Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

no text concepts found

Transcript

NEW for Examination 2015 AQA GCSE Linear Higher Tier Mathematics GCSE Content and Overview Higher Tier (Outcomes U – 9) 1 NEW for Examination 2015 AQA GCSE Linear Higher Tier Key Information This syllabus is to be taught over 2 years, starting 2015. The first examination series for this syllabus will be Summer 2017. Fully Linear course, no modules. Re-sit is only available in November series immediately following the initial Summer exam (i.e. for Y12 students). Assessment will be in the form of two written examinations in the Summer examination period of the second year (for Year 11 students). Comprising one calculator and one non-calculator paper. These will total a minimum of 3.5 hours. Assessment results will be given as an outcome ranging between U – 9 (where 9 is the highest outcome achieved). Passes will be considered as 9 - 3. Fail will be considered as 2 – U. 2 NEW for Examination 2015 AQA GCSE Linear Higher Tier Assessment Objectives The new curriculum has a greater focus on both problem solving and quality of written communication. This now comprises 25% of the total marks. The overall weighting of each of these objectives to be assessed through the final summer examination are as follows: Assessment Objectives AO1 AO2 AO3 Using and applying: Accurately recall facts and definitions. Use and interpret correct notation. Accurately carry out routine calculations or tasks requiring multistep solutions. Reason, interpret and communicate mathematically: Make deductions and form conclusions from mathematical information. Construct chains of reasoning to achieve a result. Interpret and communicate information accurately. Present arguments or proofs. Assess the validity of an argument. Problem Solving: Translate problems in mathematical or non-mathematical contexts into a series of mathematical processes. Make and use connections between different parts of mathematics. Interpret results in the context of the given problem. Evaluate methods used and results obtained. Evaluate solutions. 3 Weighting 50% 25% 25% NEW for Examination 2015 AQA GCSE Linear Higher Tier Formulae Guidance 1. Formulae included in the subject content. Candidates are expected to know these formulae; they must not be given in the assessment. The quadratic formula The solutions of 𝑎𝑥2+𝑏𝑥+𝑐= 0 where 𝑎 ≠0 Circumference and area of a circle Where r is the radius and d is the diameter: Circumference of a circle= 2𝜋𝑟= 𝜋𝑑 Area of a circle= 𝜋𝑟2 4 NEW for Examination 2015 AQA GCSE Linear Higher Tier Pythagoras’s theorem In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse: Trigonometry formulae 5 NEW for Examination 2015 AQA GCSE Linear Higher Tier 6 NEW for Examination 2015 AQA GCSE Linear Higher Tier 2. The following formulae are not specified in the content but should be derived or informally understood by candidates. These formulae must not be given in the examination. 7 NEW for Examination 2015 AQA GCSE Linear Higher Tier 3. Formulae candidates should be able to use, but need not memorise. These can be given in the exam, either in the relevant question, or in a list from which candidates select and apply as appropriate. 8 NEW for Examination 2015 AQA GCSE Linear Higher Tier Notes of Use Teaching: Content is to be taught to the highest achieving students in the cohort (i.e. set 1 pupils), dependent upon ability. Teachers are responsible for differentiating all lessons appropriately for the pupils in their classes. Resources: Any resources listed can be found on the shared Maths drive, on staff laptops, or in the resource folders. All resource folders are categorised by week and topic. Suggested resources include: Sumbooks worksheets Ten Ticks worksheets Abacus software AQA Active Teach software (teacher examples, exercises, end of unit tests and mark schemes) Interactive Essentials www.mymaths.co.uk www.worksheetworks.com http://www.superteacherworksheets.com http://www.tes.co.uk/maths-secondary-teaching-resources 9 NEW for Examination 2015 AQA GCSE Linear Higher Tier Assessment for Learning Time has been built in to this scheme of work at the end of every Term so that revision of topics taught can be undertaken. Formal assessments will be implemented at the end of every Term. Regular homework must be set in line with the mathematics department policy for all Year 10 and Year 11 students. Teachers may wish to use the GCSE homework sheets available on the shared maths drive or source a suitable alternative. Topic colour codes Number Statistics Algebra Measures Geometry 10 Number & Algebra Revision/Exams NEW for Examination 2015 AQA GCSE Linear Higher Tier Overview Year 10 Week 1 Number 1 Mental & Written Calculations Week 2 Algebra 1 Simplifying & Surds Week 3 Geometry 1 Triangles, Quadrilaterals & Angles Week 4 Geometry 2 Bearings Week 5 Statistics 1 Data Collection and Simple Charts. Week 9 Algebra 3 Using Equations and Formulae Week 17 Geometry 5 Circles Week 10 Measures 1 Metric Measures Week 11 Geometry 3 Circle Theorems Week 12 Number 4 Percentages Week 13 Algebra 4 Sequences Week 14 Week 15 Revision & Unit Tests Week 16 Geometry 4 Perimeter & Area Week 18 Algebra 5 Real Life Graphs Week 19 Number 5 Ratio and Proportion Week 20 Geometry 6 Polygons and Angles Week 21 Algebra 6 Expressions & Equations Week 24 Geometry 8 Transformations: Rotation Week 28 Statistics 2 Averages & Probability Week 36 Geometry 12 Loci Week 22 Week 23 Algebra 7 Geometry 7 Equations: Transformations: Straight Lines & Reflections & Circles. Translations Week 30 Week 31 Algebra 8 Solving Quadratic Equations Week 29 Statistics 3 Charts for Grouped Data Week 37 Week 38 Revision & Summer MOCK Exams Week 25 Geometry 9 Congruence & Similarity Week 33 Number & Algebra 1 Inequalities Week 26 Week 27 Revision & Unit Tests Week 34 Algebra 9 Plotting graphs (Linear & Quadratic) Week 35 Geometry 11 Constructions 11 Week 6 Number 2 Laws of Indices & Powers Week 7 Algebra 2 Plotting Coordinates & Linear Graphs Week 39 Number 6 FDP Week 8 Number 3 Fractions, Decimals & Rounding Week 32 Geometry 10 Representing 3D shapes Week 40 Measures 2 Using scales & Compound Measures NEW for Examination 2015 AQA GCSE Linear Higher Tier Year 11 Week 1 Geometry 13 Surface Area Week 2 Geometry 14 Volume Week 9 Algebra 10 Solving Quadratic Equations Week 17 Statistics 5 Probability: Experiments and Charts. Week 10 Algebra 11 Algebraic Fractions Week 18 Geometry 19 Sine and Cosine Rule Week 25 Revision Week 33 Revision Week 3 Number 9 Calculating with Fractions Week 4 Geometry 15 Enlargement Week 5 Geometry 16 Vectors Week 11 Week 12 Revision & MOCK Exams Week 19 Geometry 20 Cylinders, Cones and Spheres. Week 26 Week 27 Revision Revision Week 34 Week 35 Summer Exams Week 20 Algebra 13 More Real Life Graphs Week 13 Geometry 17 Pythagoras & Trigonometry Week 21 Algebra 14 Simultaneous Equations Week 28 Revision Week 36 Week 29 Revision Week 37 12 Week 6 Number & Algebra 2 Direct & Indirect Proportion Week 14 Geometry 18 Pythagoras & Trigonometry Week 22 Geometry 21 Pyramids Week 30 Revision Week 38 Week 7 Number 10 Percentages & Finance Week 8 Number 10 Percentages & Finance Week 15 Algebra 12 Quadratic and Other Graphs Week 23 Statistics 6 Probability: Venn Diagrams Week 16 Statistics 4 Scatter Graphs & Tree Diagrams Week 24 Algebra 15 Inequalities: Linear and Quadratic Week 31 Revision Week 39 Week 32 Revision Week 40 NEW for Examination 2015 AQA GCSE Linear Higher Tier Content: Year 10 Learning Objectives: Autumn 1 Date: Week 1 Resources: Lesson: 1 Number 1 Mental and Written Calculations (Integers, negatives, powers and roots) 2 3 4 Week 2 Algebra 1 1 To be able to: Recall the squares of integers up to 15 and the cubes of 2, 3, 4, 5 and 10 Recall and use corresponding squares, cubes and their roots. Recognise powers of 2, 3, 4, 5 Evaluate expressions involving other integer powers and roots (e.g. 23 + 42) Estimate powers and roots of any given positive number. Calculate accurately with negative numbers. Multiply and divide using whole and decimal numbers. Solve numerical problems involving decimals. Estimate and check answers to calculations involving decimal and negative numbers. Calculate sums using BIDMAS involving negatives, powers and decimals. Common mistakes and misconceptions Outcome Incorrectly thinking that ‘taking a square’ means multiplying by 2 and a cube as multiplying by 3. Not recognising that square roots have 2 solutions (this will become clearer when calculations with negatives are studied) Multiply together two algebraic expressions with brackets. Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments. 13 Adding and subtracting incorrectly. Mistakes made when using negatives and powers (e.g. -33 = 27 instead of -27) Not considering context. Not rounding off numbers and working accurately when asked to estimate. Not showing all working Forgetting to use the correct order. Not writing down their working and losing track of what they have done previously in the calculation. Not multiplying all terms in one bracket by the other. Forgetting to simplify answers fully. Students just square what they can see e.g. stating that (x + 3) = x2 + 9 NEW for Examination 2015 AQA GCSE Linear Higher Tier Simplifying & Surds 2 3 4 Week 3 1 Geometry 1 Triangles, Quadrilaterals & Angles 2 3 Square a linear expression, e.g. (x+1)2 Expand products of two or more binomials, e.g. (x+2)3 or (x+2)2 (x+3)3 Use the addition and subtraction rule of surds. Use the multiplication and division rules of surds. Simplify surds fully (e.g. √12 = 2√3) and rationalise denominators. Expand brackets involving surds Manipulate surds to rationalise denominators. Simplify and manipulate algebraic expressions (including those involving surds) Solve angle problems algebraically (straight lines, around a point, opposite). Use and apply rules for parallel lines to solve angles problems. Pupils do not show working out as proof (e.g. evidence of expanding brackets) Pupils forget to answer the question fully (e.g. forgetting to state Yes or No when asked whether expressions are equivalent) Thinking that (x+1)2 = x2 + 1 Completing only some of the steps to fully expanding. Identify and derive properties of special types of quadrilaterals, 14 Forgetting to multiply the entire fraction by the same surd. Not simplifying answers fully in more complicated expressions. Not using all the information in the diagram. Confusing alternate and corresponding angles. Derive and understand that angles inside a triangle sum to 180o Calculate missing angles inside triangles. Solve angle problems in triangles algebraically. Adding the numbers underneath the root signs, instead of collecting together. Not simplifying answers where possible, e.g. √4 is actually 2. Not realising when a triangle is isosceles and thinking that the problem cannot be solved. Trying to do too many steps in one go when answering algebra-based question. Not recognising, or be able to name, some of the less common NEW for Examination 2015 AQA GCSE Linear Higher Tier including square, rectangle, parallelogram, trapezium, kite and rhombus Draw diagrams from written description Calculate missing angles inside quadrilaterals Solve angle problems in quadrilaterals involving algebra 4 Week 4 1 Use three-figure bearing notation Measure the bearing from one place to another. Plot 3-figure bearings. Plot bearings from worded problems. 