Custom Worksheet curriculum coverage audit

Status: planning baseline for the hidden Custom Worksheet module.

Scope: England National Curriculum mathematics, Years 1–6 (KS1 and KS2).

Primary completeness source:

Department for Education, National curriculum in England: mathematics programmes of study.
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study

Secondary progression source:

Department for Education, Mathematics guidance: key stages 1 and 2 (2020).
https://www.gov.uk/government/publications/teaching-mathematics-in-primary-schools

The statutory programme of study is the completeness checklist. Ready-to-progress criteria are useful progression tags but are not a complete curriculum and must not replace the statutory objective map.

Current repo position

The audited Custom Worksheet modules currently contain about 175 family definitions across:

Number & place value
Number properties
Calculation
Fractions
Decimals & percentages
Ratio & proportion
Measurement
Geometry
Algebra
Statistics
Extension

This is already broad, but the public-facing taxonomy is flatter than the curriculum. Many broad families cover several statutory objectives, and several objectives have no clearly named leaf even where an existing generator could probably support them.

The next catalogue version should therefore separate:

curriculum taxonomy;
question providers;
availability/status.

A curriculum leaf must be allowed to exist even when it has no provider yet.

Recommended data model

Every curriculum leaf should have:

stable curriculum ID;
year or year range;
statutory domain;
subcategory;
short teacher-facing label;
concise objective wording;
optional DfE ready-to-progress code(s);
status: live / partial / planned;
provider type: generator / template / curated library / visual / none;
provider IDs;
notes about limitations.

Do not make a planned leaf selectable until it has at least one usable provider. Planned leaves can still be visible in the hidden Custom module with a restrained “planned” state.

Proposed catalogue hierarchy

Number & place value

Subcategories:

Counting forwards/backwards
Counting in multiples / step counting
Read & write numbers
Place value
Standard & non-standard partitioning
Compare & order
Number-line position
Represent & estimate numbers
More / less
Powers of 10
Rounding
Negative numbers
Roman numerals

Important leaves to make explicit:

Y1 count to/across 100 from any starting point
Y1 count in 2s, 5s and 10s
Y1 identify 1 more / 1 less
Y1 represent numbers and reason on a number line
Y2 non-standard partitioning of 2-digit numbers
Y2 estimate/locate 2-digit numbers on a number line
Y3 10/100 more or less
Y3 non-standard partitioning of 3-digit numbers
Y3 locate/read scaled number lines
Y4 1,000 more or less
Y4 count backwards through zero
Y4 non-standard partitioning of 4-digit numbers
Y5 count in powers of 10
Y5 decimal place value / partitioning
Y5 negative numbers in context
Y6 place value to 10,000,000 including decimals
Y6 rounding to a required degree of accuracy

Likely gaps/weakly named areas:

explicit number-line / scale partitioning by 2, 4, 5 and 10 equal parts;
standard vs non-standard partitioning as its own teacher-visible leaf;
representation/estimation tasks as a distinct leaf.

Addition & subtraction

Subcategories:

Number bonds / complements
Addition facts
Subtraction facts
Mental addition
Mental subtraction
Add/subtract across boundaries
Missing-number equations
Commutativity / inverse
Difference problems
Column addition
Column subtraction
Estimation & checking
One-step contextual problems
Two-step contextual problems
Multi-step contextual problems

Important leaves to make explicit:

Y1 equations with +, − and =
Y1 bonds and related subtraction facts within 20
Y1 one-step contextual and missing-number problems
Y2 facts to 20 and derived facts to 100
Y2 2-digit +/− ones
Y2 2-digit +/− tens
Y2 two 2-digit numbers
Y2 three 1-digit addends
Y2 difference / “how many more?”
Y2 inverse and checking
Y3 3-digit +/− ones, tens and hundreds
Y3 complements to 100
Y3 column addition/subtraction
Y4 4-digit column methods
Y4 two-step contextual problems
Y5 large-number mental calculation
Y5 multi-step contextual problems
Y6 mixed-operation / multi-step contextual problems

Likely gaps/weakly named areas:

“difference / how many more?” deserves a distinct leaf;
bridge-through-10 tasks should be visible separately;
contextual one/two/multi-step problems should no longer be represented by one retired generic word-problem family.

Multiplication & division

Subcategories:

Grouping & sharing
Arrays
Repeated addition
Times-table facts
Related division facts
Multiplication statements
Division statements
Commutativity / inverse
Derived facts / scaling
Mental multiplication
Mental division
Short multiplication
Long multiplication
Short division
Long division
Remainders & contextual interpretation
Distributive law
Scaling
Correspondence / combinations

Important leaves to make explicit:

Y1 grouping/sharing with objects and arrays
Y2 arrays/repeated addition/grouping/sharing
Y2 2, 5 and 10 facts
Y3 3, 4 and 8 facts
Y3 2-digit × 1-digit
Y3 scaling and correspondence
Y4 facts to 12×12
Y4 ×0, ×1, ÷1 and multiply three numbers
Y4 2-/3-digit × 1-digit
Y4 distributive-law problems
Y5 up to 4-digit × 1-/2-digit
Y5 up to 4-digit ÷ 1-digit and remainder interpretation
Y6 4-digit × 2-digit
Y6 4-digit ÷ 2-digit, short/long division and remainder interpretation

Likely gaps/weakly named areas:

visual arrays as their own leaf/provider;
grouping vs sharing should be distinguished in early years;
contextual remainder interpretation should be distinct from raw remainder calculation.

