# Curriculum

## Maths Curriculum at CCGS

Year 7

Pupils are assessed at the start of year to place them in appropriate sets and allow them to progress at appropriate speed.  A lot of the work in year 7 is based on mastery of the basics, constructing a solid foundation on which to build in future years. Throughout year 7 we emphasise the correct layout of solutions with the appropriate and strictly correct use of the equal sign. Answers alone are not accepted as sufficient and students will be encouraged to redo work if this happens.  Pupils work on the basic arithmetic of directed numbers building confidence in the four operations. Students build their understanding of BIDMAS with directed numbers, recap and standardise their existing methods of long multiplication and short division and use these methods with decimals. Students then progress to work on fractions again increasing their confidence with adding and subtracting both improper fractions and mixed numbers.

Students are introduced to the basics of algebra, they tackle writing expressions, substitute values into expressions and formulae. They learn how to simplify expressions understanding when two expressions are identical. They also learn how to start solving linear equations with the balance method. The mastery of this method is a priority underpinning all future solving in algebra.

When students are equipped with the basics of algebra, they are ready to work on nth term of linear sequences, solve simple problems in geometry with angles in triangles and parallel lines. They also start work on linear graphs where the focus is on mastery of accurate coordinate calculation and plotting.

The topic of statistics and probability are introduced through our data handling project where students collect data on a minigolf trip. Students calculate their own averages and produce graphs to illustrate the data they have collected.

Year 8

Students are introduced to number theory with prime number decomposition and finding LCM and HCF using Venn diagrams. They build on their knowledge from year 7 in geometry (angles in parallel lines) and learn the basics of transformations and constructions. The focus here is on neat and accurate diagrams and a competent use of geometry equipment preparing the ground for loci in year 10. All number work is revisited this year, revised to increase understanding and confidence and new skills taught, multiplication and division of fractions and decimal, ratio work and the use of standard form. They work on the understanding the use of multipliers in percentage work.

Students continue to build up their skills in algebra with the balance method still a priority. They learn how to solve equations with the unknown on both sides and with brackets. They build up to solving simultaneous equations but only tackle the basic case where the method of elimination can be used leaving the harder case for year 9 when the students will be more ready algebraically. The focus here is on the correct method and understanding what simultaneous equations mean, students are encouraged to check their own solutions by substitution to increase their independence in maths.

At the end of the year students are introduced to collecting data in grouped frequency format paving the way for further work in year 9.

Year 8 students also discover the formulae for the area and circumference of circle and apply these in basic problem solving when simple parts of circles are involved. Students will need these formulae in year 9 when tackling Volumes and SA of cylinders, cones and spheres.

Year 9

In year 9 students capitalise on their solid knowledge of number and basic algebra and attack more difficult problems across all four areas of maths: number, algebra, geometry and data handling. Often our lessons will recap work from year 7 and 8, further mastering the basics, then build with new skills on this solid foundation. Year 9 also serves as a preparation of ground for GCSE maths with many topics introduced this year to be built on in year 10 (tree diagrams, bearings, cumulative frequency graphs and Venn diagram notation)

Students work on further use of multipliers from year 8 but include the use of repeated percentage change and now also the trickier reverse percentage. The students are now ready to tackle these harder topics with confidence and will revisit them again in their GCSE revision through regular recovery starters.

In algebra, we work on multiplying two brackets and factorising simple quadratics, leaving the hardest cases till year 10. We reinforce all solving of linear equations including those with brackets, fractions and both. We build on year 8 work on simultaneous equations and learn to solve equations when one or both needs to be multiplied up. We also introduce the idea of algebraic fractions and their simplification preparing the ground for much harder work in year 11.

Students build on their previous understanding of standard form building confidence with calculations where the answer may be further adjusted. They are also introduced to limits of accuracy again preparing them for harder cases at GCSE.

We revise work on circles and extend this with Volumes and Surface areas of cylinders, cones and spheres.

Year 9 students are introduced to Pythagoras and trigonometry. Focus is again on the correct layout of solutions. Trigonometry is then embedded further with practical ‘treegonometry’ where students use inclinometers and tape measures to calculate the heights of trees and buildings in the school grounds.

Year 10

Students start the year with powers and surds, enabling students to give answers in exact surd form and avoid rounding prematurely throughout their GCSE journey. We work on overlearning basic algebraic techniques, such as simplifying expressions by expanding brackets (and stretch this skill to expanding three brackets), factorising (stretch to full quadratic factorising) and solving linear equations. We build on work from year 7 on linear sequences and use this in finding the nth term of a quadratic sequence. Work on graphs is also consolidated with all three methods of plotting straight line graphs retaught. Students spend a lot of time making connections between graphs and algebra in year 10 and deepening their knowledge of coordinate geometry. Top sets are challenged with the view of working towards their A levels, focus on harder problem solving, whereas lower sets spend the time on mastery of the basics.

We extend the work on Pythagoras and trigonometry from year 9 to work in 3D shapes. Again the previous work on similarity is extended to algebraic solutions where the previous work on linear equations comes in very handy. A big focus of year 10 is solving quadratic equations and understanding the significant points on a quadratic curve. Although this is a fairly small part of the GCSE exam, it is the most important part for our A level mathematicians so our students work on overlearning the solving of basic quadratics and are challenged with harder problem solving questions. This then allows them to tackle much harder work in year 11 when applying their skills to probability or shape work.

Year 11

Students tackle harder topics during this year, starting with statistical diagrams and extending their work on trigonometry beyond the right angle. More able mathematicians work on advanced algebraic techniques with partial fractions preparing them for A level mathematics. Students are introduced to vector geometry and extend their work with the ideas of proof. In geometry, they also explore circle theorems and their proofs. Students tackle functions and iterations, again bridging the gap to A level work.

Students practice recall of important facts and formulae and revise in class and independently preparing them for their GCSE examinations.

KS5

Students build on their previous skills and follow the A level specification from Edexcel exam board. The course is focused largely on algebra and students are encouraged to spot connections with graphs and coordinate geometry where suitable. They are encouraged to use their graphical calculator to explore graph properties and check their algebraic work with numerical answers.

Students are introduced to new statistical techniques and topics in mechanics and make connections with physics. All students are challenged with problem solving with the UKMT senior maths challenge.