When do children learn each maths topic? Curricula compared
For each maths topic: the first grade in which it appears in the official curriculum of each country, with the children's typical age. Useful when a family moves abroad or a class mixes pupils from different school systems.
How to read the table
Each cell shows the first grade in which the topic appears in that country's curriculum, named the way schools in that country name it, and the typical age of children in that grade. The data come from Imaginesis' grade-by-grade mapping of official curriculum documents and cover the topics our worksheet generator supports. An empty cell means the topic is not in our generator for that country — not that the country does not teach it. When a curriculum assigns a topic to several years at once (a cycle or a key stage), the cell shows that whole range.
| Topic | Austria | France | Germany | Italy | Netherlands | Poland | Spain | Switzerland | United Kingdom | United States |
|---|---|---|---|---|---|---|---|---|---|---|
| Algebra | ||||||||||
| Algebraic expressions | Grade 5age 10–11 | Grade 7age 12–13 | Grade 7 – 8age 12–14 | Grade 7 – 8age 12–14 | Grade 7 – 9age 12–15 | Grade 4 – 6age 10–13 | Grade 5 – 6age 10–12 | Grade 7 – 9age 12–15 | Year 6age 10–11 | Grade 5age 10–11 |
| Calculus | Grade 11age 16–17 | Grade 11age 16–17 | Grade 11 – 12age 16–18 | Grade 13age 18–19 | Grade 10age 15–16 | Year 2 of secondary schoolage 16–17 | Grade 11age 16–17 | Grade 10 – 12age 15–18 | Year 11age 15–16 | — |
| Coordinate plane | Grade 4 – 7age 9–13 | Grade 7age 12–13 | Grade 5 – 6age 10–12 | Grade 5 – 8age 10–14 | Grade 6 – 9age 11–15 | Grade 5 – 6age 11–13 | Grade 6 – 9age 11–15 | Grade 4 – 9age 9–15 | Year 4 – 6age 8–11 | Grade 5 – 6age 10–12 |
| Exponential functions | Grade 10age 15–16 | Grade 11age 16–17 | Grade 11 – 12age 16–18 | Grade 11 – 12age 16–18 | Grade 9age 14–15 | Year 2 of secondary schoolage 16–17 | Grade 10age 15–16 | Grade 9age 14–15 | Year 10 – 11age 14–16 | Grade 9age 14–15 |
| Inequalities | Grade 9age 14–15 | Grade 10age 15–16 | — | Grade 9 – 10age 14–16 | Grade 9age 14–15 | Year 1 of secondary schoolage 15–16 | Grade 10age 15–16 | Grade 10 – 12age 15–18 | Year 10age 14–15 | Grade 9age 14–15 |
| Linear equations | Grade 5 – 6age 10–12 | Grade 4 – 7age 9–13 | Grade 7 – 8age 12–14 | Grade 6age 11–12 | Grade 4 – 9age 9–15 | Grade 4 – 6age 10–13 | Grade 4 – 6age 9–12 | Grade 7 – 9age 12–15 | Year 6age 10–11 | Grade 6age 11–12 |
| Linear functions | Grade 8age 13–14 | Grade 7 – 10age 12–16 | Grade 7 – 8age 12–14 | Grade 7 – 8age 12–14 | Grade 7 – 9age 12–15 | Grade 7 – 8age 13–15 | Grade 7 – 9age 12–15 | Grade 7 – 9age 12–15 | Year 5 – 6age 9–11 | Grade 8age 13–14 |
| Matrices | — | — | Grade 11 – 12age 16–18 | Grade 10age 15–16 | — | — | Grade 12age 17–18 | — | — | Grade 12age 17–18 |
| Polynomials and rational expressions | Grade 9age 14–15 | Grade 9age 14–15 | — | Grade 9 – 10age 14–16 | Grade 9age 14–15 | Year 1 of secondary schoolage 15–16 | Grade 9 – 10age 14–16 | Grade 9age 14–15 | Year 10age 14–15 | Grade 9age 14–15 |
