Mathematics

At St. Michael’s we aim to provide our students with a thorough and comprehensive Mathematical education. Although we follow the National Curriculum and the National Numeracy Strategy we embed at all stages activities and opportunities for students to be pushed beyond the confines of the curriculum. We hope to share the enjoyment and beauty of the subject in order that students, whatever their ability, meet their potential. We help pupils to extend their knowledge, skills and understanding in familiar and unfamiliar contexts.  There is some reinforcement of basic skills, but the main emphasis is on extending understanding and reasoning, through enquiry and practical activities.

Setting

Appropriate setting is important in Mathematics. In Year 7 pupils are taught in their tutor groups, but in Year 8 pupils are divided into 4 equal ability but smaller teaching groups. In Year 9, pupils are taught mathematics in four ability sets. The groups are set 1, set 2 and two parallel, equal ability sets. In Years 10 and 11, pupils continue to be taught mathematics in sets following the pattern introduced in Year 9 (set 1, set 2 and two parallel, equal ability sets). All groups obviously follow the same programme of study based on the National Curriculum in Key Stage 3 and the higher tier GCSE syllabus in Key Stage 4.

The setting ensures that all pupils will develop at the pace that will maximise their achievement. It enables the most able pupils to move at a quicker pace and more readily access extension material. It also enables less confident pupils to spend more time to consolidate their understanding. Pupils have the opportunity to move between sets. Usually this movement takes place at the end of the academic year, but all setting is reviewed every term.

All pupils at St Michael’s Catholic Grammar School are capable mathematicians and will complete the work necessary for the higher tier GCSE examination. All pupils, irrespective of their set, have the opportunity to access and ultimately achieve the highest GCSE grades. These are, after all, the target grades for all pupils.

Course Outline

Year 7

Pupils extend their range of mental and written calculation strategies and learn to identify efficient procedures to calculate problems with integers, fractions, decimals and percentages. Algebra is introduced formally through activities that show how algebra, as an extension of number using symbols, gives precise form to mathematical relationships, formulae and calculations. Pupils discover properties of two and three-dimensional shapes, and use angle facts in calculations and constructions. In statistical work pupils construct and interpret data in tabular and diagrammatic representations, understand the many forms of an “average” and how to calculate them as well as spread of data.  Pupils tackle investigative work pupils by selecting and combining known facts and problem solving strategies to reach solutions.

Year 8

Pupils build further upon their knowledge of number, measures, algebra, shape and data handling through activities that provide frequent opportunities for pupils to discuss their work, to develop reasoning and understanding, and to explain their strategies.  Pupils learn to solve a range of numerical problems, in both familiar and unfamiliar contexts, including those involving fractions and percentage.  They use algebraic notation to describe patterns and sequences and solve equations, use formulae and construct graphs. Pupils calculate lengths, areas and volumes of two and three-dimensional shapes. In Year 8 pupils are introduced to Pythagoras’s Theorem and circle formulae for area and circumference. In statistical work they increasingly use sophisticated diagrammatic representations and make more elegant inferences from data. 

Year 9

To conclude Key Stage 3 our Year 9 pupils consolidate and advance the work in previous years and continue to develop the use of algebraic notation through describing increasingly complex number patterns and sequences, including sequences of a quadratic nature. Students learn to identify, create, use and adapt formulae and equations in a greater variety of contexts.  In ‘Shape and Space’ pupils are now introduced to trigonometry to calculate side lengths and angles, extending this to real world applications including in bearings. In statistical work they use appropriate diagrammatic representation as well as calculating averages and spread of data to make precise inferences.  Pupils also tackle extended problem solving work; that has provided opportunities for pupils to develop reasoning and understanding, and to explain their strategies and solutions.

Year 10

Our GCSE course follows the National Curriculum. in Year 10 students build upon their knowledge of number, measures, algebra, shape and data handling through activities that provide frequent opportunities to discuss their work with an increased emphasis placed on problem solving, mathematical rigor and elegance in solution, develop reasoning and understanding to explain their strategies ensuring students place as much emphasis on the method as the conclusion. In algebra students are introduced to Quadratic Equations, Inequalities, and Simultaneous Equations, whilst in ‘Shape and Space’ students study interior and exterior angles in n-sided polygons and extend their knowledge of Pythagoras and Trigonometry to 3-Dimensional problems as well as graphs of Trigonometric functions. Students also consider more elegant methods of handling data, Cumulative Frequency and methods of non-biased questionnaire use in data collection.    

Year 11
In Year 11 students are focused on refining their skills in number, algebra, shape and data handling and accessing the hardest A/A* topics as well as being introduced to Mathematical Proof. In Number students study Recurring Fractions and Surds, in Algebra students are taught further methods of solving Quadratic Equations are learn to consider the effects of direct and inverse proportionality on quantities, students also study vector algebra and graphical transformations. In ‘Shape and Space’ they discover properties of angles in relation to circle theorems, the effects of enlargement on length, area and volume, and in Data Handling students learn about Histograms and further methods of Probability.

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