Own-pace blocks · Maths
Maths, Year 4 to Year 13.
- From times tables to A level and the IB Diploma, in one stack.
- England's national curriculum is the spine.
- We check every year against US Common Core and the IB.
- Questions are written for Years 4 to 9 today.
Years 4–13England · United States · International BaccalaureateMapped
At a glance
- Years 4–13covered
- 180sprints
- 66objectives benchmarked
- 4published sources checked
Maths
How it builds.
- NumberPlace value, times tables, factors, powers and proof.
- Fractions, decimals & %Fractions, decimals and percentages, and how they connect.
- Algebra & functionsPatterns, formulae, equations, functions and graphs.
- Ratio & proportionRatio, rates and proportion.
- Geometry & measuresShapes, angles, measures, trigonometry and vectors.
- Statistics & probabilityCharts, averages, chance and testing ideas with data.
- CalculusRates of change and areas under curves.
- Mechanics (A level)Forces and motion, for A level.
- Exam practicePractice in the style of the exams.
- PlacementA short check at the start of a year to find where to begin.
- ReviewSpaced reviews of what has already been learnt.
- Year reviewA check at the end of each year.
Maths
Year by year.
Year 4Age 8–9 · US Grade 3 · IB PYPMultiplication tables check (June)
By the end of Year 4, they can:
- Read, write and round numbers up to 10,000
- Recall times tables and division facts up to 12 × 12
- Spot equivalent fractions and write tenths and hundredths as decimals
- Find perimeter and area, and name angles, triangles and quadrilaterals
- Read and draw bar charts, pictograms and time graphs
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberPlace value to 10,000; tables to 12 × 12 | Same year | Same year | Same year |
| Fractions, decimals & %Equivalent fractions; decimals to hundredths | Same year | A year either side | Same year |
| Algebra & functionsPatterns and missing numbers | Same year | Same year | Same year |
| Ratio & proportionScaling: n times as many | Same year | Same year | Same year |
| Geometry & measuresPerimeter, area by counting, angle types | Same year | Same year | Same year |
| Statistics & probabilityBar charts and time graphs | Same year | Same year | Same year |
Where it differs this year
- US expects multiplication fluency to 10 × 10 by end of Grade 3; England checks 12 × 12 in Year 4.
- US moves decimals to hundredths into Grade 4, a year later.
In the PDF: the full objectives and the sprint plan. Get the map
Year 5Age 9–10 · US Grade 4 · IB PYP
By the end of Year 5, they can:
- Order numbers to a million; find factors, primes, squares and cubes
- Multiply by 2-digit numbers and divide using short division
- Add and subtract fractions, and meet percent as "per hundred"
- Measure angles, and find area and volume by counting
- Read tables, timetables and line graphs
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberNumbers to 1,000,000; primes, squares, cubes | Same year | Same year | Same year |
| Fractions, decimals & %Add and subtract fractions; decimals to 3 places | Same year | Same year | Same year |
| Algebra & functionsNumber sequences and inverse operations | Same year | Same year | Same year |
| Ratio & proportionRates and simple scaling | Same year | Later, or not taught | Same year |
| Geometry & measuresMeasure angles; area; volume by counting cubes | Same year | Same year | Same year |
| Statistics & probabilityLine graphs and timetables | Same year | Same year | Same year |
Where it differs this year
- US introduces percent in Grade 6, one year after England.
- US adds fractions with unlike denominators in Grade 5; England handles related denominators in Year 5.
In the PDF: the full objectives and the sprint plan. Get the map
Year 6Age 10–11 · US Grade 5 · IB PYP (exhibition)KS2 SATs (May)
By the end of Year 6, they can:
- Work with numbers up to 10 million, long division and order of operations
- Use all four operations with fractions; convert fractions, decimals and percent
- Use ratio and scale factors, simple formulae and linear sequences
- Find the area of triangles and volume of cuboids; use all four quadrants
- Draw pie charts and calculate the mean
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberLong division; order of operations | Same year | A year either side | Same year |
| Fractions, decimals & %Four operations with fractions; FDP equivalence | Same year | Same year | Same year |
| Algebra & functionsSimple formulae; two unknowns | Same year | A year either side | Same year |
| Ratio & proportionRatio and scale factors | Same year | A year either side | Same year |
| Geometry & measuresArea of triangles; volume of cuboids; circle parts | Same year | A year either side | Same year |
| Statistics & probabilityPie charts and the mean | Same year | A year either side | Same year |
Where it differs this year
- England tests all of this in KS2 SATs at the end of Year 6.