2 Geometry 2 quadrilaterals (e.g. the kite and trapezium). Not reading all of the information before drawing / identifying the shape being described. Not realising that some of the angles asked for can simply be read off the diagram. Trying to do too many steps in one go when answering algebra-based question. Confusing where to measure from and to. Using the wrong scale on the protractor Bearings Week 4 Draw and interpret scale diagrams to represent journeys. Not drawing bearings for all information given. Measuring inaccurately and intersections being in the wrong places. Measuring the diagram instead of realising that the angles can be calculated. Confusing alternate and corresponding angles. Geometry 2 Bearings 3 Week 5 Calculate bearings in diagrams (including return journeys) Statistics 1 4 Data Collection and Simple Charts. 1 Consolidation: Use and apply knowledge of angles and bearings to complete exam questions. To understand the data handling cycle NOTE: The above is not specifically tested but is useful for pupil understanding Identify different types of data (discreet, continuous, qualitative, quantitative, primary, secondary) 15 Not appreciating that some data can be treated as either discrete or continuous depending on the context (e.g. age – this is really continuous, but is often treated as discrete, such as when buying child NEW for Examination 2015 AQA GCSE Linear Higher Tier or adult tickets). Week 5 2 Work out methods for gathering data efficiently Work out methods for gathering data that can take a wide range of values Sort data into class intervals Interpret and use grouped frequency tables Interpret a pie chart Statistics 1 Data Collection and Simple Charts. 3 Week 6 Number 2 Laws of Indices and Powers 4 Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use. Draw a pie chart Solve problems with pie charts. 16 Not realising that data collected by a third party (even if the results of a survey or experiment) is classed as secondary data. Using overlapping class intervals. Recording data which is on the boundary of a class interval in the wrong class. Looking at the angle in a pie chart and ignoring the fact that the pie chart can represent a different number of people. Not drawing the angles in the pie chart accurately or using the appropriate scale on the protractor. Measuring each angle from the same starting point. NEW for Examination 2015 AQA GCSE Linear Higher Tier 1 Week 6 2 Number 2 3 Laws of Indices and Powers Week 7 4 Algebra 2 Plotting Coordinates and Linear Graphs 1 Working out 27 as 2 × 7. Multiplying and dividing powers instead of adding and subtracting. Use laws of indices to multiply and divide numbers written in index notation. (e.g. x2 x x3 = x5) Calculate with roots, and with integer and fractional indices. Calculate a power of a power, e.g. (23)4 Simplify expressions involving negative indices. Simplify expressions involving fractional indices. Combine laws of indices to evaluate more complicated expressions. Use proof to show equivalence in expressions involving powers. Write numbers in standard form. Convert between standard form and decimal numbers. Calculate using numbers written in standard form. Identify straight-line graphs that are parallel to the x- or y- axis Identify and interpret gradients and yintercepts of lines in the form of y = mx + c Use the form y = mx + c to identify parallel and perpendicular lines. Find the equation of the line through two given points, or through one point with a given gradient. 17 Mixing up the rules. Forgetting to write 1/ Not simplifying fully. Simplifying and not evaluating fully when asked to. Not showing all steps when simplifying or showing equivalence. Forgetting to use a negative power when working with very small numbers. Working out only part of the calculation, forgetting to simplify the power. Ensuring final answers are in standard form, e.g. 1.2 x104 and not 12 x103. Leaving answer as a decimal number, if required. Confusing the x- and y- axis Mixing up the gradient and yintercept Not stating that the gradient is negative. NEW for Examination 2015 AQA GCSE Linear Higher Tier 2 Week 7 Sketch straight line graphs Match straight line graphs to their equations Forgetting that the bigger the gradient, the steeper the graph should look That gradients of 2 and -2 look the same, but slope in opposite directions Confusing the gradient and yintercept Incorrectly calculating with negative numbers Ignoring BIDMAS. Confusing the x- and y- coordinates Not joining up all points. Only plotting 2 points and joining these together, a 3rd should be used. Incorrectly dividing the change in xby change in y- values. Forgetting to check whether the gradient should be positive or negative once calculations have been done. Mixing up the gradient and yintercept. Algebra 2 Plotting Coordinates and Linear Graphs 3 4 Complete a table of values for linear functions (for positive and negative values of x) Plot graphs of linear functions using a table of values. Plot linear functions with or without being given a table of values. Calculate the gradient of a straight line (using change in y- / change in xvalues) Identify the equation of a line by finding the gradient and using yintercept Autumn 2 Date: Week 8 Number 3 TT L5 P2 p33-34 Resourc es: 1 Lesson: Identify and understand equivalent factions Compare fractions with different denominators using equivalence. 18 To be able to: Multiplying the denominator but not the numerator when finding equivalent fractions. Stating that 1/3 is smaller than ¼ as the denominator is smaller. NEW for Examination 2015 AQA GCSE Linear Higher Tier Fractions, Decimals and Rounding Week 8 Number 3 Sumbooks Higher worksheet (11)page 19. 2 Fractions, Decimals and Rounding TT L9-10 p1 pg 3-5 TT L9-10 p1 pg 3-5 Week 9 Sumbooks Higher worksheet (1), page 9. 3 4 Identify terminating and recurring decimals Convert fractions into terminating decimals Convert terminating decimals into fractions Change recurring decimals into their corresponding fractions and vice versa Round decimals to a given number of decimal places. Round numbers to a given number of significant figures. Apply and identify limits of accuracy when rounding. Including upper and lower bounds. Estimate and approximate calculations by rounding. Solve problems using estimation. Use inequality notation to specify simple error intervals due to truncation or rounding 19 1 Confusing 0.3 with 3. Not understanding that recurring decimals are a form of exact maths and therefore rounding answers. Giving the answer in the wrong form. Treating the digits on each side of the decimal point as separate whole numbers so giving 0.95 rounded to 1 d.p. as 0.1 Not considering context when giving final answers to problems. Not rounding values to the same degree of accuracy where appropriate. NEW for Examination 2015 AQA GCSE Linear Higher Tier Algebra 3 1 Using Equations and Formulae 2 Week 9 Algebra 3 Form simple expressions Form expressions involving powers and brackets Form and solve linear equations to solve problems. Substitute numbers to work out the value of algebraic expressions (including powers and indices) Substitute numerical values into more complicated formulae. Using Equations and Formulae Week 10 Measures 1 Metric Measures Week 10 Measures 1 Sumbooks Higher worksheet (55) page 63. 3 Find approximate solutions to equations using trial and improvement. Sumbooks Higher worksheet 41 (pg 49). L5 p 3 pg 27-34 L5 p3 pg 35- 37 4 Find approximate solutions to equations using iteration. 1 2 Change freely between related standard units (time, length, area, volume, mass, capacity, money) Change freely between metric units of area and volume. Know and use approximate metric equivalents of pounds, feet, miles, pints and gallons Note: This is no longer in the GCSE subject content but still may be useful for students. 20 Not seeing the ‘general’ case. Including brackets unnecessarily in calculations. Incorrectly substituting values into expressions (e.g. substituting a = 6 into the expression 4a, writing 46 and assuming it is forty-six). Ignoring BIDMAS. n Not realising that 10 means n ÷ 10, 1 1 or that 2 × 6 means 2 of 6 = 3. Giving answers irrespective of context. Not showing all stages of working. Not understanding the concept of rounding to get the final solution. Not showing enough stages of working out to show how the answer tends to a given solution. Ignoring the different units when comparing measurements. Not considering the relative size of units when deciding whether to multiply or divide. Forgetting the equivalent values. Multiplying instead for dividing. NEW for Examination 2015 AQA GCSE Linear Higher Tier L5 p 3 pg 29-33 3 Metric Measures Week 11 Geometry 3 Circle Theorems 1 2 Week 11 Geometry 3 Circle Theorems Week 12 Identify upper and lower limits of numbers rounded to a given degree of accuracy. Solve problems involving limits of accuracy and measures. Identify and: Use the tangent / radius theorem. Use the two tangent theorem. Use the chord / bisector theorem. Identify and: Use the angle subtended by an arc theorem. Use the semi-circle theorem. Use the same-segment theorem. 