Number properties

Subcategories:

Odd & even
Multiples
Factors
Factor pairs
Common factors
Common multiples
Prime / composite
Square numbers
Cube numbers

Current coverage is strong. Keep this as a teacher-friendly category even though the statutory programme embeds much of it in multiplication/division.

Fractions

Subcategories:

Equal parts
Recognise & name fractions
Unit fractions
Non-unit fractions
Fractions of quantities
Fractions of sets
Fractions of lengths
Fractions of shapes
Fractions on number lines
Count in fractions
Equivalent fractions
Compare & order fractions
Add fractions
Subtract fractions
Mixed & improper fractions
Simplify / common denominator
Fraction × whole number
Fraction × fraction
Fraction ÷ whole number
Fraction as division

Important leaves to make explicit:

Y1 halves
Y1 quarters
Y2 thirds, quarters, 2/4 and 3/4
Y2 2/4 = 1/2
Y2 count in halves/quarters beyond 1
Y3 tenths
Y3 fractions as numbers on a number line
Y3 equivalent fractions using diagrams
Y3 add/subtract same denominator within one whole
Y4 hundredths
Y4 fractions to divide quantities
Y4 decimal equivalents of tenths/hundredths and 1/4, 1/2, 3/4
Y5 denominators that are multiples
Y5 mixed/improper conversion
Y5 fractions × whole numbers
Y6 simplify using common factors
Y6 common denominators using common multiples
Y6 add/subtract different denominators/mixed numbers
Y6 fraction × fraction
Y6 fraction ÷ whole number
Y6 fraction as division

Likely gaps/weakly named areas:

fraction number-line questions need their own family;
equal-parts misconception questions are valuable and currently hidden inside broad fraction visuals;
recognise/finding fractions should be distinguishable by shape/set/quantity/length.

Decimals & percentages

Subcategories:

Tenths
Hundredths
Thousandths
Decimal place value
Decimal number lines
Compare & order decimals
Round decimals
Multiply/divide by 10, 100, 1,000
Decimal addition/subtraction
Decimal multiplication
Decimal division
Fraction ↔ decimal
Percentage meaning
Fraction ↔ percentage
Decimal ↔ percentage
Percentage of amount
Percentage comparison
Contextual decimal/percentage problems

Likely gaps/weakly named areas:

explicit thousandths;
decimal number-line placement;
percentage as “parts per 100” separate from percentage calculation.

Ratio & proportion

Subcategories:

Relative size / equivalent ratios
Missing ratio values
Unequal sharing & grouping
Scale factor
Similar shapes
Recipe/quantity scaling
Percentage proportion problems
Simple rates

Current coverage is reasonably strong. Percentage comparison should cross-link rather than duplicate.

Measurement

Subcategories:

Length / height
Mass / weight
Capacity
Volume
Temperature
Unit choice
Reading scales
Compare/order measures
Add/subtract measures
Metric conversions
Metric/imperial approximate equivalence
Miles ↔ kilometres
Money: recognise coins/notes
Money: compose amounts
Money: coin combinations
Money: change
Money: multi-step
Time: sequence/order language
Time: calendar/dates
Time: analogue clocks
Time: digital time
Time: 12-/24-hour
Time: duration
Time: unit conversions
Time: timetables
Perimeter
Area by counting squares
Rectangle/rectilinear area
Irregular-area estimation
Triangle area
Parallelogram area
Area/perimeter relationships
Estimate volume/capacity
Cuboid volume
Measure problem solving

Likely gaps/weakly named areas:

non-standard measurement for Y1;
separate length/mass/capacity scale reading;
irregular-area estimation Y5;
estimate volume/capacity Y5;
explicit “same area, different perimeter / same perimeter, different area”;
miles ↔ kilometres as a dedicated Y6 leaf.

Geometry – properties of shapes

Subcategories:

Recognise/name 2-D shapes
Recognise/name 3-D shapes
2-D shape properties
3-D shape properties
2-D faces on 3-D shapes
Compare/sort shapes
Draw 2-D shapes
Make/build 3-D shapes
Nets
Triangles
Quadrilaterals
Regular/irregular polygons
Symmetry
Horizontal/vertical lines
Parallel/perpendicular lines
Circles
Angles & turns
Draw shapes from dimensions/angles

Likely gaps/weakly named areas:

Y2 identify 2-D shapes on surfaces of 3-D shapes;
Y2/Y3 compare and sort shape families should be visible;
Y3 draw 2-D / recognise 3-D in different orientations;
Y5 identify 3-D shapes from 2-D representations;
Y6 draw 2-D shapes from given dimensions and angles;
Y6 recognise/build simple 3-D shapes from nets;
regular vs irregular polygons should have an explicit leaf rather than relying on broad shape properties.

