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)

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:

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

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

Questioning

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

Stages of Practice

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)

click for lionheart maths 5 year curriculum overview

Mathematics Head of Department