Free-Standing Mathematics Qualification Specification. Foundation Level. For exams June 2012 onwards For certification June 2012 onwards

Free-Standing Mathematics Qualification Specification Foundation Level For exams June 2012 onwards For certification June 2012 onwards

Free-Standing Mathematics Qualification (FSMQ) Foundation Level Money Management 4981 Using Spatial Techniques 4982 Using Data 4983 For exams and certification June 2012 onwards

Our specification is published on our website (http://www.aqa.org.uk). We will let centres know in writing about any changes to the specification. We will also publish changes on our website. The definitive version of our specification will always be the one on our website; this may differ from printed versions. You can get further copies of this specification from: AQA Logistics Centre (Manchester) Unit 2 Wheel Forge Way Ashburton Park Trafford Park Manchester M17 1EH Or, you can download a copy from our website (www.aqa.org.uk) Copyright 2010 AQA and its licensors. All rights reserved. Copyright AQA retains the copyright on all its publications, including the specifications. However, registered centres for AQA are permitted to copy material from this specification booklet for their own internal use. The Assessment and Qualifications Alliance (AQA), is a company limited by guarantee, registered in England and Wales (company number 3644723), and a registered charity (number 1073334). Registered address: AQA Devas Street, Manchester M15 6EX

Contents 4981 Money Management 3 4982 Using Spatial Techniques 21 4983 Using Data 41 1

Free-Standing Mathematics Qualification (FSMQ) Foundation Level Money Management 4981 This specification should be read in conjunction with: Specimen Papers and Mark Schemes 3

Contents 1 Introduction 6 1a Why choose AQA? 6 1b Why choose the Foundation FSMQ in Money Management? 7 1c How do I start using this specification? 7 1d How can I find out more? 8 2 Specification at a Glance 9 3 Subject Content 10 Money Management 4981 10 4 Scheme of Assessment 13 4a Aims and learning outcomes 13 4b Assessment Objectives 13 4c Pre-release data sheets 14 4d National criteria 14 4e Previous learning requirements 14 4f Access to assessment: diversity and inclusion 15 5 Administration 16 5a Availability of assessment units and certification 16 5b Entries 16 5c Private candidates 16 5d Access arrangements, reasonable adjustments and special consideration 16 5e Examination language 17 5f Qualification title 17 5g Awarding Grades and reporting results 17 5h Re-sits and how long unit results remain available to count towards certification 17 Appendices 18 A Spiritual, moral, ethical, social, legislative, sustainable development, economic and cultural issues and health and safety considerations 18 B Overlaps with other qualifications 19 C Wider Key Skills Teaching, developing and providing opportunities for generating evidence 20 5

1 Introduction 1 1a Why choose AQA? We are the United Kingdom s favourite exam board and more students get their academic qualifications from us than from any other board. But why are we so popular? We understand the different requirements of each subject by working with teachers. Our qualifications help students achieve their full potential are relevant for today s challenges are manageable for schools and colleges are easy to understand by students of all levels of ability lead to accurate results, delivered on time are affordable and give value for money. We provide a wide range of support services for teachers, including: access to subject departments training for teachers, including practical teaching strategies and methods that work, presented by senior examiners 24-hour support through our website and online with Ask AQA past question papers and mark schemes a wide range of printed and electronic resources for teachers and students free online results analysis, with Enhanced Results Analysis. We are an educational charity focused on the needs of the learner. All our income is spent on improving the quality of our specifications, examinations and support services. We don t aim to profit from education; we want you to. If you are already a customer we thank you for your support. If you are thinking of joining us we look forward to welcoming you. 6