4 apply and prove the standard circle theorems 3 Estimate measures. Solve problems involving measures and conversion. Identify and: Use the cyclic quadrilateral theorem. Use the alternate segment theorem. Misinterpreting the rounding that has taken place. Using the wrong limit when performing calculations. Forgetting that angles are equal when using the two-tangent theorem. Forgetting that bi-sect means cut in half. Using the angle subtended by an arc theorem the wrong way around, i.e. the angle at the edge is twice the one at the centre, instead of the other way around. Doubling instead of halving. Assuming that opposite angles in cycling quadrilaterals are equal. Not being able to spot the alternate segment rule. Students not able to see the bigger picture. Pupils forget to apply simple angles rules to help prove more complicated circle theorems. Number 4 4 Percentages Apply combinations of circle theorems concerning angles, radii, tangents and chords, and use them to prove related results. Prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results. 21 Ignoring context when estimating. NEW for Examination 2015 AQA GCSE Linear Higher Tier 1 Week 12 Number 4 3 Week 13 Algebra 4 Find a percentage of an amount without using a calculator Find percentages of amounts in more complex situations Compare two quantities using percentages Find a percentage of an amount with a calculator Write one quantity as a percentage of another 4 1 Sequences 2 Convert between fractions, decimals and percentages. Order fractions, decimals and percentages. 2 Percentages Calculate a percentage increase or decrease Calculate percentage increase or decrease using VAT Recognise sequences of triangular, square and cube numbers. Recognise and use sequences such as Fibonacci, quadratic and involving powers (e.g. 21, 22, 23, 24, 25…) Find any term in a sequence given the nth term Show something is false using a counter-example Find the nth term of a linear sequence 22 Forgetting that fraction lines mean ‘divide’ Multiplying by the wrong power of 10 to change between decimals and percentages. Show their working out, forgetting to order their final answer. Students divide by 10 to get 10%, so therefore divide by 1 to find 1%. Treating a percentage such as 0.05% as though it were 5%. Not using the original amount as the denominator, when finding a percentage difference. Working with quantities in different units, forgetting to convert. Adding the percentage to the cost when finding a percentage increase (e.g. £315 + 15% VAT = £330). Thinking that percentages over 100% cannot exist. Giving the actual increase/decrease as the answer, not the final total. Using the multiplier as 1.5 rather than 1.05 for an increase of 5%. Writing 3 ‘ squared’ as 2 x 3 Writing powers as 2x1, 2x2, 2x3… Not identifying an appropriate counter-example. Not appreciating that a proof shows something works for all values. Not showing every step of working out NEW for Examination 2015 AQA GCSE Linear Higher Tier Week 13 Algebra 4 3 Sequences Find the nth term for pattern sequences Identify and use sequences involving surds. Find the nth Term rule for a simple quadratic sequence. Not making the connection between the structure of the physical pattern and the form the nth term takes. Week 14 / 15 4 Find the nth Term rule for any quadratic sequence. Week 16 Geometry 4 Perimeter and Area Week 16 Geometry 4 Revision & Unit Tests / Exam Question focus? Spring 1 Not showing all steps in working out. Confusing whether they need to add or subtract a value to get from one part of a sequence to another. Missing out steps in working out. Mixing up n2 with 2n, for example. Resourc es: Lesson: 10 ticks L5 P4 p3640 Abacus Sumbooks (Y9 basics) p83 1 Calculate the perimeter of rectangles, triangles, parallelograms and trapezia 10 ticks L5 P4 p3640 http://www.workshee tworks.com/math/ge ometry/measuring- 2 Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs. Identify missing measurements on compound shapes. Calculate the perimeter of compound shapes. 23 To be able to: Outcome Counting squares instead of the number of edges exposed around the outside. Not adding all side lengths together Assuming that everything is in ‘cm’ and not checking the correct units Stating a measurement because it ‘looks the same’ as another one Not converting lengths into the same units before adding Only adding the measurements given, ignoring unlabelled sides NEW for Examination 2015 AQA GCSE Linear Higher Tier Perimeter and Area Week 17 Geometry 5 Circles figures.html Abacus Sumbooks (Exercises in Numeracy) p32 10 ticks L5 P4 p3640 Abacus Sumbooks (Y9 basics) p83 10 ticks L5 P4 p3640 http://www.workshee tworks.com/math/ge ometry/measuringfigures.html Abacus Sumbooks (Exercises in Numeracy) p32 Abacus Week 17 Geometry 5 10 ticks L6 P5 p3338 Abacus Sumbooks (Foundation book) 3 4 Writing ‘cm’ instead of ‘cm 2’ For triangles, forgetting to halve Not using the vertical height Multiplying all measurements together, instead of the ones they need Calculate the area of rectangles, triangles, parallelograms and trapezia Calculate the area of compound shapes made from rectangles. Calculate the area of compound shapes involving triangles, parallelograms and trapezia. Forgetting to add all areas together to get a total Not identifying the correct measurements to use when there are more than they need Multiplying all given measurements together 1 2 Recall the definition and properties of circles (inc. symmetry) Know and label parts of a circle (centre, radius, chord, diameter, circumference, tangent, arc, sector and segment) Draw circles accurately Calculate the circumference of a circle using 2πr or πd Calculate the perimeters of compound shapes involving circles or parts of circles Leave answers in terms of π 24 Forgetting there are an infinite number of lines of symmetry Confusing radius and diameter Confusing segment and sector Forgetting to divide by 2 when the diameter is given and the radius is needed. Not multiplying by 2 when the radius is given and the diameter is needed. Forgetting to add all lengths to get final answers. Adding measurements to the perimeter that are inside the shape NEW for Examination 2015 AQA GCSE Linear Higher Tier Circles Week 18 Algebra 5 Real Life Graphs Week 18 Algebra 5 Real Life Graphs p54 10 ticks L6 P5 p3338 Abacus Sumbooks (Foundation book) p61 Abacus 3 Calculate the area of a circle using πr2 Calculate the areas of compound shapes involving circles or parts of circles. Leave answers in terms of π. 4 Calculate arc lengths . Calculate the area of a sector. Calculate angles inside sectors of circles. 1 2 Read and interpret distance–time graphs Draw distance-time graphs Read and interpret velocity-time graphs Draw velocity-time graphs Solve problems involving speed, distance and acceleration Read and interpret real-life graphs Sketch real-life graphs Read and interpret conversion graphs Plot conversion graphs Sketch and interpret reciprocal and exponential graphs of real-life functions. Week 19 Number 5 Ratio and Proportion 25 Not leaving answers incorrect form. Multiplying by before squaring. Using the diameter instead of radius. Not leaving answers in correct form. Using the angle for the major sector when the minor is needed, and vice versa. Not being able to rearrange calculations to find the angle inside the sector Drawing and labelling axes before working out the axes range appropriate to the problem. Confusing the formula for calculating acceleration Forgetting that a positive slope is acceleration and negative slope is deceleration Not realising that the intercept represents a fixed cost. Not recognising that a straight line represents constant change, curves show rates vary Inaccurately reading from one value on a conversion graph to find another value. Drawing out axes using an unsuitable scale Not being able to use their graph to work out a solution to a problem not represented on the graph (e.g. axes go up to 200g, need to use 800g) NEW for Examination 2015 AQA GCSE Linear Higher Tier 3 4 1 Drawing a tangent to the curve inaccurately. Dividing the change in x- by y Ignoring whether it should be a positive or negative gradient. Drawing tangents to curves inaccurately. Calculate the gradients of chords and tangents numerically and algebraically. Write a ratio as a fraction. Interpret ratios in practical situations. Identify and work with fractions in ratio problems. Divide a given quantity into a ratio. Use a ratio to find one quantity when the other is known. 2 Write a ratio in the form 1 : n or n : 1 Use a ratio when comparing a scale model to the real-life object 3 Understand direct proportion Solve problems involving direct proportion. Understand value for money. Work out which product is the better buy. Week 19 Interpret the gradient at a point on a curve as the instantaneous rate of change. Turning a ratio into a fraction (e.g. 4 the ratio 4 : 5 becomes 5). Giving an answer without considering the context. Dividing by 2 as there are two parts to the ratio. Failing to find the value of the unit fraction in more complex problems. Dividing by the wrong amount to find the unit value. Writing the ratios the wrong way around. Number 5 Ratio and Proportion Week 20 Geometry 6 Polygons and Angles 26 Giving an answer without considering the context. Not multiplying or dividing both sides of the ratio by the same amount. Not finding the unit cost. Dividing by the wrong amount to find unit cost. NEW for Examination 2015 AQA GCSE Linear Higher Tier Week 20 10 ticks L5 P3 p1921 Sumbooks (Y9 basics) p65 Sumbooks (Intermediate book) p42 10 ticks L6 P5 p2729 1 10 ticks L6 P5 p2729 3 10 ticks L6 P5 p2729 4 Geometry 6 Polygons and Angles Angles re-cap: Calculate angles inside a triangle Calculate angles inside quadrilaterals (including special quadrilaterals, and algebraically) 2 Week 21 Use properties of triangles to find the sum of interior angles inside polygons. Calculate interior angles of polygons. Understand that exterior angles on polygons always sum to 360o Use exterior angles of polygons to solve problems. Algebra 6 Expressions and Equations 1 Understand indirect proportion. Solve problems involving indirect proportion. 