| Properties and operations on functions | Grade 9age 14–15 | Grade 9age 14–15 | Grade 11 – 12age 16–18 | Grade 9 – 13age 14–19 | Grade 9age 14–15 | Year 1 of secondary school – Sec. 2age 15–17 | Grade 9 – 10age 14–16 | Grade 9age 14–15 | Year 9age 13–14 | Grade 9 – 11age 14–17 |
| Quadratic functions | Grade 9age 14–15 | Grade 10age 15–16 | Grade 11 – 12age 16–18 | Grade 8age 13–14 | Grade 9age 14–15 | Year 2 of secondary schoolage 16–17 | Grade 9 – 10age 14–16 | Grade 10 – 11age 15–17 | Year 9age 13–14 | Grade 9age 14–15 |
| Sequences and series | Grade 10age 15–16 | Grade 11age 16–17 | Grade 11 – 12age 16–18 | Grade 11 – 12age 16–18 | Grade 9age 14–15 | Year 3 of secondary schoolage 17–18 | Grade 10age 15–16 | Grade 9age 14–15 | Year 9age 13–14 | Grade 9age 14–15 |
| Arithmetic | ||||||||||
| Addition and subtraction | Grade 1age 6–7 | Grade 1 – 2age 6–8 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1age 7–8 | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Year 1 – 2age 5–7 | Kindergarten – 2age 5–8 |
| Common fractions | Grade 4age 9–10 | Grade 2 – 5age 7–11 | Grade 6age 11–12 | Grade 4 – 5age 9–11 | Grade 4 – 6age 9–12 | Grade 4 – 6age 10–13 | Grade 4age 9–10 | Grade 3 – 6age 8–12 | Year 3 – 4age 7–9 | Grade 4age 9–10 |
| Comparing numbers | Grade 1 – 2age 6–8 | Grade 1age 6–7 | Grade 3 – 4age 8–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Year 1 – 2age 5–7 | Kindergarten – 1age 5–7 |
| Complex numbers | Grade 11age 16–17 | — | — | Grade 11 – 12age 16–18 | — | — | Grade 11age 16–17 | — | — | Grade 11age 16–17 |
| Decimal fractions | Grade 5age 10–11 | Grade 4 – 6age 9–12 | Grade 6age 11–12 | Grade 4 – 5age 9–11 | Grade 4 – 6age 9–12 | Grade 4 – 6age 10–13 | Grade 5 – 6age 10–12 | Grade 3 – 6age 8–12 | Year 3 – 6age 7–11 | Grade 4age 9–10 |
| Divisibility | Grade 6age 11–12 | Grade 3 – 10age 8–16 | Grade 5 – 6age 10–12 | Grade 4 – 8age 9–14 | Grade 4 – 6age 9–12 | Grade 5 – 6age 11–13 | Grade 5 – 6age 10–12 | Grade 3 – 9age 8–15 | Year 4 – 5age 8–10 | Grade 4age 9–10 |
| Integers (negative numbers) | Grade 6age 11–12 | Grade 7age 12–13 | Grade 6age 11–12 | Grade 5age 10–11 | Grade 6 – 9age 11–15 | Grade 6age 12–13 | Grade 7 – 9age 12–15 | Grade 7 – 9age 12–15 | Year 4 – 6age 8–11 | Grade 6age 11–12 |
| Logarithms | Grade 10age 15–16 | Grade 12age 17–18 | Grade 11 – 12age 16–18 | Grade 11 – 12age 16–18 | Grade 10age 15–16 | Year 1 of secondary schoolage 15–16 | Grade 11age 16–17 | Grade 10 – 12age 15–18 | — | Grade 11 – 12age 16–18 |
| Mathematical reasoning | Grade 5age 10–11 | Grade 7age 12–13 | Grade 5 – 6age 10–12 | — | Grade 5 – 6age 10–12 | Grade 5 – 6age 11–13 | Grade 5 – 9age 10–15 | Grade 7 – 9age 12–15 | — | — |
| Multiplication and division | Grade 1 – 2age 6–8 | Grade 1age 6–7 | Grade 2 – 4age 7–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 2 – 3age 8–10 | Grade 1 – 4age 6–10 | Grade 1 – 6age 6–12 | Year 1 – 4age 5–9 | Grade 1 – 3age 6–9 |
| Number systems | Grade 1age 6–7 | Grade 1age 6–7 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Year 1age 5–6 | Kindergartenage 5–6 |