1b Why choose the Foundation Free-Standing Mathematics Qualification (FSMQ) in Money Management? Each Free-Standing Mathematics Qualification (FSMQ) has been designed to encourage students to apply mathematical principles in their studies, work or interests. Foundation FSMQs provide a fresh start for students who have previously been less than successful in the mathematics classroom. FSMQs at all levels strive to be both practical and relevant to the real world, training students not only in mathematical skills but also in problem solving and modelling. It has been demonstrated that students studying mathematics within the context of money and finance are more motivated at this level. The Foundation FSMQ in Money Management will allow students to become competent in number work, the use of basic formulae and algebraic representation and the use of statistical diagrams and graphs of data pairs, while working within the context of money. This qualification will appeal particularly to those involved with courses of a vocational nature where calculating costs is an important element, eg those based in the areas of business or finance. All FSMQs feature pre-release data sheets, ensuring students are familiar with and understand contexts and vocabulary in advance of the examination. FSMQs have assessed mathematics in context since 1999. This FSMQ benefits from the experience gained through these established qualifications. This specification has evolved from the successful Mathematics Pathways project, where pilot FSMQs were used as components of the pilot GCSE Use of Mathematics. Following this pilot we have extended the range of both Higher FSMQs and Foundation FSMQs, providing parity of opportunity with GCSE tiers. Students can use this Foundation FSMQ as the first step towards achieving the AQA Certificate in Use of Mathematics, which requires two FSMQs plus a Core unit. The AQA Certificate in Use of Mathematics is equivalent in standard to GCSE Mathematics. 1 1c How do I start using this specification? You need to register at www.aqa.org.uk/ askaqa.php to ensure that you receive regular updates and have access to mark schemes, past question papers, a whole range of teacher support materials and receive details of teacher support meetings. Once you have decided to enter candidates you need to tell us so we can make sure that you get all the material you need for the examinations. This is very important as prerelease material is sent to you before the final entry deadline. You can let us know by filling in the appropriate Intention to Enter and Estimated Entry forms. If your centre is registered on e-aqa you will receive an email prompting you to submit entry information online. If you are not e-aqa registered we will send copies to your exams officer. Both forms can be downloaded from our website (www.aqa.org.uk/admin/p_entries.php). If your centre has not used AQA for any examinations in the past, please contact our centre approval team at centreapproval@ aqa.org.uk. 7

1 1d How can I find out more? You can choose to find out more about this specification or the services that AQA offer in a number of ways. Ask AQA You have 24-hour access to useful information and answers to the most commonly asked questions at www.aqa.org.uk/askaqa.php. If the answer to your question is not available, you can submit a query through Ask AQA for our team. We will respond within 2 working days. Speak to your subject team You can talk directly to the Mathematics subject team about this specification either by emailing mathematics-gce@aqa.org.uk or by calling 01483 477752. Teacher Support Meetings Details of the full range of our Teacher Support meetings are available on our website at www.aqa.org.uk/support/teachers.php. There is also a link to our fast and convenient online booking system for Teacher Support meetings at events.aqa.org.uk/ebooking. If you need to contact the Teacher Support team, you can call us on 01483 477860 or e-mail us at teachersupport@aqa.org.uk. Latest information online You can find out more including the latest news, how to register to use Enhanced Results Analysis, support and downloadable resources on our website at www.aqa.org.uk 8

2 Specification at a Glance 60 GLH (guided learning hours) Free-Standing Mathematics Qualification Foundation Level Money Management One written paper with pre-release data sheet Externally assessed 1 hour 40 marks 2 Calculator allowed Level of demand All Foundation FSMQ units are graded A to E and are set at the level of demand of GCSE grades C to G. 9

