Mathematics

Curriculum Sequencing

The current curriculum sequencing is set out below:

	autumn 1	autumn 2	spring 1	spring2	summer 1	summer 2
year 7	Additive Relationships	Multiplicative Relationships	Geometrical Reasoning	Fractions	The Grammar of Algebra	Percentages and statistics
year 8	Number	Algebra	2-D geometry	Proportional reasoning	3-D geometry	Statistics
year 9	Number 1: Types of number, estimating and approximating. Fractions and decimals.	Number 1: Types of number, estimating and approximating. Fractions and decimals.	Algebra 1: Making sense of algebra and sequences	Geometry 1: Lines, Angles & Shapes. Measures	Statistics 1: Statistical measures	Geometry 2: Nets, elevations and Pythagoras’ Theorem   Algebra 3: Using expressions and formulae
year 10	Geometry 3: Area, perimeter and volume Number 1: Surds (Higher)	Statistics 2: Collecting data. Statistics 3: Drawing graphs and charts	Algebra 4: Coordinates, plotting and sketching graph	Geometry 4: Trigonometry Statistics 4: Probability	Algebra 5: Equations with fractions and simultaneous equations	Geometry 5: Transformations Vectors
year 11	Geometry 5: Consolidate transformations (F). Vectors (H) Algebra 6: Real life graphs	Geometry 6: Constructions and loci Algebra 7: Quadratic, cubic, circular and exponential function	Algebra 7: Quadratic, cubic, circular and exponential functions (cont.)	Geometry 7: Circle theorems Revision and extension	Revision and extension	Exams

This is the LAT 5 year plan we are working towards. So far year 7 is being implemented and our year 8 is being developed

	autumn 1	autumn 2	spring 1	spring2	summer 1	summer 2
year 7	Additive Relationships	Multiplicative Relationships	Geometrical Reasoning	Fractions	The Grammar of Algebra	Percentages and statistics
year 8	Number	Algebra	2-D geometry	Proportional reasoning	3-D geometry	Statistics
year 9	Graphs and proportion	Algebra	2-D geometry	Equations and inequalities	Geometry	Statistics
year 10	Number	Geometry	Reasoning	Geometry and Number	Sampling and probability	Algebra
year 11	Algebra and geometry	Number and statistics	Revision and Extension 1	Revision and extension 2	Revision and extension 3	Exams

Sequenced to cover the whole of the NC
KS3 sequenced to lead to a deepening knowledge over time
Coverage at greater depth in KS3, emphasis on finding and filling gaps in knowledge before acceleration on to new content

Core principles (From the national curriculum)
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/239058/SECONDARY_national_curriculum_-_Mathematics.pdf

Aims
The national curriculum for mathematics aims to ensure that all pupils:

• Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• Can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Assessing Impact

• Following school policies on robust QA.
• Departmental reviews
• Work scrutinies
• Observations
• Learning walks
• Regular staff CPD to share best practice

 

Section 2: Connectedness (linking and co-ordinating)

KS3 sequenced to launch students ready for KS4 exam specification (from y10)

Key areas to be retained: Number, Algebra, Ration and Proportion, Geometry, Statistics and Probability (also all of KS2 and KS1 Maths)

From the AQA Spec

AO1: Use and apply standard techniques. Students should be able to:

• Accurately recall facts, terminology and definitions
• Use and interpret notation correctly
• Accurately carry out routine procedures or set tasks requiring multi-step solutions

AO2: Reason, interpret and communicate mathematically. Students should be able to:

• Make deductions, inferences and draw conclusions from mathematical information
• Construct chains of reasoning to achieve a given result
• Interpret and communicate information accurately
• Present arguments and proofs
• Assess the validity of an argument and critically evaluate a given way of presenting information

AO3: Solve problems within mathematics and in other contexts. Students should be able to:

• Translate problems in mathematical or non-mathematical contexts into a process or a series of
• Mathematical processes
• Make and use connections between different parts of mathematics
• Interpret results in the context of the given problem
• Evaluate methods used and results obtained
• Evaluate solutions to identify how they may have been affected by assumptions made

Opportunities for all to succeed and access mathematics. Differentiated by level of difficulty and also the amount of scaffolding given to pupils. On entry to KS4 sets will follow either H or F course, with a focus on cross-over material so that final tier of entry decided during y11

Section 3: Your subject: five year impact

We use maths every day, whether to count money or weigh calories. The curriculum as detailed above gives our pupils the opportunities, skills and knowledge to be successful in life and their future career. The maths teaching in Judgemeadow places a high emphasis on problem solving. Our ambition is for increased uptake of studying maths at Level 3.

