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The literacy and numeracy skills in this qualification

1. Reading and interpreting problems set in real-world context

   Assessed: In the exam

   All three papers set questions in personal, work, societal and scientific contexts, and Unit 1 expects learners to interpret mathematical information in infographics, schedules, tables, timetables, calendars and charts before choosing a method.

   Literacy: Reading strategies

   Getting pupils ready

   Year 7

   Pupils highlight the question, the key numbers and the units in worded problems before solving, then rewrite each problem as a one-line calculation plan.

   Year 8

   Pupils read a real leisure centre price list or a bus timetable, pick out only the information they need, and answer multi-step questions from it.

   Year 9

   Pupils tackle unstructured, multi-step problems in real contexts, such as a utility bill or an infographic on household energy use, annotating what the question asks before starting.

   Show the specification wording and the LNF statements

   Where it is in the specification: Section 3.1, Questions set in context, page 51, and Unit 1, Section 1.7.1, page 17

   “Learners will be required to respond to questions set in context and context-free questions in all three written examinations.”

   Progression step 3

   • I can read words and sentences from different texts using a range of strategies to make meaning.

   • I can use a range of strategies for finding information, e.g. skimming for gist, scanning for detail.

   Progression step 4

   • I can read, with concentration, printed and digital texts that are new to me and update, broaden and deepen my understanding of information, ideas and issues.

   • I can use a range of strategies, e.g. speed reading, close reading, annotation, prediction, to skim texts for gist, key ideas and themes, and scan for detailed information.

   Progression step 5

   • I can read and analyse a range of unseen, printed and digital texts with concentration and independence.

   • I can use a range of strategies, e.g. speed reading, close reading, annotation, prediction, to skim texts for gist, key ideas and themes, and scan for detailed information, extracting and commenting maturely on key ideas and themes.

2. Explaining working and writing a conclusion

   Assessed: In the exam

   Every paper awards one mark for communicating and organising, so learners must present a structured response, explain each step to the reader, and write a conclusion that says what the answer means.

   Literacy: Planning and organising for different purposes, audiences and context, Connectives and syntax

   Getting pupils ready

   Year 7

   Pupils set out worded problems with sentence starters such as 'First I found', 'so' and 'therefore', and finish every one with a concluding sentence.

   Year 8

   Pupils compare two mobile phone contracts and write a structured answer with each step explained, ending with a conclusion that states which is cheaper and why.

   Year 9

   Pupils mark model answers against the WJEC communicating and organising criteria, then redraft their own solution to a multi-step problem so that it meets them.

   Show the specification wording and the LNF statements

   Where it is in the specification: Section 3.1, Organising, communicating and writing accurately, page 51

   “explain to the reader what they are doing at each step of their response”

   Progression step 3

   • I can write an effective introduction that establishes context and purpose, a suitable balance between facts and viewpoints, and a precise conclusion.

   • I can use paragraphs and make links between them.

   • I can use an increasing range of connectives to organise my ideas in sentences, paragraphs and whole texts.

   Progression step 4

   • I can use summary, discussion of issues, detailed explanations and logic when covering a topic.

   • I can organise and construct my writing effectively, connecting and developing my ideas for a range of different contexts.

   • I can use a range of connectives specifically when organising my ideas in whole texts for different purposes.

   Progression step 5

   • I can organise writing in an appropriate form, ensuring content is detailed within and between paragraphs or sections, developing and sustaining ideas coherently.

   • I can summarise confidently, adapting style and form for the reader or intended audience and purpose for writing.

3. Mathematical vocabulary, notation and accurate writing

   Assessed: In the exam

   Learners must know a wide mathematical vocabulary, from geometric terms such as parallel, perpendicular, isosceles and chord to the language of probability, and the writing accurately mark on each paper requires correct mathematical form, terminology and units.

   Literacy: Vocabulary, spelling, grammar

   Getting pupils ready

   Year 7

   Pupils build a mathematics glossary and word wall, learning to spell and define terms such as parallel, perpendicular, isosceles and denominator, with a short weekly spelling check.

   Year 8

   Pupils write definitions of shapes and probability words with one example and one non-example each, then use them to describe a hidden shape to a partner without pointing.

   Year 9

   Pupils check their written answers for correct notation and units, such as cm², km/h and £ signs, and correct spellings of key terms before handing work in.

