Welcome to Maths

Early maths experiences - Classify, match, compare and order sets.

Pattern and early number:

Describe, copy, and extend simple patterns. Explore numbers to 3.

Numbers within 6 - Count, fine one more and one fewer, order and know conservation within 6.

Addition and subtraction within 6 - Add and subtraction within 6.

Measures - Estimate, order and compare capacity, weight, and lengths.

Shape and sorting - Describe and sort 2D shapes and describe positions.

Numbers within 10 - Count, represent, order and fine one fewer and one more.

Calendar and time - Know the days of the week, seasons, and sequence daily events.

Addition and subtraction within 10 - Add and subtraction within 10.

Grouping and sharing - Share into equal groups.

Number patterns within 15 - Count and explore different representations. Order and explore number patterns to 15. Find one more or fewer.

Doubling and halving - Double and half numbers and explore relationships.

Shape and pattern - Describe and sort 2D and 3D patterns. Recognise and complete patterns.

Securing addition and subtraction facts - Explore commutativity and compare two amounts.

Number patterns within 20 - Count, represent and find one more and fewer within 20.

Number patterns beyond 20 - Find one more and one less, estimate, count, group and share within 20.

Money - Recognise coins and values, explore coin combinations within 20p and find change from 10p.

Measures - Describe capacities, compare volumes/weights, and estimate and order lengths.

Explore patterns - Explore, recognise, and extend patterns.  Apply number, shape, and measures knowledge. Count forwards and backwards.

Number – Explore number, place value, addition, and subtraction within 10.

Geometry – Explore properties of shape, position, and direction.

Number – Explore addition and subtraction within 20.

Measures: Time – Tell o’clock and half-past times and sequences daily events.

Calculation strategies – Explore addition and subtraction strategies.

Number – Represent, sequence, and compare numbers within 50. Count in 2s, 5s and 10s. Describe and complete number patterns.

Additional and subtraction within 20

Fractions – Explore halves and quarters of shapes and quantities.

Measures – Compare lengths and masses and explore doubling and halving.

Numbers 50 to 100 and beyond – Read, write, represent, order, and compare numbers to 100.  Find 1 and 10 more/fewer and identify number patterns.

Additional and subtraction –

Calculate 2-digit numbers and ones. Explore regrouping and investigate number bonds to 20.

Money – Name coins, notes, and their values. Represent same values using different coins and find change.

Multiplication, division – Explore arrays, share equally, double and link halving to fractions.

Measures – Compare capacities, volumes and lengths and apply fractions to capacity.

Numbers within 100 – Read, write, represent, compare, and order to 100.  Explore patterns including odds, evens, tens and ones. 

Addition and subtraction of 2-digit numbers – Apply number bonds, represent, and explain addition and subtraction and apply to problems using bar models.

Measures: Length – Draw lengths and use < > = to compare and order lengths in cm and m.

Graphs – Represent and interpret pictograms, block diagrams, tables, and tally charts.

Multiplication and division – Explore multiplication and division through arrays and make connections to inverse, commutativity and times tables.

Measures: Time – Tell the time to quarter past/to and nearest 5-minute intervals. Calculate duration of time, sequence daily events and know the number of minutes in an hour and hours in a day.

Fractions – Explore part/whole relationships, find fractions of a set, relate fractions to division and know some fractions can be equivalent.

Addition and subtraction of 2-digit numbers - Illustrate, represent, and explain addition and subtraction involving regrouping.

Measures: Money -Recognise coins and notes, use £ and p, and calculate change.

Geometry – Identify and explore properties of shapes, position, and direction.

Numbers within 1000 – 

Represent, compare, and read scales.

Measures: Capacity and Mass – Read, measure, and estimate capacity, volume, mass, and temperature.

Calculation strategies - Apply addition and subtraction strategies to

solve equations and illustrate and explain addition and subtraction using column method.

Exploring multiplicative thinking - Pattern seek with multiples of 2, 3, 4 5 and 10 using an array, use known facts to derive facts from the 3- and 4-times tables, connect multiplication and division facts using commutativity and inverse.

