Maths Deep Dive Questions

What is a maths Ofsted examination?

The guidance notes for OFSTED inspectors are a useful tool to help senior leaders think about curriculum expectations. Although these training notes were not originally intended for classroom teachers, the 'inspection crib sheets' are a great utility for stimulating conversations about curriculum goals.

The infamous OFSTED examinations do require a good grasp of both the curriculum intent and cognitive science. There are no doubts that this professional knowledge can only improve conceptual learning and have a profound impact on the quality of teaching. But within a examination-focused inspection, for some classroom teachers, the challenge of being able to articulate their approach to teaching might prove challenging.

If your school is currently undergoing curriculum overviews then these documents are a useful tool for developing your curriculum vision. Within this post, we will outline the examination inspection methodology for mathematics. If nothing else, these OFSTED training documents can provide us with a useful tool for enhancing our mathematics curriculum.

If your school is not in England and you are not delivering the English national curriculum, then these deep-dive questions may still prove useful for your curriculum leaders. The primary mathematics aide-memoire and Ofsted examination curriculum focus points offer teaching staff a sound idea of not only what they might expect within a discussion with inspectors but also what effective teaching approaches might look like in practice.

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What is declarative knowledge in maths teaching?

Declarative knowledge in maths refers to the factual information students need to know, such as number facts, mathematical definitions, and formulas. This foundational knowledge must be explicitly taught and regularly rehearsed before students can apply it to solve problems. Teachers build this through direct instruction, worked examples, and systematic practice of key facts.

• Do plans outline the key number facts to be learned, as well as their benchmarks for automaticity?
• How well are mathematical vocabulary and sentence stems developed alongside key facts and methods?
• Are pupils equipped with rules and formulae for working with shape, distance, time, angles?
• Do plans ensure that pupils are familiarized with principles enabling the conversion of word problems into equations?
• Do pupils have a secure grasp of time, fraction and length facts?

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How do you develop procedural knowledge in mathematics?

Procedural knowledge develops through explicit modelling of mathematical methods, followed by guided practice with immediate feedback. Teachers should break complex procedures into smaller steps, ensuring students master each component before combining them. Regular practice with varied examples helps students recognise when and how to apply specific procedures.

• Do curriculum plans acknowledge the most efficient and accurate methods of calculation that pupils will use in their next stage of mathematics education?
• Is there a balance between procedures that rely on derivation and those that train recall?
• Are pupils equipped with knowledge of how to lay out calculations systematically and neatly?
• Are all pupils given procedural knowledge that enables them to work in the abstract?
• Can pupils calculate with speed and accuracy?

Conditional knowledge

• Do plans help pupils to familiarise themselves with the conditions where combinations of facts and methods will be useful?
• Do plans ensure that pupils obtain automaticity in linked facts and methods, before being expected to deploy them in problem-solving?
• Are problems chosen carefully, so that pupils are increasingly confident with seeing past the surface features and of recognising the deep structure of problems?
• Can pupils solve problems without resorting to unstructured trial and error approaches?

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How do sequences of lessons develop mathematical knowledge?

• Has the content been carefully selected to ensure pupils have the building blocks they need for later work?
• Once key facts and methods are learned, do plans allow pupils to apply their learning to different contexts?
• Is progression through the curriculum a guarantee for all and not overly influenced by choice?
• Do plans engineer the successful opportunities to connect concepts within and between topic sequences?
• Do plans rule out the acquisition of common misconceptions?
• Are pupil errors immediately highlighted and corrected?

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Why is memory important for learning mathematics?

Memory is crucial in mathematics because students must retrieve prior knowledgeto solve new problems and make connections between concepts. Without secure recall of number facts and procedures, students struggle with more complex mathematics as their working memory becomes overloaded. Effective maths teaching uses spaced practice and retrieval activities to strengthen long-term retention.

