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
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
  • Best buys
  • 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)
  • Quadratic, cubic graphs
  • Reading off graphs
  • (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
  • (Quadratic 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

TERM 1

Higher

 

Half term 1.1

Retrieval Practice

Key Learning

Number

  • Error intervals
  • Compound interest Depreciation
  • Calculations involving Upper/Lower bounds

 

Ratio & Proportion

  • Solving Mixed Ratio and Proportion problems

 

Algebra

  • Factorising mixed quadratics (including AC)
  • Linear/ Quadratic nth term
  • Solving Quadratic equations
  • Solving simultaneous linear equations
  • Complex rearranging
  • Functions/ Inverse Functions/ Composite functions
  • Iterations
  • Direct/inverse proportion equations
  •  Algebraic proof
  • Rate of change (interpreting the gradient)
  • Graphing linear inequalities

Shape, Space and Measure

·         Combined transformations – invariant points

·         Angles on parallel lines

·         Similar triangles

·         Scale factors - Length, Area, Volume.

·         Area under a speed/time graph

Statistics

·         Reverse mean

·         Estimate of the mean

·         Cumulative frequency

·         Box plots

·         Histograms – drawing and interpreting

 

Half term 1.2

Retrieval Practice

Key Learning

Number

·         Bounds and their calculations

·         Product rule for counting

 

Ratio & Proportion

·         Interpreting pie charts, ratio and proportion

·         Equations from a given ratio

 

Algebra

·         Simplifying algebraic fractions

·         Finding the equation of a Straight line

·         Types of graphs – key points

·         Set up and solve simultaneous equations

·         Harder simultaneous equations

·         Surds – Expanding, Rationalising the denominator

·         Solve quadratic inequalities> set up and solve

Shape, Space and Measure

·         Circles/ Arcs/ Sectors

·         Trigonometry – right-angled triangles

·         Trigonometric values

·         3-D Pythagoras

·         Negative/ fractional enlargement

·         Angles in a polygon

·         Problems involving Arcs/ Sectors

·         Circle theorems

·         Advanced Trigonometry – Sine rule, Cosine rule,

·         Area of a triangle = 1/2abSinC

 

Statistics

·         Histograms – drawing and interpreting

·         Conditional probability

 

 

Foundation

 

Half term 1.1

Retrieval Practice

Key Learning

Number

·         Fractions

·         FDP Conversions

·         BIDMAS

·         Finding percentages

·         Error Interval

·         Standard form calculations

·         Estimation

 

Ratio & Proportion

·         Finding ratio of amounts

·         Simplifying ratio

·         Best buys

·         Complex Ratio of amounts

·         SDT

Algebra

·         Simplifying Algebra

·         Arithmetic sequences

·         Straight line graphs/quadratic graphs

·         Horizontal/Vertical lines

·         Re-arranging equations

·         Expanding double brackets

·         Inequalities

Shape, Space and Measure

·         Angles in straight lines, around a point.

·         Complex Triangles/Quadrilaterals.

·         Angles in parallel lines.

·         Tiling questions

·         Vectors (CHALLENGE)

·         Pythagoras (CHALLENGE)

Statistics

·         Finding simple probability

·         Finding mode/median/mean

·         Relative probability

·         Pie charts

·         Complex Venn Diagrams

·         Reverse averages (CHALLENGE)

 

 

Half term 1.2

Retrieval Practice

Key Learning

Number

·         Factors, multiples and primes

·         Rounding and significant figures

·         Estimation

·         Ordering FDP

·         Flow charts

·         LCM/HCF

·         Expressing numbers as percentages

·         Compound interest (CHALLENGE)

Ratio & Proportion

·         Complex ratio of amounts

·         Combining Ratio

Algebra

·         Solving equations

·         Factorising expressions

·         Arithmetic Sequences

·         Drawing inequalities

·         Setting up and solving equations

·         Fibonacci

Shape, Space and Measure

·         Basic area including compound

·         Symmetry (Rotational, lines of)

·         Pie charts

·         Parts of a circle

·         Transformations

·         DST Graphs

·         Construction

Statistics

·         Probability lines and arrows.

·         Tree diagrams

·         Frequency trees

·         Scatter graphs

·         Mean from frequency tables

 

 

TERM 2

Key topics to be reviewed from initial Mock Exams:

 

Foundation - Estimating calculations, Multiply/ Divide – whole numbers and decimals,

Fractions, Decimals and Percentage, % increase/ decrease, ratio and proportioning topics.

Revise Equations – one-step/ two-step/ unknown on both sides. Bearings and Probability.

 

Higher – Revise Standard Form and its application, product rule for counting, setting up direct and inverse proportion equations. Iterations, link graphs- quadratic and straight-line intercepts, solving inequalities/ quadratics inequalities, gradient of a tangent/line, area under a S/T graph, exponential graphs, algebraic proof. Proving vectors are parallel

 

 

TERM 3

Key topics to be reviewed from Mock Exams:

 

Foundation – 2/3 topics revised per lesson and informed from QLAs of mock exams

 

Highers – 2/3 topics revised per lesson and informed from QLAs of mock exams

 

 

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

 

For more information please contact the head of department: chonlee@graceacademy.org.uk