Download Key Stage 4 Maths Curriculum

Key Stage 4 Maths Curriculum
At Key Stage 4 our pupils are prepared for their GCSE(s) in Mathematics. Sets 1, 2 and 3 are entered for the Linked Pair GCSE, which
means they will achieve two GCSEs one in Methods in Mathematics and the other in Applications of Mathematics. Pupils in Set 4 will be
entered for the Linear Mathematics GCSE. Each course is assessed by 100% terminal examination, which is sat at the end of Year 11
Assessments
This will be done by peer and self-assessment, where appropriate, and by regular marking from the class teacher. There will be more
formal assessments done on a half-termly basis using previous GCSE papers.
For further information please contact Mr Burley at school: Tel. (01736) 788501 or email: [email protected]
Year 11 Sets 1, 2 and 3 Maths Curriculum: Methods 2
Unit 2
M2 N
1
2
3
4
5
6
7
8
9
10
Core
(Foundation and Higher Tier)
Number
Higher Tier Only
Understand and use number operations and the relationships
between them, including inverse operations and hierarchy of
operations.
Arithmetic of real numbers.
Including exact calculation with surds and π
Numbers and their representations including powers, roots, indices
(integers).
Approximate to specified degrees of accuracy including a given
power of ten, number of decimal places and significant figures.
Use the concepts and vocabulary of factor (divisor), multiple,
common factor, common multiple, highest common factor, least
common multiple, prime number and prime factor decomposition.
Understand that factors of a number can be derived from its prime
factorisation.
Understand that 'percentage' means 'number of parts per 100' and
use this to compare proportions.
Understand and use the relationship between ratio and fractions.
Find proportional change, using fractions, decimals and percentages. Including repeated proportional change.
Use calculators effectively and efficiently.
Including trigonometric functions.
11
M2 A
1
2
Understand and use Venn diagrams to solve problems.
Algebra
Distinguish the different roles played by letter symbols in algebra,
using the correct notation.
Manipulate algebraic expressions by collecting like terms, by
multiplying a single term over a bracket, taking out common factors.
3
4
Set up, and solve simple equations.
5
Generate terms of a sequence using term-to-term and position-toterm definitions.
Form linear expressions to describe the nth term of a sequence
6
7
8
9
M2 G
1
2
3
4
5
6
7
Solve quadratic equations exactly by factorising, completing the
square and using the formula.
Form quadratic expressions to describe the nth term of a
sequence.
Use the conventions for coordinates in the plane and plot points in all
four quadrants.
Use geometric information to complete diagrams on a coordinate
grid.
Recognise and use equivalence in numerical, algebraic and
graphical representations.
Geometry
Recall and use properties of angles at a point, angles at a point on a
straight line (including right angles), perpendicular lines, and
vertically opposite angles.
Understand and use the angle properties of parallel and intersecting
lines, triangles and quadrilaterals.
Recall the properties and definitions of special types of quadrilateral,
including square, rectangle, parallelogram, trapezium, kite and
rhombus.
Recognise reflection and rotation symmetry of 2D shapes.
Calculate and use the sums of the interior and exterior angles of
polygons.
Solve problems in the context of tiling patterns and tessellation.
8
9
10
Multiplying two linear expressions, factorising quadratic
expressions including the difference of two squares, and
simplifying rational expressions.
Describe and transform 2D shapes using single or combined
rotations, reflections, translations, or enlargements by a positive
Understand, prove and use circle theorems and the intersecting
chords theorem
Understand and use the midpoint and the intercept theorems.
Understand and construct geometrical proofs using formal
arguments, including proving the congruence, or non-congruence
of two triangles in all possible cases.
Enlargements by positive fractional and negative scale factors.
11
12
13
14
15
16
17
18
19
20
scale factor and distinguish properties that are preserved under
particular transformations.
Use 2D vectors to describe translations.
Understand congruence and similarity, including the relationship
between lengths, in similar figures.
Use Pythagoras’ theorem in 2D.
Distinguish between centre, radius, chord, diameter, circumference,
tangent, arc, sector and segment.
Find circumferences of circles and areas enclosed by circles.
Calculate perimeters and areas of shapes made from triangles and
rectangles
Use vectors to solve simple geometric problems and construct
geometric arguments.