   Show the specification wording and the LNF statements

   Where it is in the specification: All units, Section 3.1, page 28, and Organising, communicating and writing accurately, page 51

   “Learners should know the following geometric terms, vocabulary and essential properties:”

   Progression step 3

   • I can use varied, appropriate and precise vocabulary including area of learning and experience/discipline-specific words for different purposes.

   • I can use strategies to correctly spell polysyllabic, complex and irregular words in the context of each area of learning and experience.

   Progression step 4

   • I have experienced a range of area of learning and experience/discipline-specific and general academic vocabulary, and can use them in my own communication.

   • I can use a variety of strategies and resources to spell familiar and unfamiliar vocabulary and area of learning and experience/discipline-specific words correctly.

   Progression step 5

   • I can use a range of discipline-specific and general academic vocabulary accurately and precisely.

   • I can use strategies to spell discipline-specific and general academic words in appropriate contexts.

   • I can understand and use formal conventions of language in a range of purposes, making effective use of reference tools and accuracy aids.

4. Personal and household finance

   Assessed: In the exam

   Unit 1 is built around financial mathematics: wages, payslips, income tax and National Insurance, VAT, budgets, bills, best buys, exchange rates, profit and loss, and at Higher Tier simple and compound interest, AER and APR.

   Numeracy: Financial literacy

   Getting pupils ready

   Year 7

   Pupils plan a class trip to Barry Island within a £300 budget, comparing coach and train prices and recording spending in a running-total table.

   Year 8

   Pupils compare supermarket pack sizes of the same product, work out the price per 100 g to find the best buy, and calculate profit for a school tuck shop.

   Year 9

   Pupils read a mock payslip and a savings advert, calculating VAT, a percentage discount and compound interest over three years using a multiplier.

   Show the specification wording and the LNF statements

   Where it is in the specification: Unit 1, Section 1.8, pages 18 to 19

   “understand the basic principles of personal/ household finance and enterprise in order to solve problems relating to”

   Progression step 3

   • I can manage money, compare costs from different retailers and determine what can be bought within a given budget.

   • I can make comparisons between prices and understand which is best value for money.

   • I can use profit and loss in buying and selling calculations.

   Progression step 4

   • I can carry out calculations relating to VAT, saving and borrowing.

   • I can appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing.

   • I can use and understand efficient methods of calculating compound interest.

   Progression step 5

   • I can understand and demonstrate the real-life process of foreign exchange.

   • I can understand and calculate income tax and understand the implications of taxation.

5. Percentages, ratio and proportion

   Assessed: In the exam

   Learners find fractions and percentages of amounts, calculate percentage change, use multipliers, solve ratio and direct and inverse proportion problems, and at Higher Tier handle repeated proportional change and reverse percentages.

   Numeracy: Calculation, Relationships within the number system

   Getting pupils ready

   Year 7

   Pupils scale a Welsh cake recipe for 6 people up to 15 using ratio, and find 10%, 5% and 15% of shop prices by building from 10%.

   Year 8

   Pupils calculate the percentage increase in local bus fares over several years and express one quantity as a percentage of another, such as goals scored out of shots taken.

   Year 9

   Pupils use single multipliers such as 0.85 and 1.2 for repeated percentage change, and work back to the original price of an item before a sale.

   Show the specification wording and the LNF statements

   Where it is in the specification: Units 1 and 3, Section 1.4, pages 14 to 15

   “calculate fractional and percentage changes (increase and decrease)”

   Progression step 3

   • I can calculate a percentage, fraction and decimal of any quantity with a calculator where appropriate.

   • I can use ratio and proportion to calculate quantities.

   • I can use equivalence of fractions, decimals and percentages to compare proportions.

   Progression step 4

   • I can calculate a percentage increase or decrease.

   • I can express one quantity as a percentage of another.

   • I can use ratio and proportion including map scales.

   Progression step 5

   • I can use multipliers as an efficient method when working with percentages, e.g. multiply by 1.2 to increase an amount by 20%.

   • I can use and understand the idea of reverse percentage to find an original quantity.

6. Calculating with and without a calculator, estimating and checking

   Assessed: In the exam

   Unit 2 is non-calculator, so learners must use written methods with whole numbers, decimals, fractions and negative numbers and estimate by rounding, while Units 1 and 3 expect efficient calculator use for order of operations, powers, roots, brackets and standard form.