- US places ratio, simple algebra, triangle area and the mean in Grade 6, one year later.
In the PDF: the full objectives and the sprint plan. Get the map
Year 7Age 11–12 · US Grade 6 · IB MYP 1
By the end of Year 7, they can:
- Calculate with negatives, mixed numbers and percentages
- Simplify, substitute and solve two-step equations; find the nth term
- Simplify ratios, share in a ratio and use unit rates
- Find trapezium and surface areas, and use angle facts
- Find averages and place events on the probability scale
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberNegatives; prime factors, HCF and LCM | Same year | Same year | Same year |
| Fractions, decimals & %Mixed numbers; percentages of amounts | Same year | Same year | Same year |
| Algebra & functionsNotation, substitution, two-step equations | Same year | Same year | Same year |
| Ratio & proportionRatio sharing and unit rates | Same year | Same year | Same year |
| Geometry & measuresTrapezium area; angle facts; surface area | Same year | Same year | Same year |
| Statistics & probabilityAverages and probability scale | Same year | Same year | Same year |
Where it differs this year
- This is the closest point of alignment: Year 7, Grade 6 and MYP 1 cover almost the same ground.
- US delays the nth term of sequences to Grade 8 functions.
In the PDF: the full objectives and the sprint plan. Get the map
Year 8Age 12–13 · US Grade 7 · IB MYP 2
By the end of Year 8, they can:
- Use index laws and standard form
- Work out percentage change and reverse percentages
- Expand, factorise and solve equations; plot straight-line graphs
- Solve proportion problems; measure circles, prisms and cylinders
- Find the probability of combined events and read scatter graphs
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberIndex laws and standard form | Same year | A year either side | Same year |
| Fractions, decimals & %Percentage change; reverse percentages | Same year | Same year | Same year |
| Algebra & functionsExpand, factorise, solve, inequalities | Same year | Same year | Same year |
| Ratio & proportionDirect proportion; speed and density | Same year | Same year | Same year |
| Geometry & measuresCircles; prisms and cylinders | Same year | Same year | Same year |
| Statistics & probabilityCombined events; scatter graphs | Same year | Same year | Same year |
Where it differs this year
- US teaches standard form (scientific notation) and linear graphs in Grade 8, a year later.
- Circles, proportional relationships and probability match closely across all three.
In the PDF: the full objectives and the sprint plan. Get the map
Year 9Age 13–14 · US Grade 8 · IB MYP 3
By the end of Year 9, they can:
- Tell rational from irrational numbers and convert recurring decimals
- Use y = mx + c, solve simultaneous equations and factorise quadratics
- Solve inverse proportion, compound interest and depreciation problems
- Use Pythagoras, right-angled trigonometry, similarity and congruence
- Use Venn diagrams, two-way tables and lines of best fit
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberRational and irrational numbers | Same year | Same year | Same year |
| Fractions, decimals & %Compound interest and depreciation | Same year | A year either side | Same year |
| Algebra & functionsy = mx + c; simultaneous equations | Same year | Same year | Same year |
| Ratio & proportionInverse proportion; similarity | Same year | A year either side | Same year |
| Geometry & measuresPythagoras; first trigonometry | Same year | A year either side | Same year |
| Statistics & probabilityVenn diagrams and two-way tables | Same year | Same year | Same year |
Where it differs this year
- US covers Pythagoras in Grade 8 but leaves trigonometry to Geometry (Grade 10).
- US meets quadratics in Algebra I (Grade 9), a year later.
In the PDF: the full objectives and the sprint plan. Get the map
Year 10Age 14–15 · US Grade 9 (Algebra I) · IB MYP 4
By the end of Year 10, they can:
- Solve quadratics by factorising, the formula and completing the square
- Simplify surds, use fractional indices and simplify algebraic fractions
- Write proportion equations and model exponential growth
- Use exact trig values, 3D trigonometry, similar shapes and vectors
- Use tree diagrams, cumulative frequency and box plots
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberSurds; fractional and negative indices | Same year | A year either side | Same year |
| Algebra & functionsQuadratics: factorise, formula, complete the square | Same year | Same year | Same year |
| Ratio & proportionGrowth, decay and proportion equations | Same year | Same year | Same year |
| Geometry & measuresTrig in 3D; similar areas and volumes | Same year | A year either side | Same year |
| Statistics & probabilityTree diagrams; cumulative frequency | Same year | A year either side | Same year |
Where it differs this year
- IB MYP splits into standard and extended maths here; GCSE Higher content sits closest to extended.