Maths helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. Reasoning is our ability to think logically about a situation. Analytical and reasoning skills are important because they help us solve problems and look for solutions. While it may seem farfetched to think that solving maths problems in school can help you solve a problem in your life, the skills that you use in framing the problem, identifying the knowns and unknowns, and taking steps to solve the problem can be a very important strategy that can be applied to other problems in life.

Maths is important for balancing your budget because you will have a good understanding of how to make sure that your costs are less than the money you have. Balancing one’s bank account, for example, is an important life skill that requires maths in order to subtract balances. People who know maths are therefore less likely to go into debt because they did not know how much money they had versus how much money they spent. There have been studies by the DFE showing that good grades in GCSE maths lead to average higher future earnings for school-leavers.

Not only is maths used in daily life, but many careers use maths on a daily basis. You can find jobs that use maths in a variety of industries, such as financial services, health care and science. The complexity of maths varies from one career to the next. Obviously, mathematicians and scientists rely on mathematical principles to do the most basic aspects of their work such as test hypotheses. While scientific careers famously involve maths, they are not the only careers to do so. Even operating a cash register requires that one understands basic arithmetic. People working in a factory must be able to do mental arithmetic to keep track of the parts on the assembly line and must, in some cases, manipulate fabrication software utilising geometric properties (such as the dimensions of a part) in order to build their products. Really, any job requires maths because you must know how to interpret your pay-slip and bank account statement to balance your budget.

Research indicates that children who know maths are able to recruit certain brain regions more reliably, and have greater grey matter volume in those regions, than those who perform more poorly in maths. The brain regions involved in higher maths skills in high-performing children were associated with various cognitive tasks involving visual attention and decision-making. While correlation may not imply causation, this study indicates that the same brain regions that help you do maths are recruited in decision-making and attentional processes.

Section 4: Teaching and Learning

1. Interleaving: The maths department carry out frequent low stakes testing through interleaved sets of retrieval questions. This may be mostly during starters when pupils are given questions from mixed topics, revisiting key areas and concepts. This also incorporates retrieval practice.

2. Dual Coding: Through whole school and departmental CPD, maths staff have developed their teaching resources, i.e. powerpoints and flipcharts to simplify these as much as possible; emphasising diagrams, key text and concepts without cluttered displays, and using different colours only when needed for clarification.

3. Retrieval Practice: Retrieval of key conceptual and procedural knowledge through:

• Interleaved questions sets in lessons
• Weekly Homework (Yr8-11) based on retrieval of prior learning as well as current topics
• Year 7 daily homework booklets which are standard across the LAT.
• Regular topic testing
• Online quizzes for independent practice
• Year 7 daily homework

4. Elaboration: Questioning is key in encouraging elaboration. We encourage pupils to do this by:

• Think, pair, share
• Pause, pounce, bounce
• Allowing sufficient thinking time
• Using a balance of closed and open questions
• Students are encouraged to use correct vocabulary and explain ideas in detail

5. Concrete examples: Detailed modelled examples are copied into books for pupils to reference.

Key vocabulary is taught explicitly using Frayer Models (Yr 7) with consistent definitions

Pupils are encouraged to use correct vocabulary and explain their ideas in detail. There is consistent use of correct mathematical vocabulary by staff and pupils.