| Order of operations | Grade 1 – 2age 6–8 | Grade 1 – 5age 6–11 | Grade 3 – 4age 8–10 | Grade 6age 11–12 | Grade 1 – 6age 6–12 | Grade 3age 9–10 | Grade 1 – 4age 6–10 | Grade 1 – 6age 6–12 | Year 1 – 5age 5–10 | Kindergarten – 3age 5–9 |
| Powers and roots | Grade 7age 12–13 | Grade 7age 12–13 | Grade 9 – 10age 14–16 | Grade 7 – 8age 12–14 | Grade 7 – 9age 12–15 | Grade 4 – 6age 10–13 | Grade 5 – 6age 10–12 | Grade 7 – 9age 12–15 | Year 5age 9–10 | Grade 6age 11–12 |
| Ratios and proportions | Grade 4 – 6age 9–12 | Grade 4 – 7age 9–13 | Grade 7 – 8age 12–14 | Grade 5 – 8age 10–14 | Grade 5 – 9age 10–15 | Grade 5 – 6age 11–13 | Grade 5 – 9age 10–15 | Grade 4 – 6age 9–12 | Year 5age 9–10 | Grade 6age 11–12 |
| Word problems | Grade 1 – 2age 6–8 | Grade 1 – 3age 6–9 | Grade 1 – 4age 6–10 | Grade 4 – 5age 9–11 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 4age 6–10 | Grade 1 – 6age 6–12 | Year 1 – 3age 5–8 | Kindergarten – 3age 5–9 |
| Written algorithms | Grade 3age 8–9 | Grade 1 – 3age 6–9 | Grade 3 – 4age 8–10 | Grade 3age 8–9 | Grade 3 – 6age 8–12 | Grade 4 – 6age 10–13 | Grade 3 – 4age 8–10 | Grade 3 – 6age 8–12 | Year 3age 7–8 | Grade 3age 8–9 |
| Data and chance | ||||||||||
| Chance and likelihood | Grade 3 – 4age 8–10 | Grade 4age 9–10 | Grade 2 – 4age 7–10 | Grade 4 – 5age 9–11 | Grade 7 – 9age 12–15 | Grade 7 – 8age 13–15 | Grade 3 – 4age 8–10 | Grade 3 – 5age 8–11 | Year 7age 11–12 | Grade 7age 12–13 |
| Working with data | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 4age 6–10 | Grade 2 – 5age 7–11 | Grade 1 – 6age 6–12 | Grade 4 – 6age 10–13 | Grade 1 – 4age 6–10 | Grade 1 – 2age 6–8 | Year 2 – 3age 6–8 | Kindergartenage 5–6 |
| Geometry | ||||||||||
| Angles | Grade 3 – 5age 8–11 | Grade 3 – 6age 8–12 | Grade 5 – 6age 10–12 | Grade 4 – 5age 9–11 | Grade 4 – 6age 9–12 | Grade 4 – 6age 10–13 | Grade 4age 9–10 | Grade 3 – 6age 8–12 | Year 3age 7–8 | Grade 4age 9–10 |
| Area | Grade 4age 9–10 | Grade 4 – 5age 9–11 | Grade 3 – 4age 8–10 | Grade 4 – 5age 9–11 | Grade 3 – 6age 8–12 | Grade 4 – 6age 10–13 | Grade 3 – 6age 8–12 | Grade 3 – 6age 8–12 | Year 4age 8–9 | Grade 2 – 3age 7–9 |
| Circles: chords, tangents, angles, sectors | Grade 8age 13–14 | Grade 11age 16–17 | — | Grade 10 – 12age 15–18 | — | Year 2 of secondary schoolage 16–17 | — | Grade 9age 14–15 | Year 10age 14–15 | Grade 10age 15–16 |
| Graphs | — | — | — | — | — | — | Grade 11age 16–17 | — | — | — |
| Intercept theorem and similarity | Grade 7age 12–13 | Grade 8 – 9age 13–15 | — | Grade 8age 13–14 | Grade 8 – 9age 13–15 | Year 1 of secondary schoolage 15–16 | Grade 8 – 9age 13–15 | Grade 7 – 9age 12–15 | Year 9age 13–14 | Grade 10age 15–16 |
| Measuring length | Grade 2age 7–8 | Grade 1 – 3age 6–9 | Grade 3 – 4age 8–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 3age 9–10 | Grade 1 – 4age 6–10 | Grade 1 – 2age 6–8 | Year 1 – 3age 5–8 | Grade 1 – 2age 6–8 |
| Perimeter | Grade 3age 8–9 | Grade 3age 8–9 | Grade 3 – 4age 8–10 | Grade 4 – 5age 9–11 | Grade 3 – 6age 8–12 | Grade 3age 9–10 | Grade 3 – 4age 8–10 | Grade 3 – 6age 8–12 | Year 3age 7–8 | Grade 3age 8–9 |
