# Mathematics

We aim to develop talented mathematicians with excellent problem solving skills. ## Subject Area Curriculum Intent

### 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)

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:

### reviewing material

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

### Sequencing Concepts & Modelling

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

for pupils to correct

Examples of increasing difficulty

Fading of examples to improve scaffolding for pupils

Better use of dual coding when presenting examples

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

### Questioning

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

### Stages of Practice

Guide pupil practice
current planned

Modelled examples (copied into books for pupils to reference)

Walking, talking mocks

Additional detail in explanations when needed (identified through circulation and questioning)

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

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
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
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)

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
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
standard form
Enlargement; Negative
scale factors of
enlargement
Coordinates
(including midpoints,
problems)
Surface area and volume
of pyramids, cones and
spheres (including exact
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