Mathematics

Head of Department: Mr K Williams

At Oldershaw we aim to give all our students the opportunity to learn and enjoy mathematics in a safe, pleasant and stimulating environment. By providing a well planned and structured curriculum students are able to engage in lessons where interactive whole class teaching, problem solving and rich tasks challenge the full range of ages and abilities. All learners at the Academy have the opportunity to develop skills in Numeracy, Algebra, Shape and Space and Data Handling as well as the use and application of mathematics and consequently we meet all the statutory requirements of the National Curriculum.

The Mathematics Department aims to:

Provide all students with a deep and broad understanding of the application of mathematics in everyday life through developing tasks which are relatable for our pupils and the community in which we teach.
Ensure that all students have the opportunity to make sufficient progress with their mathematical skills. Staff teach mathematics through the use of concrete, abstract and pictorial mediums to ensure every learner has to opportunity to succeed in making progress.
Be ambitious for our students by providing stretch and challenge to all pupils in a range of different ways while also supporting and guiding them on a path where success is achievable for all.
Frequently review and evaluate the progress of our learners through a range of methods. Pupils are required to complete work in which they understand demonstrates their learnt skills along with formative and summative assessments. Any pupils who are identified to not be making the required progress are provided with structured and tailored intervention where possible.
Incorporate cultural capital into lessons in all year groups. We aim to prepare students for the real world by ensuring that they develop the skills required to apply mathematics in everyday life.

Our curriculum is implemented by ensuring that:

Teaching is tailored to match the ability and skills of all learners
Teachers ensure that students can apply mathematical skills to a range of
Students are set homework on a regular basis. All students have access to the on-line “My Maths” homework resource and are expected to complete tasks set by their mathematics teacher in order to consolidate their learning.

In Year 7

Pupils entering Oldershaw Academy are initially taught in mixed ability groups. During this time, they are baseline tested and these scores alongside KS2 results are used to place the pupils in sets by ability.

At Key Stage 3, pupils cover a curriculum that is shaped by four underlying principles: one curriculum for all; topics covered by pupils are the same but where differentiation is used to make them accessible is implemented; a deep understanding and a good number sense underpinning all with the ability to problem solve. All topics are covered in depth to promote mastery and understanding. Our approach to learning enables learners to develop the tools necessary in order to reason and problem solve. The initial content focuses heavily (though not exclusively) on number work and algebra as these are considered essential building blocks for the rest of the content. Students who enter below the expected standard follow a course which specifically targets the main areas of weakness with a particular emphasis on numeracy.

Mastery enables pupils to continually apply their prior knowledge from Key Stage 2 alongside new learning in lessons. Continual recapping supports a deep conceptual understanding of how concepts interact with each other in mathematics.

During DIRT week, pupils have the opportunity to reflect over their work with their class teacher. This time also provides students with the opportunity to complete a mathematically rich activity, as part of our culture capital programme, specifically looking at functional mathematics in everyday life through a variety of mediums.

Assessments are completed on a half-termly basis with analysis completed on each pupil based on their result. Students who have significantly under-performed or are not making the required progress to meet their end of Key Stage 3 target are provided with structured intervention in order to support their learning. Interventions include working in small groups after school or being placed on our IDL numeracy programme. All interventions are monitored to ensure that they are enabling students to improve their performance.

Autumn Term

Students spend the term developing a greater sense of number systems and being able to make generalisations about them to improve their number sense. This is split into the following sub-topics:

Numbers and Numerals: Students explore time to see that numeral systems can be used to group number in ways other than base 10. This provides students with a context in which to explore decomposition and regrouping of number. Students also meet the Indian and Mayan number systems. By exploring number systems with different bases, students become more aware of the patterns that exists in base 10.

Axioms and Arrays: Students develop their understanding of different models for multiplication and division. Students also explore the axioms of number and which operations they apply to. The unit begins by looking at structures which lead to multiplication and the different models that can be associated with these structures. The array model is developed to explore the commutativity of multiplication. The array model is again used to introduce the associativity and distributivity axioms.

Factors and Multiples: students are given the opportunity to explore the ‘structure’ of the natural numbers. Students will be introduced to factors, multiples and important sets of numbers such as prime numbers, square numbers and cube numbers. Once the fundamental concepts have been introduced students are given the opportunity to develop their understanding, conjecture, problem solve and generalise.

Order of Operations: students use a range of representations to show combined calculations using the four operations. These include written calculations, worded statements, function machines and area models. By converting between these representations’ students will understand how the priority order of the four operations is embedded into the ‘grammar’ of written calculations

Positive and Negative Numbers: Students learn to interpret negative quantities in practical situations allowing students experiences to shift their thinking from the idea that “measures” must be positive. Students will have experienced negative numbers in context from primary education and know that the number line extends beyond zero.

