# Maths

## Maths

Departmental Intent

The mathematics curriculum will encourage students to use critical thinking skills and logical reasoning required for future education, training and employment.

Students will be equipped with the skills to make links with the wider curriculum and appreciate the impact and influence that mathematics has on their daily lives. Students will develop their fluency of numerical skills in order to confidently select the appropriate tools to solve problems in a real-life context.

YEAR 7
YEAR 8
YEAR 9
YEAR 10
YEAR 11 (Higher)
YEAR 11 (Foundation)
YEAR 7

## TERM 1

Number:

An introduction to the number work students will need to access the Grace Academy Maths curriculum. Throughout lessons there will be lots of opportunities to problem solve and apply the topics to multiple contexts.

Topics Include:

• BIDMAS
• Adding/Subtracting/Multiplying and Dividing with positive and negative numbers
• Rounding to decimal places, significant figures and truncating
• Estimating calculations
• Multiplying and dividing with decimals
• Squares, Cubes, Roots, Indices introduction and its use in calculations
• Factors, multiples and primes including highest common factor, lowest common multiple and prime factorisation
• Adding/Subtracting/Multiplying and Dividing fractions including mixed numbers and improper
• Fractions of amounts and reciprocals

## TERM 2

Perimeter/Area, Angles and Percentages: An introduction to geometry and a chance to apply their prior learning into new contexts. All of the previous number work will be developed into the geometry unit.

Topics Include:

• Perimeter of rectangles, parallelograms, triangles, trapeziums and compound shapes
• Area of rectangles, parallelograms, triangles, trapeziums and compound shapes
• Angles around a point, angles in triangles, quadrilaterals and other polygons
• Angles on parallel lines
• Converting between fractions, decimals and percentages
• Finding percentages of amounts, increasing and decreasing by a given percentage and application in real-life contexts

## TERM 3

Ratio and Proportion and Algebra: Students will start to develop their proportional reasoning skills. These skills will play a vital part in the rest of their studies at Grace. Students will also be introduced to algebraic expressions and how we use letters to represent variables.

Topics Include:

• Simplifying ratios, dividing into given ratios
• The unitary method and proportional reasoning; application to recipe questions and real-world problems
• Writing algebraic expressions
• Collecting like terms
• Substituting into expressions
• Expanding brackets
• Factorising
• Introducing links between algebra and shapes
YEAR 8

## TERM 1

Indices, Standard Form, Algebra, Volume and Surface Area: Students will develop their skills involving indices, build on their algebraic knowledge, and build on their area knowledge with volume and surface area.

Topics include:

• Multiplication/ Division and Power Laws of indices
• Writing to and from Standard Form
• Calculations in Standard Form
• Build on introductory algebraic skills
• Expand and simplify expressions with single brackets
• Volume of 3-D shapes including cuboids, triangular prisms and cylinders
• Surface Area of 3-D shapes including cuboids, triangular prisms and cylinders

### TERM 2

Graphs, Equations, Construction, Ratio, Proportion, Probability and Sequences: Students will apply their algebraic skills to drawing graphs including distance/time graphs. Students will use geometric equipment to construct triangles and bisectors accurately. The ratio and proportion unit will develop key skills student need to use for many branches of maths

Topics include:

• Recognising and plotting straight line and curved graphs
• Solve linear equations
• Rearranging formulae
• Constructing triangles, perpendicular bisectors and angle bisectors
• Using ratio to solve problems
• Proportioning techniques linking to Speed, Distance, Time and Recipes
• Introduction to probability - Finding the probability of single events happening/ not happening
• Using experimental and theoretical probability
• Introduction to different sequences

### TERM 3

Converting, Pythagoras and Statistics: Students will be able to convert between units of length, mass and capacity, apply Pythagoras’s theorem and learn how to represent and analyse data

Topics include:

• Metric conversions
• Upper/ Lower bounds
• Currency conversion
• Calculating missing sides using Pythagoras’s theorem
• Representing data on Frequency polygons, pie charts and Scatter Graphs
• Calculating averages from a list of data and frequency tables

YEAR 9

### TERM 1

Expressions, Angles, Similar Shapes, Fractions, Decimals, Percentages, Ratio and Proportion: Students will consolidate some previous key concepts and apply them to solving more complex problems at Foundation GCSE level. (Higher topics are bracketed)

Topics include:

• Review index Laws
• Writing expressions from shapes
• Set up and solve equations
• (Algebraic Fractions – Add/ Subtract/ Multiply/ Divide and Simplify)
• Compare and convert between Fractions, Decimals and Percentages, Fractions of… Percentage of…
• Using percentage multipliers, simple/ compound interest, reverse %
• (Converting recurring decimals to fractions)
• Angles in parallel lines
• Interior/ Exterior angles of polygons
• Bearings
• (Congruent and similar shapes)

