Mathematics - KS4 - Core

10

What students will learn

How it builds on learning

Number 1: Number skills including order of operations, place value, negative numbers, decimal numbers, indices, surds and standard form. Investigating and discovering special properties of certain numbers.

Builds on the content and skills learnt in Number 1 across Key Stage 3

Algebra 1: Expressions, including linear and quadratic, and manipulating algebra including using letters to represent numbers. Manipulation of more complex expressions, in particular fractions.

Builds on the content and skills learnt in Algebra 1 across Key Stage 3

Geometry 1: Angles and angle facts at a variety of levels from looking at angles along a straight line to angles in polygons of various sizes and circle theorems. Accurately drawing shapes using a ruler and a protractor. Pythagoras’ theorem. Trigonometry for both right-angled and, at some levels, non-right-angled triangles.

Builds on the content and skills learnt in Data Handling 1 across Key Stage 3

Data Handling 1: Representing data using tables, charts and graphs. Understanding correlation. Methods of sampling. Use of quartiles and representing data using boxplots and cumulative frequency diagrams.

Builds on the content and skills learnt in Geometry 1 across Key Stage 3

Number 2:  Calculations including different methods of multiplication or division and rounding. Developing skills at using a calculator. Compound measures and upper and lower bounds. Using the product rule for counting.

Builds on the content and skills learnt in Number 2 across Key Stage 3

Algebra 2: Forming equations, looking at ways to solve them including using a number machine and writing the problem as a sentence. Solving equations as well as inequalities. Solving linear simultaneous equations and for some groups more advanced simultaneous equations. Drawing more complicated graphs, eg. the reciprocal and exponential functions. Using iteration to find solutions to equations.

Builds on the content and skills learnt in Algebra 2 across Key Stage 3

Geometry 2: Area and perimeter of shapes, ranging from rectangles to compound shapes and then circles, including arcs, sectors and segments. Volume and surface area of 3D shapes.

Builds on the content and skills learnt in Data Handling 2 across Key Stage 3

Data handling 2: Analysing data using averages and measures of how spread out the data is. At some levels this will include finding averages from data presented in frequency tables or graphs and presenting data in histograms.

Builds on the content and skills learnt in Geometry 2 across Key Stage 3

Number 3: Fractions, decimals and percentages, including recurring decimals.

Builds on the content and skills learnt in Number 3 across Key Stage 3

Algebra 3: Sequences including spotting patterns; filling in gaps, finding the rule to generate the sequence and finding the nth term. Plotting coordinates onto a graph and plotting ones which follow a set rule with a view to looking at how this links in with straight line graphs. Further work with straight line graphs, including mid points of line segments, linear inequalities, perpendicular gradients and kinematics graphs. At some levels transformations of graphs is introduced.

Builds on the content and skills learnt in Algebra 3 across Key Stage 3

Ratio and Proportion 3: Looking at the differences between ratio and proportion, then linking this to skills done previously with percentages. Percentages of amounts. Simple and compound interest. Creating and using scale drawings. Iterative processes. Direct and inverse proportion.

Builds on the content and skills learnt in the Ratio & Proportion parts of Number 3 across Key Stage 3

Geometry 3: Reflective and rotational symmetry, similarity including congruency, and a selection of the different transformations depending on the level of the pupil – from translations, reflections, rotations and enlargements. Properties of 2D and 3D shapes will also be considered. Use of vectors. Combinations of transformations of shapes, including the use of matrices for such transformations.

Builds on the content and skills learnt in Geometry 3 across Key Stage 3

Data handling 3: Continuing to investigate probability ranging from words to describe likelihood, working out numerical probabilities and drawing diagrams to display all possible outcomes. Conditional probability.

Builds on the content and skills learnt in Data Handling 3 across Key Stage 3

11

What students will learn

How it builds on learning

Algebra 1: Expressions, including linear and quadratic, and manipulating algebra including using letters to represent numbers. Manipulation of more complex expressions, in particular fractions. Identities and proof. Factor theorem. Composite functions.

Builds on the content and skills learnt in Year 10 Algebra 1

Geometry 1: Angles and angle facts at a variety of levels from looking at angles along a straight line to angles in polygons of various sizes and circle theorems. Accurately drawing shapes using a ruler and a protractor. Pythagoras’ theorem including in 3D for some groups. Trigonometry for both right-angled and, at some levels, in 3D and for non-right-angled triangles. More advanced students will also investigate the trigonometric functions in more depth and meet differentiation and some of its applications.

Builds on the content and skills learnt in Year 10 Geometry 1

Data Handling 1: Representing data using tables, charts and graphs. Understanding correlation. Methods of sampling. Use of quartiles and representing data using boxplots and cumulative frequency diagrams.

Builds on the content and skills learnt in Year 10 Data Handling 1

Number 2:  Calculations including different methods of multiplication or division and rounding. Developing skills at using a calculator. Compound measures and upper and lower bounds. Using the product rule for counting.

Builds on the content and skills learnt in Year 10 Number 2

Algebra 2: Forming equations, looking at ways to solve them including using a number machine and writing the problem as a sentence. Solving equations as well as inequalities; for some groups solving quadratic inequalities. Solving linear simultaneous equations and for some groups more advanced simultaneous equations. Drawing more complicated graphs, e.g. the reciprocal and exponential functions. Using iteration to find solutions to equations. Inverse functions

Builds on the content and skills learnt in Year 10 Algebra 2

Geometry 2: Area and perimeter of shapes, ranging from rectangles to compound shapes and then circles, including arcs, sectors and segments. Volume and surface area of 3D shapes.

Builds on the content and skills learnt in Year 10 Geometry 2

Data handling 2: Analysing data using averages and measures of how spread out the data is. At some levels this will include finding averages from data presented in frequency tables or graphs and presenting data in histograms.

Builds on the content and skills learnt in Year 10 Data Handling 2

The summer term will be spent revising.

Consolidation and review of all learning from across Key Stage 3 and Key Stage 4 in preparation for GCSE assessment.

Tier

Grades available

Higher

4, 5, 6, 7, 8, 9

Foundation

1, 2, 3, 4, 5