Expressions and Equations: students use algebraic notation to express the multiples of integers and see collecting like terms as a development of the distributive property. Students first use a range of representations and contexts including Cuisenaire rods, bar models, number pyramids to manipulate expressions into their simplest form as well as representing equality statements. Seen alongside ‘tracking calculations’, students will develop flexibility in expressing relationships algebraically as well as being comfortable substituting constant values for variables.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Christmas.

Spring Term

Students spend the term developing a greater sense 2D Shapes and the Cartesian Plane. This is split into the following sub-topics:

Angles: estimating, measuring, drawing and calculating angles. Students describe, classify and identify types of angles using clear vocabulary, and measure and draw angles accurately. Students revise facts involving angles around a point, angles at a point on a straight line and vertically opposite angles from experiences in primary school. Students will begin to generalise these angle facts.

Classifying 2D Shapes: analysing the geometric properties of polygons before focusing more closely on triangles and quadrilaterals. Students begin by classifying polygons by their properties including number of sides, number of line and rotational symmetries, types of internal angles, number of equal sides, and number of parallel sides. They are encouraged to conjecture and prove which properties are the result of other properties. For example, if a polygon has as many line symmetries as sides then it must be regular.

Constructing Triangles and Quadrilaterals: students draw and construct triangles and quadrilaterals. In addition, there is time allocated for a further analysis of their geometrical properties. Students draw and measure angles within this context allowing them to practise the skills learned in the previous unit.

Coordinates: students develop their understanding of the cartesian coordinate grid and solve problems in all four quadrants. Students will be familiar with coordinates from work at primary school and in other subjects. The tasks in this unit will give students opportunities to apply their understanding from previous units including negative numbers and geometric properties of triangles and quadrilaterals.

Area of 2D Shapes: the concept of area as a measurable quantity is introduced. This begins by revisiting arrays introduced in previous units for multiplication. Starting with rectilinear shapes, this is built upon to explore the area of other shapes including, triangles and special quadrilaterals. Reasoning about calculating the area of shapes is built up by decomposing shapes and connecting to existing knowledge.

Transforming Shapes: students are expected to consider how different transformations acting on an object produce different images. Reflection, rotation, translation, and enlargement are first applied to an object on a grid before moving onto a coordinate axis. Reflection and rotation are introduced through previous experience of line and rotational symmetry.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Easter.

Summer Term

Students spend the term developing a greater sense of working with Fractions and Ratio and Proportion. This will be split into sub topics: Prime Factor Decomposition, Conceptualising and Comparing Fractions, Calculating with Fractions, Ratio and Percentages.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning a Summer holiday

In Year 8

Autumn Term

Students spend the term developing a greater sense of number systems and being able to make generalisations about them to improve their number sense. Areas taught are as follows:

Numbers and Numerals: Students extend their knowledge of numeral systems and how they can be used to group number in ways other than base 10. This provides students with a context in which they can further explore decomposition and regrouping of number. Students also meet the different number systems. By exploring number systems with different bases, students become more aware of the patterns that exists in base 10.

Axioms and Arrays: Students extend their understanding of different models for multiplication and division. Students also continue to explore the axioms of number and which operations they apply to. The unit looks at structures which lead to multiplication and the different models that can be associated with these structures. The array model is developed to explore the commutativity of multiplication. The array model is again used to introduce the associativity and distributivity axioms.

Factors and Multiples: students are given the opportunity to further extend their knowledge of the ‘structure’ of the natural numbers. Students will be reminded of factors, multiples and important sets of numbers such as prime numbers, square numbers and cube numbers. Once the fundamental concepts have been recapped students are given the opportunity to develop their understanding, conjecture, problem solve and generalise.

Expressions and Equations: students will build on their understanding of algebraic notation to express the multiples of integers and see collecting like terms as a development of the distributive property. Students will use a range of representations and contexts including Cuisenaire rods, bar models, number pyramids to manipulate expressions into their simplest form as well as representing equality statements. Seen alongside ‘tracking calculations’, students will develop flexibility in expressing relationships algebraically as well as being comfortable substituting constant values for variables.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Christmas.

Spring Term

Students will spend the term extending their knowledge to develop a greater sense 2D Shapes and the Cartesian Plane. The following areas are studied in detail:

Angles: Students spend time estimating, measuring, drawing and calculating angles. Students describe, classify and identify types of angles using clear vocabulary, and measure and draw angles accurately. Students revise facts involving angles around a point, angles at a point on a straight line and vertically opposite angles from experiences in primary school. Students will begin to generalise these angle facts.

