Reading notes · Pre-enrolment · 27 August 2026
Re-learning maths: tracing the primary curriculum
I start my PGCE next week! I am incredibly excited and somewhat nervous. One of my pre-enrolment tasks was to cover a main subject and part of the National Curriculum. With maths probably being my weaker subject, I opted for this.
I found reading through the development of mathematics quite dry, to be honest. Still, it was useful to get a feel for the progression—and it made me excited about all the maths I am going to re-learn. I never thought I would say that!
Purpose of the National Curriculum
My initial thoughts were about its emphasis on giving children a spiritual, emotional and intellectual education: an introduction to the best ideas, principles, knowledge and tools that humanity has been able to come up with so far.
As I read, I felt a sense of responsibility, but also fascination and gratitude that we have a profession which aims to impart this to children. How wonderful. I am excited to become acquainted with it and tackle the challenge of sharing, cultivating and furnishing the minds of the next generation with this foundation as effectively as I can muster and manage.
The emphasis on the spiritual dimension feels like something that may be increasingly questioned. Yet, to me, it feels wise to incorporate rituals of togetherness, origin and depth too.
Inclusion
The document makes clear that teachers play an important role in meeting a child where they are and tailoring resources, teaching and support to enable that child to access the treasures the National Curriculum has to offer.
This requires taking account of identity, SEND, disability and children for whom English is not a first language. It is about carefully adapting plans and teaching to deliver well for a range of differences.
I was slightly concerned that there appeared to be a greater emphasis on ensuring children do not fall behind than on enabling those with the greatest attainment to flourish too.
“They should plan stretching work for pupils whose attainment is significantly above the expected standard. They have an even greater obligation to plan lessons for pupils who have low levels of prior attainment or come from disadvantaged backgrounds.”
Numeracy
Numeracy is presented as a foundational tool for grasping other subjects. Foundations therefore need to be laid effectively in arithmetic, measurement, geometry, algebra, probability, risk, uncertainty, and the collection and presentation of data.
Years 1–5
How mathematical understanding develops
These notes condense the sequence I saw across the primary years. Each strand moves from practical recognition towards increasingly independent selection, connection and reasoning.
Number and place value
Count to 100 forwards and backwards, find one more or one less than a given number, and count in 2s, 5s and 10s.
Count in 2s, 3s, 5s and 10s; recognise tens and ones; represent and compare numbers; and write numbers to 100.
Count in multiples of 4, 8, 50 and 100; recognise hundreds, tens and ones; order numbers to 1,000; and solve related problems.
Count in multiples of 6, 7, 9, 25 and 1,000; cross zero into negative numbers; compare four-digit numbers; round; solve problems; and read Roman numerals to 100.
Work with numbers to 1,000,000; count in powers of 10; interpret negative numbers; compare and round large numbers; solve problems; and read Roman numerals to 1,000.
The progression: Children move from counting and recognising small numbers to understanding increasingly large numbers, place value, rounding and negative numbers. The emphasis shifts towards comparing, ordering and using number knowledge to solve problems.
Addition and subtraction
Use mathematical statements and the symbols +, − and =; use number bonds to 20.
Continue using concrete objects while beginning written methods; know addition and subtraction facts to 20; and explore relationships between calculations.
Add and subtract three-digit numbers using formal column methods; estimate and use the inverse to check; and solve missing-number problems.
Use formal column methods with up to four digits; estimate and check answers; and solve two-step problems in context.
Add and subtract numbers with more than four digits; choose formal or mental methods; use rounding to check accuracy; and solve multi-step problems.
The progression: Children progress from number bonds and simple calculations to formal written methods, mental strategies and multi-step problems. They increasingly choose suitable methods, estimate answers and use inverse operations to check their work.
Multiplication and division
Solve one-step problems using objects and pictorial representations.
Use the 2-, 5- and 10-times tables and the symbols ×, ÷ and =; understand that multiplication is commutative while division is not.
Recall facts for 3, 4 and 8; multiply two-digit numbers by one digit; and solve missing-number and scaling problems.