Including the relationship between areas and volumes of similar
shapes.
Extend to 3D.
Use the trigonometric ratios to solve 2D and 3D problems. Use the
sine and cosine rules to solve problems in 2D and 3D.
Extend to other compound shapes.
Calculate the area of a triangle using ½ ab sin C.
Calculate volumes of right prisms and of shapes made from cubes
and cuboids.
21
Solve mensuration problems involving more complex shapes and
solids.
Year 11 Sets 1, 2 and 3 Maths Curriculum: Applications 2
Unit 2
A2 N
1
Core
(Foundation and Higher Tier)
Number
5
Understand and use number operations and the relationships
between them, including inverse operations and hierarchy of
operations.
Use the concepts and vocabulary of factor (divisor), multiple,
common factor, common multiple, highest common factor, least
common multiple, prime number and prime factor decomposition.
Approximate to specified degrees of accuracy including a given
power of ten, number of decimal places and significant figures.
Understand that 'percentage' means 'number of parts per 100' and
use this to compare proportions.
Find proportional change.
6
7
Divide a quantity in a given ratio.
Use calculators effectively and efficiently.
2
3
4
Higher Tier Only
Repeated proportional change, exponential growth/decay, its
relationship with repeated proportional change including financial
and scientific applications.
Including trigonometric functions.
A2 M
1
2
3
4
5
6
A2 A
1
2
3
4
5
6
7
8
9
10
A2 G
1
2
3
4
5
6
7
Measures
Interpret scales on a range of measuring instruments and recognise
the inaccuracy of measurements.
Convert measurements from one unit to another.
Make sensible estimates of a range of measures.
Understand and use compound measures in familiar and unfamiliar
contexts.
Understand and use bearings.
Measure and draw lines and angles.
Algebra
Set up, and solve simple equations.
Use the conventions for coordinates in the plane and plot points in all
four quadrants.
Recognise and plot equations that correspond to straight-line graphs
in the coordinate plane.
Find approximate solutions of equations using graphical methods
and systematic trial and improvement.
Find and interpret gradients and intercepts of straight line graphs in
practical contexts.
Construct linear functions from real-life problems and plot their
corresponding graphs.
Recognise and use graphs that illustrate direct proportion.
Discuss, plot and interpret graphs (which may be nonlinear)
modelling real situations, including journeys / travel graphs.
Calculate areas under graphs consisting only of straight lines and
interpret the result.
Extend to quadratic and other functions.
Interpret the gradient at a point on a curve as the rate of change.
Extend to inverse proportion.
Including periodic graphs.
Extend to estimates of areas under curves.
Geometry
Recall and use properties of angles at a point, angles at a point on a
straight line (including right angles), perpendicular lines, and
vertically opposite angles.
Understand and use the angle properties of parallel and intersecting
lines, triangles and quadrilaterals.
Recall the properties and definitions of special types of quadrilateral,
including square, rectangle, parallelogram, trapezium, kite and
rhombus.
Recognise reflection and rotation symmetry of 2D shapes.
Understand congruence and similarity, including the relationship
between lengths, in similar figures.
Use Pythagoras’ theorem in 2D.
Distinguish between centre, radius, chord, diameter, circumference,
Including the relationship between areas and volumes of similar
shapes.
Extend to 3D.
tangent, arc, sector and segment.
8
9
10
11
12
13
14
15
16
Use the trigonometric ratios to solve 2D and 3D problems.
Use 2D representations of 3D shapes
Use and interpret maps and scale drawings.
Draw triangles and other 2D shapes using a ruler, pair of compasses
and protractor.
Use straight edge and a pair of compasses to do constructions.
Construct loci.
Find circumferences of circles and areas enclosed by circles.
Calculate perimeters and areas of shapes made from triangles and
rectangles
Calculate volumes of right prisms and of shapes made from cubes
and cuboids.
17
Extend to other compound shapes.
Solve mensuration problems involving more complex shapes and
solids.
Year 11 and Year 10 Set 4 Maths Curriculum: Linear Mathematics GCSE
Number and Algebra
N1 Working with number
N1.1
N1.2
N1.3
N1.4
N1.5
N1.6
N1.7
N1.8
N1.9
N1.14
Understand integers and place value to deal with arbitrarily large positive numbers.