Classifying 2D Shapes: analysing the geometric properties of polygons before focusing more closely on triangles and quadrilaterals. Students begin by classifying polygons by their properties including number of sides, number of line and rotational symmetries, types of internal angles, number of equal sides, and number of parallel sides. Students are encouraged to conjecture and prove which properties are the result of other properties. For example, if a polygon has as many line symmetries as sides then it must be regular.

Constructing Triangles and Quadrilaterals: students draw and construct triangles and quadrilaterals. In addition, time is allocated for a further analysis of their geometrical properties. Students draw and measure angles within this context allowing them to practise the skills learned in the previous unit.

Coordinates: students develop their understanding of the cartesian coordinate grid and solve problems in all four quadrants. Students will be familiar with coordinates from work at primary school and in other subjects. The tasks in this unit provides students with opportunities to apply their understanding from previous units including negative numbers and geometric properties of triangles and quadrilaterals.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Easter.

Summer Term

Students spend the term extending and developing a greater sense of working with Fractions and Ratio and Proportion. There is a focus on the following sub-topics: Prime Factor Decomposition, Conceptualising and Comparing Fractions, Calculating with Fractions, Ratio and Percentages.

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning a Summer break

In Year 9

Our Year 9 curriculum primarily focuses on the transition between Key Stage 3 and Key Stage 4. Students continue to follow the key stage 3 National Curriculum however we are continually looking for opportunities to stretch and challenge the most able whilst ensuring that key skills are retained and mastered. Consequently we have created a curriculum that allows pupils to further develop knowledge obtained in earlier years, whilst also giving them the initial exposure to topics that will be covered in depth in Years 10 and 11.

Over the course of the academic year, pupils will have the opportunity to gain an initial understanding of algebra and statistics, whilst continuing to build on key topics from Key Stage 3 such as number, ratio and geometry. During DIRT week, pupils have the opportunity to look back over their work and make corrections with the class teacher. Pupils are also given the opportunity to complete a mathematically rich activity, as part of our culture capital programme such as the Christmas project. In these tasks we provide students with the opportunities to plan, measure, cost and evaluate , specifically looking at functional maths in everyday life.

Developing fluency

Students develop confidence and strength in their mathematical skills with the following approaches:

consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers and roots
gain knowledge of algebra including simplification, manipulation, writing expressions and solving equations
move freely between different numerical, algebraic, graphical and diagrammatic representations
use language and properties precisely to analyse numbers

Reason mathematically

extend and formalise their knowledge of ratio and proportion, including working with measures and geometry
reason deductively in geometry, number and algebra, including using geometrical constructions
interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
assess the validity of an argument and the accuracy of a given way of presenting information

Solve problems

develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts
make and use connections between different parts of mathematics to solve problems
model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions
select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems; interpret their solution in the context of the given problem

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Christmas parties , Easter festivities and Summer holidays.

In Year 10

Students at Key Stage 4 study in greater depth the same aspects of Mathematics that are taught at Key Stage 3. All students are assessed against the OCR J560 GSCE specification (grades 9 – 1). Assessment is by examination at the end of Year 11, where students take three papers, each 1 hour 30 minutes. The first paper is a non-calculator paper, whilst the second and third allow the use of a calculator.

Our Year 10 curriculum focuses primarily on the delivery of the GCSE examination content. The curriculum has been created using the Key Stage 4 National Curriculum guidelines, focusing on the key topics and modules that will provide pupils with a strong foundation of knowledge such as; number, ratio and algebra. By allowing pupils to become more aware of the key topics outlined above, pupils build confidence with the material as they progress with their studies and head toward their final examination in Year 11. Our set 1 follow a programme created to target the higher-level topics (grade 5 – 9), whilst sets 2 through to 5 follow a programme tailored toward foundation level (grade 1 – 5). In addition to this, our Enhanced Curriculum group follow a differentiated programme, whilst still working at a Key Stage 4 level. The Enhanced Curriculum group provides an opportunity for pupils with more challenging learning needs to progress at the right level toward their GCSE. Please see below for more information on our Enhanced Curriculum.

Pupils are given the opportunity to attend maths intervention of an evening if they feel they require additional help with a specific topic. Further to this, our team of expert tutors provide small group support for those pupils who are demonstrating weaknesses. Pupils will be identified for tutor intervention through the most recent examination analysis by the Head of Department and Head of KS4 Mathematics.

Develop fluency

consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include more complex powers and roots
select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π, use of standard form and application and interpretation of limits of accuracy
consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions
extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities
move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic and reciprocal functions
use language and properties precisely to analyse numbers

Reason mathematically

extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically
extend their ability to identify variables and express relations between variables algebraically and graphically
reason deductively in geometry, number and algebra, including using geometrical constructions
interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally
assess the validity of an argument and the accuracy of a given way of presenting information

Solve problems

develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts
make and use connections between different parts of mathematics to solve problems
model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions
select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems; interpret their solution in the context of the given problem

Cultural Capital: students embark on a short project whereby they develop mathematical skills planning for Christmas.

