Head of Department
Ms C O'Neill
Year 7
| Autumn 1 | Autumn 2 |
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Making generalisations about the number system 1 Place value Arithmetic Factors and multiples Order of operations A good understanding of number and algebra underpins all processes in mathematics. As such, our focus this half term is about building on the number skills learnt in primary school to develop fluency and ensure solid foundations are in place using, following and amending the Mathematics Mastery approach and programme for our students |
Making generalisations about the number system 2 Positive and negative numbers Expressions, equations and inequalities Pupils continue to develop their number skills, applying them to new contexts. We also start to apply skills to the essential concepts of algebra which underpins all aspects of pure mathematics developing students ability to reason and express themselves using abstract notation. |
| Spring 1 | Spring 2 |
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2D geometry Angles Classifying 2D shapes Area of 2D shapes Coordinates The focus for this term is geometry. All of the number and algebra skills which have been studied so far this year, can now start to be applied to topics such as perimeter, area and volume as well as angles in different 2D shapes. We also start to introduce problem solving skills when looking at complex geometric problems at the end of each topic. |
The Cartesian plane Transforming 2D figures Constructing triangles and quadrilaterals Students continue to develop their understanding of geometry and shape and space by developing the understanding of the Cartesian plane and representing shapes using this method. In addition, qualities of 2D shapes are explored further allowing students to construct shapes (looking at different polygons when challenging and extending the most able). |
| Summer 1 | Summer 2 |
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Fractions Prime factor decomposition Conceptualising and comparing fractions Manipulating and calculating with fractions Pupils continue to develop their number skills, whilst applying them to new contexts such as fractions, learning to manipulate and calculator with fractions. We also look at prime factorisation as the system in which all numbers can be constructed and formed (extending this to prime numbers and prime factorisation). |
Ratio and proportion Ratio Percentages We start to apply number skills to the essential concepts of ratio and proportion which are essential for developing mathematical reasoning skills. We end this half term by starting to look at some real-world applications of mathematics through problem solving and word problem tasks. |
Year 8
| Autumn 1 | Autumn 2 |
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Equations and inequalities Sequences Forming and solving equations and inequalities We revisit the algebra topics before extending this to solving inequalities and equations that were first met in Year 7. Pupils will recap the basic skills, before deepening their understanding by applying them to more challenging topics. In addition, time is taken to recap on sequences, looking at forming algebraic sequences |
Graphical representations Coordinates and linear graphs Real life graphs Accuracy and estimation We revisit the topics studied at in Year 7, but start to apply them to more complex situations, building on the 3D work that was introduced previously for example by studying transformations of 2D objects. More work is completed on interpreting and analysing real life graphs which are then used to extend understanding and ideas related to rates of change. |
| Spring 1 | Spring 2 |
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Proportional reasoning Ratio Real life graphs and rates of change Direct and inverse proportion We revisit the essential number skills of ratio and proportion, whilst extending to more complex topics. Students will also extend this to representing these on graphs and solving real-life problems. Pupils will also start to look at more complex ideas within proportion, looking at direct and inverse proportionality. |
Representations and reasoning with Data Univariate data bivariate data The focus of this half term, is applying the number skills developed so far to real-life contexts through the topics of compound measures, data and statistics. Pupils further develop an understanding of how statistics and graphs can be used in the real-world to analyse and represent data. Students are also introduced to methods of rounding and problems using estimation in their calculations. |
| Summer 1 | Summer 2 |
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Angles Angles in polygons Bearings Students begin this unit revisiting concepts in more depth in preparations for Week 2 where they look at formal methods for finding the sum of angles in polygon. These lessons focus on issues like ‘What is a polygon?’ and ‘What is an interior angle?” Students continue looking at compounded triangles, and are introduced to methods for finding the sum of interior angles of a polygon. Students also look at alternate methods and again look at what is and isn’t an interior angle. Students are introduced to exterior exteriors, and look at interior and exterior angles within regular polygons. Formal notation is introduced. Students are introduced to bearings and consider how to work out and estimate bearings using a number of different representations. Students should build a sense that a bearing and distance describe a position. Students continue their work on bearings in 2 new contexts. Firstly, students will formalise the relationship between A from B and B from A, then students will look at how pairs of bearings, and bearings and loci can help find exact positions. |