Add, subtract, multiply and divide any number.
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
Approximate to a given power of 10, up to three decimal places and one significant figure
Order rational numbers.
The concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, highest multiple, prime number and
prime factor decomposition.
The terms square, positive and negative square root, cube and cube root.
Index notation for squares, cubes and powers of 10.
Index laws for multiplication and division of integer powers.
Use calculators effectively and efficiently, including statistical functions.
N2 Fractions, Decimals and Percentages
N2.1
N2.2
N2.3
N2.4
N2.5
N2.6
N2.7
Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
Add and subtract fractions.
Use decimal notation and recognise that each terminating decimal is a fraction.
Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals.
Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
Interpret fractions, decimals, percentages as operators.
Calculate with fractions, decimals and percentages.
N3 Ratio and Proportion
N3.1
N3.2
N3.3
Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
Divide a quantity in a given ratio.
Solve problems involving ratio and proportion, including the unitary method of solution.
N4 The Language of Algebra
N4.1
N4.2
Distinguish the different roles played by letter symbols in algebra, using the correct notation.
Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5 Expressions and Equations
N5.1
N5.4
N5.6
N5.7
N5.8
N5.9
Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
Set up and solve simple linear equations.
Derive a formula, substitute numbers into a formula and change the subject of a formula.
Solve linear inequalities in one variable and represent the solution set on a number line.
Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving
them.
Use algebra to support and construct arguments.
N6 Sequences, Functions and Graphs
N6.1
N6.2
N6.3
N6.4
N6.11
N6.12
N6.13
Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
Use linear expressions to describe the nth term of an arithmetic sequence.
Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information.
Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, gradient including finding their gradients.
Construct linear functions from real-life problems and plot their corresponding graphs.
Discuss, plot and interpret graphs (which may be non-linear) modelling real situations, including statistics contexts.
Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.
Geometry and Measures
G1 Properties of Angles and Shapes
G1.1
G1.2
G1.3
G1.4
G1.5
G1.6
G1.7
G1.8
Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite
angles at a vertex.
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
Calculate and use the sums of the interior and exterior angles of polygons.
Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and
rhombus.
Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
Recognise reflection and rotation symmetry of 2D shapes.
Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor
and distinguish properties that are preserved under particular transformations.
Understand congruence and similarity.
G2 Geometrical Reasoning and Calculation
G2.1
G2.3
Use Pythagoras’ theorem.
Justify simple geometrical properties.
G2.4
Use 2D representations of 3D shapes.
G3 Measures and Construction
G3.1
G3.2
G3.3
G3.4
G3.5
G3.6
G3.7
G3.8
G3.9
G3.10
G3.11
Use and interpret maps and scale drawings.
Understand the effect of enlargement for perimeter, area and volume of shapes and solids.
Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements.
Convert measurements from one unit to another.
Make sensible estimates of a range of measures.
Understand and use bearings.
Understand and use compound measures.
Measure and draw lines and angles.
Draw triangles and other 2D shapes using a ruler and protractor.
Use straight edge and a pair of compasses to do constructions.
Construct loci.
G4 Mensuration
G4.1
G4.3
G4.4
Calculate perimeters and areas of shapes made from triangles and rectangles.
Calculate circumferences and areas of circles.
Calculate volumes of right prisms and of shapes made from cubes and cuboids.
G5 Vectors
G5.1
Understand and use vector notation for translations.
Statistics and Probability
S1 The Handling data Cycle
S1.1
Understand and use the statistical problem solving process which involves
• specifying the problem and planning
• collecting data
• processing and presenting the data
• interpreting and discussing the results.
S2 Data Collection
S2.1
S2.2
S2.3
S2.4
S2.5
Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data.
Identify possible sources of bias.
Design an experiment or survey.
Design data-collection sheets distinguishing between different types of data.
Extract data from printed tables and lists.
S3 Data Presentation and Analysis
S3.1
S3.2
S3.4
Design and use two-way tables for grouped and ungrouped data.
Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts,
pie charts, line graphs, frequency polygons, histograms with equal class intervals.
Calculate median, mean, range, mode and modal class.
S4 Data Interpretation
S4.1
Interpret a wide range of graphs and diagrams and draw conclusions.
