3 are strand level only. They are "Number", "Algebra" and so on.
Board versions are fixed. These are AQA 8300 and 7357, Edexcel 1MA1 and 9MA0, and OCR J560 and H240, at the versions listed in the source project.

Sources and Copyright

Concept names and specification references are derived from curriculum documents published by:

AQA (aqa.org.uk)
Pearson Edexcel (qualifications.pearson.com)
OCR (ocr.org.uk)
Department for Education (gov.uk/dfe) — Crown Copyright, Open Government Licence v3.0

The graph structure, prerequisite relationships and cross-stage progression edges are original work by QuantOsimo, published under Apache 2.0.

Concept names range from short topic titles (e.g. "Trigonometry", "Quadratic equations") to longer excerpts from specification statements. Short topic names are factual descriptions of mathematical topics. Longer specification excerpts remain the copyright of their respective owners and are included here solely to identify curriculum concepts — not to reproduce the specifications.

If you are an exam board and have concerns about any content in this dataset please contact: support@quantosimo.com