## The Importance of Mathematics

Maths is important for all members of modern society. Mathematical thinking and the use of mathematical techniques is part of the essential equipment that all students need to enter the world of work and decision making.

We believe that Maths should also be a stimulating and enjoyable experience for all of our students, helping them to learn the basic skills and to develop the ability to solve problems in a creative way.

We strive to create an atmosphere where students are challenged and encouraged to do their best.

## Key Stage 3

**Contact**: Mrs M. Weighill

### Course Aims

In Years 7, 8 & 9 students pursue a course in Mathematics in line with the new National Curriculum. In these first three years of secondary school Mathematics we aim to enthuse and encourage all students. During KS3 we lay the foundations in algebra, number, geometry and data handling for work at GCSE level.

We encourage students to think mathematically and we offer them appropriate challenges throughout.

### Course Content

In Year 7, students will cover the following topics in Maths: Multiples, factors and prime numbers; Powers, roots and reciprocals; Conventional notation for the priority of operations; Ordering and inequalities; Written methods of calculation; Algebraic notation; Straight line graphs; Linear equations; Sequences; Ratio and proportion; Fractions, decimals and percentages; Geometry and measures; Coordinates; Naming 2D and 3D shapes; Properties of quadrilaterals and triangles; Perimeter, area and volume; Angles; Transformations including: reflection, translation and rotation; Probability; Venn diagrams; Statistics; Mean, median, mode and range; Comparison of data sets; Frequency tables; Pie charts and scatter graphs.

In Year 8, students will cover the following topics in Maths: Rounding to a given level of accuracy; Standard form; Negative numbers. Long division; Powers; Inverse of a linear function; Nth terms of sequences; Straight line equations; Common factors; Changing simple formulae; Fractional coefficients; Ratio and proportion; Fractions; Percentages; Geometry and measures; Angles on parallel lines; Geometrical properties of quadrilaterals; Circle geometry; Volume of a prism; Probability; Estimatation of probabilities; Statistics: Calculate mean, median, mode or modal class and range from a frequency table, including from grouped continuous data.

In Year 9, students will cover the following topics in Maths: Number: Calculator efficiency; Index laws; Using a multiplier to solve percentage problems; Decimals to fraction conversion; Square a linear expression; Linear factors; Factorisation; Quadratic sequences; Simultaneous equations ; Ratio and proportion; Geometry and measures; Pythagoras’ theorem; Pythagorean triples; Compound units for speed, pressure and density; Trigonometry in right angled triangles; Surface area and volume of prisms, including cylinders; Reflections, rotation, translation and enlargement; Probability; Tree diagrams and tables to record outcomes of two successive events; Enumerate sets and unions/intersections of sets using venn diagrams; Statistics.

### Extra Curricular Activities

Weekly maths challenges; UK Maths Challenge.

### Course Assessment

Grade | Assessment Detail |
---|---|

9 | Students can solve quadratic inequalities in one variable. Students can represent the solution set of inequalities on a number line, using set notation and on a graph. Students can sketch translations and reflections of a given function, and can find the equation of a tangent to a circle at a given point. Students can interpret the succession of two functions as a ‘composite function’. Students use circle theorums to prove related results. |

8 | Students can solve quadratic equations by completing the square. Students can solve two simultaneous equations in two variables (linear/quadratic) algebraically, and can find approximate solutions to equations numerically using iteration. Students can recognise, sketch and interpret the trigometric functions y=sinx, y=cosx and y=tanx for angles of any size. Students can calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs) and interpret results in cases such as distance-time graphs. Students can argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct proofs. |

7 | Students can simplify surd expressions involving squares, and can calculate upper and lower bounds. Students can factorise quadratic expressions, and solve quadratic equations using the quadratic formula. Students can use vectors to construct geometric arguments and proofs, and can understand 3D pythagoras. Students know and can apply the sine rule and cosine rule to find unknown lengths and angles. Students can construct and interpret diagrams for grouped discrete data and continuous data i.e. histograms with equal and unequal class intervals and cumulative frequency graphs. |

6 | Students can change recurring decimals into their corresponding fractions and vice versa. Students can calculate fractional indices. Students can simplify the laws of indices, and solve quadratic equations. Students can find approximate solutions using a graph. Students can to identify perpendicular lines. Students can deduce expressions to calculate the nth tetm of a quadratic sequence. Students can solve direct and inverse proportion problems. Students can apply the standard circle theorums concerning angles, radii, tangents and chords. Students can apply the concepts of congruence and similarity, including the relationships between areas and volumes in similar figures. Students can calculate and interpret conditional probabilities through representation using expected frequencies with a variety of tables and graphs. |

5 | Students use inequality notation and can interpret fractions and percentages as operators. Students can solve linear equations in one unknown algebraically, and solve two simultaneous equations in two variables algebraically. Students can solve linear inequalities in two variables. Students can find the equation of the line through two given points or through one point with a given gradient. Students can rearrange formulae to change the subject and can interpret the gradient of a straight line graph as a rate of change. Students can solve original value problems. Students can use the basic congruence criteria for triangles and know the formulae for the trigonometric ratios. Students can calculate surface area and volumes of spheres, pyramids, cones and composite solids. Students can calculate probabilty of events and can find the median from cumulative frequency graphs. |

4 | Students can use the concepts and vocabulary of prime factorisation, and check calculations using approximations. Students can round numbers to an approximate degree of accuracy, and can calculate with integer indices. Students can solve linear equations in one unknown algebraically. Students can find approximate solutions using a graph. Students can recognise, sketch and interpret graphs of linear functions, and can identify parallel lines. Students can divide a quanity into two parts in a given ratio, and can solve problems using simple percentages. Students understand the sum of angles within a triangle and are familiar with Pythagoras’ theorem. Students can find the mean, median and modal averages from a data set, and draw estimated lines of best fit. |

3 | Students can apply the four operations, and can round numbers to a degree of accuracy. Students can use positive integer powers and associated real roots. Students can substitute numerical values into formulae and expressions. Students can multiply a single term over a bracket. Students can plot simple graphs with given co-ordinates. Students can solve problems using percentages. Students can describe translations as 2D vectors, and can apply formulae to calculate volumes, and circle geometry. Students can compare data using averages and range. |

2 | Students can order decimals and fractions, and collect like terms. Students can express one quantity as a percentage of another. Students can apply properties of angles at a point, and on a straight line, which being able to measure angles to calculate the area of basic shapes. Students can find the mean from a list of data, and make comparisons using charts. |

1 | Students can order positive and negative integers. Students can define a percentage as ‘number of parts per hundred’. Students can measure line segments, and calculate the area of a triangle. Students can apply averages to a list of data, and draw and interpret line graphs, bar charts and pictograms. Students can make lists and tally charts. |

If you have any questions or queries relating to the Maths curriculum please email HeadOfMaths@ecclesbourne.derbyshire.sch.uk for more information.