Mathematics
subject OVERVIEW
Mathematics can be applied in practical tasks, reallife problems and within mathematics itself. The course aims to develop deep learning through the mastery of mathematical vocabulary, conceptual understanding and mathematical reasoning used to solve a variety of problems.
The course of study should help you whether working individually or collaboratively to reason logically, plan strategies and improve your confidence in solving complex problems.
During Maths lessons you will learn how to:
 Use and apply maths in practical tasks, real life problems and within mathematics itself.
 Develop and use a range of methods of computation and apply these to a variety of problems.
 Develop mathematical vocabulary and improve mental calculation.
 Consider how algebra can be used to model real life situations and solve problems.
 Explore shape and space through drawing and practical work using a range of materials and a variety of different representations.
 Use statistical methods to formulate questions about data, represent data and draw conclusions.
Engage in practical and experimental activities in order to appreciate principles of probability. There is no coursework
autumn 1  fractions and percentages
Skills 

Knowledge 

Rationale 
All the content is from Year 7. These units were part of Year 7 Summer 1 and are to be retaught. In this module learners formally explore fractions and their relation to decimals. The extension of the number system to rational numbers is a highly important stage in learners’ mathematical development. To begin, the uniqueness of the prime number decomposition is explored. This is used to show properties of particular numbers. Prime factorisation is used to determine the highest common factor and lowest common multiple. The next two units are dedicated to fractions, building on knowledge of fractions from KS2. Fractions are considered simultaneously as a number, as a way of expressing division, as a continuous partwhole model and as a discrete part of a larger set. Learners compare two or more fractions in a set and order them by their size. Learners extend their understanding of applying the four operations to noninteger values.Bar models, line models and rectangular representations are used heavily throughout to represent the fractional amounts. 
autumn 2  algebra
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Rationale 
This module gives learners the opportunity to develop and formalise the algebra they have become familiar with in Year 7. It has an increased level of challenge and complexity. This module begins by studying sequences. In the autumn term of year 7 students were introduced to algebraic notation and met sequences in the form of geometric patterns. In this unit, sequences are derived from the same geometric patterns and other contexts. Students start with the term to term rules, before expressing the position to term rules algebraically. Different types of sequences are explored including linear, nonlinear, arithmetic and geometric. In year 7 students explored the nature of equality and solved equations with one unknown where the unknown appeared on one side. In Unit 2 learners formalise methods for solving equations. Learners use inverse operations to transform equations with one and two steps and encounter equations involving a single bracket. Equations are derived from familiar contexts and the solutions to these equations are interpreted within that context. In unit 3, inequalities are derived from the same contexts that were met in the previous unit. Solutions are built up by substituting numbers that satisfy the inequality. This develops an understanding that the solution to an inequality has a range of values. The unit continues with more formal strategies for solving inequalities. The same strategies for solving equations are developed in the context of inequalities. 
spring 1  graphical representations
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Rationale 
All the content in italics is from the Year 7 curriculum. The transformations unit was disrupted in the Spring of 2020. In this module, learners apply what they have learned about algebra and geometry in the Cartesian grid. Learners are expected to consider how transformations acting on an object produce different images. Reflection and rotation are introduced through previous experience of line and rotational symmetry. There is a focus on language and consideration of the amount of information required to perform each transformation. The transformations are sorted by whether they result in a congruent image. This is the foundation for exploring similarity and trigonometry later. THe next unit is students’ first formal introduction to straight line graphs. This begins with the plotting of discrete points beginning with 𝑛 = 1. The 𝑛axis is replaced by the 𝑥axis and discrete points are replaced with a continuous line to represent all coordinate pairs. Functions derived from real life contexts are used to help give meaning to the features of a linear graph. Students develop strategies for identifying and drawing graphs of linear functions. The concept of gradient is introduced as the rate of change of the 𝑦 coordinates. Learners are also able to explore the contexts of parallel lines and similar triangles. Students work on coordinate geometry problems by finding the equation of a line through two points and finding the equation of a line through a point with a given gradient. 
spring 2  ratio and proportion
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Rationale 
All the content in italics is from the Year 7 curriculum. In this module we combine the ratio unit in year 7 with the units on ratio and rate from year 8. This is a natural combination since the year 8 module involved a thorough recap of the year 7 content originally. Time is spent in the first unit reinforcing the notion of a ratio as an expression of a constant multiplicative relationship which can be between quantities in the same unit e.g. fractions or between two quantities in different units e.g. speed measured in miles per hour. A variety of contexts are used to explore and clarify concepts. Having established ratio as an expression of a relationship between two quantities, this is applied to ratio problems where students are required to divide an amount into a given ratio and find different quantities given a ratio. Next, learners examine proportional relationships in familiar contexts before looking at the meaning of direct proportion in abstract. Students are encouraged to compare different approaches to solving problems involving direct proportion. In the second week of this unit, learners will meet the concept of inverse proportion. Learners will encounter this in different contexts, notably by studying perimeter for a constant area. 
Summer 1  represent and reason with data
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This module explores a variety of methods of presenting data, with an emphasis on interpretation as well as production. In the first unit, learners study univariate data. The unit presents a series of inquiry questions and students make hypotheses in relation to these. Each of the statistical methods taught in this unit are used to construct an argument for or against some given hypotheses. Students begin by considering different ways of representing a data set such as in tables, bar charts, pictograms, line graphs and pie charts. Students organize data into different frequency distributions. Misleading graphical representations of the data are presented and critiqued. In the second part of this unit, students begin to look at statistical measures and interpret these in terms of the data. Students calculate the mean, median, mode and range of ungrouped and grouped data. Time is spent discussing the different measures of centrality. In the second unit of the half term, students extend their understanding of statistical diagrams and measures to bivariate data. Students present the data in tables and in a scatter graph. They examine relationships between point to make simple inferences about association and covariation. The difference between correlation and causation are introduced and the idea of an explanatory variable. 
summer 2  area, volume and surface area
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Rationale 
In this module we have rearranged the unit on accuracy and rounding to go before work on measures of area and volume. This enabled time to be spent on year 7 units earlier in the year, and the accuracy unit complements the other units on measure. The units on angles originally in Year 8 will be taught in Year 9. ‘Accuracy and estimation’ provides an opportunity to consolidate understanding of rounding to a given decimal place which most learners will have met at primary school. Significant figures are introduced through measuring contexts. Rather than meeting significant figures as a set of rules to follow, students are required to work out why the zero is 45.0 is significant. Estimation is encountered in a variety of contexts and is an opportunity to practice rounding and unit conversions. Next, learners study circles. Learners explore the connection between the circumference of a circle and its diameter and through this are introduced to pi. Software and other visuals are used to give students the opportunity to see how formulae are derived. The unit ends with opportunities for students to apply their understanding to geometric problems involving the area and circumference of a circle. Finally, learners formally meet volume as a measure of the space inside a 3D object. Students may need to revisit the names and properties of 2D shapes before moving onto 3D. Time is spent building and breaking down 3D shapes, both with blocks and as nets. Students develop their own methods for finding the volume of prisms and before any exposure to the conventional formulae for cuboids, cylinders and other uniform prisms. 
knowledge organisers
A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and ALevel exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments, and calculations.
We encourage all pupils to use them by doing the following:
 Quiz themselves at home, using the read, write, cover, check method.
 Practise spelling key vocabulary
 Further researching people, events and processes most relevant to the unit.