Recall tables to 12 × 12; use factor pairs, commutativity and mental methods; and multiply up to three-digit numbers by one digit.
Work with factors, multiples and primes; use formal multiplication and division; interpret remainders; work with powers of 10, square numbers and cube numbers.
The progression: Learning develops from equal groups and simple times-table facts to secure recall, formal calculation and understanding factors, multiples, primes and remainders. Multiplication and division become increasingly connected to wider problem-solving.
Fractions
Recognise halves and quarters as two or four equal parts of an object.
Write and solve simple fractions; understand thirds and quarters.
Count in tenths; recognise fractions as numbers; add and subtract fractions with the same denominator; compare, order and solve problems.
Recognise equivalence; count in hundredths; calculate fractions of quantities; connect common fractions and decimals; compare and round decimals.
Compare and order fractions; convert mixed and improper fractions; calculate with related fractions; and work with thousandths, decimals and percentages.
The progression: Children move from recognising simple fractions of objects to treating fractions as numbers. They increasingly work with equivalence, decimals and percentages and use these relationships to compare quantities and solve problems.
Measurement
Compare and describe measures; record measurements; recognise coins; sequence events; and recognise dates.
Use standard units; combine coins; solve practical problems using measures; and tell the time to five-minute intervals.
Work with length, mass and capacity; measure perimeter; calculate money and change; read clocks to the nearest minute; and compare durations.
Convert units; calculate perimeter and area; work with money; convert 12- and 24-hour time; and solve measurement problems.
Convert metric units and use approximate imperial equivalents; calculate perimeter and area; estimate volume; and convert units of time.
The progression: Children progress from recognising and comparing everyday measures to calculating, converting and solving problems using standard units. They increasingly connect measurement with number, decimals, area, perimeter and volume.
Geometry
Name common 2D and 3D shapes and describe whole and half turns.
Use terms including right angle, quarter turn, clockwise and anticlockwise; order and arrange mathematical objects.
Draw 2D and make 3D shapes; identify angles, right angles, horizontal and vertical lines, and perpendicular and parallel lines.
Classify triangles and quadrilaterals; identify acute and obtuse angles; use symmetry; work with first-quadrant coordinates and translations.
Identify 3D shapes from 2D representations; measure and compare angles; reason about rectangles and polygons; and describe reflections and translations.
The progression: Children move from naming shapes and describing simple movement to analysing properties, angles, symmetry and position. Later they use coordinates, reflection and translation and reason more precisely about geometric relationships.
Statistics
Use pictograms, tally charts, block diagrams and simple tables; sort objects and compare categorical data.
Use bar charts, pictograms and tables and solve one-step and two-step questions.
Present and interpret discrete and continuous data using charts and graphs; solve comparison, sum and difference problems.
Solve problems using line graphs; complete and interpret tables and timetables.
The progression: Children progress from presenting simple categorical data to interpreting increasingly complex graphs and tables. The emphasis shifts towards comparison and using data to answer multi-step questions.
The upper-primary shift
Year 6
By Year 6, pupils bring strands together, choose methods more independently and reason about relationships between quantities.
Number and place value
Read, order and compare numbers to 10 million; round accurately; use negative numbers in context; and solve increasingly complex number problems.
Four operations
Multiply and divide up to four-digit numbers using formal methods; interpret remainders; calculate mentally; identify factors, multiples and primes; use the order of operations; solve multi-step problems; and connect fractions, decimals and percentages.
Ratio and proportion
Solve problems involving relative quantities, percentages, scale factors, unequal sharing and grouping.
Algebra
Use simple formulae; generate linear sequences; express missing-number problems algebraically; and explore values that satisfy equations.
Measurement
Convert standard units using decimals; relate miles and kilometres; reason about area and perimeter; and calculate areas and volumes.
Geometry
Construct and classify shapes; find unknown angles; understand circles; use all four coordinate quadrants; and translate and reflect shapes.
Statistics
Interpret and construct pie charts and line graphs; solve problems with them; and calculate and interpret the mean.
