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AQA Mathematics - Foundation Tier General Topic No. of Hours Objectives Grade By the end of the module students should be able to … Autumn Term Statistical measures Area and volume (1) Integers Find the mode for a set of numbers Find the median for an odd set of numbers Work out the range for a set of numbers Calculate the mean for a set of numbers Find the median for an even set of numbers Write down the mode from a graph Compare the mean and range of two distributions Calculate the ‘fx’ column for a frequency distribution Calculate the mean for a frequency distribution Find the modal class for grouped data Find the mean for grouped data Find the median class for grouped data Find the perimeter of a shape by counting sides of squares Find the area of a square by counting squares Work out the area and perimeter of a simple rectangle, such as 3 m by 8 m Work out the area and perimeter of a harder rectangle, such as 3.6 m by 7.2 m Find the area and perimeter of compound shapes Find the area of a triangle and a parallelogram Estimate the area of an irregular shape by counting squares and part squares Find the area and perimeter of compound shapes Find the area of a kite and a trapezium Name the parts of a circle Calculate the circumference of a circle, given the radius or diameter, to an appropriate degree of accuracy Find the perimeter of a semicircle Calculate the area of a circle, given the radius or diameter, to an appropriate degree of accuracy Find the area of a semicircle Understand positive and negative integers Add and subtract negative integers Multiply and divide negative integers Find the factors of a number Two-Tier GCSE Mathematics - Medium Term Plan G F E D C G F E D G E D G D C D C G F E G Resources used / Notes AQA Mathematics - Foundation Tier Rounding Angles Find the least common multiple (LCM) of two simple numbers Find the highest common factor (HCF) of two simple numbers Recognise prime numbers Write a number as a product of prime factors Find the reciprocal of a number Round to the nearest integer Write an integer correct to the nearest 10 or the nearest 100 Round numbers to given powers of 10 and to given numbers of decimal places Round a number to one significant figure Estimate answers to problems involving decimals Estimate square roots Estimate answers to calculations involving division Estimate answers to calculations involving division by numbers less than one Find minimum and maximum values Express fractions of full turns in degrees and vice versa Recognise acute, obtuse and reflex angles, estimate angles and measure them accurately Use properties of angles at a point and angles on a straight line, understand the terms ‘perpendicular lines’ and ‘parallel lines’ Recognise corresponding angles and alternate angles Understand and use three-figure bearings Simplify expressions with one variable such as a + 2a + 3a Simplify expressions with more than one variable such as 2a + 5b + a – 2b Multiply out expressions with brackets Expand (and simplify) harder expressions Factorise expressions Write down the place value of a digit, for example, what is the value of the 4 in 0.24? Order decimals, for example, which is bigger, 0.24 or 0.3? Add and subtract decimals Multiply two decimals, such as 2.4 × 0.7 Divide a number by a decimal, such as 1 ÷ 0.2 and 2.8 ÷ 0.07 Convert decimals to fractions and fractions to decimals Use of symbols Decimals Two-Tier GCSE Mathematics - Medium Term Plan C G F E G F D C F D F E D C D F E D C D AQA Mathematics - Foundation Tier Spring Term Spring Term, Year 10 Properties of triangles (F tier only) Fractions Representing data Scatter graphs Properties of polygons Show that the angles of a triangle add up to 180° and use this to find angles Show that an exterior angle of a triangle is equal to the sum of the interior opposite angles Identify isosceles, equilateral and right-angled triangles Use the word ‘congruent’ when triangles are identical Use angle properties of isosceles, equilateral and right-angled triangles Find equivalent fractions 24 Simplify fractions such as 36 Arrange fractions in order of size Work out fractions of quantities such as Find one number as a fraction of another Do calculations with simple fractions involving addition Do calculations with simple fractions involving subtraction Do calculations with mixed numbers Do calculations with simple fractions involving multiplication Do calculations with simple fractions involving division Construct and interpret a pictogram Construct and interpret a bar chart Construct and interpret a dual bar chart Interpret a pie chart Construct a pie chart Interpret a stem-and-leaf diagram Construct a stem-and-leaf diagram (ordered) Construct a frequency diagram Interpret a time series graph Draw a scatter graph by plotting points on a graph Interpret the scatter graph Identify the type and strength of the correlation Draw a line of best fit on the scatter graph Interpret the line of best fit Recognise and name shapes, such as isosceles triangle, parallelogram, rhombus, trapezium