Autumn 1

Solve word problems (add and subtract)

Autumn 2

Explain and

investigate (multiply and divide)

Spring 1

Geometry

Spring 2

Fractions

Summer 1

Applications of algebra

Summer 2

Percentages and statistics

All should be confident and competent in Key Stage 2 material. Review of these prerequisites may be useful for each unit:

• Number bonds
• Convert units
• Money +/−
• Measurement

• Mental strategies
• Multiplication facts
• Multiplication strategies
• Solve number problems

• Lengths and units
• Parallel and perpendicular
• Work with angles
• Division and the mean

• Equal parts
• Factors and multiples
• Tenths and hundredths
• Word problems
• Fractional areas

• Areas of rectangles and triangles
• Number patterns
• Algebraic notation
• Triangle and quadrilateral properties

• Decimals and problem solving
• Fractions of shapes
• Equivalence
• Order of operations

All will have access to this specific Key Stage 3 content:

• Place value (including decimals)
• Add and subtract (including decimals)
• Rounding
• Perimeter
• Mental strategies

• Factors and multiples
• Multiply and divide (including decimals)
• Area of rectangle, triangle and parallelogram
• Calculate the mean
• Further mental strategies

• Draw and measure angles
• Find unknown angles (straight lines, at a point, vertically opposite)
• Properties of triangles and quadrilaterals
• Unit conversions (linear)
• Symmetry and tessellation

• Equivalent fractions
• Compare and order fractions and decimals
• Change mixed numbers to improper fractions and vice versa
• Fraction of a quantity
• Multiply and divide fractions

• Order of operations
• Substitution
• Form and simplify algebraic expressions
• Expand over a single bracket, and factorise
• Sequences (term-to- term, not nth term)

• Construct and interpret statistical diagrams including pie charts
• Convert between percentages, vulgar fractions and decimals
• Percentage of a quantity
• Find the whole, given the part and the percentage

As well as looking at the termly projects, highest attaining students may be stretched through depth by consideration of the following:

• Different counting systems or bases
• Generalisation
• Upper and lower bounds

• Shikaku puzzles
• Different counting systems or bases
• Alternative methods of multiplication
• Generalisation

• Tessellating triangles and quadrilaterals
• Tangram investigations
• Rigid shapes

• Terminating and recurring decimals
• Fractions of tangrams
• Shape block challenges

• Four fours
• Patterns and generalising
• Algebraic mean questions

• Comparing and converting between representations
• Applications of percentages

Autumn 1

Number

Autumn 2

Algebraic expressions

Spring 1

2-D geometry

Spring 2

Proportional reasoning

Summer 1

3-D geometry

Summer 2

Statistics

All should be confident and competent with Year 7 material. Review of these prerequisites may be useful for each unit:

• Factors, multiples and primes
• Multiplication and division
• Fraction equivalence and calculations

• Problem solving with fractions
• Order of operations
• Form algebraic expressions
• Substitution

• Angle types
• Angle facts
• Rectangle and triangle areas
• ×/÷ by powers of 10
• Problem solving with negative numbers

• Rounding
• Bar modelling with factions
• Fraction ×/÷
• Bar modelling with equations
• FDP equivalence

• Rectilinear areas
• Fraction +/−
• Problem solving with fractions
• Percentage increase and decrease
• Substitution with negatives

• Statistical diagrams
• Ratio and rate
• The mean
• Calculator skills and rounding

All will have access to this specific Key Stage 3 content:

• Primes and indices
• Prime factorisation, squares and cubes
• Use of Venn diagrams to find LCM and HCF
• Add and subtract fractions

• Order and calculate with negative numbers
• Form and solve linear equations (unknowns on one side)
• Use more complex algebraic expressions
• Linear sequences: nth term

• Construct triangles and quadrilaterals
• Calculate unknown angles (including parallel lines)
• Unit conversions (including area)
• Area of a trapezium
• Areas and perimeters of composite figures

• Percentage increase and decrease, including multipliers
• Reverse percentage problems
• Ratio (equivalent, of a quantity) and rate
• Scaling and multipliers
• Speed, distance, time

• Use of significant figures and estimation
• Circumference and area of a circle
• Visualise and identify 3-D shapes and their nets
• Volume of cuboid, prism, cylinder, composite solids
• Surface area

• Collect and organise data, including surveys
• Interpret and compare statistical representations
• Mean, median and mode averages
• The range and outliers

As well as looking at the termly projects, highest attaining students may be stretched through depth by consideration of the following:

• Egyptian fractions
• Continued fractions
• HCF and LCM generalisation

• Explore non-linear sequences
• T-totals

• Similarity and ratio
• Complex constructions
• Simple angle proofs

• Density
• Area scale factors
• Loan repayment

• Platonic solids
• Percentage errors
• Plans and elevations

• Misleading graphs
• Equal width histograms
• Sampling methods

Autumn 1

Graphs and proportion

Autumn 2

Algebraic expressions

Spring 1

2-D geometry

Spring 2

Equations and inequalities

Summer 1

Statistics

Summer 2

Geometry

All should be confident and competent with Year 7 and 8 materials. Review of these prerequisites may be useful for each unit:

• Read scales
• Linear equations
• Proportion
• Percentage increase and decrease

• Make expressions
• Expressions and area
• Substitution
• Powers and roots
• Problem solving with a calculator

• Area and circumference
• Angles on lines and in triangles
• Angles in parallel lines
• Pie charts

• Linear graphs
• Sequences
• Manipulate formulae
• Problem solving with algebra

• FDP conversion
• Number problems with fractions and decimals
• Averages and the range
• Venn diagrams and two-way tables