4 Solve more complex angle problems involving exterior and interior angles of polygons. Know the difference between and equation, expression and an identity Where appropriate interpret simple expressions as functions with inputs 27 Not considering real-life context before answering questions. Incorrectly multiplying instead of dividing. Not showing working. Not stating the angles rule they have used. Not remembering properties of regular / irregular polygons and other properties of shapes. Confusing the rule for triangles and quadrilaterals. Incorrectly splitting the polygon into triangles. Working things out mentally without writing down the calculations. Thinking that exterior angles are only 360o on quadrilaterals. Confusing the rules for interior and exterior angles. Forgetting the formula for the exterior angles of a polygon and how to apply it. Failing to spot that all angles are equal on a regular polygon when only one angle is given. Forgetting that interior and exterior sum to 180o Pupils do not use the correct notation for angles (e.g. angle ABC = angle DEF because…) Incorrectly combining number work involving fractions and decimals with equation solving. Getting the wrong signs when NEW for Examination 2015 AQA GCSE Linear Higher Tier and outputs Interpret the reverse process as the ‘inverse function’ Interpret the succession of two functions as a ‘composite function’. Solve two-step equations. Solve equations involving brackets. Solve equations with an unknown on both sides. Solve equations with unknown on both sides and brackets. Week 21 Algebra 6 Expressions and Equations 10 ticks L6 P1 p6-8 http://www.workshee tworks.com/math/pre -algebra.html Sumbooks (Y9 basics) p5310 ticks L6 P1 p6-8 http://www.workshee tworks.com/math/pre -algebra.html Abacus 2 3 Solve equations involving fractions on one side. Solve equations involving fractions on both sides. 4 1 Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs Find the equation of a straight line Rearrange formulae to change the subject. Rearrange formulae where the subject appears twice. 28 multiplying negative numbers. Incorrectly simplifying after expanding the bracket. Introducing errors when there are a negative number of unknowns on either side of the equation. Not multiplying by the denominator of the fraction. Not multiplying by the LCM of each fraction when they appear o both sides. Inaccurately multiplying so having errors in final answer. Not using the inverse operation (e.g. x + y = z becomes x = z + y). Not using brackets or a clear division (e.g. rewriting c = 2a + 5 as a = c − 5 ÷ 2). Incorrectly working out the change in NEW for Examination 2015 AQA GCSE Linear Higher Tier through two points Week 22 x- or y- values when finding the gradient. Forgetting that they needs to substitute in values for x- and yusing the coordinates given. Not being able to solve the equation to find the y-intercept. Algebra 7 Equations: Straight Lines & Circles. 2 Week 22 Algebra 7 3 Equations: Straight Lines & Circles. 4 Spring 2 Geometry 7 Transformations: Reflections and Translations Week 23 Find the equation of the line through one point with a given gradient Solve problems involving equations of straight lines. Recognise and use the equation of a circle centre (0,0) Abacus Week 23 Find the equation of a tangent to a circle at a given point. Forgetting that when x=o, y is the intercept. Substituting in the wrong values into the equation. Forgetting the formula. Not square rooting to find the radius. Learning Objectiv es: Resourc es: 10 ticks L4 P7 p2936 Sumbooks (Foundation book) p37 1 10 ticks L6 P2 p1112 2 Lesson: Recognise and draw lines of symmetry in plane shapes. Draw a reflection of a shape in a mirror line (horizontal, vertical or diagonal) Draw reflections in the x- or y- axis on a coordinate grid. Identify lines that are parallel to the xor y- axes. 29 To be able to: Outcome Only drawing on one line of symmetry when there are several Drawing the image a different distance from the mirror line than the object. Mixing up x = and y = lines Confusing whether the line is NEW for Examination 2015 AQA GCSE Linear Higher Tier Geometry 7 Transformations: Reflections and Translations Reflect shapes on coordinate grids in lines parallel to the x- or y- axis Reflect shapes in lines such as y = x Sumbooks (Foundation book) p37 10 ticks L7-8 P4 p32 Identify lines of reflection on a coordinate grid by finding midpoints. Describe fully reflections on a coordinate grid. 3 10 ticks L5 P4 p3132 10 ticks L6 P2 p3-10 Sumbooks (Foundation book) p48 4 Translate shapes according to a given vector. Describe translations fully using vectors. Week 24 Geometry 8 Transformations: Rotation Week 24 Geometry 8 10 ticks L4 P7 p3738 Sumbooks (Y9 basics) p78 Sumbooks (Foundation book) p46 10 ticks L6 P2 p1316 Sumbooks 1 2 Describe the changes and invariance achieved by combinations of rotations, reflections and translations. Recognise rotational symmetry in regular 2-D shapes. Recognise rotational symmetry in other shapes. Complete images to give a given order of rotational symmetry. Use fractions of turns, angles and compass directions (e.g. ¼ turn clockwise, 90o anticlockwise, turn through 180o) 30 horizontal or vertical when drawing on the line of reflection. Automatically reflecting in the x- or y- axes. Assuming the mirror line is either the x- or y- axis. Incorrectly identifying mirror lines parallel to the x- or y-axis. Forgetting to give enough information, i.e. ‘reflection in the line…) Only finding the new location of one corner of the shape and then drawing in the rest incorrectly. Forgetting that negative numbers mean left or down. Confusing the left/right value for the up/down value in column vectors. Using coordinate notation instead of vector notation. Describing the translation of shape A to shape B, when the opposite was required. Forgetting the definition of regular polygons. Stating order 4 for shapes with 4 sides. Pupils make images symmetrical, instead of giving order of rotational symmetry. Mixing up clockwise and anticlockwise. Not realising 180o turns end in the NEW for Examination 2015 AQA GCSE Linear Higher Tier Transformations: Rotation Week 25 (Foundation book) p47 10 ticks L6 P2 p1316 3 10 ticks L6 P2 p1316 4 10 ticks L7-8 P5 p11-14 Abacus 1 10 ticks L7-8 P5 p11-14 Abacus Sumbooks (Foundation book) p77 10 ticks L7-8 P5 p23-24 2 Geometry 9 Congruence and Similarity Week 25 Geometry 9 Congruence and Similarity 3 Rotate simple shapes on a grid around a given point. Draw the position of a shape after rotation about the origin (0,0) on a coordinate grid. Rotate a shape on a coordinate grid given any centre of rotation. Identify the centre of rotation between two shapes. Describe a rotation fully giving the size and direction of turn and the centre of rotation. Understand the meaning of congruence. Identify congruent shapes (squares, circles, regular polygons) Identify congruent shapes on coordinate grids (i.e. that have been rotated, reflected, translated or enlarged including fractional and negative scale factors) Know the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Recognise and explain how triangles are congruent. same position independent of direction. Rotating the shape around the wrong point. Working out the angle of rotation incorrectly. Assuming that (0,0) is the centre of rotation instead of reading the question carefully. Not giving enough information, i.e. centre, direction and angle. If not using tracing paper: Not joining up corresponding corners. Perpendicular lines not drawn accurately, crossing in the wrong place. Not realising that shapes are still congruent even if they have been rotated or reflected. Understand the meaning of similar shapes. Calculate scale factors in similar shapes. 31 Mixing up the rules of congruence (e.g. thinking that AAS = ASA) Stating congruence even when corresponding sides / angles are not equal. Not checking that all lengths are similar. Dividing measurements that are not corresponding. NEW for Examination 2015 AQA GCSE Linear Higher Tier Week 26/27 Abacus 10 ticks L7-8 P5 p23-29 4 Abacus Revision & Unit Tests / Exam Question focus? (Easter) Summer 1 Week 28 Identify similarity in simple shapes. Describe and construct similar shapes (e.g. circles, squares, rectangles) Use similarity when working with area Apply the concepts of congruence and similarity to solve problems. Resourc es: Lesson: 1 Find MMR from a frequency table. Find the modal class and median from a grouped frequency table. Statistics 2 Using the wrong scale factor. Dividing lengths that are not corresponding to check similarity. Not using a squared scale factor when working with area. To be able to: Outcome Adding up the total frequency incorrectly. Forgetting to divide by the total by the number of data items. Averages & Probability Week 28 2 Statistics 2 Find an estimate of the mean for grouped data. Compare a set of discreet data using mode, range, median and mean. Averages & Probability Week 29 3 Understand the meaning of independent events. 32 Not using the midpoint of a class interval. Adding the frequencies together before multiplying by the midpoint. Selecting an inappropriate measure for the data provided. Showing calculations without making a conclusion or proving a hypothesis. Working in a haphazard way when giving possible combinations, thus NEW for Examination 2015 AQA GCSE Linear Higher Tier Statistics 3 Charts for Grouped Data 4 1 Week 29 2 Statistics 3 3 Charts for Grouped Data Week 30 Algebra 8 Systematically list all outcomes for combined independent events (in a list or table). Calculate the probability of combined independent events. Construct theoretical possibility spaces (sample space) combined events. Calculate probabilities using possibility spaces (sample space). Set up tree diagrams for combined independent events. List outcomes using tree diagrams. NOTE: (you may wish to calculate simple probabilities from a tree diagram here) Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use Interpret and solve problems involving histograms. Plot cumulative frequency curves. Interpret cumulative frequency curves. Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through tendency (median, mean, mode and 33 missing one or more combinations. Not simplifying fractions where required. Not listing all outcomes of each event. Miscounting the number of possibilities in the sample space. Not including enough ‘branches’ for outcomes. Not reading across every possible combination of branches and therefore missing outcomes. Assuming that all column widths should be equal. Forgetting that bar height represents frequency density and not frequency. Multiplying or dividing incorrectly when trying to find missing values needed. Using unsuitable scales on the axes. Not being able to identify the scale that has been used. Forgetting to add frequencies together. Plotting coordinates and joining together like a frequency polygon. NEW for Examination 2015 AQA GCSE Linear Higher Tier Solving Quadratic Equations 4 Week 30 Algebra 8 10 ticks L7-8 P3 p9 Sumbooks (Intermediate book) p31 1 10 ticks L7-8 P3 p9 Sumbooks (Intermediate book) p31 Sumbooks (Higher book) p34 2 Week 31 3 Solving Quadratic Expand and simplify expressions involving brackets and surds. Factorise linear expressions. Factorise expressions involving surds. Factorise quadratic expressions. Factorise using the difference of two squares. Factorise quadratic expressions with coefficients greater than 1 (e.g. starting 2x2) Factorise quadratic expressions of the form ax2 + bx + c including the difference of two squares. Plot graphs of quadratic functions (recap) Solve quadratic equations graphically. Solve quadratic equations by factorising algebraically (including Solving Quadratic Equations Algebra 8 modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range) Draw box plots from cumulative frequency curves. Interpret box blots. Understand and discuss the effect of outliers. 