Mathematics

In Key Stage 3, pupils follow the programs of study prescribed by the National Curriculum. They learn new techniques in each of the set areas of Number & Measure, Geometry, Algebra, Statistics, Probability, Ratio and proportion and Rates of Change and apply these to problems. We challenge and extend their thinking often going beyond that set out below. The pupils are encouraged to explain their thinking and to set this down on paper. They meet simple proofs and are encouraged to develop their talents of reasoning, interpretation and problem solving in the context of real life problems.

More detail as to the content is set out below:

Year 7

Secure Skills Include:

Number & Measure:

• Factors, Multiples, Squares, Square Roots, Primes and Divisibility tests. Powers and roots. Finding HCF and LCM logically.
• Simple estimation and rounding to decimal places and significant figures.
• Multiplication – standard methods up to 4 digit by 2 digit.
• Negative numbers including +/-/x/÷and order of operations.
• Conversion between metric units.
• Time including time in decimal form.
• Fractions, decimals, and percentage problems.

Geometry:

• Angle facts.
• Properties of 2D and 3D shapes.
• Area and perimeter of rectangles, triangles, parallelograms and composite shapes.
• Volume and surface area of cubes and cuboids.
• Metric and Imperial Units and their connections.
• Reflective and rotational symmetry in shapes, transformations & formal constructions.
• Coordinates and straight line graphs.

Algebra:

• Using letters in place of unknowns & variables and simplifying expressions. Create and use formulae.
• Solving simple equations.
• Generate sequences from term-to-term and position to term rules.

Statistics:

• Work confidently with discrete data. Representing and interpreting data in graphical form. Comparing two data sets.

Ratio, Proportion and Rates of Change:

• Understand the relationship between ratio and proportion.
• Solve proportional and ratio problems.

Year 8

Secure Skills Include:

Number & Measure:

• Use integer powers of 2, 3, 4, 5 and their associated roots.
• Four rules of fractions and negative numbers and questions involving BIDMAS.
• Multiply and divide an integer by a decimal and a decimal by a decimal.
• Prime factor form including application to highest common factor and lowest common multiple.
• Use multipliers to calculate a percentage increase/decrease.

Geometry:

• Angles associated with parallel lines.
• The sums of the interior and exterior angles of regular/irregular polygons.
• Transform 2-D shapes by simple combinations of rotations, reflections, enlargements and translations, on paper and using ICT.
• Formal constructions and loci, both by reasoning and by using ICT, to produce shapes and paths.
• Use bearings including the eight compass point bearings and three-figure bearings.
• Extend area to trapezium; calculate areas of compound shapes.

Algebra:

• Recognise and plot equations of the form y = mx + c correspond to straight-line graphs.
• Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations.
• Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets).
• Begin to work with inequalities such as listing integer values that satisfy -4 ≤ x< 3 and appreciating all the real values of x that satisfy this.
• Use linear expressions to describe the nth term of a linear sequence.

Probability:

• Find and record all mutually exclusive outcomes for single events and two successive events in a systematic way, using two-way tables, tree diagrams and Venn diagrams.

Statistics:

• Scatter graphs and linear correlation.
• Understand what is meant by a sample.
• Design questionnaires.
• Produce and interpret stem and leaf diagrams, pie charts, bar charts and frequency diagrams.
• Averages from a frequency table.
• Compare two or more sets of data.

Ratio, Proportion and Rates of Change:

• Use Scale drawings and map scales.
• Use the unitary method to solve simple word problems involving ratio and direct proportion.
• Divide a quantity into two or more parts in a given ratio, find missing quantities from a ratio and express a ratio in the form 1: n

Year 9

Secure Skills Include:

Number & Measure:

• Cancel common factors before multiplying or dividing fractions.
• Multiply and divide by decimals.
• Use a calculator efficiently to perform complex calculations with numbers of any size including fractions and negative numbers, knowing not to round during intermediate steps of a calculation; use p and sign change keys, function keys for powers, roots and fractions, brackets and the memory.  Interpret the display in context.
• Estimate square roots and cube roots.

Geometry:

• Extend angles in polygons work.
• Convert between area and volume measures (mm2 to cm2, cm2 to m2, mm3 to cm3, cm3 to m3, and vice versa).
• Find the circumference and area of a circle.
• Calculate the surface area and volume of right prisms.
• Understand congruence.
• Visualise and use 2-D representations of 3-D objects; including plans and elevations.
• Enlarge 2-D shapes, given a centre of enlargement and any scale factor, on paper and using ICT; identify the scale factor of an enlargement and recognise that enlargements preserve angle but not length.
• Pythagoras’ Theorem.
• Trigonometry in right-angled triangles

Algebra:

• Find the inverse of a linear function.
• Construct and solve linear equations with integer coefficients.
• Use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20.
• Solve problems involving direct proportion using algebraic methods.
• Generate points and plot graphs of linear functions where y is given implicitly in terms of x, e.g. ay + bx = 0, y + bx + c = 0.
• Distance–time graphs.
• Factorise by common factors.
• Use formulae from mathematics and other subjects.
• List integer values that satisfy a given inequality and represent inequalities on number lines.

Probability:

• Use frequency trees and link to probabilities

Statistics:

• Work confidently with continuous data including: grouping data, estimating the mean, modal class and the interval containing the median.

Ratio, Proportion and Rates of Change:

• Find percentage changes.
• Calculate simple interest, VAT, discounts, pay rises and simple compound interest.
• Interpret and use ratio in a range of contexts, including solving word problems.
• Extend working with map scales.