Key Stage 4.

The following table outlines the schemes of work that are followed by each group in key stage 4.  An outline of the content can be found in the tables below.

 

    Year 10 (1st half) Year 10 (2nd half) Year 11 Autumn term
         
Set 1   Higher Bronze Higher Silver Higher Gold
Set 2   Higher Bronze  Higher Silver Higher Gold
Set 3   Higher Initial Higher Bronze Higher Silver
Set 4   Higher Initial Higher Bronze Higher Silver
Set 5   Foundation Bronze Foundation Silver Foundation Gold
Set 6   Foundation Initial Foundation Bronze Foundation Silver


Higher Bronze and Foundation Gold. Grades D & C

Number

  • Use the index laws with numerical and algebraic expressions involving multiplication and division of positive integer powers.  Use the terms cube root and negative square root.
  • Use the four operations on fractions, including mixed numbers.
  • Convert a simple fraction to a decimal using division.  Use and understand terminating and recurring decimals including exact fraction equivalents.
  • Use percentages to compare proportion.  Use and find percentage change.
  • Check solutions to calculations using various methods including approximating, using inverse operations and recognising the effect of multiplying and dividing by numbers less than one and greater than one.  Estimate answers using appropriate techniques.
  • Use and understand the terms reciprocal, highest common factor, lowest common multiple, prime number.  Find the prime factor decomposition of positive integers.

Algebra

  • Generate integer sequences using a rule for the nth term.  Use linear expressions to describe the nth term of an arithmetic sequence.
  • Solve simple linear inequalities in one variable and represent the solution set on a number line, using the convention for distinguishing ≤ and ≥ from < and >.
  • Change the subject of a formula in cases where the subject only appears once.
  • Plot graphs of linear functions in which y is given explicitly or implicitly in terms of x. Find the gradient of linear graphs.
  • Draw and interpret graphs modelling real situations, which may be non-linear, including simple quadratic graphs.
  • Generate points and plot graphs of simple quadratic functions and use these to find approximate solutions of simple related equations.

Geometry and Measure

  • Recognise that a measurement given to the nearest whole unit may be inaccurate by up to one half of a unit in either direction.
  • Understand and use rates and compound measures, for example speed, density, rate of flow.
  • Calculate and use the sums of the interior and exterior angles of polygons, for both regular and irregular polygons.
  • Understand, recall and use Pythagoras’ theorem in 2-D contexts.
  • Calculate the surface area and volume of right prisms, including cylinders.  Convert between measures for area or for volume/capacity, for example between mm2  and cm2  or between cm3  and litres.
  • Construct loci to show paths and shapes.  Use straight edge and a pair of compasses to produce standard constructions, including the midpoint and perpendicular bisector of a line segment and the bisector of an angle.
  • Recognise, visualise and construct enlargements of objects using positive integer scale factors and a centre of enlargement.  Identify the centre and the scale factor of an enlargement.  Understand the implications of enlargement for perimeter/length.
  • Transform 2-D shapes by simple combinations of transformations.

Statistics

  • Understand and use estimates of probability from theoretical models or relative frequency.  Compare experimental data and theoretical probabilities.  Understand that if an experiment is repeated, the outcomes may - and usually will - be different, and that increasing the sample size generally leads to better estimates of probability and population characteristics.
  • Calculate the mean from grouped continuous data.

 

 

Higher Initial and Foundation Silver. Grades E, D & C

Number

  • Multiply and divide simple fractions. Add and subtract mixed numbers.
  • Express one quantity as a fraction or percentage of another.
  • Increase and decrease quantities by a percentage.
  • Use the four operations on decimals without the use of a calculator.
  • Use ratio notation including reduction to its simplest form.  Understand and use ratio and proportion, including dividing a quantity in a given ratio.
  • Use a calculator effectively and efficiently, entering a range of measures including
  • 'time', interpreting the display and rounding off a final answer to a reasonable degree of accuracy.  Perform calculations using the order of operations.

Algebra

  • Use and generate formulae.  Substitute positive and negative numbers into a formula or an expression.
  • Set-up and solve linear equations with integer coefficients.  This will include equations in which the unknown appears on both sides of the equation, or with brackets.
  • Manipulate algebraic expressions by multiplying a single term over a bracket and by taking out common factors.
  • Use tables to plot graphs of linear functions given explicitly.
  • Use trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.

