# Maths

## Curriculum Overview** **

### Intent

*Mathematics is the most beautiful and most powerful creation of the human spirit.*

*Stefan Banach*

At Newcastle Academy we encourage all pupils to develop a love and understanding of Mathematics. Our broad and balanced curriculum introduces key concepts in a logical order and encourages mastery through looking at the concept from a variety of standpoints and contexts. Our aim is to develop mathematicians who:

- are numerically and algebraically fluent
- communicate mathematically
- demonstrate critical thinking, logic and curiosity
- are resilient and persistent
- are creative problems solvers

The mathematical skills of problem solving, logical thinking, and investigation will help children make progress in all areas of study. In addition to these general skills, maths is required for learning in a wide range of areas – anything from plumbing to economics to psychology. It is a particularly key subject for pursuing STEM pathways.

The programme of study for pupils reinforces and develops key concepts introduced in KS1 and KS2 across KS3 before embarking on a KS4 course that leads to the Edexcel GCSE in Mathematics. With the option to take a GCSE course at an appropriate level, our Higher Tier programme ensures pupils have the mathematical skills for any A-level Mathematics qualification, whilst both Higher and Foundation Tier programmes ensures a solid base of knowledge and competencies for study of Level 3 Core Maths, Functional Skills and/or the mathematics skills needed for other level 3 qualifications. The mathematical knowledge, skills and understanding that is taught is useful in the personal life, future study and employment of all pupils. An appreciation of the patterns and power of mathematics will also be taught while fostering an enjoyment of the subject.

The content taught is from the five core strands of mathematics: number; ratio, proportion and rates of change; algebra; statistics and probability; geometry and measures. Lessons are planned to include a variety of teaching and learning styles that inspire and involve students, including digital activities, mathematical games and puzzles as well as the use of course textbooks.

## Implementation

**The Curriculum**

The mathematics programme of study is a 5-year spiral curriculum that builds on the skills and knowledge that pupils learn previously. In Y7 and Y8, pupils follow a broad and balanced Mathematics curriculum that provides them with the key skills and problem-solving experience needed for success at GCSE. In Y9-11, pupils follow the Pearson SOW for the Edexcel 9-1 Mathematics GCSE.

The full curriculum overview is below. The coloured text shows some of the spiral of the curriculum where topics are revisited, and concepts are further developed. It must be noted that some later topics encompass knowledge taught in several disparate earlier units and is therefore a guide to the spiral; it is not a comprehensive overview. Further detail for each of the units is found in the detailed descriptions for each year group.

**Year 7 and 8**

On entry into Y7, pupils are placed into sets using their KS2 scores. Following this, pupils are only moved into different sets when we believe it appropriate based on their performance in class, homework and regular unit assessments. Y7 catch-up intervention is completed by Learning Support Practitioners during the school day with selected pupils.

Y7 and Y8 pupils have 7 periods of Mathematics a fortnight. Pupils study 8 units across each year consisting of a mixture of GCSE-ready content and a mastery of key skills.

**Year 7 Curriculum**

__Unit 1: Data Handling. __

This unit develops the skills that underpin statistical work in Science and Geography at both KS3 and KS4. It covers:

- Collecting data: manipulating discrete and continuous data into frequency tables. This builds on tally charts from KS2 and is a prerequisite for the use of frequency tables at GCSE and in the real world (histograms, frequency polygons, averages from a table).
- Averages and range: in KS2 the mean is taught as an average, in year 7 pupils explore other types of average, as well as the range and use them to compare and contrast data sets. Higher ability pupils are expected to find averages and range from frequency tables, a skill required at GCSE.
- Representing data: pupils will be expected to construct their own statistical diagrams to represent a range of data. Although this is covered at KS2, there is an expectation that pupils: choose appropriate diagrams; construct their own axis; understand the limits of various statistical representations.