and hexagon Calculate interior and exterior angles of a quadrilateral Investigate tessellations Classify a quadrilateral by geometric properties Calculate exterior and interior angles of a regular polygon 5 8 E G E G F of £20 Two-Tier GCSE Mathematics - Medium Term Plan E D C E C G F E D D C D C G E C AQA Mathematics - Foundation Tier Indices and Standard form Summer Term Sequences Coordinates Collecting data Percentages Calculate squares and square roots (with and without the use of a calculator) Calculate cubes and cube roots (with and without the use of a calculator) Use function keys on a calculator for powers and roots Use the terms square, positive square root, negative square root, cube and cube root Recall integer squares from 2 × 2 to 15 × 15 and the corresponding square roots Recall the cubes of 2, 3, 4, 5 and 10 Use index notation and index laws for positive and negative powers Continue a sequence of numbers or diagrams Write down terms of a simple sequence Find a particular term in a sequence involving positive numbers Write the term-to-term rule in a sequence involving positive numbers Find a particular term in a sequence involving negative or fractional numbers Write the term-to-term rule in a sequence involving negative or fractional numbers Write the terms of a sequence or a series of diagrams given the nth term Write the nth term of a sequence or a series of diagrams Use coordinates in the first quadrant, such as plot the point (3, 2) Use coordinates in all four quadrants, such as plot the points (3, –2), (–2, 1) and (–4, –3) Draw lines such as x = 3 and y = x + 2 Solve problems involving straight lines Draw lines such as y = 2x + 3 Find the midpoint of a line segment Use and understand coordinates in three dimensions Design and use tally charts for discrete and grouped data Design and use two-way tables for discrete and grouped data Classify and know the difference between various types of data Design and use data collection sheets and questionnaires Identify possible sources of bias in the design and use of data collection sheets and questionnaires Use a variety of different sampling methods Understand that percentage means ‘out of 100’ Change a percentage to a fraction or a decimal and vice versa Two-Tier GCSE Mathematics - Medium Term Plan F E D C G F E D C G F E D C G E D C D F AQA Mathematics - Foundation Tier Area and volume 2 Compare percentages, fractions and decimals Work out a percentage of a given quantity Calculate simple interest Increase or decrease a quantity by a given percentage Express one quantity as a percentage of another Work out a percentage increase or decrease Find the volume of a solid by counting cubes and stating units Find the volume of water in a given cube or cuboid Find the height of a cuboid, given volume, length and breadth Solve problems involving surface areas of prisms and cylinders Change between area measures such as change 2.7m² to cm² Calculate volumes of prisms and cylinders Change between volumes of measures such as change 2.6m³ to cm³ or change 2700cm³ to litres E D C G E D C Year 11 Solve an equation such as 3x = 12 or x + 5 = 9 Solve an equation such as Solve an equation such as 3x 4 = 5 + x or 2(5x + 1) = 28 Solve an equation such as 3x 12 = 2(x 5), draw a line of symmetry on a 2-D shape draw the reflection of a shape about a mirror line draw all the lines of symmetry on a 2-D shape draw the line of reflection for two shapes give the order of rotation symmetry of a 2-D shape name, draw or complete 2-D shapes from information about their symmetry reflect shapes in the axes of a graph reflect shapes in lines like x = 2 or y = -1 describe reflections and rotations about the origin fully identify reflection symmetry in 3-D shapes reflect shapes in y = x and y = -x rotate shapes about any point on a graph find the centre of a rotation and describe the rotation fully combine reflections and rotations identify lengths and angles that remain the same in reflections and rotations. Autumn Term Equations Rotations and reflections x 7 or 3x 1 = 9 2 2x x 7x 5 or 2 3 4 3 Two-Tier GCSE Mathematics - Medium Term Plan F E D C G F E D C AQA Mathematics - Foundation Tier Solve simple ratio and proportion problems, for example finding the ratio of teachers to pupils in a school finding the amount of flour in a recipe for pastry when the ratio of fat to flour is 1:2. Solve more complex ratio and proportion problems, for example sharing out money between two groups in the ratio of the numbers in each group. Solve equations such as x3 + x = 12 using trial and improvement methods Give a scale factor of an enlarged shape Enlarge a shape by a positive scale factor Find the measurements of the dimensions of an enlarged shape Use map scales to find distance Compare the area of an enlarged shape with the original shape Enlarge a shape by a positive scale factor from a given centre Translate a shape using a description such as 4 units right and 3 units down Enlarge a shape by a fractional scale factor Translate a shape by a vector such as Transform shapes by a combination of translation, rotation