Geometry and Measure

  • Understand and use the angle properties of parallel and intersecting lines.
  • Construct triangles and other 2-D shapes using a ruler and a protractor, given information about their sides and angles.  Use a straight edge and a pair of compasses to do constructions.  Construct inscribed regular polygons.  Construct nets of cubes, regular tetrahedra, square-based pyramids and other 3-D shapes.
  • Recall the meaning of circle, chord, tangent, arc, sector and segment.  Recall and use the formulae for the circumference and the area of a circle.
  • Recall and use the formula for the area of a parallelogram and a triangle.  Use the formula for the area of a trapezium.  Calculate perimeters and areas of shapes made from triangles and rectangles.  Find the surface area of simple solid shapes using the area formulae for triangles and rectangles.
  • Use 2-D representations of 3-D shapes, including plans and elevations.
  • Transform triangles and other 2-D shapes by rotation, reflection, or translation using column vectors.  Recognise and visualise rotations, reflections and translations. Understand the properties preserved by these transformations; understand the congruence of these transformations.

Statistics

  • Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1.
  • Identify the modal class of grouped data.  Calculate the mean of grouped discrete data.
  • Draw and interpret a wide range of graphs and diagrams for discrete and continuous data, including frequency polygons and stem and leaf diagrams.  Compare distributions and make inferences, using the shapes of the distributions and measures of average and range.
  • Design and use two-way tables for discrete and grouped data.
  • Design and criticise questions for use in a survey, taking possible bias into account.

 


Foundation Bronze. Grades F & E

Number

  • Factors, multiples, common factors and prime numbers.
  • Round numbers
  • Significant figures
  • Decimal places
  • Estimate answers to one-stage calculations.
  • Squares, square roots, cubes and cube roots.
  • Index notation for simple integer powers.`
  • Fractions; simplifying, equivalence, improper, mixed numbers, common denominators, addition and subtraction.
  • Use the equivalence between fractions, decimals and percentages.
  • Find a percentage of a quantity, interpreting percentage as an operator.
  • Use the four operations with positive and negative integers.
  • Use simple proportion, particularly in the context of recipes.

Algebra

  • Continue and explain patterns in number and spatial arrangements. 
  • Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
  • Substitute positive numbers into simple algebraic formulae.  Derive a simple formula.
  • Manipulate algebraic expressions by collecting like terms.
  • Solve simple equations involving two steps.
  • Interpret information presented in a range of linear and non-linear graphs, including travel (distance/time) graphs.

Geometry and Measure

  • Angle properties of all triangles.
  • Sum of the interior angles of a quadrilateral is 360. 
  • Use isometric drawings and nets of 3-D shapes.
  • Volumes of cubes and cuboids with formula.  Calculate volumes of shapes made from cubes and cuboids.
  • Recall the geometric properties and definitions of the special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
  • Construct and interpret maps and scale drawings.
  • Rotation symmetry of 2-D shapes.  Identification and use.
  • Understand and use positive integer scale factors.

Statistics

  • Understand and use measures of probability from equally likely outcomes.
  • List all outcomes for two successive events in a systematic way and derive related probabilities
  • Use and interpret the statistical measures: mode, median, mean and range for discrete and continuous data, including comparing distributions.
  • Construct and interpret pie charts.
  • Interpret graphs representing real data, including recognising misleading diagrams.

 

Foundation Initial. Grades G & F 

Number

  • Round numbers to a given power of 10.
  • Add and subtract three-digit numbers, without the use of a calculator.  Add and subtract using numbers with up to two decimal places without the use of a calculator.
  • Multiply and divide numbers with no more than one decimal digit by an integer between 1 and 10, without the use of a calculator.  Multiply and divide any number by
  • 10, 100 and 1000 without the use of a calculator.
  • Multiply and divide a three-digit number by a two-digit number.  Multiply numbers with up to two decimal places by an integer, with or without a calculator.
  • Calculate a fraction of a given quantity.  Identify fractions of a shape.
  • Recall the fraction to decimal conversions of familiar simple fractions (tenths, hundredths, half, quarters, fifths).  Convert simple fractions of a whole to percentages of the whole and vice versa.
  • Calculate simple percentages of quantities, without the use of a calculator.
  • Order decimals (ordering up to five decimals and knowing that, eg, 5•07 is smaller than 5•3).
  • Solve problems using the four operations on integer and decimal numbers using a calculator.
  • Work out starting times, finishing times and intervals.
  • Perform calculations involving the use of brackets and the order of operations.
  • Order positive and negative temperatures.  Solve problems involving temperature changes.

 

 

Algebra

  • Continue simple sequences.  Explain how to find the next number in a simple pattern. Recognise and describe patterns in number.
  • Use formulae expressed in words or symbols, substituting positive numbers into the formula to find the value of the subject (usually in context).
  • Use simple function machines to deal with inputs and outputs, recognising basic inverse functions.  Solve simple equations involving one operation.
  • Use axes and coordinates in four quadrants, including using points identified by geometrical information.
  • Construct and interpret simple graphs, including conversion graphs.