   Numeracy: The number system, Calculation, Fluency, Strategic competence

   Getting pupils ready

   Year 7

   Pupils write a rounded estimate before every written calculation in a daily non-calculator starter, then check the answer with an inverse operation.

   Year 8

   Pupils predict the answer to calculations such as 3 + 4 × 2² using the order of operations before keying them in, and explain any mismatch.

   Year 9

   Pupils sort a mixed question sheet into mental, written and calculator methods, then use the power, root and standard form keys on a scientific calculator.

   Show the specification wording and the LNF statements

   Where it is in the specification: Unit 2, Section 1.1.9, page 12, and Units 1 and 3, Section 1.5.5, page 16

   “estimate solutions to numerical calculations by approximating the numbers in the calculations”

   Progression step 3

   • I can estimate by rounding to the nearest 10, 100, 1000 or whole number.

   • I can use a range of strategies to check calculations including the use of inverse operations, equivalent calculations and the rules of divisibility.

   • I can use a calculator effectively and efficiently to carry out calculations.

   Progression step 4

   • I can make and justify estimates and approximations of calculations.

   • I can use a scientific calculator effectively and efficiently to carry out calculations using the available range of function keys.

   • I can use the order of operations including brackets and powers.

   Progression step 5

   • I can use firmly established, memorable and usable facts and techniques in order to apply the most efficient methods.

   • I can use a scientific calculator effectively and efficiently to carry out calculations using the available range of function keys.

   • I can choose an appropriate mental or written strategy and know when it is appropriate to use a calculator.

7. Units, compound measures and accuracy of measurement

   Assessed: In the exam

   Learners convert metric and imperial units and units of time, work with time zones, use compound measures such as speed, fuel consumption, density and population density, and at Higher Tier find upper and lower bounds.

   Numeracy: Measurement, The number system, Communicating with symbols

   Getting pupils ready

   Year 7

   Pupils measure classroom objects and convert between mm, cm, m and km, then plan a day trip to Cardiff using the real train timetable from Aberdare.

   Year 8

   Pupils calculate average speed and fuel consumption for car journeys from Aberdare to Cardiff and Swansea, writing units such as km/h and mpg every time.

   Year 9

   Pupils work out the population density of Rhondda Cynon Taf from census figures, and state the upper and lower bounds of lengths measured to the nearest centimetre.

   Show the specification wording and the LNF statements

   Where it is in the specification: Units 1 and 3, Section 3.5, pages 34 to 35, and Unit 1, Section 1.6, pages 16 to 17

   “recall and use compound measures for speed and fuel consumption”

   Progression step 3

   • I can read and interpret scales or divisions on a range of measuring instruments.

   • I can convert metric units of length to smaller units, e.g. cm to mm, m to cm, km to m.

   • I can use and interpret calendars, timetables and schedules to plan events and activities, and make calculations as part of the planning journey.

   Progression step 4

   • I can represent and use compound measures, using standard units.

   • I can use the common units of measure, convert between related units of the metric system and carry out calculations.

   • I can use timetables and time zones to calculate travel time.

   Progression step 5

   • I can understand and use a variety of compound measures.

   • I can recognise and define limitations on accuracy of measurements, e.g. upper and lower bounds.

   • I can use appropriate notation, symbols and units of measurement, including compound measures.

8. Scale drawings, maps and bearings

   Assessed: In the exam

   Units 1 and 3 require learners to read scales, use maps, produce scale drawings with scales such as 1:500 and use three-figure bearings, and Unit 3 adds constructions and loci with ruler, protractor and compasses.

   Numeracy: Angle, Position, Measurement, Calculation, Shape and space

   Getting pupils ready

   Year 7

   Pupils measure the classroom with trundle wheels and tape measures and draw an accurate floor plan on squared paper at a scale of 1 cm to 1 m.

   Year 8

   Pupils use an Ordnance Survey map of the Cynon Valley to measure real distances with the map scale and give three-figure bearings between landmarks.

   Year 9

   Pupils construct a scale drawing of the school field with ruler and compasses and shade the region within 20 m of a sprinkler using loci.