In Year 11

Our Year 11 curriculum focuses on the delivery of the remaining content of the KS4 National Curriculum. Time is also designated to examination preparation and revision in order to guide pupils toward obtaining a grade 5. Throughout the examination preparation period, pupils will spend time looking at past questions and build up their examination technique. Pupils will look at the language of a question, presentation of answers and mark schemes to gain a better understanding of what is being asked of them in the examination. Furthermore, all pupils have the opportunity to attend mathematics carousels and masterclasses during lesson time, where the mathematics department deliver a number of workshops focusing on the key topics needed for the GCSE examination.

Develop fluency

consolidate their numerical and mathematical capability from key stage 3 and extend their understanding of the number system to include powers and roots
select and use appropriate calculation strategies to solve increasingly complex problems, including exact calculations involving multiples of π, use of standard form and application and interpretation of limits of accuracy
consolidate their algebraic capability from key stage 3 and extend their understanding of algebraic simplification and manipulation to include quadratic expressions, and expressions involving algebraic fractions
extend fluency with expressions and equations from key stage 3, to include quadratic equations, simultaneous equations and inequalities
move freely between different numerical, algebraic, graphical and diagrammatic representations, including of linear, quadratic and reciprocal functions
use language and properties precisely to analyse numbers

Reason mathematically

extend and formalise their knowledge of ratio and proportion, including trigonometric ratios, in working with measures and geometry, and in working with proportional relations algebraically and graphically
extend their ability to identify variables and express relations between variables algebraically and graphically
make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments
reason deductively in geometry, number and algebra, including using geometrical constructions
interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning
explore what can and cannot be inferred in statistical and probabilistic settings, and express their arguments formally
assess the validity of an argument and the accuracy of a given way of presenting information

Solve problems

develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
develop their use of formal mathematical knowledge to interpret and solve problems, including in financial contexts
make and use connections between different parts of mathematics to solve problems
model situations mathematically and express the results using a range of formal mathematical representations, reflecting on how their solutions may have been affected by any modelling assumptions
select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine problems; interpret their solution in the context of the given problem

6th Form

Year 12

Students may choose to study A level Mathematics and are assessed against the AQA specification. All students study Pure Mathematics topics ((2/3 of content), such as higher algebra, trigonometry and calculus, as well as applications: Mechanics and Statistics (1/6 of content each). The course helps develop logical thinking skills and teaches mathematical techniques to support studies in other subjects, such as the sciences. In year 12 students study the first year of the Advanced Mathematics course and are given the opportunity to gain an AS qualification in mathematics at the end of that year. Students benefit from small classes and are assessed twice termly.

Year 13

Students study a wide range of pure mathematics, mechanics and statistics topics from the AQA Advanced Level Mathematics year 2 programme of study. Regular homework and assessments allow students to revise and consolidate their learning as they prepare for the Advanced Level mathematics examinations at the end of year 13.

Sixth form re-sit

Students who have not been successful at GCSE mathematics in year 11 enrol on the mathematics re-sit course. Students are provided with further teaching of key topics and are prepared for examination in November and June of year 12 with further opportunities in year 13 for those students who need additional learning.

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Cultural Capital

The implementation of the Mathematicscurriculum includes opportunities for learners to develop skills relevant to the real world such as finance and retail. At the end of each term students embark on a short project whereby they develop mathematical skills in real life settings such as holiday planning and daily budgeting.

Pupils who are striving for a grade 5 are offered the chance to take part in the PiXL mathematics trip to Harrogate. The trip involves pupils taking part in interactive workshops over the course of the day, focusing on the key topics that pupils need in order to obtain a grade 5 in GCSE mathematics, with a strong bias towards the use of mathematics in everyday life.

Our subject curriculum has enabled our learners to:

Become confident with Mathematics and understand its place in the real world
Be engaged in lessons which are interesting and varied and where experiences are enriched through project work, problem solving and investigation.

Take part in the UK Maths Challenge from as young as Year 7.
achieve qualifications in mathematics at GCSE (Students attain as high as grade 9) and GCE Advanced Level (Students attain as high as grade A)
progress into further and higher education at many institutions including The University of Liverpool, Liverpool John Moores University and Chester College.
establish careers in many areas including Business, Finance, Medicine, Astro-Physics and Teaching
the department has an excellent track record of preparing students for further study of mathematics at University. We are proud too of the fact that in the past three years a number of students have embarked on mathematics degrees after completing Advanced Level courses at Oldershaw Academy.