S4.2
S4.3
S4.4
Look at data to find patterns and exceptions.
Recognise correlation and draw and/or use lines of best fit by eye, understanding what these represent.
Compare distributions and make inferences.
S5 Probability
S5.1
S5.2
S5.3
S5.4
S5.7
S5.8
S5.9
Understand and use the vocabulary of probability and the probability scale.
Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative
frequency.
List all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities.
Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.
Compare experimental data and theoretical probabilities.
Understand that if an experiment is repeated, this may – and usually will – result in different outcomes.
Understand that increasing sample size generally leads to better estimates of probability and population characteristics.
Year 10 Sets 1, 2 and 3 Maths Curriculum: Methods 1
Unit 2
M2 N
1
2
3
4
5
6
7
8
9
10
11
12
Core
(Foundation and Higher Tier)
Number
Understand and use number operations and the relationships
between them, including inverse operations and hierarchy of
operations.
Arithmetic of real numbers: add, subtract, multiply and divide any
number
Numbers and their representations including powers, roots, indices
(integers).
Use the concepts and vocabulary of factor (divisor), multiple and
prime numbers.
Understand that 'percentage' means 'number of parts per 100' and
use this to compare proportions.
Use multipliers for percentage change.
Interpret fractions, decimals and percentages as operators.
Understand and use the relationship between ratio, fractions and
decimal representations
Understand and use direct proportion.
Divide a quantity in a given ratio.
Use calculators effectively and efficiently.
Higher Tier Only
Simplification of surds including rationalising a denominator.
Extend to fractional and negative indices, and use of standard
index form.
Approximate to appropriate degrees of accuracy
Work with repeated percentage change; solve reverse percentage
problems.
Including recurring and terminating decimals.
Extend to include inverse proportion.
M1 A
1
2
3
4
5
Algebra
Distinguish the different roles played by letter symbols in algebra,
using the correct notation.
Distinguish in meaning between the words equation, inequality,
formula and expression.
Manipulate algebraic expressions by collecting like terms, by
multiplying a single term over a bracket, taking out common factors.
Set up, and solve simple equations.
Set up and use equations that describe direct and inverse
proportion.
Set up, and solve simultaneous equations in two unknowns where
one of the equations might include squared terms in one or both
unknowns.
6
7
8
9
10
11
Solve quadratic equations approximately using a graph.
Derive a formula, substitute numbers into a formula and change the
subject of a formula.
Use algebra to support and construct arguments.
Use the conventions for coordinates in the plane and plot points in all
four quadrants.
Recognise and plot equations that correspond to straight-line graphs
in the coordinate plane.
12
14
15
16
1
2
3
4
Use algebra to construct simple proofs
3D coordinate systems
Use y = mx + c and understand the relationship between gradients
of parallel and perpendicular lines.
Draw, sketch, recognise graphs of linear, quadratic simple cubic
functions, the reciprocal function y = 1/x with x
y
= kx for integer values of x and simple positive values of k, the
trigonometric functions y = sin x, y = cos x and y = tan x.
Understand and use the Cartesian equation of a circle centred at
the origin and link to the trigonometric functions.
Construct the graphs of simple loci.
Sketch simple transformations of a given function.
13
M1 P
The meaning of identity and knowledge of the identity symbol will
also be expected.
Multiplying two linear expressions, factorising quadratic
expressions including the difference of two squares, and
simplifying rational expressions.
Probability
Understand and use the vocabulary of probability and the probability
scale.
Understand and use theoretical models for probabilities including the
model of equally likely outcomes.
Understand and use estimates of probability from relative frequency.
Use of sample spaces for situations where outcomes are single
events and for situations where outcomes are two successive
events.
5
6
7
Identify different mutually exclusive and exhaustive outcomes and
know that the sum of the probabilities of all these outcomes is 1
Understand and use set notation to describe events and compound
events.
Use Venn diagrams to represent the number of possibilities and
hence find probabilities.
8
Use tree diagrams to represent outcomes of compound events,
recognising when events are independent or dependent.
Know when to add or multiply probabilities: if A and B are mutually
exclusive, then the probability of A or B occurring is P(A) + P(B); if
A and B are independent events, the probability of A and B
occurring is P(A)× P(B).