Number sense and exploring calculation strategies – Read, write, compare, and order numbers and use know facts to mentally calculate.

Place value - Read, write, represent, partition, order and compare 3-digit numbers. Find 10 and 100 more or less and round to the nearest 10 and 100.

Graphs - Collect, interpret, and present data using charts and tables.

Addition and subtraction - Develop and use a range of mental calculation strategies and use and explain formal written methods – column method.

Measures: Length and perimeter - Measure, draw and compare lengths, add, and subtract lengths and calculate perimeter.

Multiplication and division – Understand commutativity and inverse and explore multiplication and division facts for 2, 3, 4, 5, 6, 8 and 10.

Calculating with multiplication and division - multiply and divide by 10, multiply a 2-digit number by a 1-digit number, divide 2-digit by a 1-digit and solve correspondence problems

Measures: Time - Tell, record, write and order the time analogue and digital, including 12-hour representations. Measure, calculate and compare durations.

Fractions – Add, subtract, compare, and order fractions.

Geometry: Angles and shape - Identify angles including right angles, identify and draw parallel and perpendicular lines, draw/make, classify, and compare 2-D and 3-D shapes, and measure perimeters.

Measures - Read scales with different intervals, weigh, compare and estimate masses and capacities with mixed units.

Applying multiplicative

thinking – Represent and solve multiplication and division problems.

Exploring calculation strategies and place value - Add and subtract mentally, find 10, 100 and 1000 more or less, order and compare beyond 1000 and round number.

Reasoning with large

numbers - Read, write, represent, order and

compare 4-digit numbers, find 10, 100 or 1000 more or less, round numbers to the nearest 10, 100 or 1000.

Addition and subtraction - Select appropriate strategies to add and subtract, illustrate, and explain appropriate addition and subtraction strategies including column method with regrouping.

Multiplication and division - Identify and explore patterns in multiplication tables including 7 and 9 and explore mental x and \ strategies. Illustrate and explain short multiplication.

Discrete and continuous data - Read, interpret, compare, and construct pictograms, bar charts and time graphs.

Calculating with

multiplication and division – illustrate short division and divide using partitioning.

Fractions - Explore different interpretations and representations of fractions, find equivalent fractions, represent fractions greater than one as mixed number and improper fractions and add and subtract fractions with the same denominator including fractions greater than one.

Measures: Time - Read and convert analogue to digital and 12-hour and 24-hour times. Convert between units of time.

Decimals – Convert decimal equivalents to tenths, quarters, and halves.  Compare numbers with same number of decimal places. Multiply and divide by 10 and 100 including decimals.

Area and perimeter – Calculate for rectangles and rectilinear shapes.

Measures: Solving measures and money problems – Convert and select appropriate units of measure.  Use strategies to investigate problems.

Geometry:  Shape and symmetry - Classify, compare, and order angles.  Compare and classify 2-D shapes.  Identify lines of symmetry.

Geometry: Position and direction - Describe and plot using coordinates. Describe translations.

Reasoning with pattern and sequences – Read and recognise Roman numerals up to 100.  Explore sequences and patterns.

Geometry: 3-D shape - Use understanding of 3-D shapes, identify 3-D shapes from 2-D representations

Reasoning with large whole integers - Read, write, order and compare numbers up to one million.  Round numbers within one million to the nearest multiple of powers of ten. Read Roman numerals up to M.

Integer addition and subtraction - Use rounding to estimate.  Use a range of mental calculation strategies to add and subtract integers.  Illustrate the written method of column addition and subtraction.  Select efficient calculation strategies.

Statistics:  Line graphs and timetables - Complete, read and interpret data from line graphs.  Read and interpret timetables including calculating intervals.

Multiplication and division - Identify multiples and factors.  Investigate prime numbers.  Multiply and divide by 10, 100 and 1000 (integers).  Multiply and divide using derived facts.  Use written methods to multiply and divide. Use a range of mental calculation strategies.

Perimeter and area -Investigate and estimate area and perimeter of rectilinear shapes. Estimate the area of non-rectilinear shapes.