Area, volume and surface area Circles and composite shapes Volume of prisms Surface area of prisms We revisit the geometry topics which were first met in Year 7. The emphasis is on building on the basic skills and formulae that were learnt, whilst bringing in more complex concepts such as algebra, and linking back to solving equations formed from geometric problems as well as developing basic awareness of circles, volume and surface area of 3D shapes. |
Year 9
| Autumn 1 | Autumn 2 |
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Probability FDP review Probability Sets, Venns and sample space diagrams We revisit number work from KS2 and KS3 to refresh their understanding of the interconnection of methods of calculation for fractions, decimals and percentage in preparation for work on probability in the next unit. We introduce theoretical probability in a variety of contexts and with a variety of representations. Combined events are considered with the use of sample spaces, two-way tables and probability tree diagrams. Students add frequency tree diagrams and two-way tables to their repertoire of probability representations and look at non-random situations. They compare experimental to theoretical probability. Students build on their existing understanding of Venn diagrams by being introduced to set notation. The second week of this unit builds on the first by introducing probability presented in Venn diagrams and set notation. Students interpret and convert between representations to solve problems. |
Linear simultaneous equations Solving linear simultaneous equations algebraically and graphically. Students work on algebraic manipulation, including some revision of solving linear equations. Students are formally introduced to some formal algebraic manipulation methods such as equation scaling and addition and subtraction of equations within a system. Students solve simultaneous equations by adding or subtracting to remove a variable, firstly looking at cases in which this happens, and then using equivalent equations to manufacture these cases. We also solve simultaneous equations through substitution from one equation into another. Students explore linear graphs to connect understanding of solutions to linear equations in two variables to the coordinates of points that lie on their graphs, including intersections as simultaneous equations. |
| Spring 1 | Spring 2 |
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Geometry of Triangles Angle review, Constructions, congruence and loci Pythagoras theorem In addition, at the end of this half-term, we re-visit geometry, this time specifically looking at right-angled triangles and the topics of Pythagoras’ Theorem. Students revisit angle theorems to calculate missing angles using longer chains of reasoning, justifying their deductions. Opportunities exist throughout the unit for estimating, naming, measuring and drawing angles using a protractor. Formal notation is developed Students are introduced to loci and use the properties of circles to find the locus of points that are a specific distance from a point. Students develop this to find the locus of points that are equidistant from two points and use this to construct perpendicular biscectors. In week 2 of this unit, students are introduced to the conditions for congruence in triangles. This is derived from students understanding of the different ways to construct triangles. These conditions are then used to prove when two triangles are congruent. Students explore tiled squares leading to a formal introduction to Pythagoras’ Theorem. Students start to look at different contexts in which Pythagoras' theorem can be used, such as within 2-D shapes, 3-D shapes, and the Cartesian plane. |
Ratio and proportion Ratio review, similarity and enlargement and trigonometry Ratio is revisited this week with a focus on understanding the difference between part : part and part : whole relationships, representing those relationships as fractions, using the constant of proportionality and scale factor to find equivalent ratios, and connecting the constant of proportionality to the unit ratio Students are introduced to the idea of similarity in the context of enlargement. They use then learn how to find the scale factor from the unit ratio. After working with intershape relationships, they revisit the idea of constants of proportionality as inter-shape relationships and learn that these are the same within similar shapes. Students’ attention is drawn to the similarities and differences of intra shape and inter shape relationships. They are introduced to the centre of enlargement firstly through examining enlarged shapes and their relationship to the centre and then by enlarging shapes from a given centre. They examine the relationship between the scale factor and the area of the enlarged shape. Students investigate a right-angled triangle in a unit circle in quadrant 1 and use what is known about similar shapes to find missing lengths of right-angled triangles. After being introduced to sine and cosine functions, students can find the opposite/adjacent of a right-angled triangle from a given angle and hypotenuse length, and vice-versa. Students explore the relationship between the opposite and adjacent is looked at as the tangent of an angle is uncovered. Secondly, students look at finding unknown angles through inverse trig functions. |
| Summer 1 | Summer 2 |
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Quadratics Algebra review, quadratic expressions and equations. We revisit the algebra topics from Year 7 and Year 8, aiming to recap the basic skills that were learnt and build fluency, before studying each topic to a greater depth, thus improving understanding and providing the opportunity to tackle more challenging concepts. Students look specifically at quadratic expressions and equations, including those written in the standard form ax 2+b x +c(=0). Students also begin looking at quadratic graphs and common visual features of them, such as the curve and turning point. Students look at interpreting information from a quadratic graph, then students begin looking at quadratics written in double brackets and considering equivalence with quadratics in their standard form. Students continue to work on expanding brackets, as the questions gradually increase in complexity, they eventually move onto expanding more than two brackets. |