### TERM 2

Formulae and Functions, Working in 2D, Probability with combined Events, Measures and Accuracy:

Topics include:

• Substituting into and rearranging formulae
• Expand double brackets and factorise into double brackets
• (Expand Triple Brackets, using function notation, AC method, Algebraic Proof)
• Mixed Areas
• Transformations – Reflection, Rotation, Translation, Enlargement
• (Negative Enlargements)
• Probability; Relative frequency, Venn diagrams and Tree diagrams
• (Set notation)
• Using appropriate accuracy, estimating calculations, using a calculator effectively
• Density, Mass, Volume
• Error Intervals
• (Upper and Lower bound calculations)

### TERM 3

Solving Equations and Inequalities, Handling Data:

Topics include:

• Set up and solve equations
• Solve inequalities, represent on a number line
• Simultaneous equations
• (Solving Simultaneous equations and inequalities graphically. Quadratic inequalities. Equations involving indices)
• Mean from frequency table, Estimate of the mean from grouped frequency table
• (Quartiles, IQR, Cumulative Frequency, Box plots, Histograms)

YEAR 10

### TERM 1

Equations, Inequalities, Prime factorisation, Pythagoras and Trigonometry, Calculations

Topics include:

• Equations revision
• Inequalities revision
• Simultaneous equations
• (Complex Simultaneous equations and inequalities graphically. Quadratic inequalities. Equations involving indices)
• Highest Common Factors/ Lowest Common Multiples, prime factorisation
• (Simplify/ Multiply/ Rationalise Surds)
• Indices, Standard form and Exact calculations
• (Fractional/ Negative powers, surd form)
• Use and apply Pythagoras and SOHCAHTOA
• Vectors introduction
• Exact Values of trigonometry
• (3-D Pythagoras, Sine rule, Cosine rule, 1/2absinC)
• Vectors
• (Vector proofs)

### TERM 2

Circles, Constructions and Graphs, Sequences:

Topics include:

• Compound shapes involving circles
• Constructing triangles, perpendicular and angle bisectors
• (Circle theorems, arc length/ sector area)
• (Trigonometric, reciprocal, exponential, circle graphs. Tangent to a curve. Estimating an area under a velocity/time graph)
• Plotting straight-linear graphs, Y = mx + c
• Distance/Time graphs
• (Properties of quadratic graphs, roots, minimum points, completing the square, iterations)
• Using and finding an nth term of an arithmetic sequence
• Fibonacci, geometric sequences

### TERM 3

Compound units and Proportion, Working in 3-D, Sequences:

Topics include:

• Compound Units, Rates of change
• Scale factors of length
• (Proportion equations, scale factors of area and volume)
• Plans and elevations
• Volume/ surface area of prisms
• (Volume of a pyramid/ sphere)

YEAR 11 (Higher)

Year 11 students will continuously retrieve previous learning in order for them to remember more. The Key Learning topics interleave with previous learnt knowledge into their current learning preparing students thoroughly for GCSE exam-type questions.

### TERM 1

Retrieval Practice

• Error intervals, Compound interest/ Depreciation, solving mixed Ratio and Proportion problems
• Factorising quadratics (including AC method), Linear/ Quadratic nth terms, Solving Quadratic equations, Solving simultaneous linear equations
• Combined transformations, Angles on parallel lines, Similar triangle problems
• Reverse mean, Estimate of the mean, Cumulative frequency, Box plots

Key Learning

• Number, Ratio, Proportion - Calculations involving Upper and Lower bounds
• Algebra - Complex rearranging, Functions – Inverse, Composite, Iterations, Direct and Inverse proportion equations, Algebraic proof, Rate of change (interpreting the gradient), Graphing linear inequalities
• Geometry - Scale factors - Length, Area, Volume, Area under a speed/time graph
• Statistics – Histograms; drawing and interpreting

### TERM 2

Retrieval Practice

• Interpreting pie charts, ratio and proportion problems, Bounds and their calculations
• Simplifying algebraic fractions, Finding the equation of a Straight line, Types of graphs – key points
• Circles/ Arcs/ Sectors, Trigonometry – right-angled triangles, Exact trigonometric values, 3-D Pythagoras, Negative/ Fractional enlargement
• Drawing and interpreting histograms