9
10
11
Compare experimental data and theoretical probabilities, and make
informal inferences about the validity of the model giving rise to the
theoretical probabilities.
Understand that when a statistical experiment or survey is repeated
there will usually be different outcomes, and that increasing sample
size generally leads to better estimates of probability and population
characteristics.
Year 10 Sets 1, 2 and 3 Maths Curriculum: Methods 2
Unit 2
M2 N
1
2
3
4
5
6
7
Core
(Foundation and Higher Tier)
Number
Understand and use number operations and the relationships
between them, including inverse operations and hierarchy of
operations.
Arithmetic of real numbers.
Numbers and their representations including powers, roots, indices
(integers).
Approximate to specified degrees of accuracy including a given
power of ten, number of decimal places and significant figures.
Use the concepts and vocabulary of factor (divisor), multiple,
common factor, common multiple, highest common factor, least
common multiple, prime number and prime factor decomposition.
Understand that factors of a number can be derived from its prime
factorisation.
Understand that 'percentage' means 'number of parts per 100' and
Higher Tier Only
Including exact calculation with surds and π
8
9
10
11
M2 A
1
2
use this to compare proportions.
Understand and use the relationship between ratio and fractions.
Find proportional change, using fractions, decimals and percentages. Including repeated proportional change.
Use calculators effectively and efficiently.
Including trigonometric functions.
Understand and use Venn diagrams to solve problems.
Algebra
Distinguish the different roles played by letter symbols in algebra,
using the correct notation.
Manipulate algebraic expressions by collecting like terms, by
multiplying a single term over a bracket, taking out common factors.
3
4
Set up, and solve simple equations.
5
Generate terms of a sequence using term-to-term and position-toterm definitions.
Form linear expressions to describe the nth term of a sequence
6
7
8
9
M2 G
1
2
3
4
5
6
7
8
9
Multiplying two linear expressions, factorising quadratic
expressions including the difference of two squares, and
simplifying rational expressions.
Solve quadratic equations exactly by factorising, completing the
square and using the formula.
Form quadratic expressions to describe the nth term of a
sequence.
Use the conventions for coordinates in the plane and plot points in all
four quadrants.
Use geometric information to complete diagrams on a coordinate
grid.
Recognise and use equivalence in numerical, algebraic and
graphical representations.
Geometry
Recall and use properties of angles at a point, angles at a point on a
straight line (including right angles), perpendicular lines, and
vertically opposite angles.
Understand and use the angle properties of parallel and intersecting
lines, triangles and quadrilaterals.
Recall the properties and definitions of special types of quadrilateral,
including square, rectangle, parallelogram, trapezium, kite and
rhombus.
Recognise reflection and rotation symmetry of 2D shapes.
Calculate and use the sums of the interior and exterior angles of
polygons.
Solve problems in the context of tiling patterns and tessellation.
Understand, prove and use circle theorems and the intersecting
chords theorem
Understand and use the midpoint and the intercept theorems.
Understand and construct geometrical proofs using formal
10
11
12
13
14
15
16
17
18
19
20
21
Describe and transform 2D shapes using single or combined
rotations, reflections, translations, or enlargements by a positive
scale factor and distinguish properties that are preserved under
particular transformations.
Use 2D vectors to describe translations.
Understand congruence and similarity, including the relationship
between lengths, in similar figures.
Use Pythagoras’ theorem in 2D.
Distinguish between centre, radius, chord, diameter, circumference,
tangent, arc, sector and segment.
Find circumferences of circles and areas enclosed by circles.
Calculate perimeters and areas of shapes made from triangles and
rectangles
arguments, including proving the congruence, or non-congruence
of two triangles in all possible cases.
Enlargements by positive fractional and negative scale factors.
Use vectors to solve simple geometric problems and construct
geometric arguments.
Including the relationship between areas and volumes of similar
shapes.
Extend to 3D.
Use the trigonometric ratios to solve 2D and 3D problems. Use the
sine and cosine rules to solve problems in 2D and 3D.
Extend to other compound shapes.
Calculate the area of a triangle using ½ ab sin C.
Calculate volumes of right prisms and of shapes made from cubes
and cuboids.
Solve mensuration problems involving more complex shapes and
solids.