Geometry and Measure

  • Use: kilometres, metres, centimetres and millimetres; kilograms and grams; litres and millilitres.  Convert measurements from one metric unit to another.  Interpret scales
  • on a range of measuring instruments.
  • Make sensible estimates of a range of measures in everyday settings.
  • Measure and draw angles to the nearest degree.  Identify acute, obtuse, reflex and right angles.  Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines and opposite angles at a vertex.
  • Recognise regular polygons (pentagon, hexagon, octagon).  Recognise simple solids (cube, cuboid, sphere, cylinder, cone).  Recognise the terms circle, centre, radius, diameter and circumference.  Recognise types of triangle (isosceles, equilateral, scalene).
  • Find the perimeter of straight-sided shapes.   Find areas of irregular shapes and volumes of simple solids.  Find the area of a rectangle.
  • Use and interpret street plans and simple maps, including: simple grid references (of the form A6, J3 etc), left and right, clockwise and anticlockwise and compass directions.
  • Recognise and complete reflection symmetry of 2-D shapes.
  • Understand that reflections are specified by a mirror line.  Transform triangles and other 2-D shapes by reflection, using a given line.

 

Statistics

Understand and use the vocabulary of probability, including terms such as ‘fair’,

‘evens’, ‘certain’, ‘likely’, ‘unlikely’ and ‘impossible’.  Understand and use the probability scale.

Find all possible ways of listing up to four objects.

Calculate the mean, median, mode and range of discrete data.

Draw and interpret simple frequency tables, charts, pictograms and bar charts for discrete data.

Extract and use information from common two-way tables including timetables.

 

 

 Higher Silver. Grades C, B & A

Number

  • Use a multiplier to solve percentage increase and decrease problems.  Calculate the original amount when given the transformed amount after a percentage change.
  • Use repeated proportional or percentage changes.  Represent repeated proportional change using a multiplier raised to a power.
  • Use standard index form expressed in conventional notation and on a calculator display.  Convert between ordinary and standard index form representations. Calculate with standard index form.
  • Check the order of magnitude of compound calculations using estimation methods, without the use of a calculator.

Algebra

  • Solve harder linear equations including with fractional coefficients.
  • Manipulate algebraic expressions by expanding the product of two linear expressions, simplifying the result. 
  • Factorise quadratic expressions, usingthe difference of two squares.  Solve by factorising quadratic equations of the form ax2 +bx + c = 0
  • Simplify algebraic expressions by taking out common factors.  Simplify rational expressions.
  • Rearrange formulae, including where the subject appears twice, or where a power of the subject appears.
  • Set up two linear simultaneous equations.  Solve by eliminating a variable; interpret the equations as lines and their common solution as the point of intersection.
  • Plot, sketch and recognise graphs of quadratics, simple cubic functions, and reciprocal functions 
  • y = k  with x ≠ 0, including graphs arising from real situations and their interpretation.
  • Solve several linear inequalities in two variables and find the solution set, representing this on a suitable diagram.  Shade such regions on a graph, using the convention for distinguishing ≤ and ≥ from < and >.
  • Construct the graphs of simple loci.
  • Understand that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y-intercept.  Write the equation of a straight line in the form y = mx + c.  Understand the gradients of parallel lines.

Geometry and Measure

  • Understand and construct geometrical proofs using circle theorems:  Understand that the tangent at any point on a circle is perpendicular to the radius at that point; understand that tangents from an external point are equal in length;  understand that the angle subtended by an arc at the centre of the circle is twice the angle subtended at any point on the circumference;  understand that the angle subtended at the circumference by a semicircle is a right angle;  understand that angles in the same segment in a circle are equal;  understand that opposite angles in a cyclic quadrilateral sum to 180°;  understand the alternate segment theorem.
  • Understand and use 3-D coordinates.
  • Find the coordinates of the midpoint of a line segment AB given points A and B in 2-D. Use Pythagoras’ theorem to find the length of a line segment AB given the points A and B in 2-D.
  • Understand, recall and use trigonometrical ratios in right-angled triangles in 2-D.
  • Understand similarity of triangles and other plane figures and use this to make geometrical inferences.
  • Construct enlargements using any scale factor, including positive fractional and negative scale factors; identify scale factors.
  • Understand and use the effect of enlargement on the area and volume of shapes and solids.
  • Fully describe combinations of transformations (rotation, reflection, translation, enlargement) using a single transformation.

Statistics

  • Use tree diagrams to represent outcomes of combined events, recognising when events are independent.  Find probabilities using tree diagrams.
  • Draw and interpret cumulative frequency tables and diagrams and box plots for grouped data.  Find the median, quartiles and interquartile range.
  • Compare distributions and make inferences, using the shapes of the distributions and measures of average and spread, including median and quartiles.
  • Calculate an appropriate moving average.  Identify seasonality and trends in time series, from tables or diagrams.

 

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