Judgemeadow Maths Department current and planned pedagogical approaches

The following outlines how the teaching in mathematics incorporates aspects of Rosenshine’s Principles of Instruction:

DAILY REVIEW
Current	Planned
Retrieval of key conceptual and procedural knowledge through interleaved questions sets in lessons & Year 7 daily homework	Greater consistency across the department Daily homework will extend to other year groups with the new curriculum
weekly and monthly review
current	planned
Weekly Homework (Yr8-11) based on retrieval of prior learning as well as current topics Regular topic testing Online quizzes for independent practice	Systematic follow-up work on identified misconceptions and errors
New material in small steps
current	planned
New KS3 curriculum breaks content into identified small steps Topics are built up from basic examples through to more complex Key vocabulary taught explicitly using Frayer Models (Yr 7) with consistent definitions	More consistency and careful teaching of vocabulary (Yr8-11) Consideration of how to reduce extrinsic cognitive load and embed concepts into long-term memory
Provide models
current	planned
Lots of expert modelling Modelled answers with misconceptions for pupils to correct Examples of increasing difficulty	Fading of examples to improve scaffolding for pupils Better use of dual coding when presenting examples
Scaffolds for difficult tasks
current	planned
Increased detail in modelled examples where necessary	Fading of examples to improve scaffolding for pupils Example-problem pairs and use of careful procedural and conceptual variation
Ask questions ‘ask more questions to more students in more depth'
Current	planned
Think, pair, share Pause, pounce, bounce Allow sufficient thinking time Balance of closed and open questions Students encouraged to use correct vocabulary and explain ideas in detail	Follow up questioning – expect more depth More consistent use of correct mathematical vocabulary by staff and pupils
Check pupil understanding
current	planned
Expect pupils to elaborate (explain why/how) when answering questions Regular medium stakes (topic) testing Frequent low stakes testing through interleaved sets of retrieval questions	More use of diagnostic multiple choice questions with distractors selected to identify misconceptions Exit tickets
Guide pupil practice
current	planned
Detailed feedback on homework tasks Modelled examples (copied into books for pupils to reference) Walking, talking mocks Additional detail in explanations when needed (identified through circulation and questioning)	Fading of examples Higher quality expert / live modelling More use of visualisers to aid live modelling Example-problem pairs and use of careful procedural and conceptual variation
Obtain high success rate
current	planned
Very high expectations of behaviour and attitude Keeping attention on the learning Regular repetition of work on key conceptual and procedural knowledge Detailed feedback on homework tasks and assessments Diagnostic assessment (in class and as homework) and planned re-teaching to address identified gaps (particularly yr 11)	More consistency of planning for what pupils are thinking about rather than what they are doing Higher expectations of detail in pupils’ working Follow-up work on multiple occasions (where necessary) from homework and tests Increase use of diagnostic testing
Independent practice
current	planned
Independent practice during learning Homework booklets Access to online quizzes and questions GCSE past paper practice	Explicit teaching around the importance of pupils practicing without support (from teacher, notes or peers) Valuing and building in desirable difficulties and valuing learning over performance

Bibliography:
“Principles of Instruction” – Barak Rosenshine 2010 & 2012
“Rosenshine’s Principles in Action” – Tom Sherrington 2019
“How I wish I’d taught maths” – Craig Barton 2018
“What makes great teaching? Review of the underpinning research” – Coe et al 2014 (CEM)

curriculum overview

year 7
The Grammar of Algebra	Additive Relationships	Multiplicative Relationships	Geometrical Reasoning 1	Fractions
Sequences (term-to-term, not position-to-term)	Place value (including decimals)	Multiplication Facts & Properties of Arithmetic	Draw, Measure and Classify Angles	Fractional Thinking
Algebra as a language	Addition and Subtraction of Whole Numbers and Positive Decimals	Area, Factors and Multiples	Find Unknown Angles	Equivalence of Fractions
Functions	Addition and Subtraction Involving Negative Numbers	Formal Methods of Multiplication	Properties of triangles and quadrilaterals	Multiplication and Division of Fractions
Priority of operations	Median (as a positional value) Range (as a subtractive calculation)	Division Facts & Priority of Operations	Symmetry and Tessellation	Fractions of Amounts
Expressions	Perimeter of polygons	Models of Division & Properties of Division
		Formal Methods of Division
		Arithmetic Mean