Fractions and decimals - Read, write, order and compare decimals.  Round decimals to the nearest whole number. Represent, identify, name, write, order and compare fractions (including improper and mixed numbers). Calculate fractions of amounts.

Geometry: Angles - Classify, compare, and order angles.  Measure a draw angle with a protractor.  Understand and use angle facts to calculate missing angles.

Fractions and percentages - Add, subtract fractions with denominators that are multiples of the same number.  Multiply fractions (and mixed numbers) by a whole number.  Explore percentage, decimal, fractions equivalence. 

Geometry: Transformations - Read and identify coordinates in all four

Quadrants. Translate and reflected co-ordinates and shapes.  Calculate intervals across zero as a context for negative numbers.

Measures:  Converting units of

measure - Convert between metric units of length, mass and capacity and units of time. Know and use approximate conversion between imperial and metric. 

Calculating with whole numbers and decimals - Mental strategies to add and subtract involving decimals.  Use formal written strategies to add, subtract and multiply involving decimals.  Multiply and divide decimal numbers by ten, 100 and 1,000.  Derive addition, subtraction and multiplication facts involving decimals.

Geometry:  2-D and 3-D shape - Classify 2-D shapes and reason about regular and irregular polygons. Know the properties of diagonals of quadrilaterals. Classify 3-D shapes and create 2-D representations of 3-D shapes.

Measures: Volume - Use cube numbers and notation, estimate volume, convert units of volume.

Problem solving – Solve problem involving negative numbers and calculating intervals across zero.  Calculate the mean, interpret remainders, investigate numbers (consecutive, palindromic and multiples).

Integers and decimals - Represent, read, write, order, and compare numbers up to ten million.  Round numbers, make estimates and use this to solve problems in context.  Solve multi-step problems involving addition and subtraction.

Multiplication and division - Identify and use properties of number, focusing on primes.  Multiply larger integers and decimal numbers using a range of strategies.  Divide integers by 1-digit and 2-digit numbers representing remainders appropriately.  Illustrate and explain formal multiplication and division strategies.

Calculation problems - Understand the use of brackets.  Use knowledge of the order of operations to carry out calculations.  Generate and describe linear number sequences. Express missing number problems algebraically. Solve equations with unknown values.

Fractions - Order, simplify, find equivalents, and compare fractions, including those greater than one.  Recall equivalence between common fractions and decimals.  Find decimal quotients using short division.  Add and subtract fractions.

Measures: Missing angles and length - Compare and classify a range of geometric shapes.  Use angle facts to find unknown angles

Geometry: Coordinates and shapes - Draw a range of geometric shapes using given dimensions and angles.  Describe, draw, translate and reflect shapes on a co-ordinate plane.  Recognise and construct 3-D shapes.  Name and illustrate parts of a circle.

Fractions - Represent multiplication involving fractions. Multiply two proper fractions. Divide a fraction by an integer.

Decimals and measure: Use, read, write, and convert between standard units of measures; length, mass, time, money, and volume as well as imperial units.

Geometry - Calculate the area of parallelograms and triangles.  Calculate, estimate and compare the volume of cuboids.

Percentage and statistics - Calculate and compare percentages of amounts.  Connect percentages with fractions.  Explore the equivalence of fractions, decimals and percentages. Calculate the mean. Construct and interpret lines graphs and pie charts.  Compare pie charts.

Proportion problems - Use fractions to express proportion.  Identify ratio as a relationship between quantities and as a scale factor. Explore unequal sharing involving ratio.