__Unit 2: Place Value.__

This unit allows pupils to reflect on how our number system works using numbers of Arabic origin in base 10 (due to the number of digits we have on both hands) and clarifies ‘borrowing’, ‘carrying’ and ‘dropping a zero’. It covers:

- Understanding and using place value: building from KS2 and preparing for GCSE problems such as standard form.
- Rounding numbers: again, building from KS2 and extending to the concept of significant figures.
- Addition and subtraction: applying place value to build and extend KS2 arithmetic in order to prepare pupils for problem solving in KS4.
- Perimeter: application of techniques used to find the perimeter of common 2D shapes covered at KS2 and extending it to compound 2D shapes.

__Unit 3: Coordinates.__

This unit looks at the cross over between shape, data and algebra by looking at Cartesian coordinates on an axis, developing fluency throughout the curriculum. It covers:

- Drawing and interpreting coordinates: at KS2 pupils are expected to interpret, write and draw coordinates. We build on this by looking at midpoints and completing shapes. Higher ability pupils will be challenged to find distances between two coordinates.
- Equations of horizontal and vertical lines: recognising that a straight line that is parallel to an axis will always have one constant coordinate and using this to develop algebraic notation. Knowing the equation of a horizontal or vertical line is a requirement for GCSE topics on transformations and regions defined by inequalities at KS4.
- Scatter graphs: utilising knowledge from Unit 1, pupils apply coordinate knowledge to draw, interpret, interpolate and extrapolate data from scatter graphs; a key requirement for GCSE in multiple subjects.
- Line graphs: pupils now have the prior knowledge required from coordinates and graph plotting to draw and interpret different line graphs. These skills are essential for looking at data in Science, Geography and even historical data. At GCSE, pupils will develop this by considering frequency polygons and cumulative frequency graphs.

__Unit 4: Multiplication and Division__

This unit looks at the development of multiplication and division as a replacement for repeated addition and repeated subtraction, and at its application. It covers:

- Mental multiplication and division: through the use of multiples and factors and the development of the concepts of prime numbers, lowest common multiple and highest common factor
- Written methods for multiplication and division: exploring the use of different methods and how they demonstrate the same process differently, giving pupils a better understanding of our number system. These methods are applied to algebraic expressions in later units.
- Multiplying and dividing by 10, 100 and 1000: applying place value knowledge from Unit 2 and checking pupils understand the concept first introduced at KS2 and are not just applying set rules. The concept is extended to converting metric units and looking at the consequence of multiplying and dividing by 0.1, 0.01 and 0.001.
- Correct order of operations: incorporating work from unit 2 and prior KS2 work on BODMAS. Pupils are introduced to calculator processes, an essential component of many GCSE courses.
- Area: applying the techniques learnt to finding the area of common 2D shapes covered at KS2 and extending it to compound 2D shapes.

__Unit 5: Expressions__

This unit connects work from Unit 2 and Unit 4 via the use of function machines to incorporate understanding, forming and manipulating expressions. It covers:

- Forming expressions: a topic briefly introduced at KS2 but is foundational for algebraic reasoning and advanced problem solving at GCSE.
- Substitution: a skill covered through expressions at KS2 and extended here to include key mathematical and scientific formulae.
- Understanding equivalency: through the use of substitution and algebraic manipulation.
- Simplifying expressions: by collecting like terms and understanding where terms are unlike.
- Expanding and factorising expressions: a new skill for pupils but necessary in the GCSE curriculum.

__Unit 6: Angles__

This unit builds on work at KS2 on understanding, naming, measuring and drawing angles. It covers:

- Basic angle facts: angles on straight lines and around a point, and vertically opposite angles whilst incorporating work from Unit 5.
- Angle sums for different shapes: starting with special triangles and quadrilaterals and extending into higher order regular and irregular polygons.
- Measuring and drawing angles: through construction of geometric figures to prepare pupils for GCSE topics of loci, congruence and similarity.
- Pie charts: building on work in Unit 1 and Unit 4 to master another way to represent and interpret data. This is a key skill for many subjects at GCSE.