• Do plans ensure that consolidation and overlearning of content takes place at frequent intervals?
• Are pupils able to refer to work completed and content learned in previous lessons?
• Do plans strike a balance between rehearsal of explanations or proof of understanding and rehearsal of core facts and methods needed to complete exercises and solve problems?
• Do plans prioritise thinking about core content by ensuring that pupils know what to do?
• Do plans actively prevent the need for guessing, casting around for clues and unstructured trial and error?
• Can pupils recall, rather than derive, facts and formulae, without the use of memory aids?

Early Years

• Do plans close the school entry gap in knowledge of number?
• Do plans allow for learning of key number facts and an efficient and accurate method of counting before pupils are expected to solve everyday problems?
• Are pupils given key mathematical language?
• Are curriculum plans equitable?

Disciplinary rigour

• Do pupils know that proficiency in mathematics requires sustained effort and focus?
• Are pupils encouraged to be precise, accurate and systematic in their mathematical endeavours?
• Do plans give pupils undisturbed opportunities to hone their effort and focus?

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What are the most effective pedagogical approaches for teaching maths?

Effective maths pedagogy combines explicit instructionwith carefully structured practice, moving from concrete representations to abstract concepts. Teachers should use variation theory to highlight mathematical structures and connections while maintaining high expectations for all students. Regular formative assessment helps teachers adapt their instruction to address misconceptions immediately.

Instruction

• Are instructional approaches systematic, with new content introduced in a logical order, building on what pupils know?
• Can pupils answer questions without needing to guess or cast around for clues?
• Does instruction make sense to pupils?
• Are diagrams and physical apparatus helpful?

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How should retrieval practice be used in maths assessment?

Retrieval practicein maths should include daily low-stakes quizzing on previously taught content, not just recent topics. Teachers can use starter activities, exit tickets, and homework to regularly test key facts and procedures from across the curriculum. This approach strengthens memory and helps identify gaps in understanding before they become barriers to new learning.

Component parts (facts and methods)

• Are pupils regularly tested on their recall of core maths facts?
• Are the prescribed benchmarks for accuracy and speed of recall true indicators of automaticity?
• Do pupils know they are improving?
• Do plans incorporate opportunities for assessing pupils’ knowledge of core methods such as finding equivalent fractions, converting measurements or using short division outside of requirements to use these methods for problem-solving?

Composite skills (applied facts and methods)

• Are pupils prepared for tests of composite skills?
• Are summative tests of this nature kept to a minimum?
• Are pupils familiar with the typical language used in these tests?

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What makes a strong maths curriculum culture in schools?

A strong maths curriculum culture ensures all teachers understand and implement the intended curriculum sequence, with consistent approaches across year groups. Leadership should provide regular training on cognitive science principles and mathematical pedagogy while monitoring implementation through learning walks and book scrutiny. The culture must prioritise deep understanding over superficial coverage and celebrate mathematical thinking.

• Is the homework policy equitable and effective, supporting the consolidation of learning and closing knowledge and retention gaps?
• Are adequate resources available?
• Does the calculation policy prioritise learning/use of efficient and accurate methods of calculation for all pupils?
• Is the marking policy reasonable and clear?
• Is proficiency in mathematics celebrated?
• Do pupils appreciate the ways in which mathematics underpins advances in technology and science?
• Is quiet, focused scholarship in mathematics promoted?
• Do pupils know that creativity, motivation and love of mathematics follow success born of hard work?
• What enrichment activities are offered?

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When should schools introduce key mathematical facts and definitions?

Mathematical facts and definitions should be introduced systematically according to a carefully planned curriculum sequence that builds from foundational concepts. Schools must ensure prerequisite declarative knowledge is secure before introducing new content, typically following a concrete-pictorial-abstract progression. Regular assessment of factual recall helps identify when students are ready to progress to more complex concepts.