• Compound areas
• Powers of 10 and standard form
• Problem solving with algebra

All will have access to this specific Key Stage 3 content:

• Cartesian coordinates including midpoint of a line segment
• Linear graphs
• Direct and inverse proportion
• Calculate with scales
• Standard form

• Sequences including arithmetic and geometric
• Expand binomials and factorise simple quadratics
• Change the subject of familiar formulae

• Construction and loci
• Congruence and similarity
• Pythagoras’ theorem
• Angles in polygons

• Construct and solve equations and inequalities (unknowns on both sides)
• Graphical solutions to simultaneous linear equations
• Quadratic and other graphs

• Probability
• Mean of grouped data
• Compare two data sets
• Scatter graphs

• Similarity and Enlargement’
• Transformations (translation, rotation, reflection)
• Exploring trigonometry

As well as looking at the termly projects, highest attaining students may be stretched through depth by consideration of the following:

• 3-D coordinates
• Explore linear and non-linear graphs

• Algebraic proof

• Geometrical proof
• Euclidean geometry
• 3-D Pythagoras
• Complex constructions

• Regions on graphs
• Linear programming
• Modelling

• Equations of lines of best fit
• Probability problems

• Further trigonometry
• Multiple transformations

Throughout Year 9

Approximation and significant figures

Addition, subtraction, multiplication and division with whole numbers, fractions and decimals

Percentage increase and decrease, finding the whole given the part and the percentage

Autumn 1

Number

Autumn 2

Geometry

Spring 1

Reasoning

Spring 2

Geometry & number

Summer 1

Sampling & probability

Summer 2

Applications of algebra

All should be confident and competent in Key Stage 3 material. Review of these prerequisites may be useful for each unit:

• Calculate with fractions
• Convert and solve problems with fractions and percentages
• Review indices

• Ratio notation, links to vulgar fractions, decimals and percentages
• Reflection, rotation and translation
• Pythagoras’ theorem

• Algebraic notation and substitution, including kinematics formulae
• Angles and shapes
• Straight-line graphs
• Equations and inequalities
• Rearranging formule

• Decimal calculations and rounding
• Units
• Area and perimeter of plane shapes, including composite shapes
• Congruence

• Sample spaces
• The probability scale
• Vulgar fractions, decimals and percentages

• Real-life graphs
• Deriving and using expressions, formulae and equations

All will be assessed on this specific Key Stage 4 content

• Calculations with and rules of indices
• Calculations with standard form
• Geometric change including compound interest, growth and decay
• Standard non-linear sequences

• Enlargement
• Similar shapes
• Bearings
• Trigonometry in right angled triangles

• Algebraic arguments
• Geometric reasoning
• Equations of parallel lines
• Vectors

• Properties of 3-D shapes; their plans and elevations
• Surface area and volume of pyramids, cones and spheres (including exact answers)
• Estimation and limits of accuracy
• Loci
• Geometric proof

• Populations and samples
• Theoretical and experimental probability
• Probability of combined events, including tree diagrams and use of Venn diagrams
• Sample spaces and listing

• Expand and factorise binomials
• Quadratic equations
• Cubic and reciprocal graphs
• Linear simultaneous equations
• Graphical solutions of equations

Highest attaining students will also be assessed on the following material, which provides good preparation for Key Stage 5

• Recurrence relations
• Surds
• Recurring decimals
• Fractional indices
• Quadratic sequences

• Negative scale factors of enlargement
• Combine transformatios
• 3-D trigonometry and Pythagoras’ theorem

• Vector proofs
• Trigonometry graphs
• Equations of perpendicular lines
• Further inequalities

• Similar areas and volumes
• Upper and lower bounds
• Trigonometry in all triangles

• Conditional probabiliy

• Complete the square, quadratic formula, quadratic inequalities
• Further simultaneous equations
• Algebraic fractions
• Exponential graphs

Throughout KS4: Students will need to keep working on key skills as they occur within other topics, as well as when the skills are being explicitly addressed. These include: Addition, subtraction, multiplication and division; order of operations; fractions, decimals and percentages; rounding and estimation; and algebraic notation.

Autumn 1

Algebra and geometry

Autumn 2

Number & statistics

Spring 1

Revision, extension 1

Spring 2

Revision, extension 2

Summer 1

Revision, extension 3

Summer 2

Examinations

All should be confident and competent in Key Stage 3 material. Review of these prerequisites may be useful for each unit:

• Ratio calculations
• Direct and inverse proportion
• Derive and use expressions, formulae and equations

• Simple statistical diagrams
• Averages and the range
• Solve number problems

• Review and revision

• Review and revision

• Review and revision

• Review and revision

All will be assessed on this specific Key Stage 4 content

• Arcs and sectors of circles
• Direct and inverse variation
• Proof in algebra and geometry

• Represent and describe distributions
• Identify misleading graphs
• Time series
• Correlation and lines of best fit
• Solve problems
• involving compound units

• Review and revision

• Review and revision

• Review and revision

• Review and revision

Highest attaining students will also be assessed on the following material, which provides good preparation for Key Stage 5

• Apply and prove circle theorems
• Equation of a circle and the tangent to a circle
• Variation with powers

• Histograms with equal and unequal class intervals
• Cumulative frequency graphs and box plots

• Functions and their inverses
• Composite functions
• Transformation of graphs

• Solve equations by Numerical methods
• Gradients of curves and areas under graphs

• Review and revision

• Review and revision

Throughout KS4: Students will need to keep working on key skills as they occur within other topics, as well as when the skills are being explicitly addressed. These

include: Addition, subtraction, multiplication and division; order of operations; fractions, decimals and percentages; rounding and estimation; and algebraic notation.