Reasoning with number Surds, indices, standard form and growth and decay Students are introduced to rational and irrational numbers, and surds. This unit can be thought of as “surdslite” as students will be introduced to surds in a way that is key stage appropriate. During the first week of this unit students look at indices and roots, including looking at cases with negative indices and an index of zero. Students then focus on the index laws, looking at multiplication, division, and raising to further powers. Students are introduced to numbers written in standard form as tools to consider and compare very large and very small numbers. They draw connections between powers of ten and place value, compare the size of numbers by considering the power of ten and use multiplication and division to adjust numbers into standard form. Decimal multipliers to calculate percentage change is built on by considering repeated change, first with different percentages and then with the same percentage (compound change). Graphical representations of growth and decay are considered to illustrate that exponential growth (/decay) means the rate of growth (/decay) increases over time. |
Year 10
| Autumn 1 | Autumn 2 |
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Higher tier Calculations, checking and rounding Indices, roots, reciprocals and hierarchy of operations, Factors, multiples, primes, standard form and surds Algebra: the basics, setting up, rearranging, and solving equations Sequences |
Higher tier Averages and range Representing and interpreting data and scatter graphs Fractions and percentages Ratio and proportion |
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Foundation tier Integers and place value Decimals Indices, powers and roots Factors, multiples and primes Algebra: the basics Expressions and substitution into formulae |
Foundation tier Tables, charts and graphs Pie charts Scatter graphs Fractions, decimals and percentages Percentage |
| Spring 1 | Spring 2 |
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Higher tier Polygons, angles and parallel lines Pythagoras’ Theorem and trigonometry Graphs: the basics and real-life graphs Linear graphs and coordinate geometry |
Higher tier Quadratic, cubic and other graphs Perimeter, area and circles 3D Forms and Volume Accuracy and bounds |
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Foundation tier Equations and inequalities Sequences Properties of shapes, parallel lines and angle facts |
Foundation tier Interior and exterior angles of polygon Perimeter, area and volume Statistics, sampling and the averages |
| Summer 1 | Summer 2 |
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Higher tier Transformations Constructions, loci and bearings Quadratic and simultaneous equations |
Higher tier Inequalities Probability |
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Foundation tier Real-life graphs Straight-line graphs Transformations Ratio |
Foundation tier Proportion Right-angled triangles: Pythagoras and trigonometry |
Throughout Year 10 the same topics are studied as in Key Stage 3, with an aim to recapping the more basic skills, before moving on to applying the concepts to more challenging contexts and the next and new level of complexity studied at a GCSE level. By revisiting and reviewing each topic, our students will form stronger links between topics, and become more confident in applying their skills to unfamiliar situations and to real-life problem-solving questions.
Year 11
| Autumn 1 | Autumn 2 |
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Higher tier Algebraic reasoning Linear Graphs, Other Graphs Probability |
Higher tier Sequences, bounds and iterations Data representation |
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Foundation tier Fractions Percentages Arithmetic Types of number including use of Venn diagrams for PFD |
Foundation tier Linear Graphs Area and Volume Transformations Pythagoras Trigonometry |
| Spring 1 | Spring 2 |
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Higher tier Trigonometry Data representation Surds |
Higher tier Percentages Ratio and proportion Circle Theorems Circle Graphs Vectors Constructions and loci |
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Foundation tier Ratio and Proportion (including conversion graphs) Standard Form Perimeter and Area including circles Angle review Algebraic reasoning |
Foundation tier Transformations Constructions and loci Data representation Probability |
| Summer 1 | Summer 2 |
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Higher tier Angle review Revision through to GCSE exams |
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Foundation tier Revision through to GCSE exams |
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| In this half term, the focus shifts to revision, to ensure that students are fully prepared for their GCSE exams at whichever tier of entry best suits their needs and their opportunity to achieve the best rest. Students complete weekly mocks which their teachers mark and give feedback of areas of strength and areas which need more focus. These areas are then targeted through revision lessons as well as intervention to ensure that students become more confident and able to tackle examination style questions. |
Throughout Year 11 the same topics are studied as in Year 10, but at a faster pace to ensure there is plenty of time for revision during half term 5 to prepare for the exams at the end of the year. There is a continued aim of ensuring that strong foundations are in place for each topic, before building on these with ever-increasing depth and a particular focus on application to unfamiliar contexts and developing problem-solving techniques.