   Show the specification wording and the LNF statements

   Where it is in the specification: Units 1 and 3, Section 3.3, page 31, and Section 3.2, page 30

   “interpret and produce scale drawings; scales may be written in the form 1 cm represents 5 m, or 1:500”

   Progression step 3

   • I can use angle as a measure of rotation.

   • I can use grid references to specify location.

   • I can read and interpret scales or divisions on a range of measuring instruments.

   Progression step 4

   • I can measure and draw angles.

   • I can apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale.

   • I can use ratio and proportion including map scales.

   Progression step 5

   • I can measure and draw angles.

   • I can apply proportional change to two-dimensional designs.

9. Using formulae, including perimeter, area and volume

   Assessed: In the exam

   Learners substitute into formulae written in words or symbols, change the subject of a formula, and apply perimeter, area and volume formulae to 2-D and 3-D shapes, recalling most formulae because the Foundation formula lists give only the trapezium and prism.

   Numeracy: Shape and space, Communicating with symbols, Measurement, Strategic competence

   Getting pupils ready

   Year 7

   Pupils write word formulae for real situations, such as a taxi fare, rewrite them in symbols, and use formulae to find the perimeter and area of rectangles.

   Year 8

   Pupils find the area of composite shapes and circles on a school garden plan, showing the formula, the substitution and the units at each step.

   Year 9

   Pupils calculate the volume and capacity of prisms and cylinders, such as a rainwater tank, and rearrange formulae to find a missing length.

   Show the specification wording and the LNF statements

   Where it is in the specification: All units, Section 2.1.2, page 21, and Units 1 and 3, Section 3.6, page 36

   “substitute positive and negative whole numbers, fractions and decimals into simple formulae and expressions written in words or in symbols”

   Progression step 3

   • I can measure and calculate perimeter.

   • I can find areas by counting squares, progressing to calculating the area of squares and rectangles using formulae.

   • I can use appropriate notation, symbols and units of measurement.

   Progression step 4

   • I can demonstrate an understanding of the relationship between a formula representing a measurement and the units used.

   • I can calculate the areas of two-dimensional simple and compound shapes, including circles.

   • I can apply the formulae for the volume of simple prisms.

   Progression step 5

   • I can communicate my answers using correct mathematical form.

   • I can use appropriate notation, symbols and units of measurement, including compound measures.

   • I can recognise, model and apply the underlying mathematical structures and ideas within problems, in order to formulate and solve them.

10. Geometric reasoning and proof

    Assessed: In the exam

    Unit 2 requires learners to recall angle facts and, at Higher Tier, construct geometric proofs including circle theorems, and AO3, worth 20%, asks for arguments and proofs built by logical reasoning and deduction.

    Numeracy: Logical reasoning

    Getting pupils ready

    Year 7

    Pupils find missing angles on straight lines and around a point and give the reason for each step in a full sentence, such as 'angles on a straight line add up to 180°'.

    Year 8

    Pupils solve chains of angles in parallel lines, writing a numbered reason for every step, then check a partner's argument for any missing reason.

    Year 9

    Pupils prove simple results, such as the angles in a quadrilateral summing to 360°, and judge 'always, sometimes or never true' statements using counter-examples.

    Show the specification wording and the LNF statements

    Where it is in the specification: Unit 2, Section 3.4.5, page 33, and Section 3.1, AO3, page 50

    “construct geometric proofs using angle properties and facts, including circle theorems”

    Progression step 3

    • I can construct and develop a mathematical argument.

    • I can justify my procedures and predictions.

    • I can explain results and procedures precisely using appropriate mathematical language.

    Progression step 4

    • I can construct and develop a mathematical argument.

    • I can justify my procedures, predictions and conjectures.

    • I can explain results and procedures precisely using appropriate mathematical language.

    Progression step 5

    • I can construct and develop a mathematical argument.

    • I can verify and prove results and solutions.

    • I can explain results and procedures precisely using appropriate mathematical language.

11. Planning an enquiry and collecting data

    Assessed: In the exam

    Units 1 and 3 require the statistical problem-solving process: learners specify and test hypotheses, design and criticise questionnaire questions for fairness and bias, choose sampling methods and consider how sample size affects reliability.

    Numeracy: Collecting data

    Getting pupils ready

    Year 7

    Pupils pose a question about their year group, such as how pupils travel to school, and collect the answers in a tally chart and frequency table.