To know, understand and solve problems involving:

- Base 10 integers

- Addition and subtraction

- Base 10 and decimals

-Multiplying and dividing by 10 and 100

To know, understand and solve problems involving:

-Multiplication

-Commutativity

-Multiplication and division

-Associativity

-Distributivity

-Multiplication facts

-Number pyramids

To know, understand and solve problems involving:

-Factors, primes and squares

-Squares

-Factor polygons

-Common multiples

-Number grids

-Prime patterns

To know, understand and solve problems involving:

- Indices

- Prime factorisation

- Highest common factor

- Lowest common multiple

To know, understand and solve problems involving:

-Equal and non-equal priority

-Combined operations

-Distributivity and order of operations

-Unknowns in written calculations

To know, understand and solve problems involving:

-Negative numbers in context

-Order and absolute value

-Modelling addition

-Further addition

-Subtracting positive and negative numbers

-Multiplication as scaling

-Negative scale factors

-Further Multiplication

-Division

-Axioms and negative numbers

To know, understand and solve problems involving:

- Simplification

- Indices

- Substitution

- Using a calculator with algebra

- Collecting like terms

- Expanding brackets

- Factorising

- Equality

- Inverse operations

- Solving one and two step equations

To know, understand and solve problems involving:

-The 2D axes

-Line segments

-Midpoints

-Geometric problems

-Equations of lines

- Exploring horizontal and vertical lines

To know, understand and solve problems involving:

- Describing and comparing angles

- Measuring and drawing angles

- Finding unknown angles

- Alternate angles

- Corresponding and allied angles

To know, understand and solve problems involving:

- Rotational symmetry

- Reflectional symmetry

- Classifying triangles

- Interior angles of triangles

- Comparing quadrilaterals

- Tessellation patterns

To know, understand and solve problems involving:

- Describing perimeters

- Describing area

- Areas of parallelograms

- Area of triangles

To know, understand and solve problems involving:

- Equal parts of a whole

- Fractions and units of measure

- Equivalence

- Comparing fractions

- Ordering decimal fractions

To know, understand and solve problems involving:

- Multiplying fractions

- Dividing fractions by integers

- Dividing with fractions in mixed contexts

- Adding and subtracting

- Distributivity

To know, understand and solve problems involving:

- In the same ratio

- Equivalent ratios

- Ratio and proportion in geometry

- Dividing into a ratio

To know, understand and solve problems involving:

- Translation

- Rotation

- Reflection

- Enlargement

To know, understand and solve problems involving:

- Generalising linear sequences

- Position-to-term rules

To know, understand and solve problems involving:

- Simplification

- Indices

- Substitution

- Using a calculator with algebra

- Collecting like terms

- Expanding brackets

- Factorising

- Equality

- Inverse operations

- Solving one and two step equations

To know, understand and solve problems involving:

-Coordinate grids

-Linear graphs

-Gradient

-Equation of a line

To know, understand and solve problems involving:

- Rounding using a number line

- Rounding to decimal places

- Estimation

- Significant figures

- Rounding to one significant figure

To know, understand and solve problems involving:

- Parts and wholes

- Sharing in a ratio

- Equal proportion

To know, understand and solve problems involving:

- Representing linear relationships

- Sketching graphical relationships

- Speed as rate

- Distance-time graphs

To know, understand and solve problems involving:

- Introduction to conversion

- Direct proportion in the Cartesian plane

- Gradient and the constant of proportionality

- Direct proportion – unitary method

- Inverse proportion

- Speed, distance and, time

- Percentage change with speed, distance and, time

To know, understand and solve problems involving:

- Types of data

- Data collection

- Representing data

- Comparing representations

- Mean

- A changing mean

- Means from frequency tables

- Mode, median and range

- Finding averages from bar charts

To know, understand and solve problems involving:

- Correlation

- Lines of best fit

- Median and range from scatter charts

- Correlation and causation

To know, understand and solve problems involving:

- Polygons

- Interior angles

- Sum of interior angles of a polygon

- Exterior angles

- Angle notation

To know, understand and solve problems involving:

- Combined multiplication and indices

- Substitution with indices and division

- Simplification with division and indices

- Expanding and collecting like terms

- Further factorising

- Solving equations with expanding

- Solving equations with unknowns both sides

- Changing the subject

To know, understand and solve problems involving:

- Anatomy of a circle

- Circle constructions

- Circumference

- Perimeter of compound shapes

- Area of circles

- Area and perimeter of compound shapes

To know, understand and solve problems involving:

- Faces, edges and vertices

- Nets of cubes

- Nets of cuboids

- Surface area of cuboids

- Prisms

- Nets of prisms

- Surface area of prisms

- Cylinders

- Volume of cuboids

- Volume of prisms

To know, understand and solve problems involving:

-FDP conversions

-Arithmetic with FDP

To know, understand and solve problems involving:

- Chance and probability

- Theoretical probability

- Comparing probabilities

- Complementary events

- Sample space diagrams

- Probability of combined events

- Probability tree diagrams

- Frequency tree diagrams

- Two-way tables

- Relative frequency

- Expectation and bias

To know, understand and solve problems involving:

-Intersections

- Unions

- The universal set

- Set notation

- Probability in set notation

- Venn diagrams and experimental probability

- Expected outcomes and Venn diagrams

To know, understand and solve problems involving:

- Equivalent equations

- Adding and subtracting equations

- Solving simultaneous equations

- Solving simultaneous equations – Scaling

- Solving simultaneous equations - Rearranging

- Substitution of expressions

- Solving simultaneous equations through substitution

To know, understand and solve problems involving:

- Graphing y=mx+c

- Graphing ax+by=c

- Solving graphically

- Visualising linear relationships

- Areas of enclosed regions

- Parallel lines

- Solving simultaneous inequalities graphically

-0, 1 or 2 solutions

To know, understand and solve problems involving:

- Angles and triangles

- Angles in polygons

To know, understand and solve problems involving:

- Circle loci

- Equidistant points

- Perpendicular bisectors

- Bisecting angles

- Constructing triangles

- Congruence

- Congruence proof

- Constructing angles

To know, understand and solve problems involving:

- The hypotenuse

- Pythagoras’ theorem

- Pythagoras in 3-D shapes

- Pythagoras and the Cartesian plane

To know, understand and solve problems involving:

- Parts and wholes

- Ratios and fractions

- Scale factors and constants of proportionality

- Unit ratios

To know, understand and solve problems involving:

- Congruence

- Enlargement

- Similarity

- Constants of proportionality

- Centre of enlargement

- Enlargement on a coordinate grid

- Area and enlargement

To know, understand and solve problems involving:

- The unit circle - similar triangles

- Sine and cosine graphs

- Trigonometry and generalising right angle triangles

- Opposite and adjacent

- Generalising with sin cos tan

- Finding the angle

- Generalising right-angled trigonometry

To know, understand and solve problems involving:

- Algebraic conventions

- Simplifying by collecting like terms

- Expanding brackets

- Factorising expressions

- Substitution

- Rearranging and solving equations

- Equations with two variables

To know, understand and solve problems involving:

- Quadratic expressions

- Substituting into a quadratic

- Plotting quadratic graphs 1

- Interpreting quadratic graphs:

- Find y from x

- Factorised form of quadratics

- Expanding double brackets

- Expanding 3 or more binomials

- Comparing representations

To know, understand and solve problems involving:

-Rational and irrational numbers

- Exact and approximate values

- Surds

- Accuracy

To know, understand and solve problems involving:

- Indices

- Roots

-0 and negative indices

- Base 10

- Multiplication of indices

- Division of indices

To know, understand and solve problems involving:

-Powers of ten

-Comparing numbers

-Writing standard form

-Connecting standard form

To know, understand and solve problems involving:

- Decimal multipliers

- Compound growth and decay

- Graphs of growth and decay

- Reverse compound change

To know, understand and solve problems involving:

-Number problems and reasoning

-Place value and estimation

-Bounds

-HCF and LCM

-Indices

-Standard form

-Surds

To know, understand and solve problems involving:

-Expanding and factorising

-Solving equations

-Formulae

-Sequences

To know, understand and solve problems involving:

-Pie charts

-Back-to-back stem and leaf diagrams

-Frequency polygons

-Scatter graphs

-Averages and the range

-Averages from frequency tables

-Two-way tables

To know, understand and solve problems involving:

-Fraction and arithmetic

-Reciprocals

-Ratio

-Proportion

-Percentages

-Fraction, decimal, percentages, and ratio equivalence

-Growth and decay

-Compound measures

-Recurring decimals to fractions

To know, understand and solve problems involving:

-Angle properties

-Angles in polygons

-Angles in parallel lines

-Pythagoras

-Trigonometry

-Exact values

To know, understand and solve problems involving:

-Linear graphs

-Rates of change

-Equation of a line

-Quadratic graphs

-Cubic graphs

-Reciprocal graphs

To know, understand and solve problems involving:

-Solving inequalities

-Quadratic equations

-Quadratic inequalities

-Completing the square

-Simultaneous equations

To know, understand and solve problems involving:

-Perimeter and area

-Volume and surface area of prisms

-Circles

-Sector area and arc length

-Volume and surface area of cylinders, spheres, cones, and pyramids

To know, understand and solve problems involving:

-Translation

-Reflection

-Rotation

-Enlargement

-Scale drawings and bearings

-Constructions

-Loci

To know, understand and solve problems involving:

-Congruence

-Geometric proof

-Similarity in 2D

-Similarity in 3D

To know, understand and solve problems involving:

-Single events

-Combined events

-Mutually exclusivity and independence

-Tree diagrams

-Conditional probability

-Venn diagrams and set notation

To review units from the year identified, bespoke to each class.

To know, understand and solve problems involving:

- Place Value

- Negative numbers

- Order of operations

- Rounding and estimation

- Decimal calculations

- Squares cubes and roots

- Factors and multiples

- Indices

- Standard form

To know, understand and solve problems involving:

- Algebraic expressions

- Simplifying expressions

- Substitution

- Formulae

- Expanding brackets

- Factorising

- Using expressions and formulae

To know, understand and solve problems involving:

- Solving equations

- Inequalities

- Generating sequences

- Nth term of a sequence

To know, understand and solve problems involving:

- Frequency tables

- Two-Way tables

- Representing Data

- Time Series

- Stem and leaf diagrams

- Pie Charts

- Scatter graphs

- Line of best fit

To know, understand and solve problems involving:

- Mean and range

- Mode, median, IQR

- Mean from a frequency table

- Sampling

To know, understand and solve problems involving:

- Compare fractions

- Add and subtract fractions

- Multiplying and dividing fractions

- Fractions and decimals

- Fractions and percentages

- Finding percentage of a quantity

- Simple Interest

- Compound interest

- Percentage increase and decrease

To know, understand and solve problems involving:

- Writing ratios

- Dividing quantities in a given ratio

- Comparing ratios and writing 1:n

- Proportion

- Unitary method

- Direct and Inverse proportion graphs

- Compound measures

To know, understand and solve problems involving:

- Properties of shapes

- Angles in parallel lines

- Angles in triangles

- Exterior and Interior angles

To know, understand and solve problems involving:

- Pythagoras’ Theorem

- Trigonometry SOH, CAH, TOA

To know, understand and solve problems involving:

- Rectangles, parallelograms, triangles

- Trapezia

- Area of compound shapes

- Surface area of 3D solids

- Volume of prisms

To know, understand and solve problems involving:

-Calculating probabilities

- Experimental probabilities

- Venn diagrams

- Tree diagrams

To know, understand and solve problems involving:

- Co-ordinates

- Linear Graph

- Gradient and y=mx+c

- Real life graphs

- Distance time graphs

To review units from the year identified, bespoke to each class

To know, understand and solve problems involving:

-Congruence

-Geometric proof

-Similarity in 2D

-Similarity in 3D

To know, understand and solve problems involving:

-Trigonometric Graphs

-Sine rule

-Cosine rule

-Area of a triangle

-Solving Pythagoras and trigonometry problems in 3D

To know, understand and solve problems involving:

-Sampling

-Cumulative frequency

-Box plots

-Histograms

-Comparing data

To know, understand and solve problems involving:

-Solving simultaneous equations graphically

-Quadratic equations

-Quadratic graphs

-Cubic equations

-Iteration

To know, understand and solve problems involving:

-Rearranging formulae

-Algebraic fractions

-Proof

-Functions

To know, understand and solve problems involving:

-Direct and inverse proportion

-Exponential functions

-Non-linear graphs

-Transformation of functions

To know, understand and solve problems involving:

-Radii and chords

-Tangents

-Angles in circles

To know, understand and solve problems involving:

-Vector notation

-Vector arithmetic

-Parallel vectors

-Collinear points

-Solving geometric problems

All units – bespoke scheme of learning created for each class

All units – bespoke scheme of learning created for each class

All units – bespoke scheme of learning created for each class

To know, understand and solve problems involving:

- Translation

- Reflection

- Rotation

- Enlargement

- Combining transformations

To know, understand and solve problems involving:

- Similarity and enlargement

- Properties of similar shapes

-  Congruent shapes

- Rules of Congruence

To know, understand and solve problems involving:

- Plans and elevations

- Scale drawings

- Constructions

- Loci and regions

- Bearings

To know, understand and solve problems involving:

- Area and Circumference of a Circle

- Semi-circles and sectors

- Composite shapes

- Volume and surface area of cylinders

- Volume and surface area of pyramids, cones, and spheres

To know, understand and solve problems involving:

- Expanding double brackets

- Plotting graphs

- Factorising Quadratics

- Solving Quadratics

To know, understand and solve problems involving:

- Graphs of cubic and reciprocals

- Non – linear graphs

- Solving simultaneous equations graphically

- Simultaneous equations algebraically

- Rearranging formulae

All units – bespoke scheme of learning created for each class

All units – bespoke scheme of learning created for each class

All units – bespoke scheme of learning created for each class

To know, understand and solve problems involving:

-Expanding brackets

-Factorising

-Indices, Surds, rationalising the denominator

To know, understand and solve problems involving:

-Solving quadratics

-Completing the square

-Functions

-Quadratic Graphs

-The discriminant

-Modelling with quadratics

To know, understand and solve problems involving:

-Linear simultaneous equations

-Quadratic simultaneous equations

-Simultaneous equations and graphs

-Linear inequalities

-Quadratic inequalities

-Inequalities on graphs

To know, understand and solve problems involving:

-Equation of a line

-Parallel and perpendicular lines

-Length and area

-Modelling with straight lines

To know, understand and solve problems involving:

-Midpoints and perpendicular bisectors

-Equation of a circle

-Intersections of lines and circles

-Tangent and chord properties

-Circles and tangents

To know, understand and solve problems involving:

-Pascal’s triangle

-Factorials

-The binomial expansion

-Solving binomial problems

-Binomial estimation

To know, understand and solve problems involving:

-Cubic graphs

-Quartic graphs

-Reciprocal graphs

-Points of intersection

-Translating graphs

-Sketching graphs

-Transforming functions

To know, understand and solve problems involving:

-Gradients of curves

-Finding the derivative

-Differentiation of terms

-Gradients, tangents and normal

-Increasing and decreasing functions

-Second order derivatives

-Stationary points

-Sketching gradient functions

-Modelling with differentiation

To know, understand and solve problems involving:

-Integrating terms

-Indefinite integrals

-Finding functions

-Definite integrals

-Areas under curves

-Area under the x-axis

-Area between curves and lines

To know, understand and solve problems involving:

-Exponential functions

-Exponential modelling

-Logarithms

-Laws of logs

-Solving equations using logs

-Working with natural logs

-Logs and non-linear data

To know, understand and solve problems involving:

-Sine rule

-Cosine rule

-Area of triangles

-Solving triangle problems

-Graphs of trig functions

-Transformation of trig graphs

To know, understand and solve problems involving:

-Angles in four quadrants

-Exact values of trig ratios

-Trig identities

-Solving trig equations

-Equations and identities

To know, understand and solve problems involving:

-Algebraic fractions

-Dividing polynomials

-The factor theorem

-Proof

-Repeated factors

-Algebraic division

To know, understand and solve problems involving:

-Sec, cosec and cot

-Trig identities

-Inverse trig functions

-Addition formulae

-Double angle formulae

-Solving further trig equations

-Simplifying acosx+bsinx

-Proving trig identities

-Modelling with trig functions

To know, understand and solve problems involving:

-Calculating probabilities

-Venn Diagrams

-Mutually exclusive and independent events

-Tree diagrams

To know, understand and solve problems involving:

-Set notation

-Conditional probability

-Probability formulae

To know, understand and solve problems involving:

-Probability distributions

-The binomial distribution

-Cumulative probabilities

To know, understand and solve problems involving:

-Hypothesis testing

-Critical values and regions

-One tailed and two tailed tests

To know, understand and solve problems involving:

-Vectors

-Magnitude and direction

-Position vectors

-Solving geometric problems

-Modelling with vectors

To know, understand and solve problems involving:

-Constructing a model

-Modelling assumptions

-Quantities and units

-Working with vectors

To know, understand and solve problems involving:

-Displacement time graphs

-Velocity time graphs

-Constant acceleration formulae

-Vertical motion under gravity

To know, understand and solve problems involving:

-Force diagrams

-Forces as vectors

-Force and acceleration

-Motion in 2D

-Connected particles

-Pulleys

To know, understand and solve problems involving:

-Functions of time

-Differentiation

-Maxima and minima problems

-Using integration

-Constant acceleration formulae

To know, understand and solve problems involving:

-Population and samples

-Non-random sampling

-Types of data

-Large data set

To know, understand and solve problems involving:

-Measures of central tendency

-Other measures of location

-Measures of spread

-Variance and standard deviation

-Coding

To know, understand and solve problems involving:

-Outliers

-Box plots

Cumulative frequency

-Histograms

-Comparing data

To know, understand and solve problems involving:

-Exponential models

-Measuring correlation

-Hypothesis testing for zero correlation

All AS units – bespoke SOL

To know, understand and solve problems involving:

-Radian measure

-Arc length

-Sector area

-Solving trig equations in radians

-Small angle approximations

To know, understand and solve problems involving:

-Correlation

-Linear regression

To know, understand and solve problems involving:

-Resultant moments

-Equilibrium

-Centre of mass

-Tilting

To know, understand and solve problems involving:

-Differentiating trig

-Differentiation exponentials and logs

-The chain rule

-The product rule

-The quotient rule

-Implicit differentiation

-Using second derivatives

-Rates of change

To know, understand and solve problems involving:

-Integrating standard functions

-Integrating f(ax+b)

-Using trig identities

-Reverse chain rule

-Substitution

-By parts

-Partial fractions

-Finding areas

-Trapezium rule

-Solving differential equations

-Modelling with differential equations

-Integration as the limit of a sum

To know, understand and solve problems involving:

-Parametric equations

-Using trig identities

-Curve sketching

-Points of intersection

-Modelling with parametric equations

To know, understand and solve problems involving:

-Partial fractions

To know, understand and solve problems involving:

-The modulus function

-Functions and mappings

-Composite functions

-Combining transformations

-Solving modulus problems

To know, understand and solve problems involving:

-3D coordinate

-Vectors in 3D

-Solving geometric problems

-Application to mechanics

To know, understand and solve problems involving:

-Arithmetic sequences and series

-Geometric sequences and series

-Sum to infinity

-Sigma notation

-Recurrence relations

-Modelling with series

To know, understand and solve problems involving:

-Locating roots

-Iteration

-Newton Raphson method

-Applications to modelling

To know, understand and solve problems involving:

-Proof by contradiction

To know, understand and solve problems involving:

-Resolving forces

-Inclined planes

-Friction

To know, understand and solve problems involving:

-Static particles

-Modelling with statics

-Friction and static particles

-Static rigid bodies

-Dynamics and inclined planes

-Connected particles

To know, understand and solve problems involving:

-Horizontal projection

-Horizontal and vertical components

-Projection at any angle

-Projectile motion formulae

To know, understand and solve problems involving:

-Vectors in kinematics

-Vector methods with projectiles

-Variable acceleration in one dimension

-Differentiating vectors

-Integrating vectors

To know, understand and solve problems involving:

-Probability using the normal distribution

-The inverse normal distribution

-The standard normal distribution

-Finding the mean and standard deviation

-Approximating the binomial distribution

-Hypothesis testing with the normal distribution