Early years

Numbers and number bonds to 10; concepts and vocabulary for talking about maths and mathematical patterns (size, weight, capacity, quantity, position, distance, time)

Key Stage 1

• Concepts, representations and associated vocabulary:
• Simple fractions
• Basic arithmetic: the numbering system and its symbols, place value, conventions for expressions and equations, counting, addition, subtraction, equal sharing, doubling, balancing simple arithmetic equations, classifying numbers (odd, even, teens), inverse operations, estimation, numerical patterns
• Basic measurement: length; capacity; time; position; relative size, position, direction, motion, quantity
• Currency and coinage
• Basic geometry: 2D and 3D shapes, geometric patterns
• Categorical data
• Maths facts: all number bonds within and between 20; key number bonds within and between 100, all multiplication facts for the 2, 5 and 10 multiplication tables, key ‘fraction facts’ such as ‘half of 6 is 3’, key ‘time facts’ such as the number of minutes in an hour

Lower Key Stage 2

Concepts, representations and associated vocabulary:

• Arithmetic: enhanced knowledge of the code for number (to 1000s) including patterns and associated rules for addition and subtraction of numbers, decimal numbers, place value, negative numbers, associative and distributive laws
• Maths facts: all multiplication facts for the 3, 4, 6, 7, 8, 9, 11, 12 multiplication tables, decimal equivalents of key fractions
• Equivalent fractions
• Formulae: Units of measurement conversion rules, formulae for perimeter and area
• Roman Numeral system and associated historical facts
• Geometry facts: right angles, acute and obtuse angles, right angles in whole and half turns, symmetry, triangle and quadrilateral classifications; horizontal, perpendicular, parallel and perpendicular lines
• Links between words/phrases in word problems and their corresponding operations in mathematics (e.g. ‘spending’ is associated with ‘subtraction from an amount’)
• The rules for multiplying and dividing by 10, 100 and 1000
• First quadrant grid coordinate principles

Upper Key Stage 2

Concepts, representations and associated vocabulary:

• Enhanced knowledge of the code for number: up to and within 1 000 000, multiples, factors, decimals, prime number facts to 100, composite numbers, indexation for square and cubed numbers
• Properties of linear sequences
• Conversion facts metric to imperial measurements and vice versa
• Key circle, quadrilateral and triangle facts and formulae (e.g. Angles on a straight line sum to 180 degrees)
• Rules and principles governing order of operations

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How can teachers ensure deep learning of mathematical procedures?

Deep procedural learning occurs when students understand why procedures work, not just how to execute them mechanically. Teachers should explicitly connect procedures to underlying mathematical concepts and provide opportunities for students to explain their reasoning. Varying problem contexts while maintaining the same procedure helps students recognise deep mathematical structures.

Early years

Accurate counting, single-digit addition and subtraction, halving doubling and sharing

Key Stage 1

Efficient and accurate methods:

• Counting up and down in 1s, 2, 5s, 10s and 1/2s; addition; subtraction, equal sharing, division and multiplication
• Reading, writing of the digits/symbols, vocabulary and phrases required for working with simple fractions, arithmetic expressions and equations
• Measuring length, capacity, time and monetary value
• Presentation and layout of calculations
• Using a ruler
• Spotting and making geometric and numerical patterns
• Construction and interpretation of categorical data: pictograms, charts, tables

Lower Key Stage 2

Efficient and accurate methods:

• Counting up and down in multiples of 3, 4, 6, 7, 8, 9, 11, 12, 25, 50, 100, 1000, in tenths, in ones through to negative numbers
• Column addition and subtraction
• Mental addition and subtraction using patterns and rules of number
• Short division and multiplication
• Mental multiplication using derived facts
• Fractions: finding unit and non-unit fractions of amounts, common equivalents, addition, subtraction and comparison of fractions with the same denominator
• Measure, compare, add, subtract: lengths, mass, capacity (all units of measurement)
• Read, write and compare roman numerals
• Draw 2D and 3D shapes
• Interpret and present data
• Estimation and rounding
• First quadrant grid construction, plotting and translation of points

Upper Key Stage 2

Efficient and accurate methods

• Scaling, coordinate geometry in all four quadrants
• Division with remainders as fractions, decimals and where rounding is needed
• Fractions: conversion mixed to improper and vice versa, add, subtract and multiply
• Finding percentages of amounts
• Converting units of measurement
• Measurement of length, angles, area, perimeter, volume
• Use of order of operations
• Convert between fractions, decimals and percentages Linear algebra, basic trigonometry Long multiplication and division

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What is conditional knowledge in mathematics and why does it matter?