__Unit 7: 3D shapes__

In this unit pupils develop their knowledge and understanding of 3D shapes from KS2. It covers:

- Recognising 3D shapes: naming the regular polyhedra; recognising faces, edges and vertices and applying it to Euler’s formula including the duality between different regular polyhedra.
- Representing 3D shapes in 2D: through drawing plans and elevations and making isometric drawings, skills needed for GCSE and applicable in Design Technology.
- Drawing nets: utilising work from Unit 6 to construct nets of cuboids and common prisms and recognising a variety of nets that make the required shape.

__Unit 8: Fractions__

In this unit pupils revisit content from KS2 on fractions and develop fluency by applying fractions rules to algebra and representing fractions in different forms. It covers:

- Representing fractions: pictorially and looking at equivalent numerical fractions
- Four operations: addition, subtract, multiplication and division of fractions extending it to look at mixed numbers
- Comparing fractions: including ordering sets of fractions

**Year 8 Curriculum**

__Unit 9: Algebraic thinking__

In this unit pupils revisit the concepts introduced Units 4 and 5 in order to promote mastery and develop fluency. It covers:

- Correct order of operations: incorporating work from unit 2 and prior KS2 work on BODMAS. Pupils are introduced to calculator processes, an essential component of many GCSE courses and focus more on the impact that indices have.
- Forming expressions: a topic briefly introduced at KS2 but is foundational for algebraic reasoning and advanced problem solving at GCSE. This is extended to look at forming formulae.
- Substitution: a skill covered through expressions at KS2 and extended here to include key mathematical and scientific formulae.
- Understanding equivalency: through the use of substitution and algebraic manipulation.
- Simplifying expressions: by collecting like terms and understanding where terms are unlike. This is extended to include expanding and simplifying two or more single brackets.
- Expanding and factorising expressions: starting with single bracket expressions then extended to double brackets for quadratic expressions.

__Unit 10: Sequences and Graphs__

In this unit pupils further develop their skills with sequences to look at applications to graphs and to finding terms algebraically. It covers:

- Describing and continuing sequences: linear to start but extended to non-linear including geometric, quadratic (including square and triangular numbers) and Fibonacci-like sequences.
- Linear graphs: building on work from Unit 3 to generate linear and non-linear graphs from a sequence.
- n
^{th}term: both finding the n^{th}term of a sequence and using the n^{th }term to find a particular number in a sequence. Extended to quadratic sequences for high ability pupils.

__Unit 11: Equations and formulae__

In this unit pupils look at the concept of equality and are introduced to the concept of bar models applied to solving equations. The concept of balancing equations is developed alongside the bar model framework. It covers:

- Understanding equality: uncovering the bidirectional nature of equality so pupils understand that both sides of an equation are worth the same amount.
- Solving equations: using the bar model to first solve one step equations progressing to solving multistep equations involving brackets with the unknown on both sides, extended to changing the subject of a formula.

__Unit 12: Types of number__

In this unit pupils revisit the concepts introduced in Unit 4 and extend them to include the fundamental theorem of arithmetic. It covers:

- Squares and Cubes: pupils also cover the equivalent roots; this is extended to look at the law of indices
- Multiples, Factors and Primes: defining and identifying numbers
- Prime Factor Decomposition: applying the fundamental theorem of arithmetic to be able to deconstruct numbers and represent them as a product of prime factors
- Highest Common Factor and Lowest Common Multiple: the logical extension of multiples and factors, this is extended to use prime factor decomposition and Venn diagrams to find HCF and LCM of 3 large numbers

__Unit 13: Ratio and Proportion__

In this unit pupils build on their knowledge of ratio from KS2 and relies on concepts from Units 4, 8 and 12, especially bar modelling. It covers:

- Equivalent ratios: utilising equivalent ratios to solve problems including recipe, exchange rate and best buy problems utilising simplifying ratios and writing ratios in the form 1:n. Use of bar modelling is an essential strategy.
- Dividing a quantity in a given ratio: including problems where the difference between the quantities is given.