34 Drawing the box inaccurately, so it represents the lowest and highest value instead of the interquartile range. Placing the median in the middle of the axes, instead of at the correct value. Not finishing off whiskers. Not showing outliers where required. Errors made when working with negative numbers. Not multiplying all terms in the bracket by the number / term on the outside. Forgetting basic rules of surds. Not taking out the highest common factors. Forgetting that x2 is a factor of x3 Forgetting that √2 is a factor of √10 and √12, for example. Errors made when multiplying out brackets to check answers. Forgetting to write the opposite sign when writing the solution, e.g. (x + 1) gives solution of x= -1 not x=1. Not writing down both solutions. NEW for Examination 2015 AQA GCSE Linear Higher Tier those that need rearranging). Equations 4 1 Week 31 2 Algebra 8 3 4 1 Solving Quadratic Equations Week 32 10 ticks L4 P8 p2228 Geometry 10 Complete the square. Solve quadratic equations by completing the square. Substitute into formulae (including negatives and indices) (re-cap) Recognise and interpret the quadratic formula. Substitute into the quadratic formula. Solve quadratic equations using the quadratic formula, finding both solutions. Consolidation Consolidation Identify 3D shapes: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres. Describe 3D shapes by their properties. Identify planes of symmetry of 3-D objects. Forgetting to halve the value in front of the ‘x’ Errors made when multiplying out what is inside the bracket. Incorrectly writing add or subtract after the bracket, when the opposite is necessary. Forgetting there are always 2 solutions. Errors made when squaring or multiplying with negatives. Forgetting to change the sign in from of the ‘b’ value to a positive or negative where required. Not writing both solutions on the answer line. Miscalculating with negatives. Giving correct answers but not explaining the properties used. Using incorrect terminology, e.g. corners instead of vertices. Representing 3D shapes Week 32 Geometry 10 Representing 3D 10 ticks L4 P8 p2228 10 ticks L6 P4 p3340 Sumbooks (Y9 basics) p71 2 Recognise the net of a 3-D object Draw the net of a 3-D object 35 Incorrectly visualising 3-D objects in 2-D. NEW for Examination 2015 AQA GCSE Linear Higher Tier shapes Week 33 Number & Algebra 1 Inequalities Sumbooks (Foundation book) p35 10 ticks L6 P2 p3742 Sumbooks (Y9 basics) p74 Sumbooks (Foundation book) p35 10 ticks L5 P6 p3034 10 ticks L6 P2 p3742 Sumbooks (Foundation book) p78 L 6 p 1 p9 Week 33 3 4 Make a drawing of a 3-D object on isometric paper. Make isometric drawings of a 3-D object when given certain criteria (e.g. 24 cubes, draw a cube that has 125 cubes, draw a cuboid…) Set up linear equations. Solve linear equations. 2 Sumbooks higher p 245 3 Number & Algebra 1 Use the symbols <, >, ≤, ≥ to show numerical inequalities. Write down integer values that satisfy inequalities. Show inequalities on a number line. Inequalities Week 34 Algebra 9 Plotting graphs Solve linear inequalities in one variable. Solve linear inequalities and show solutions on a number line. 36 Using isometric paper in landscape not in portrait. Not joining lines dot-to-dot. Forgetting that there are cubes on the inside of a shape (e.g. asked to draw a cuboid that has 24 cubes) and only considering the cubes you can see. Construct and interpret plans and elevations of 3-D objects 1 L6 p 6 pg 7 L7-8 p 4 pg 13-15 Missing out hidden cubes when converting from a 3-D view to a plan or elevation. Confusing the different views. Misinterpreting the problem. Not making links between one part of the question and another. Correct equation formed but solved incorrectly. Confusing the convention of an open circle for a strict inequality and a closed circle for an included boundary. Not remembering how to use inequality symbols. Not reversing the sign when multiplying or dividing by a negative. Colouring in the circle when it is not needed. Misinterpreting the symbols given in the inequality. Not changing the symbols around NEW for Examination 2015 AQA GCSE Linear Higher Tier (Linear and Quadratic) Week 34 Sumbooks higher p 245 4 L6 p 1 pg25 1 L6 p 1 pg27-29 L6 p 1 pg 35 L7-8 p 3 pg 29 2 AQA Higher book, Ex. 35D, page 551. 3 Solve linear inequalities in one or two variables and represent solutions on a number line. Plot graphs of linear functions (with or without a table of values) Plot graphs of two linear functions and identify points of intersection. Solve linear equations graphically. Plot graphs of quadratic functions. Solve linear or quadratic equations graphically. Algebra 9 Plotting graphs (Linear and Quadratic) 4 Solving problems with quadratic equations (graphically or algebraically). Plot graphs of other functions (e.g. cubic, reciprocal, exponential for positive values of k) NOTE: This is not specifically tested, but is useful for when students need to sketch graphs of various functions. Learning Objectiv es: 37 when multiplying or dividing by a negative. Writing x= on answer lines instead of using the appropriate symbol. Substituting incorrectly. Not using BIDMAS. Making mistakes when calculating with negative numbers. Not using a third point as a check when drawing a straight line. Not plotting enough points. Not joining points together. Joining coordinates with a straight line instead of a smooth curve. Not visualising the problem. Incorrectly setting up equations. Students do not apply basic knowledge of mathematics to help solve problems (e.g. multiplying out algebraic expressions given as lengths, to find an expression or equation for area). Joining non-linear graphs with straight lines. Not checking ‘rogue’ coordinates they have plotted (e.g. they can see what the graph should look like, but do not check working out when there is a coordinate that does not fit with the rest). NEW for Examination 2015 AQA GCSE Linear Higher Tier Summer 2 Week 35 Geometry 11 10 ticks L7-8 P5 p57 10 ticks L6 P4 p32 Resourc es: Lesson: 1 Construct acute, obtuse angles. Construct reflex angles. Construct the bisector of an angle. 2 Constructions Week 35 Geometry 11 Constructions Week 36 Geometry 12 Loci Week 36 Geometry 12 10 ticks L6 P4 p3132 10 ticks L6 P4 p3132 10 ticks L7-8 P5 p34 3 Sumbooks (Intermediate book) p87 Sumbooks (Year 9 basics) p69-70 4 Worksheet in resources folder 1 Worksheet in resources folder 2 Draw triangles accurately when at least one angle is given. Draw triangles accurately when given the length of all three sides. Know that the perpendicular bisector of a line segment is the shortest route between two points. Construct a perpendicular bisector of a line. Construct a perpendicular to a given line from/at a given point. Make an accurate drawing of given shapes using constructions. To be able to: Outcome Labelling the wrong part of the angle once drawn. Using the wrong scale on the protractor. Not keeping the arms of compasses an equal distance apart when bisecting. Not completing the triangle by drawing the third side. Rubbing out construction lines. Not completing the triangle by drawing the third side. Not opening the compasses so that they are greater than the midpoint. Rubbing out construction lines. Not keeping a consistent distance between the points of the compass when drawing arcs. Using the wrong type of construction. Not using compasses and drawing ‘freehand’ Not drawing according to all given criteria. Construct a locus around a point. Construct a locus around a line of points. Construct a locus that is equidistant between two points. Construct a locus that is equidistant between two lines. 38 Failing to keep the settings of compasses constant. Rubbing out construction lines. Confusing a distance from a point with the distance from a line. NEW for Examination 2015 AQA GCSE Linear Higher Tier Loci Week 37/38 Sumbooks (Intermediate book) p57-58 10 ticks L7-8 P5 p710 Sumbooks (Intermediate book) p57-58 10 ticks L7-8 P5 p710 Sumbooks (Higher book) p51 (including bearings) Revision & Summer MOCK Exams? 3 4 Solve problems involving constructions and loci. Not using compasses. Making inaccurate constructions. Shading the wrong region. Solve locus problems, including the use of bearings and scale. Forgetting that bearings use 3figures. Not using a North line. Confusing clockwise and anticlockwise. 1 10 ticks L5 P3 p29-34 10 ticks L4 P3 p27-42 Week 39 Measures 2 Using scales & Compound measures (speed, rates of pay, area) 2 Week 39 Measures 2 Using scales & Compound measures (speed, 10 ticks L6 P5 p9-12 Sumbooks 3 Calculate amounts such as daily or weekly wages. Calculate rates of pay (including overtime rates) Solve problems involving salaries and pay. Know the formula linking speed, distance and time. 39 Assuming that rates of pay are the same each day or time. Doubling rates of pay instead of multiplying by 1.5, for example. Incomplete calculations, e.g. working weekly pay but forgetting the weekend hours worked. Not remembering the formula. Dividing instead of multiplying, NEW for Examination 2015 AQA GCSE Linear Higher Tier rates of pay, area) Week 40 (Foundation book) p58 Perform calculations involving speed, distance and time. Number 6 FDP Week 40 Number 6 FDP 10 ticks L4 P3 p2742 4 10 ticks L6 P3 p3-12 http://www.workshee tworks.com/math/per cent.html Abacus Sumbooks (Y9 basics) p2910 ticks L6 P3 p1316 Abacus Sumbooks (Y9 basics) p32 Sumbooks (Foundation book) p9-11 10 ticks L6 P3 p1316 Abacus 1 2 3 Change freely between related standard units and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts. Convert metric units of measurement (re-cap) Convert between units of compound measures such as area, rates of pay and speed. Use compound measures such as area, rates of pay and speed. Calculate percentages of amounts. Calculate with percentages in real-life contexts. Calculate percentage increase and decrease. where appropriate. Not checking that measurements are using the same units (e.g. distance in Km but time in metres per hour) Multiplying or dividing by the wrong power of 10. Assuming that area in m2 need to be x100 to convert into cm 2. Forgetting to convert both sets of units, e.g. when converting km per hour into metres per minute. Use decimals as multipliers and to calculate quantities (with or without a calculator) Convert between decimals and percentages. 