year 8
Percentages	Sets and Building Numbers	Describing using Algebra	2-D geometry One	Proportional reasoning	3-D geometry	Organising and Representing Data
Developing Understanding of Percentages	Primes and Prime Factorisation	Review: Negative numbers and inequality statements	Construct Triangles and Quadrilaterals	Convert between percentages, vulgar fractions, and decimals	Rounding, significant figures and estimation	Collect and organise data
Percentage of a quantity	Venn Diagrams and Sets	Formulate and evaluate expressions	Find unknown angles (including parallel and transversal lines)	Percentage increase and decrease	Calculator skills	Interpret and compare statistical representations
Find the Whole, Given the Part (Fraction, Decimal or Percentage)	Adding and Subtracting Fractions	Linear equations (inc one and two step, unknown on both sides using all types of numbers) [NB Binomial expansion comes in yr 9]	Conversion of Units	Finding the whole given the part and the percentage	Circumference and area of a circle	Mean, median and mode averages
		Arithmetic (Linear) Sequences	Areas and perimeters of composite figures	Ratio and Rate	Visualise and identify 3-D shapes and their nets	The range and outliers
			rea of More Complex Shapes	Speed, Distance, Time	Volume of cuboid, prism, cylinder, composite solids
				Area scale factors	Volume scale factors

year 9
Graphs and proportion	Understanding Probability	Algebraic Manipulation	2-D geometry two	Linear Equations and inequalities	Geometry of Triangles One	Comparing Data
The Cartesian Plane	What is probability (inc representations)	Sequences including arithmetic and geometric	Triangles and quadrilaterals	Construct and solve linear equations and inequalities	Pythagoras’ theorem	Mean of grouped data
Direct and Inverse Proportion	Basic probability	Algebraic manipulation review	Angles in polygons	Graphical solutions to simultaneous linear equations	The unit circle	Comparing two data sets
Calculation with Scales	Theoretical and experimental (relative frequency)	Change the subject of a formula	Construction and loci		Similar triangles	Scatter graphs
Calculations with standard form	Venn diagrams		Congruence and similarity		Exploring trigonometry with a 30-60-90 triangle
					Use known angle and shape facts to obtain simple proofs

year 10
Non-linear Algebra	Number	Geometry	Reasoning	Geometry and Number	Sampling & probability
Expand and factorise binomials and trinomials	Ratio and Proportion	Transformations (translation, rotation, reflection); Combine Transformations	Vectors	Loci	Populations and samples
Algebraic fractions	Estimation; Limits of accuracy; Upper and lower bounds	Similar shapes	Key angle and shape facts	Properties of 3-D shapes; their plans and elevations	Theoretical and experimental probability
Quadratic equations and graphs; Complete the square; quadratic formula	Calculations with standard form	Enlargement; Negative scale factors of enlargement	Coordinates (including midpoints, problems)	Surface area and volume of pyramids, cones and spheres (including exact answers)	Listing
Simultaneous equations	Calculations with and rules of indices	Trigonometry in right angled triangles	Algebraic arguments	Similar areas and volumes	Set notation
Graphical solutions of equations	Fractional indices	3-D trigonometry and Pythagoras’ theorem	Equations of parallel & perpendicular lines	Trigonometric graphs	Combined events, including tree diagrams
Quadratic inequlities	Surds	Bearings	Further inequalities	Trigonometry in all triangles	Conditional probability
Cubic and reciprocal graphs	Compound interest		Angle proofs
Exponential graphs	Growth and decay		Vector proofs
	Recurring decimals

year 11
Algebra and geometry	Number and statistics	Kinomatics	Exams
Using angle and shape facts to derive results	Represent and describe distributions	Gradients of curves and areas under graphs
Proof in algebra and geometry (inc vectors)	Identify misleading graphs	Standard non-linear sequences
Arcs and sectors of circles	Time series	Quadratic sequences
Equation of a circle and the tangent to a circle	Correlation and lines of best fit	Recurrence relations
Apply and prove circle theorems	Histograms with equal and unequal class intervals	Solve equations by iteration
Variation	Cumulative frequency graphs and box plots	Functions and their inverses
Variation with powers	Solve problems involving compound units	Composite functions
		Transformations of functions