and reflection Plot points of a conversion graph and read off positive values Read from a conversion graph for negative values Interpret distance/time graphs Calculate simple average speeds from a distance/time graphs over hours Calculate complex average speeds from a distance/time graphs over minutes decide which metric unit to use for everyday measurements convert between imperial and metric units know rough metric equivalents of pounds, feet, miles, pints and gallons make sensible estimates of a range of measures in everyday settings use speed in calculations involving distance and time (with times restricted to 1 1 1 4 hour, 3 hour, 2 hour and whole numbers of hours). solve more difficult speed problems understand and use other compound measures such as density recognize that measurements given to the nearest whole unit may be half a unit larger or smaller Use a formula written in words such as cost = 20 x distance travelled Use a simple formula such as p = 2l +2w Substitute positive numbers into a simple formula Ratio and proportion Trial and improvement Spring Term Spring Term, Year 10 Translation and enlargements Real life graphs Measures Formulae 4 3 Two-Tier GCSE Mathematics - Medium Term Plan D C C F E D C F E D C G F E C G F AQA Mathematics - Foundation Tier Construction Write an expression from a problem Substitute negative numbers into a simple formula Use formulae from mathematics and other subjects Find a solution to a problem by forming an equation and solving it Substitute numbers into more complicated formulae such as Rearrange a linear formula such as p = 3q + 5 measure a line accurately to within 2 millimetres recognise the net of a simple solid such as a cuboid measure or draw an angle accurately to within 2 degrees measure and scale a line draw the net of a simple solid such as a cuboid draw a triangle given the lengths of: three sides, or two angles and a side, or two sides and the included angle draw a quadrilateral such as a kite or a parallelogram to given measurements understand that giving the lengths of two sides and a non-included angle may not produce a unique triangle construct and recognise the nets of 3-D shapes such as pyramids and triangular prisms construct the perpendicular bisector of a line construct the perpendicular from a point to a line construct the perpendicular from a point on a line bisect an angle Understand and use the vocabulary of probability, such as certain, impossible, likely, unlikely, evens. Understand and use a probability scale. Express a probability as a fraction, such as the probability of getting a six Probability when a fair die is thrown is c E A 1 D 9 1 . 6 Display outcomes systematically, such as the results when two coins are tossed. Two-Tier GCSE Mathematics - Medium Term Plan D C G F E D C G F AQA Mathematics - Foundation Tier Graphs of linear functions Pythagoras’ theorem Quadratic functions Loci 3-D shapes Algebraic Proofs Understand the difference between experimental and theoretical probability, such as getting 56 heads and 44 tails rather than 50 – 50. Use a two-way table to find a probability such as getting a combined total of 7 from throwing two dice. Understand and use relative frequency. Understand the meaning of mutually exclusive outcomes, such as getting a head or a tail. Use the fact that the probabilities of mutually exclusive outcomes add up to 1. Use probability to estimate outcomes for a population. Plot the graphs of straight lines such as y 4 Complete a table of values for y 2x 3 and draw the graph Solve problems involving graphs such as finding where the line y x 2 crosses the line y 1 Recognise the equations of straight line graphs such as y 4x 2 Find the gradients of straight line graphs Use Pythagoras’ theorem to find the hypotenuse of a right-angled triangle Use Pythagoras’ theorem to find any side of a right-angled triangle Use Pythagoras’ theorem to find the height of an isosceles triangle Use Pythagoras’ theorem in practical problems Draw graphs of simple quadratic functions such as y 3x 2 and y x 2 4 Draw graphs of harder quadratic functions such as y x 2 x 1 Find the points of intersection of quadratic graphs with lines Use graphs to find the approximate solutions of quadratic equations Understand the idea of a locus Construct accurate loci, such as those of points equidistant from two fixed points Solve loci problems, such as identifying points less than 3 cm from a point P Recognise and name three-dimsensional (3-D) solids Sketch three-dimsensional (3-D) solids Draw a cuboid on an isometric grid and mark its dimensions Draw plans and elevations of three-dimsensional (3-D) solids Decide with a reason whether a simple statement is true or false Decide with a reason whether a harder statement is true or false Identify a counter example Understand the difference between a demonstration and a proof Show step-by-step deductions in providing a basic algebraic explanation E D C E D C D C D 2 Two-Tier GCSE Mathematics - Medium Term Plan C D C G E D E D C AQA Mathematics - Foundation Tier Two-Tier GCSE Mathematics - Medium Term Plan