40 Forgetting to put decimal places back in when performing without calculator. Multiplying or dividing by the wrong power of 10. Not realising that 1/10 = 10/100. Writing 0.1 as 1%, for example. Forgetting to convert into the same Convert between fractions and terminating decimals. Order fractions, decimals and Dividing by the wrong power of 10. Mistaking 0.3 for 3%, for example. Calculating the increase / decrease but forgetting to add it to original amount to get a total. NEW for Examination 2015 AQA GCSE Linear Higher Tier Sumbooks (Y9 basics) p32 Sumbooks (Exercises in Numeracy) p24 Sumbooks (Foundation book) p9-11 10 ticks L5 P2 p3 10 ticks L6 P3 p1316 Abacus Sumbooks (Foundation book) p9-11 percentages. 4 Recognise fractions as multipliers. Calculate fractions of amounts. Compare quantities using fractions, decimals and percentages. 41 type of number before trying to compare. Not spotting that ½ = 0.5, so multiplying by 0.5 is the same as multiplying by ½ Multiplying by the denominator instead of the numerator, and vice versa. Multiplication or division errors made but method correct. NEW for Examination 2015 AQA GCSE Linear Higher Tier Content: Year 11 Learning Objectives: Autumn 1 Date: Week 1 Geometry 13 Surface Area (Cubes, cuboids, other prisms) Resources: Lesson: Geometry 14 Sumbooks Higher worksheet (92-93) page 100-101. (includes parts of circles) L7-8 p 6 p3-11 1 L5 p 6 pg 36 3 Whiteboard maths mensuration 93 4 L5 p 3 pg 31-3 1 2 NOTE: Not cylinders Week 2 To be able to: Calculate the areas of compound shapes. Calculate the surface area of a cube. Calculate the surface area of a cuboid. Calculate the surface area of triangular prisms. Calculate the surface area of other prisms. Convert between metric units of area. Solve problems involving surface area. Apply properties of similarity and congruence when working with area. Calculate the volume of a cube or cuboid. Calculate the volume of a triangular prism. Calculate the volume of other prisms. 42 Common mistakes and misconceptions Outcome Not being able to visualise how to split shapes up into smaller components. Using the incorrect units or measurements. Not accounting for every side of the shape. Forgetting to divide by 2 for triangles, or dividing the area of the whole shape by 2 to get final answers. Not giving answers in the units required. Not being able to rearrange a formula or calculation to find missing measurements. Working with a mixture of units instead of converting them to the same type. Not comparing corresponding sides of shapes to check similar lengths. Confusing volume and surface area. Not splitting shapes up into smaller parts to find cross-sectional area. NEW for Examination 2015 AQA GCSE Linear Higher Tier Volume (Cubes, cuboids, other prisms) Sumbooks Higher worksheet (94) page 102. 2 3 NOTE: Not cylinders Solve problems involving volume and capacity. Convert between units when working with area and volume. Compare lengths, areas and volumes using ratio notation. Make links to similarity (including trigonometric ratios) and scale factors 4 Week 3 1 Number 9 Calculating with Fractions 2 Calculate exactly with fractions, surds and multiples of π 3 calculate exactly with fractions, surds ) and rationalise denominators and multiples of π simplify surd expressions involving squares (e.g. 12 = 4×3 = 4× 3 = 2 3 Writing ratios in the wrong order. Not simplifying ratios. Using linear ratios when they should be squared or cubed. Consolidation Write amounts as one fraction of another (e.g. 2/5 shaded, 3/5 not shaded) Add and subtract fractions with the same denominator. Add and subtract mixed numbers. Write two or more fractions with the same denominator. Add and subtract fractions when one or more denominators need to be changed. Multiply a fraction by a fraction Multiply a fraction by a whole number. Multiply a fraction by a mixed number, or a mixed number by a mixed number. Incorrectly converting a mixed number to an improper fraction. Not converting the final answer back to a mixed number where required. Not multiplying numerator and denominators by the same thing. Multiplying diagonally as though ‘crossmultiplying’ is being done, 2 5 12 e.g. 3 × 6 = 15 Multiplying the numerator and the denominator by the whole number e.g. 4 Divide a whole number or a fraction by a fraction Divide mixed numbers by whole numbers. Find the reciprocal of a whole number, a decimal or a fraction 43 1 20 × 20 = . 4 80 Leaving denominators as decimal numbers. Not simplifying answers when asked to do so. Finding the reciprocal of the wrong NEW for Examination 2015 AQA GCSE Linear Higher Tier fraction, or finding the reciprocal of both fractions. Week 4 L6 p 2 pg 19-21 Identify the scale factor of an enlargement (including fractional / decimal) Enlarge a shape on a grid Enlarge a shape by a fractional scale factor. 1 L7-8 p 4 pg 34-37 Geometry 15 Enlargement L7-8 p 4 pg 34-37 2 L9-10 p 3 pg 3-5 L7-8 p 4 pg 34-37 3 L9-10 p 3 pg 3-5 L9-10 p 3 p6-18 Week 5 4 1 Geometry 16 Vectors 2 3 Enlarge a shape using a centre of enlargement. Enlarge a shape on a coordinate grid, using a centre of enlargement as (0,0) or another coordinate. (as above, including fractional scale factors) Find a centre of enlargement. Describe enlargements fully, giving scale factor and centre. Dividing the measurements of the original by the image, instead of image by original. Inaccurately counting squares. Adding the scale factor instead of multiplying by the scale factor. Not using the centre of enlargement. Not enlarging all sides of the shape by the same scale factor. Using the wrong centre of enlargement. Construct similar or congruent shapes on a coordinate grid using rotation, reflection, translation or enlargement. Understand and describe the effects of enlargement on perimeter, area and volume of shapes. Understand vector notation. Represent column vectors pictorially. Describe vectors using column notation. Apply addition and subtraction of column vectors. Draw the result vector after an addition or subtraction of vectors. Use multiplication of vectors by a scalar. 44 Not joining corresponding corners of shapes. Giving only part of the information required. Assuming that a scale factor of 2 doubles the area of the shape. Not carrying out multiple transformations where required. Writing vectors as coordinates. Mixing up the left right direction with the up / down. Not writing left / down as a negative value. Mistakes made when adding or subtracting with negative numbers. Not drawing the resultant vector to show final answer. Not multiplying both values by the scalar multiple. NEW for Examination 2015 AQA GCSE Linear Higher Tier 4 Week 6 L 7-8 p 1 pg 35 Number & Algebra 2 Sumbook higher 17 1 Direct and Indirect Proportion Sumbook higher 17 2 3 L9-10 p 1 pg 11 4 Use diagrammatic and column representations of vectors. Identify parallel vectors from column vectors or diagrams. Consolidation: Solve simple problems involving vectors. Use vectors to construct geometric arguments and proofs. Know that when y is directly proportional to x, y α x and y = k x Interpret the gradient of a straight line graph as a rate of change. Calculate the constant of proportionality (k) given values for x and y. Write a formula in terms of x and y for direct proportion problems. Know that when y is inversely proportional to x, y α 1/x and y = k/x Calculate the constant of proportionality (k) given values for x and y when they are inversely proportional. Write a formula in terms of x and y for inverse proportion problems. Recognise and sketch graphs of direct and indirect proportion. Construct and interpret equations that describe direct and inverse proportion. Solve problems involving direct and indirect proportion algebraically and graphically. 45 Not sketching the vectors to help identify which ones are parallel. Failing to identify common factors of vectors written in column notation. Mixing up the rules of adding / subtracting or using multiples of vectors. Not understanding that if we travel the wrong way across a vector, it changes it into a negative, for example. Forgetting the formula. Multiplying instead of dividing to find ‘k’. Mixing up the value of x and y when substituting. Not substituting the value of ‘k’ back in to original formula. Using the formula for direct instead of indirect (inverse) proportion. Dividing instead of multiplying to find ‘k’. Not substituting the value of ‘k’ back in to original formula. Confusing graphs of direct and inverse proportion. Not substituting values into equations to check the effect on the shape of the graph. Misinterpreting a problem as direct proportion, when it is inverse. NEW for Examination 2015 AQA GCSE Linear Higher Tier ? ? Week 7 1 Number 10 Percentages & Finance 2 3 4 Week 8 1 interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes. Calculate percentages of amounts. (re-cap) Calculate percentage increase and decrease. (re-cap) Find the original value after a percentage increase or decrease. Solve problems involving percentage increase / decrease or overall percentage change. Calculate using simple interest. Solve problems involving credit. Calculate repeated percentage change. Solve problems involving repeated percentage change / compound interest. Calculate a percentage profit or loss Calculate original values using profit or loss. Number 10 46 Dividing by the wrong power of 10. Forgetting to add on the increase or deduct the decrease. Using the wrong multiplier, i.e. 1.2 for 2% increase. Not understanding that it is possible to have more than 100% when using percentages in context. Assuming that an increase of 30%, then a decrease of 10% is equal to an increase of 20%. Not seeing that 17.5% = 10% + 5% + 2.5%. Forgetting to add on the initial deposit in credit calculations. Incorrectly calculating 1.5 x 2 instead of 1.52. Not checking whether it is a repeated increase or decrease. Writing the profit or loss in a monetary value instead of a final percentage. Dividing by the selling price instead of the original cost price. NEW for Examination 2015 AQA GCSE Linear Higher Tier Percentages & Finance 2 3 4 Week 9 1 Understand the Retail Price Index and its use in real-life context. Interpret changes in the retail price index in terms of the base year (i.e. +5%, -10%, +23%). Interpret and make comparisons in the changes in the value of goods using the Retail Price Index (e.g. price of food has increased by 10%, but this is below the expected increase for that year). Calculate simple price changes using the Retail Price Index (increase or decrease) Calculate base year prices given the relevant price index. Solve more complex problems involving the Retail Price Index. Re-cap: Solve equations with unknowns on both sides. Solve equations involving brackets or fractions. Factorise quadratic expressions. Solve quadratic equations by factorising (including coefficients greater than 1). Algebra 10 Solving Quadratic Equations (recap) 2 3 Complete the square. Solve equations by completing the square. 