__Unit 14: Area, Perimeter and Volume__

In this unit pupils build on KS2 knowledge and revisit concepts from Units 2, 4 and 7. It introduces the concepts of Volume and Surface Area for rectilinear 3D shapes and prisms. It covers:

- Perimeter: including compound shapes. It extends to the circumference of a circle and sectors. For higher ability pupils Pythagoras’ Theorem is introduced to find the perimeter of right-angled triangles.
- Area: triangles, common quadrilaterals and compound shapes. It extends to circles and sectors. For higher ability pupils Pythagoras’ Theorem is applied to find the area of isosceles and equilateral triangles.
- Volume and Surface Area: cuboids, prisms and compound prisms. For higher ability pupils spheres, cones and pyramids are considered.

__Unit 15: FDP and Percentages__

In this unit pupils build on knowledge of simple fractions, decimals and percentage equivalents and calculating with percentages from KS2. It utilises bar modelling methodology and introduces the concept of reverse percentages to find the original amount. It covers:

- Fraction, decimal and percentage equivalence: building to recurring decimals and more complex terminating decimals.
- Percentage of a quantity: both non-calculator and calculator methods are taught. The concepts are extended to increase/decrease by a percentage, including efficient calculator methods, and reverse percentages.

__Unit 16: Probability__

In this unit pupils apply concepts introduced in Units 8 and 12 to probability. Pupils are introduced to the field of set theory, now an important topic at GCSE, and look at the implications of uncertainty. It covers:

- Venn diagrams: as used for probability and introducing the concepts of intersection, union and complements of sets including multiple combinations of the different sets.
- Probability of an event: starting with representing a common occurrence with a word, as a fraction and on a probability scale before extending to multiple events using sample spaces.

**Years 9, 10 and 11**

Pupils consolidate and extend their learning by following curriculum which is designed to equip them with the skills necessary to achieve their full potential across all their chosen GCSEs and to be functionally numerate throughout their lives. At the end of Y11, pupils will sit the Edexcel 9-1 Mathematics GCSE. A copy of the specification is available to download from the Edexcel website: http://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html.

Y9 have 7 hours of Maths a fortnight whereas Y10 and Y11 groups have 9 periods of Mathematics a fortnight. Y9 and Y10 have 3 sets, whereas Y11 currently has 4 sets. They are following the Edexcel GCSE (9-1) Pearson scheme of work, with assessments at the end of each unit. The following table outlines the content covered:

In addition, Y11 complete a weekly half exam paper for homework. This is followed up with an intervention lesson with personalised DIRT tasks for pupils to complete to rectify misconceptions. This is re-tested with a follow-up shadow paper to check for understanding and recall of knowledge and to inform further intervention.

### Impact

As a result of the successful implementation of our curriculum, pupils will increase in confidence with, and knowledge of, the mathematical skills they have been taught. Specifically, we will see the following impact:

- An increase over time in pupil attainment at all grades but specifically in the headline figures of grade 4+, grade 5+ and grade 7+. In 2020, the percentages of grades awarded at 4+ and 5+ exceeded the national average.
- An increase over time in the progress 8 measure for Mathematics.
- An increase over time of pupils taking and completing level 3 Mathematics qualifications.

This will be the result of pupils:

- having a well-developed tool kit for solving problems.
- being numerically and algebraically fluent having mastered key concepts.

## Assessment

### How grades are decided for input; what are the grades based upon?

In all year groups, at the end of a unit pupils follow a DIET process:

**D** – Diagnosis – Pupils complete a diagnosis assessment to find any gaps in knowledge

**I **– Intervention – Pupils complete intervention tasks to fill the gaps in knowledge

**E** – Extension – Pupils complete extension tasks to further their understanding of the topic

**T** – Test – Pupils complete a test to summarise their knowledge, inform their Current Working Grade (CWG) and to identify any future learning. The test uses similar questions to the diagnosis but the numbers in the questions are changed.