| Plane figures | Grade 1age 6–7 | Grade 1 – 3age 6–9 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 4age 6–10 | Grade 1 – 2age 6–8 | Year 1 – 2age 5–7 | Kindergartenage 5–6 |
| Right triangles | Grade 8age 13–14 | Grade 8 – 9age 13–15 | Grade 9 – 10age 14–16 | Grade 7 – 8age 12–14 | Grade 7 – 9age 12–15 | Grade 7 – 8age 13–15 | Grade 7 – 9age 12–15 | Grade 7 – 9age 12–15 | Year 7 – 9age 11–14 | Grade 8age 13–14 |
| Solids | Grade 1 – 3age 6–9 | Grade 1 – 3age 6–9 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 4 – 6age 10–13 | Grade 3 – 4age 8–10 | Grade 1 – 6age 6–12 | Year 1 – 2age 5–7 | Kindergartenage 5–6 |
| Symmetry on a grid | Grade 1 – 2age 6–8 | — | Grade 2 – 4age 7–10 | Grade 4 – 5age 9–11 | Grade 2 – 6age 7–12 | Grade 3age 9–10 | Grade 3 – 4age 8–10 | Grade 1 – 2age 6–8 | — | — |
| Trigonometry | Grade 9age 14–15 | Grade 9age 14–15 | Grade 11 – 12age 16–18 | Grade 10age 15–16 | Grade 9age 14–15 | Year 2 of secondary schoolage 16–17 | Grade 10age 15–16 | Grade 10 – 12age 15–18 | Year 9age 13–14 | Grade 10age 15–16 |
| Vectors | Grade 9age 14–15 | Grade 10age 15–16 | Grade 11 – 12age 16–18 | Grade 10age 15–16 | Grade 10age 15–16 | Year 3 of secondary schoolage 17–18 | Grade 11age 16–17 | Grade 10age 15–16 | Year 11age 15–16 | Grade 12age 17–18 |
| Applying mathematics in everyday life | ||||||||||
| Estimation and strategy games | Grade 1 – 3age 6–9 | Grade 1 – 4age 6–10 | Grade 2 – 4age 7–10 | Grade 2 – 3age 7–9 | Grade 2 – 6age 7–12 | Grade 1 – 3age 7–10 | Grade 2 – 4age 7–10 | Grade 1 – 6age 6–12 | Year 3age 7–8 | Grade 2age 7–8 |
| Mass, capacity and temperature | Grade 2 – 3age 7–9 | Grade 2 – 3age 7–9 | Grade 3 – 4age 8–10 | Grade 3age 8–9 | Grade 2 – 6age 7–12 | Grade 3age 9–10 | Grade 2 – 4age 7–10 | Grade 1 – 6age 6–12 | Year 1 – 3age 5–8 | Grade 3age 8–9 |
| Money | Grade 1 – 2age 6–8 | Grade 1 – 3age 6–9 | Grade 2 – 4age 7–10 | Grade 2 – 3age 7–9 | Grade 2 – 6age 7–12 | Grade 1 – 3age 7–10 | Grade 2 – 4age 7–10 | Grade 1 – 6age 6–12 | Year 1 – 3age 5–8 | Grade 2age 7–8 |
| Patterns and rhythms | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Grade 1 – 4age 6–10 | Grade 4 – 5age 9–11 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 4age 6–10 | Grade 1 – 2age 6–8 | Year 2age 6–7 | Grade 3age 8–9 |
| Time and the clock | Grade 1 – 3age 6–9 | Grade 1 – 5age 6–11 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 4age 6–10 | Grade 1 – 6age 6–12 | Year 1 – 3age 5–8 | Grade 1 – 3age 6–9 |
| Spatial relations and size attributes | ||||||||||
| Classifying and comparing sizes | Grade 1age 6–7 | Grade 1 – 2age 6–8 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Year 1 – 2age 5–7 | Kindergartenage 5–6 |
| Position and direction | Grade 1age 6–7 | Grade 1 – 2age 6–8 | Grade 1 – 4age 6–10 | Grade 1age 6–7 | Grade 1 – 6age 6–12 | Grade 1 – 3age 7–10 | Grade 1 – 2age 6–8 | Grade 1 – 2age 6–8 | Year 3age 7–8 | Kindergartenage 5–6 |
Source: Imaginesis analysis of official national curricula. Updated automatically when a curriculum mapping changes.
Open data (CC BY 4.0): doi:10.5281/zenodo.23217841 · GitHub