Conditional knowledge in mathematics is knowing when and why to use specific strategies or procedures to solve problems. This knowledge develops through exposure to varied problem types where students must select appropriate methods rather than following prescribed steps. Teachers build conditional knowledge by explicitly discussing strategy selection and providing mixed practice where students must choose between multiple approaches.

Early years

Use combinations of number facts, shape facts, pattern facts, methods of counting, addition and subtraction to

• Play games
• Sing songs
• Answer questions
• Talk about everyday objects
• Solve problems using objects within continuous provision

Key Stage 1

Use combinations of taught and rehearsed facts and methods to:

• Complete written exercises
• Solve missing number problems
• Solve simple word problems involving arithmetic, money, time and fractions
• Solve data and measurement problems

Lower Key Stage 2

Employ a mix of learned and practiced information and methods to:

• Complete written exercises
• Solve missing number, length problems
• Solve word problems involving arithmetic, fractions, data handling, shape, length, mass and capacity

Upper Key Stage 2

Utilise a blend of memorised and prepared tools and techniques for: finishing written tasks

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Frequently Asked Questions

What exactly is a maths Ofsted examination and how does it differ from regular inspections?

A maths Ofsted examination is a focused inspection methodology that examines the mathematics curriculum through detailed conversations with teachers about their curriculum intent and implementation. It requires teachers to articulate their approach to teaching mathematics and demonstrate understanding of both curriculum goals and cognitive science principles that support effective maths learning.

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How can teachers effectively prepare for examination conversations with Ofsted inspectors?

Teachers should be ready to discuss how they develop declarative, procedural, and conditional knowledge in their pupils, including specific examples of how they teach number facts, mathematical vocabulary, and problem-solving strategies. They need to articulate how their lesson sequences build mathematical knowledge systematically and how they use memory techniques like spaced practice and retrieval activities to ensure long-term retention.

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What is the Memory Mathematics Framework and how does it transform lesson planning?

The Memory Mathematics Framework applies cognitive science principles to mathematics teaching, ensuring pupils retain rather than just encounter mathematical knowledge. It emphasises the importance of explicit teaching of declarative knowledge, systematic practice of procedures, and regular consolidation through retrieval practice to strengthen long-term memory and prevent working memory overload.

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Why do pupils struggle with word problems and what teaching approach helps them overcome this?

Pupils struggle with word problems because they focus on surface features rather than recognising the underlying mathematical structure. The solution is to carefully select problems that help pupils see past surface details, ensure they have automaticity in key facts and methods before problem-solving, and teach them to convert word problems into equations systematically.

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How should schools balance the teaching of mathematical facts versus understanding in their curriculum?

Schools should ensure pupils master declarative knowledge (facts, vocabulary, formulas) through explicit teaching and regular rehearsal before expecting them to apply this knowledge to problem-solving. Plans should balance procedures that rely on derivation with those that require automatic recall, ensuring pupils can access abstract mathematical thinking without being hindered by poor recall of basic facts.

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What specific questions should curriculum leaders ask to audit their maths provision effectively?

Leaders should examine whether plans outline key number facts with automaticity benchmarks, ensure mathematical vocabulary is developed alongside methods, and check that pupils are equipped with rules for working with shape, time, and measurement. They should also verify that lesson sequences prevent common misconceptions and provide frequent opportunities for consolidation and overlearning.

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How can retrieval practice be implemented effectively in mathematics teaching and assessment?

Retrieval practice should include daily low-stakes quizzing on previously taught content from across the curriculum, not just recent topics. Teachers can use starter activities, exit tickets, and homework to regularly test key facts and procedures, which strengthens memory pathways and helps identify gaps in understanding before they become problematic.