Key Stage 3
The national curriculum for mathematics aims to ensure that all pupils:
• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
At KS3 decisions about progression is based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly are challenged by further rich and sophisticated problems before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent are encouraged to consolidate their understanding, through additional practice, before moving on.
In this unit pupils have the opportunity to learn how to devise and use rules for sequences. They are introduced to algebraic expressions and manipulation. They begin to plot linear graphs and learn how to describe straight lines in terms of algebra. They construct and solve linear equations using formal methods. The mystery symbols activity allows pupils to explore methods informally at first and then develop these into a formal method of solving equations.
In this unit pupils will recognise the importance of organising data appropriately and learn to calculate the mean, median mode and range of small data sets. They will learn how to interpret these measures in a context. They are taught how to compare two sets of data using different techniques and make comparison. They learn to use the vocabulary associated with probability. Pupils learn to calculate the theoretical probabilities of simple events.
Shape and Measures
This unit will review the vocabulary associated with angle and shape. Pupils will learn and use the correct labelling conventions and associated language through a range of problems. Pupils will develop their knowledge of the geometric properties of shape
They will learn how to interpret scales on different measuring equipment, recognise the relationship between different metric units and convert between one metric unit and another. There are opportunities for pupils to refine their estimating skills applied to length and area, and to formalise the rules for calculating these for simple and compound shapes.
They will have the opportunity to recognise, visualise and explore the transformation and symmetry of 2D shape. They will learn how to reflect and rotate shapes and will learn the language and notation associated with these transformations.
In this unit pupils begin to explore the effects of multiplying and dividing decimal numbers by powers of 10. They will learn how to compare and order decimal numbers and negative numbers in context and consolidate efficient written methods for adding and subtracting whole numbers and decimals with up to 2 places. They are introduced to equivalence of fractions, decimals and percentages (FDP) and learn how to convert between the different forms. Rounding, decimals efficient use of calculators, BIDMAS, and ratio are all covered in this unit of work.
Pupils will develop further their understanding of algebraic manipulation including use of indices, brackets and factorising. They will learn how to plot the graphs of linear functions with an increasing degree of sophistication. Pupils will also learn how to construct linear functions arising from real-life problems and plot their corresponding graphs. They learn to construct and solve equations and this will extend to solving equations with unknowns on both sides.
In this unit, calculating mean, median, mode and range of small data sets is revisited. They will learn how to interpret these measures in a context. Pupils will also explore how they can deduce mean, mode median and range from data given in a frequency table (no grouped data at this stage)
They continue to develop the concepts of theoretical and experimental probability and understand that results from experiments do not always match what is expected from theory. Pupils learn to calculate the theoretical probabilities of single and combined events.
Shape and Measures
Pupils will continue to deduce formulas and strategies for finding the perimeter, area and volume of various shapes. They continue to develop their knowledge and understanding of angle and other associated geometric properties of shapes. They will explore additional angle facts and geometrical concepts and be able to tackle angle problems of an increasing level of sophistication.
They will learn how to complete formal constructions and will explore properties of 3D shapes and visualise 3D objects in a range of representations.
In this unit pupils will continue to explore the effects of multiplying and dividing decimal numbers by powers of 10. They will continue to learn how to compare and order decimal numbers and negative numbers in context and consolidate efficient written methods for adding and subtracting whole numbers and decimals with up to 2 places. They should become more proficient in performing calculations with fractions and understand how to calculate percentages with and without a calculator.
Pupils will develop further their understanding of sequence, algebraic manipulation including use of brackets and factorising. This will develop their skills from year 7 by introducing extended use on indices. They will explore the graphs of linear functions with an increasing degree of sophistication. Pupils will also learn how to create tables of values for quadratic and cubic functions and plot their graphs.
They will further extend their understanding of forming and solving equations. Use and represent inequalities and solve quadratic and cubic equations using a systematic trial and improvement method.
Pupils will also explore how they can calculate an estimate for the mean, and locate the class interval where the mode and median lie from grouped data. Throughout the unit pupils will be encouraged to think about comparing two sets of data using the techniques outlined. They will develop their understanding of scatter graphs and how pairs of scatter graphs can be used to compare strength of correlation.
They continue to develop the concepts of theoretical and experimental probability
Shape and Measure
In this unit they will explore and extend methods for finding the area and volume of shapes. Pupils will spend most of their time investigating circles and prisms and applying methods and formulas to problems.
They will continue to develop their knowledge and understanding of the angle and other associated geometric properties of shapes. They focus on transformations on coordinate axes and how shapes and their properties change under single and combined transformations.
Extensive work is carried out on multiplying and dividing decimal numbers by powers of 10. They will continue to learn how to compare and order decimal numbers and negative numbers in context and consolidate efficient written methods for adding and subtracting whole numbers and decimals with up to 2 places. Decimals and percentages are revisited.
Key Stage 4
What qualification will the course lead to? GCSE Mathematics
Which Examination Board? Edexcel
This is a linear qualification, with three terminal exams that must be taken at the end of the course in year 11.
The grading scale will be from nine to one (nine representing the highest grade). There are two tiers of entry available: Foundation (grades one to five) and Higher (grades four to nine).
The assessment for each tier of entry consists of three written exam papers. Each paper has an assessment time of one and a half hours and is worth 33.3% of the final grade. Paper one is non calculator and papers two and three are calculator.
There will be a greater emphasis on mathematical reasoning, communication and problem solving skills.
The content is divided in to six main areas:
3. Ratio, proportion and rates of change
4. Geometry and measures