Overall reflection so far
From handling quantities to reasoning with relationships
Maths appears to progress from concrete and practical foundations towards increasingly abstract, connected and independent mathematical reasoning. In the earlier years, children focus on number and place value, simple calculation, and hands-on exploration of measures and shapes. As those foundations become secure, different areas begin to overlap more clearly.
By Years 5 and 6, children increasingly use fractions, decimals, percentages, ratio and proportion together to solve multi-step problems. There is greater emphasis on choosing appropriate methods, following rules such as the order of operations, checking whether answers are reasonable, and explaining how and why a method works.
Year 6 brings a further shift towards generalisation and mathematical relationships. Algebra represents unknown values, sequences and relationships, while ratio, scale and percentages require children to think about how quantities relate rather than simply what their individual values are.
Overall, I see a gradual increase in abstraction: from manipulating physical quantities and recognising basic numerical relationships towards missing values, transformations, symbols, sequences and proportions. Mathematics becomes less about performing isolated calculations and increasingly about representing, connecting, selecting and reasoning with mathematical ideas.
Reference
Glossary of key terms
- Acute angle
- An angle smaller than 90°.
- Associative law
- Numbers can be regrouped in addition or multiplication without changing the answer.
- Categorical data
- Data grouped into named categories rather than measured amounts.
- Commutativity
- Numbers can be added or multiplied in either order without changing the answer.
- Composite number
- A whole number greater than 1 with more than two factors.
- Continuous data
- Measured data that can take any value within a range.
- Coordinates
- A pair of numbers describing a position on a grid, written (x, y).
- Cube number
- A number multiplied by itself twice, such as 3 × 3 × 3 = 27.
- Discrete data
- Data consisting of separate, countable values.
- Equivalent fractions
- Fractions with the same value, such as ½ and 2/4.
- Factor
- A whole number that divides exactly into another number.
- Factor pair
- Two numbers that multiply together to make another number.
- First quadrant
- The area of a coordinate grid where both coordinates are positive.
- Improper fraction
- A fraction whose numerator is equal to or greater than its denominator.
- Integer
- A whole number, including positive numbers, negative numbers and zero.
- Integer multiplication
- Multiplication involving whole numbers, including positive and negative integers.
- Mean
- An average found by adding the values and dividing by the number of values.
- Mixed number
- A whole number and a fraction combined, such as 2½.
- Multiple
- A number produced by multiplying another number by a whole number.
- Non-unit fraction
- A fraction with a numerator greater than 1, such as ¾.
- Number bonds
- Pairs of numbers that combine to make a given total.
- Obtuse angle
- An angle greater than 90° but less than 180°.
- Parallelogram
- A quadrilateral with two pairs of parallel sides.
- Place value
- The value of a digit according to its position in a number.
- Positive integer scaling
- Multiplying a quantity by a positive whole number, such as three times as many.
- Prime factor
- A factor that is also a prime number.
- Prime number
- A number greater than 1 with exactly two factors: 1 and itself.
- Reflex angle
- An angle greater than 180° but less than 360°.
- Remainder
- The amount left over when a number cannot be divided exactly.
- Scale factor
- The amount by which a shape or quantity is enlarged or reduced.
- Square number
- A number multiplied by itself, such as 5 × 5 = 25.
- Unit fraction
- A fraction with a numerator of 1, such as ¼.
Subject knowledge
Areas for my own potential growth
A modest BBC Bitesize revision plan to help me rebuild confidence before and during training.
- 1Fractions, decimals and percentages
Equivalent fractions, mixed and improper fractions, conversions and fractions or percentages of quantities.
- 2Ratio, proportion and scale factor
Relative quantities, scaling, unequal sharing and percentages.
- 3Factors, multiples and prime numbers
Factor pairs, common factors, primes, square numbers and cube numbers.
- 4Algebra and order of operations
Formulae, missing values, sequences, symbols and calculation order.
- 5Angles, coordinates and transformations
Acute, obtuse and reflex angles; four-quadrant coordinates; reflection and translation.
- 6Data and averages
Discrete and continuous data, line graphs, pie charts and the mean.
Priority: spend most time on areas 1–4, with 5–6 as lighter revision.