Geometry – position & direction

Subcategories:

Positional language
Movement
Turns
Shape/object patterns
First-quadrant coordinates
Plot points / complete polygons
Translation
Reflection
Four-quadrant coordinates
Coordinate transformations

Likely gap:

Y2 arrange mathematical objects in patterns/sequences is not clearly represented.

Angles

Keep the current visual angle subsystem, but expose it through the geometry hierarchy:

Turns & orientation Y1–2
Right angles & turns Y3
Identify/compare/order angles Y4
Estimate/measure/draw degrees Y5
Angles on lines/around points Y5–6
Angles in triangles Y6
Angles in quadrilaterals/polygons Y6
Angle reasoning Y5–6

This is currently one of the strongest areas of the Custom module.

Statistics

Subcategories:

Categorise/sort data
Tally charts
Pictograms
Block diagrams
Tables
Bar charts
Time graphs
Line graphs
Timetables
Pie charts
Mean
Comparison/sum/difference from data
Construct representations
Interpret representations
Choose an appropriate representation

Likely gaps/weakly named areas:

construction and interpretation should be distinguishable;
Y2 “sort categories by quantity / total / compare categorical data” should have a low-reading-age leaf;
Y4 continuous-data presentation should be explicit;
“choose appropriate representation” is non-statutory guidance but useful as an extension/reasoning family.

Algebra

Subcategories:

Missing-number statements
Use simple formulae
Substitute into formulae
Linear sequences
Express missing-number problems algebraically
One-unknown equations
Two-unknown equations
Find pairs satisfying an equation
Enumerate combinations of two variables
Equivalent expressions / generalisation

Likely gap:

“enumerate possibilities of combinations of two variables” should be a separate Y6 leaf.

Coverage priorities

Priority A — taxonomy gaps, likely easy to support from existing engines

bridge-through-10 addition/subtraction
difference / how-many-more
non-standard place-value partitioning
number-line location / scale partitioning
grouping vs sharing
arrays
fraction number lines
decimal number lines
explicit tenths/hundredths/thousandths
contextual remainder interpretation
equal-area/different-perimeter reasoning
regular/irregular polygon classification
two-variable enumeration
categorical-data comparison

Priority B — new visual/template generators

early arrays
non-standard measurement
2-D face on 3-D shape
shape sorting
shape patterns/sequences
Y3 draw/recognise shapes in varied orientation
Y5 3-D from 2-D representations
irregular-area estimation
volume/capacity estimation
Y6 draw 2-D shape from dimensions/angles

Priority C — curated question libraries

Use original, locally stored question banks for objectives where a fully general generator gives little benefit or risks awkward wording.

Good candidates:

contextual one/two/multi-step problems
measure reasoning
money reasoning
calendar/timetable interpretation
“which method / why?” reasoning
classify/explain/justify questions
misconception diagnosis
multi-clue number-property problems
algebraic/generalisation word problems
data interpretation with richer contexts

Curated question-bank architecture

Do not store hundreds of unstructured strings in one file.

Recommended structure:

one library file per domain or tightly related group;
each question has a stable ID;
objective IDs and year tags;
difficulty;
prompt;
answer;
worked solution;
marking mode;
optional choices;
optional visual specification;
keywords / misconception tags;
provenance = original;
review status.

Suggested provider modes:

seeded-generator
parameterised-template
curated-library
visual-generator

A parameterised template is preferable where possible because it combines natural language with mathematically verified variation.

Example fields:

{
  id: 'Y4-MEAS-MONEY-017',
  objectiveIds: ['Y4-MEAS-MONEY-02'],
  years: [4],
  difficulty: 'standard',
  mode: 'curated-library',
  prompt: '...',
  answer: { type: 'money', value: 6.35 },
  solution: [
    '...',
    '...'
  ],
  tags: ['money', 'two-step', 'change'],
  review: 'approved',
  provenance: 'original'
}

QA requirements

Add automated checks that:

every statutory curriculum leaf has a stable ID;
every statutory leaf has status live / partial / planned;
every live leaf has at least one valid provider;
every provider references valid curriculum IDs;
generated/template questions validate mathematically;
curated questions include a non-empty answer and worked solution;
IDs are unique;
no empty/planned leaf is selectable;
no exact question repeats in one generated sheet;
coverage reports show live/partial/planned counts by year and domain.

A human sample review remains required for wording, age appropriateness and diagram clarity.

Product implication

The Custom Worksheet selector should become a curriculum browser: Domain → subcategory → objective/question family.

Teachers should not need to understand internal generator names.

Existing broad generator families can continue to serve several curriculum leaves behind the scenes. The curriculum structure and the generation implementation should no longer be the same thing.