Key Learning

• Number, Ratio, Proportion - Product rule for counting
• Algebra - Equations from a given ratio, set up and solve simultaneous equations, Non-linear simultaneous equations, Surds; Expanding, Rationalising the denominator, solving quadratic inequalities, set up and solve inequalities
• Geometry - Angles in a polygon, Problems involving Arcs/ Sectors, Circle theorems, Advanced Trigonometry – Sine rule, Cosine rule, Area of a triangle = 1/2abSinC
• Probability – Venn diagrams; Conditional probability

### TERM 3

Retrieval Practice

• Product rule for counting, Standard Form calculations,
• Equations from a given ratio, Surds, Non-linear simultaneous equations
• Angles in a polygon, Circle theorems, Advanced Trigonometry – Sine rule, Cosine rule, 1/2abSinC
• Stem and leaf diagrams, Frequency polygons

Key Learning

• Number, Ratio, Proportion - Capture-recapture
• Algebra - Equations of parallel and perpendicular lines, simultaneous equations graphically, solving quadratic equations from graphs, solving exponential equations, Area under a curve – trapezia (over and under estimates), Gradient of a point on a curve
• Geometry – Density/ Mass/ Volume, Vectors and Vector proof
• Probability - Tree diagrams; independent/ dependent events

YEAR 11 (Foundation)

Year 11 students will continuously retrieve previous learning in order for them to remember more. The Key Learning topics interleave with previous learnt knowledge into their current learning preparing students thoroughly for GCSE exam-type questions.

### TERM 1

Retrieval Practice

• BIDMAS, Fractions calculations, FDP Conversions, percentage calculations, simplifying ratios, sharing an amount into a given ratio, Best buys
• Simplifying algebraic expressions, Arithmetic sequences, Horizontal/ Vertical lines, Straight line graphs/quadratic graphs,
• Angles on a straight line, angles around a point.
• Writing probabilities, Relative frequency (probability), finding the Mode/ Median/ Mean, drawing and interpreting Pie charts

Key Learning

• Number, Ratio, Proportion - Error Intervals, Standard form calculations, Estimation, Complex Ratio of amounts, Speed/ Distance/ Time
• Algebra - Re-arranging equations, expanding Double brackets, representing and solving Inequalities
• Geometry – Multi-step angles in a Triangle/ Quadrilateral, Angles on parallel lines, Area (tiling) questions, Vectors, Pythagoras, Venn Diagrams
• Statistics - Reverse Averages

### TERM 2

Retrieval Practice

• Factors, multiples and primes, Rounding and significant figures, Estimation, Ordering FDP, Flow charts, Complex ratio of amounts
• Solving equations, Factorising expressions, Arithmetic Sequences
• Lines of Symmetry, Rotational symmetry, Parts of a circle, Area of different shapes including compound shapes
• Pie charts, Probability scales, Tree diagrams

Key Learning

• Number, Ratio, Proportion – Lowest Common Multiple (LCM)/ Highest Common Factor (HCF), writing one amount as a percentage of another, Compound interest, Combining ratios
• Algebra - Drawing inequalities, set up and solve equations, Fibonacci sequence
• Geometry – Transformations, Distance Time Graphs, Constructions
• Statistics - Frequency trees, Scatter graphs, Mean from frequency tables

### TERM 3

Retrieval Practice

• Fractions calculations, Decimal multiplication and division, LCM/HCF, Error Intervals, Estimation, Speed Distance Time
• Simplifying expressions, Expanding brackets, Terminology: Terms, Identities, Expressions, Equations
• Unit conversions, Area of circles, Transformations, Pythagoras, Constructions

Key Learning

• Number, Ratio, Proportion – Negative/ Fractional indices, Reverse percentages, Simple vs Compound Interest, Indices
• Algebra - Sketching graphs, Area/perimeter and algebra (setting up and solving), SUVAT Equations, solving quadratic equations factorising, solving Simultaneous Equations
• Geometry – Pressure/ Force/ Area , Trigonometry, Area of sectors, Volume of prisms, Reverse area problems

Course Title: GCSE Mathematics

Exam Board: OCR for the foundation tier (1-5) and Edexcel for the higher tier (4 – 9). Tiering decisions are initially made at Christmas in year 10, but will be reviewed half termly to ensure the correct tier is chosen for each individual.

Examination Description: 100% exam based. Students sit three exams (one Non-Calculator allowed paper and two Calculator allowed papers) and their average across the three papers will inform their grade.

 Foundation – OCR Higher – Edexcel Paper 1 – Calculator allowed Paper 1 – Calculator Not allowed Paper 2 – Calculator Not allowed Paper 2 – Calculator allowed Paper 3 – Calculator allowed Paper 3 – Calculator allowed