- US box plots arrive in Grade 6, much earlier; England teaches them now.
In the PDF: the full objectives and the sprint plan. Get the map
Year 11Age 15–16 · US Grade 10 (Geometry) · IB MYP 5GCSE / IGCSE
By the end of Year 11, they can:
- Use function notation, composite and inverse functions and transformations
- Apply the sine and cosine rules and circle theorems; prove results with vectors
- Estimate gradients and areas under graphs as rates of change
- Interpret histograms, sampling and conditional probability
- Calculate with upper and lower bounds
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberBounds and accuracy | Same year | A year either side | Same year |
| Algebra & functionsFunctions: composite, inverse, transformations | Same year | A year either side | Same year |
| Ratio & proportionRates of change from graphs | Same year | A year either side | Same year |
| Geometry & measuresSine and cosine rules; circle theorems; vectors | Same year | Same year | Same year |
| Statistics & probabilityHistograms; conditional probability | Same year | A year either side | Same year |
| CalculusGradients and areas under graphs | Same year | Later, or not taught | A year either side |
Where it differs this year
- GCSE and IGCSE exams sit at the end of this year; MYP 5 ends with the eAssessment.
- US Geometry covers circle theorems and trigonometry now; function work sits in Algebra I–II.
In the PDF: the full objectives and the sprint plan. Get the map
Year 12Age 16–17 · US Grade 11 (Algebra II) · IB DP 1AS level (optional)
By the end of Year 12, they can:
- Prove by deduction and exhaustion, and disprove by counterexample
- Divide polynomials, use the factor theorem and the coordinate geometry of circles
- Use exponentials and logarithms in modelling
- Differentiate and integrate polynomials; solve optimisation problems
- Use the binomial distribution, hypothesis tests, trig identities and 2D vectors
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberProof by deduction and counterexample | Same year | A year either side | Same year |
| Algebra & functionsPolynomials; exponentials and logarithms | Same year | Same year | Same year |
| Geometry & measuresTrig identities; 2D vectors | Same year | A year either side | Same year |
| Statistics & probabilityBinomial distribution; hypothesis tests | Same year | A year either side | Same year |
| CalculusDifferentiate and integrate polynomials | Same year | A year either side | Same year |
Where it differs this year
- A level and IB DP both start calculus now; most US students meet it in Grade 12 (AP Calculus).
- Statistics is compulsory in A level and IB; in the US it is a separate optional course (AP Statistics).
In the PDF: the full objectives and the sprint plan. Get the map
Year 13Age 17–18 · US Grade 12 (Precalculus / AP Calculus) · IB DP 2A level / IB Diploma / AP
By the end of Year 13, they can:
- Use the chain, product and quotient rules; integrate by substitution and parts
- Solve differential equations and use numerical methods
- Use radians, compound angles, 3D vectors and series
- Use the normal distribution, correlation and regression
- Calculate with complex numbers
Where each thread sits
● Same year◐ A year either side○ Later, or not taught
| Thread | England | US | IB |
|---|---|---|---|
| NumberComplex numbers (Further / HL) | A year either side | Same year | Same year |
| Algebra & functionsSeries; binomial for any n | Same year | Same year | Same year |
| Geometry & measuresRadians, compound angles, 3D vectors | Same year | Same year | Same year |
| Statistics & probabilityNormal distribution; regression | Same year | A year either side | Same year |
| CalculusCalculus techniques; differential equations | Same year | Same year | Same year |
Where it differs this year
- Complex numbers are in IB HL and US Precalculus but only in A level Further Maths.
- The new IB DP maths syllabus starts teaching in August 2027 (first exams May 2029), so it applies to every learner.
In the PDF: the full objectives and the sprint plan. Get the map
Maths
Where the curricula differ
- We follow England's order. When the US or IB teach a topic earlier or later, we say so in that year.
- Year 7 is where the three line up most closely.
- From Year 10, IB MYP splits into standard and extended. England's GCSE Higher content sits closest to extended.
Maths
How we checked.
- England's programmes of study are the spine. Each objective is checked against United States and International Baccalaureate.
- 4 published sources, listed in the PDF.
- Last checked October 2026.
Changes ahead
- England's reformed national curriculum is due from September 2028. We will check this map again when it is published.
- The new IB Diploma maths syllabus is first taught in August 2027, with first exams in May 2029.
Get the detailed map
The full year-by-year objectives, mapped against England, the US and the IB, with the sprint plan and every source we used.
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