    Year 8

    Pupils design a short questionnaire on school meals, then critique each other's questions for leading wording, overlapping answer boxes and bias.

    Year 9

    Pupils test a hypothesis such as 'Year 9 pupils sleep less than Year 7 pupils', choosing a random or stratified sample and explaining how sample size affects reliability.

    Show the specification wording and the LNF statements

    Where it is in the specification: Units 1 and 3, Section 4.1, pages 40 to 41

    “design and criticise questions for a questionnaire, including notions of fairness and bias”

    Progression step 3

    • I can collect relevant data to answer posed questions.

    Progression step 4

    • I can collect own data for a survey, e.g. through designing a questionnaire.

    • I can plan how to collect data to test a simple hypotheses.

    • I can collect both quantitative and qualitative data.

    Progression step 5

    • I can collect data in a suitable way according to my hypothesis.

12. Drawing graphs, charts and diagrams

    Assessed: In the exam

    Learners construct pictograms, bar charts, pie charts, line graphs, scatter diagrams with lines of best fit and grouped frequency diagrams, and draw conversion and travel graphs, with Higher Tier adding cumulative frequency, box plots and histograms.

    Numeracy: Representing data

    Getting pupils ready

    Year 7

    Pupils draw bar charts and pie charts by hand from their travel-to-school data, choosing a suitable scale and labelling both axes.

    Year 8

    Pupils draw a conversion graph between pounds and euros and a travel graph of a walk to Dare Valley Country Park, then read values from each.

    Year 9

    Pupils measure arm span and height, plot a scatter diagram, draw a line of best fit through the mean point and describe the correlation.

    Show the specification wording and the LNF statements

    Where it is in the specification: Unit 3, Section 4.2, pages 41 to 44, and Unit 1, Section 2.5.1, page 27

    “construct scatter diagrams for data on paired variables”

    Progression step 3

    • I can select and construct appropriate charts, diagrams and graphs with suitable scales.

    • I can represent data using:

      • lists, tally charts, tables, diagrams and frequency tables
      • bar charts, grouped data charts, line graphs and conversion graphs
      • pictograms where one symbol represents more than one unit using a key
      • Venn and Carroll diagrams.

    Progression step 4

    • I can construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate.

    • I can construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, choosing an appropriate scale.

    • I can construct graphs to represent data including scatter diagrams to investigate correlation.

    Progression step 5

    • I can select and construct appropriate charts, diagrams and graphs with suitable scales.

13. Interpreting data, averages and probability

    Assessed: In the exam

    Learners compare distributions using averages and spread, recognise misleading graphs and draw conclusions related back to the original problem, while Unit 2 holds all probability, from the 0 to 1 scale to tree diagrams, which the LNF covers only through interpreting data.

    Numeracy: Interpreting data

    Getting pupils ready

    Year 7

    Pupils compare the mean and range of two classes' times-table test scores and write one sentence saying which class did better and why.

    Year 8

    Pupils critique misleading newspaper graphs with cut-off axes, then run a dice experiment comparing relative frequency with the theoretical probability.

    Year 9

    Pupils compare two data sets using the median and interquartile range, then write a conclusion that answers the original question and names one limitation of the data.

    Show the specification wording and the LNF statements

    Where it is in the specification: Units 1 and 3, Section 4.2.21 to 4.2.23, page 44, and Unit 2, Sections 4.3 to 4.4, pages 45 to 47

    “draw inferences and conclusions from summary measures and data representations, relate results back to the original problem”

    Progression step 3

    • I can extract and interpret information from an increasing range of diagrams, timetables and graphs (including pie charts).

    • I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain.

    • I can use mean to interpret a simple data set.

    Progression step 4

    • I can interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading.

    • I can use mean, median, mode and range to compare data (continuous and discrete), and can choose the most appropriate average.

    • I can examine results critically, select and justify choice of statistics, recognising the limitations of any assumptions and their effect on the conclusions drawn.

    Progression step 5

    • I can interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading.

    • I can interpret mathematical information; drawing inferences from graphs, diagrams and data, including discussion on limitations of data.

    • I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain.

Source: WJEC GCSE Mathematics and Numeracy (Double Award) Specification, for teaching from September 2025, Version 5, September 2025.