4 Solve quadratic equations graphically. Solve quadratic equations using the 47 Forgetting that the base year always has an index of 100 (100%) 105 means an increase of 5%, not 105% from the base year. An index less than 100 means a decrease in value. Using the last price in the table to calculate an increase, instead of the base year price. Not understanding when the multiplier should be greater than or less than 1. Using the multiplier as 1.5 rather than 1.05 for an increase of 5%. Misinterpreting the problem. Not showing all stages or working out, or missing stages of working out not believing they are relevant. Errors made when working with negative numbers. Not multiplying all terms in the bracket by the number / term on the outside. Forgetting that x2 is a factor of x3 Forgetting to change the sign around when giving solutions. Not multiplying out brackets to check factorisation has been done correctly. Not halving the coefficient in front of the ‘x’. Incorrectly rearranging. Not writing down both solutions. Forgetting to write the opposite sign when writing the solution, e.g. (x + 1) gives solution of x= -1 not x=1. NEW for Examination 2015 AQA GCSE Linear Higher Tier formula. Week 10 TT L 9 to 10, Pack 4, Page 28. 1 TT L 9 to 10, Pack 4, Page 29. 2 Sumbooks Higher worksheet (10) page 18. TT L 9 to 10, Pack 4, Page 30. TT L 9 to 10, Pack 4, Page 31. 3 Add or subtract algebraic fractions, simplifying answers fully 4 Solve equations involving algebraic fractions. Use basic laws of indices (re-cap) Simplify algebraic fractions Algebra 11 Algebraic Fractions Week 11/12 Week 13 Geometry 17 Pythagoras & Trigonometry Multiply and divide algebraic fractions, simplifying fully Incorrectly substituting in values for a, b and c. Not changing the sign of the ‘b’ value where necessary. Mixing up the multiplication and division laws of indices. Not simplifying fully. Forgetting the rules of multiplying with simple fractions. Not switching the second fraction upside down when dividing. Not making denominators match before trying to add or subtract. Forgetting to simplify answers where possible. Mixing up the rules for adding, subtracting, multiplying and dividing. Revision & MOCK Exams? L7-8 p 2 pg 3 L7-8 p 2 pg 5-7 1 Know and understand Pythagoras’ theorem a2 + b2 = c2 Calculate the length of the hypotenuse of a right-angled triangle. Calculate the length of shorter sides in a right-angled triangle. Use Pythagoras’ Theorem to solve problems in real-life context. 48 Forgetting to take the square root to find the final answer. Not correctly identifying the hypotenuse. Drawing a scale diagram to ‘calculate’ the length of a hypotenuse. Adding instead of subtracting to find the shorter sides. Thinking that square root is not needed when finding shorter sides. Failing to identify whether they are finding the longer or shorter side when problem solving. Students do not sketch out the problem to help them visualise it. NEW for Examination 2015 AQA GCSE Linear Higher Tier 2 TT L7-8 p5 pg 2831. TT L7-8 p 5 pg 33-35. Sumbooks Higher worksheet (101) page 109. 3 Calculate the length of a line segment AB (e.g. on a coordinate grid) using Pythagoras’ Theorem. Calculate lengths in other geometrical figures using Pythagoras’ Theorem. Identify and label sides of triangles in terms of Trigonometric ratios (i.e. opposite, adjacent and hypotenuse) Know and use the trigonometric ratios. (SOHCAHTOA) to find missing lengths. 4 TT L7-8 p 5 pg 36-37. Sumbooks Higher worksheet (102) page 110. Week 14 Sumbooks Higher worksheet (100) page 108. 1 Calculate missing angles inside rightangled triangles using Trigonometry. Solve problems involving trigonometry. Know the formulae for Pythagoras and trigonometry ratios and apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures Solve problems involving Pythagoras and Trigonometry. Geometry 17 2 Use and apply the rules of Pythagoras and Trigonometry in 3D problems. 3 Know the exact values of sinθ and cosθ for θ = 00, 300, 450 , 600 and 900; Know the exact value of tanθ for θ = 00, 300, 450 and 600 Use exact values for sin, cos or tanθ Pythagoras & Trigonometry 49 Pupils do not sketch out the problem to visualise it. Trying to make an accurate drawing and ‘measure’ lengths instead of calculating it. Mixing up the ratios and not following SOHCAHTOA. Using the right-angle as a starting point instead of another given angle. Multiplying instead of dividing where necessary. Using the wrong ratio. Forgetting whether to multiply or divide, dependent upon whether calculating a side or an angle. Trying to apply Pythagoras when there are not enough side lengths given. Using the wrong trigonometric ratio. Not being able to visualise the problem. Pupils do not sketch the problem they are working on to help see what length or angle they are finding. Confusing the values of the different ratios. Not being able to apply the knowledge to the problem in front of them. NEW for Examination 2015 AQA GCSE Linear Higher Tier 1 when solving Trigonometry problems. Recognise, sketch and interpret graphs of trigonometric functions (y=sinx, y=cosx, y=tanx) for angles in any size. Recognise and sketch graphs of quadratic functions. Recognise lines of symmetry in quadratic graphs. Sketch translations and reflections of a given function (eg quadratic functions). 2 4 Week 15 Algebra 11 Quadratic and Other Graphs 3 Interpret and use graphs of quadratic functions in real-life context. Identify and interpret intercepts, turning points and roots of quadratic functions graphically. Deduce roots algebraically and turning points by completing the square. Draw graphs of cubic and reciprocal functions. Sketch and recognise graphs of cubic and reciprocal functions (e.g. y = 1/x with x ≠ 0) Confusing what each graph should look like with another. Moving the parabola across the xaxis instead of up or down the yaxis. Not realising parabolas should be symmetrical. Not considering how wide the curve should be depending on the coefficient, and sketching graphs that look too similar. Not applying context when using quadratic graphs (e.g. not recognising that the turning point is where a ball stops climbing in height and stops moving). 4 Week 16 Statistics 4 1 Interpret graphs of quadratic, cubic and reciprocal functions. Draw and interpret cubic and reciprocal graphs in real-life contexts. Identify types of correlation graphically. Describe the correlation between two data sets (not from a graph) Make predictions about bivariate 50 Confusing what quadratic, cubic or reciprocal graphs should look like. Not plotting a few points to remind themselves of what each type of graph might look like before sketching. Forgetting that 1/x means 1 ÷ x. Misinterpreting the problem. Not thinking about how the change in x- affects the change in y-, and vice versa. Not understanding that correlation does not imply causation between two data sets. Not considering real-life context when considering whether it is a NEW for Examination 2015 AQA GCSE Linear Higher Tier Scatter Graphs & Tree Diagrams 2 3 data. Interpret points on a scatter graph. Identify points that may be classed as outliers. Plot bivariate data as a scatter diagram. Draw estimated lines of best fit. Estimate using a line of best fit. Understand and describe interpolation and extrapolation as a method of estimation. Re-cap: Represent the outcomes of two independent events using a tree diagram. Calculate the probability of two independent events from a tree diagram. Work out the probability of an event that can happen in more than one way using a tree diagram (the AND OR rules). Represent the outcomes of dependent events using a tree diagram (conditional probability) Calculate probabilities of dependent events from a tree diagram. 4 Week 17 Statistics 5 Probability: 10 ticks L7 P1 p712 1 Understand that the greater the number of experimental trials the more reliable the results. Estimate probability from a set of experimental data. Compare estimated probability with theoretical probability (using 51 positive or negative correlation. Plotting as (y, x) instead of (x, y) coordinates. Missing off points as not working systematically. Assuming the line of best fit has to go through (0,0). Not attempting to split the points evenly either side of the line. Not using a suitable scale for each axis. Incorrectly setting up the two events. Adding instead of multiplying across branches. Not simplifying fractions where required. Not recognising when a question involves independent events and so adding rather than multiplying the fractions. Adding across branches, multiplying at the end. Incorrectly stating that the more trials means there is less bias. Not understanding that as it is based on an experiment; the probability can change with each experiment and is therefore only ever an estimate. NEW for Examination 2015 AQA GCSE Linear Higher Tier Experiments and Charts. 10 ticks L7 P1 p11-13 2 Whiteboard maths: Bar charts, pictograms, pie charts, two-way tables. 3 4 Week 18 TT L9-10 P2 p7. 1 TT L9-10 P2 p8. 2 appropriate language and the probability scale). Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size. Calculate relative frequency of an outcome from an experiment. Predict the likely number of successful events of an outcome. Calculate probability of single events from charts (e.g. bar chart, pictograms, pie charts, two way tables). Calculate the probability of two or more events from charts. Calculate probabilities from a set of grouped data (e.g. grouped frequency tables. Know and apply the sine rule to find lengths and angles. Geometry 18 Sine and Cosine Rule (non-rightangled triangles) Know and apply the cosine rule to find lengths and angles. Mixed Sine & Cosine activities: Sumbooks Higher worksheet (103) page 111. TT L9-10 P2 p 52 Comparing theoretical probability with relative frequency without taking into account the number of trials carried out. Incorrectly reading the vertical axis of bar charts Not understanding a grouped frequency table. Labelling up their triangle incorrectly (not naming corresponding angles and sides with the same letter). Not switching the formula around depending on whether you want to find a length or an angle. Using the wrong ratio (e.g. cos instead of sin) Not realising that the cosine rule can also be applied to right-angled triangles. Not sketching out the problem given. Rearranging incorrectly to find alternative lengths or angles. Rounding off calculations before getting to final answers, making it inaccurate. NEW for Examination 2015 AQA GCSE Linear Higher Tier Sumbooks Higher worksheet (104) page 112. Sumbooks Higher worksheet (105) page 113. 3 Know and apply ½ ab sin C to find the area or sides of any triangle. 4 Solve geometrical problems. NOTE: Includes Pythagoras, trigonometry, Sine and Cosine rules, area of triangles. Exam style questions: TT L9-10 P2 p1316. Week 19 Geometry 19 Cylinders, Cones and Spheres. 10 ticks L6 P5 p33-38 10 ticks L9-10 P4 p10-25 (mix of surface area and volume of 3D shapes) Sumbooks (Intermediate book) p62 Abacus 10 ticks L9-10 P4 p10-25 (mix of surface area and volume of 3D shapes) Abacus 1 Calculate the circumference and area of a circle (re-cap). Calculate the volume of a cylinder. Calculate the surface area of a cylinder. Solve problems involving the volume and surface area of cylinders 2 Substituting in values in the wrong places. Rearranging the formula incorrectly. Not being able to identify which method to use to solve a problem (i.e. Pythagoras, Trigonometry, sine or cosine rules). Not sketching out the problem to help visualise it. Forgetting to use inverse sin, cos or tan where necessary. Not showing all stages of working out. Making rounding errors. Forgetting to divide by 2 when the diameter is given and the radius is needed. Multiplying by before squaring. Using the wrong measurement for the radius or diameter. Not being able to identify the measurements they need to use. Calculate the volume of a cone. Calculate the surface area of a cone. 3 Calculate the volume of a frustum. Solve problems involving cones or frustums. NOTE: Ratio or similarity may also be included in these problems. 53 Forgetting to divide by 3 (or x 1/3) when finding volume. Using the vertical or slanted height the wrong way around. Calculating only part of the problem, forgetting to finish it off or show final answers. Using incorrect measurements. Not being able to work backwards or rearrange formulae to find missing NEW for Examination 2015 AQA GCSE Linear Higher Tier Week 20 10 ticks L9-10 P4 p15 4 Calculate the volume of a sphere. Calculate the surface area of a sphere. Solve problems involving spheres. TT Level 7 to 8, Pack 6, Start Page 37. 1 AQA Methods & Applications PDF file, page 212. 2 AQA Methods & Applications PDF file, page 206209. 3 AQA Methods & Applications PDF file, page 218. 4 Sumbooks (Intermediate book) p32-34 10 ticks L7-8 1 Algebra 13 More Real Life Graphs Week 21 Algebra 14 Read and interpret graphs for time series data and know their appropriate use. Calculate averages using time series data. Calculate gradients of linear graphs. Use and interpret gradients of linear graphs. Calculate gradients of non-linear graphs. Estimate gradients of non-linear graphs. Calculate or estimate areas beneath non-linear graphs. Interpret gradients and areas underneath graphs showing real life contexts. Interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts Manipulate linear equations to make variables match. Eliminate one variable in any pair of simultaneous equations. NOTE: Students may have to manipulate 54 measurements. Students often forget to apply the 4/3 of… Multiplying by 3 and dividing by 4. Incorrectly substituting measurements into the formulae. Using a grouped label on the horizontal axis rather than a continuous scale. Misinterpreting positive and negative gradients. Dividing the change in x- by the change in y- axis. Giving answers in the wrong units (m/s) Misreading the scale on the axes. Not splitting up the area under the graph accurately Not splitting up the area of the curve appropriately. Misreading the scales on the axes and therefore making errors. Not interpreting areas as being under or over estimates. Incorrectly adding or subtracting the equations. Making mistakes when using negative numbers. NEW for Examination 2015 AQA GCSE Linear Higher Tier P4 p3-12 10 ticks L7-8 P4 p3-12 2 10 ticks L7-8 P4 p3-12 3 10 ticks L7-8 P4 p3-12 Sumbooks (Higher book) p92 4 Week 22 10 ticks L9-10 P4 p14 1 Geometry 20 Worksheet in resources folder Volume and Surface Area of Pyramids 10 ticks L9-10 P4 p14 Worksheet in resources folder one or both equations. Solve simultaneous linear equations. Simultaneous Equations Solve linear / quadratic simultaneous equations graphically. Solve linear / quadratic equations algebraically. Form pairs of simultaneous equations for a real-life problem. Set up and solve simultaneous linear or quadratic equations to solve problems. Plot graphs of linear or quadratic functions (re-cap) Find approximate solutions to simultaneous equations graphically. Calculate the volume of a pyramid. Solve problems involving the volume of pyramids. 2 Calculate the surface area of pyramids. Solve problems involving the surface area of pyramids. 55 Not multiplying or dividing the entire equation by the same thing. Forgetting to find both solutions. Errors made when substituting, especially with negatives. Accuracy errors when attempting to match variables in equations. Plotting points incorrectly. Misreading scales on axes. Not being able to manipulate equations to solve algebraically. Misinterpreting problems and setting up inappropriate equations. Not considering real-life context when finding solutions, e.g. which would be the best solution for the length of this garden, -7 or +5m? Making mistakes when completing a table of values or substituting. Not joining up points with a ruler and therefore intersection is inaccurate. Not plotting more than 2 points to check a straight line is formed. Using the sloping height instead of vertical height. Not dividing by 3 at the end, of multiplying by 1/3 Not checking the shape of the base, i.e. is it square or triangular? Using the wrong units. Mixing up the formulae for volume and surface area. Not including all sides of the shape. Working in a mixture of units. NEW for Examination 2015 AQA GCSE Linear Higher Tier Sumbooks Higher worksheet (94-95) page 102-103. 3 Calculate volume and surface area of composite solids 10 ticks L9-10 P3 p6-14 4 Use similarity when working with area and volume of 2D or 3D shapes. 1 Week 23 Statistics 6 Sort numerical data into a simple Venn diagram. Solve numerical problems using Venn diagrams or algebraically. Probability: Venn Diagrams 2 3 Not sure where to put this either Understand the term ‘union’ and ‘intersection’ in a Venn diagram. Use set notation to describe areas of a Venn diagram. Shade in areas on a Venn diagram to satisfy given criteria. Calculate probabilities from a Venn diagram. Calculate conditional probabilities using Venn diagrams. Calculate and interpret conditional probabilities through representation using expected frequencies with twoway tables, tree diagrams and Venn diagrams. 56 Not being able to visualise how to split the overall shape into it’s separate components to find volume. Not checking measurements or volumes to help visualise what happens to area / volume when standard lengths change. Forgetting to count items on the outside of the circles. Not counting items that have already been placed. Not understanding that some people in numerical problems are counted twice when they are in the middle of the diagram. Confusing union and intersection. Forgetting which symbol to use, i.e. ‘U’ for union. Shading in the area that isn’t needed, instead of showing the one that is. Forgetting that probabilities should sum to 1. Miscalculating when subtracting probabilities from 1. Writing answers in the wrong form, e.g. a fraction when a decimal is required. Not simplifying answers where necessary. NEW for Examination 2015 AQA GCSE Linear Higher Tier 4 Week 24 Algebra 15 Sumbooks Higher worksheet (56 and 57) page 6465. 1 2 Inequalities: Linear and Quadratic 3 AQA Methods & Applications PDF file, chapter 5.1 page 92. 4 Recognise prime numbers (including two-digit) Write a number as a product of prime factors using index notation Use prime factors to find HCFs and LCMs (using a Venn or otherwise) Solve linear inequalities in one or two variables. Represent solutions on a number line. Solve quadratic inequalities in one variable and represent on a number line. Represent solutions to inequalities (linear or quadratic) using set notation. Represent solutions to linear or quadratic inequalities graphically. Week 25 Revision Week 26 Revision Week 27 Revision 57 Thinking that 1 is a prime number. Failing to recognise that a number is not prime, when finding prime factors Shading in a circle instead of leaving it empty. Misinterpreting inequality symbols. Placing values in the wrong areas of the diagram. Confusing unions with intersections. Shading in the wrong section of the graph, i.e. shading in the bit needed, instead of the part not needed. Only representing part of the solution on the graph, forgetting to show all inequalities to get a final region. NEW for Examination 2015 AQA GCSE Linear Higher Tier Week 28 Revision Week 29 Revision Week 30 Revision Week 31 Revision Week 32 Revision Week 33 Revision Week 34 58 NEW for Examination 2015 AQA GCSE Linear Higher Tier Exam Week? Week 35 Exam Week? Week 36 Week 37 Week 38 Week 39 59