3 Subject Content Foundation FSMQ: Money Management There are no specific requirements for this qualification in respect of prior learning. What you need to learn Using calculators and computers A basic calculator with a memory facility will be sufficient for you to use with this qualification. However, any calculator may be used in this qualification provided that it conforms with JCQ Regulations. You should learn to use your calculator effectively and efficiently. Whenever you use a calculator you should record your working as well as the result. It is important that you are also able to carry out simple calculations without using a calculator. 3 You should learn how to use a spreadsheet. You should learn to use a This includes: spreadsheet to: draw tables and record data formatting column widths so as to input headings and data formatting cells, when necessary, so that data is expressed correctly record processed data in tables record financial transactions carry out calculations draw charts and diagrams using columns to record details of transactions credits debits running totals using spreadsheet formulae such as =E3+C4+D4 to calculate a running total in cell E4 using the fill down facility pie charts bar charts line graphs (using scatter graph facilities) Reading, recording You should learn to: This includes: and classifying financial transactions read and use information given in tables use tables to record financial transactions by hand by spreadsheet using separate columns to record credits, debits and running total using negative numbers for debits, debts and negative credit 10

timetables classify transactions of one type (for example debits) into different categories (for example spending on leisure, travel, food, etc.) Reading and using timetables given in 24 and 12 hour clock finding the length of time of a journey using tally charts Carrying out You should learn to: This includes: calculations understand and use decimal notation the usual notations for money carry out calculations based on credits and debits to calculate a current balance carry out calculations involving the addition, subtraction, multiplication and division of money express one quantity as a fraction of another (for example total spent on travel as a fraction of all debits) express one quantity as a percentage of another express two or three quantities as a ratio by hand with a calculator by spreadsheet using spreadsheet formulae such as =E3+C4+D4 debits and debts expressed as negative numbers as a decimal reducing to simplest form reducing to simplest form 3 divide a quantity in a given ratio for example dividing 50 in the ratio 2 :3 :5 convert between fractions, decimals and percentages knowing common equivalencies: 1 2 1 4 1 3 1 10 1 5 = 0.5 = 50% = 0.25 = 25% 1 3 = 0.3 = 33 % = 0.1 = 10% = 0.2 = 20% and multiples of these. use decimals and percentages to make comparisons use ratios to make comparisons putting decimals and percentages in order of size finding best buys two or three values that are being compared 11

carry out calculations that involve working without a calculator for fractions finding fractions or percentages of involving a whole-number denominator quantities (for example finding 15% less than or equal to 10 1 of 250, 25% of 400, of 12.80) 4 exchange rates calculate prices using exchange rates 3 calculate increases and decreases given a starting value and the percentage rate (for example when 250 is increased by 10% the increase is 25) calculate new values given a starting value and a rate of percentage increase or decrease calculate (simple) interest over a single time period calculate interest which is compounded over at least two time periods use of multi-stage calculations only rather than using formulae Accuracy, estimating You should learn to: This includes: and checking round values of money to the most appropriate value (for example the nearest penny, pound or 100) check calculations using inverse operations check calculations using estimates by hand and mentally by hand and mentally check calculations by using another method (for example reaching a total in two different ways) Displaying information You should learn to: This includes: use tables to display data you have found and explain the results of your work use and draw charts to show financial data draw line graphs to show how a quantity (for example current balance) varies with time using tally charts pictograms, pie charts and bar charts drawn by hand and spreadsheet by hand by spreadsheet 12

4 Scheme of Assessment 4a Aims and learning outcomes Free-Standing Mathematics Qualifications aim to promote: the development of a mathematics curriculum that is integrated with other areas of learners studies, work or interests the development of skills that enable learners to communicate, use and interpret their mathematics the development of learners confidence in, together with a positive attitude towards, using mathematics the recognition of mathematics as a useful tool in other areas of study, the world of work and society in general The Free-Standing Mathematics Qualification in Money Management should enable learners to: develop knowledge, skills and understanding of mathematical methods and concepts develop mathematical reasoning skills acquire the ability to solve open-ended problems develop and use mathematics as a model of reality and have an awareness of any limitations this may introduce into their analysis of a situation recognise when it is appropriate to use ICT, such as calculators and computer spreadsheets, and when it is appropriate to use pencil and paper methods solve substantial and realistic problems encountered by adults communicate clearly, using logical reasoning and appropriate notation interpret what their mathematics tells them about the situation they are analysing or the problem they are solving, using this information to summarise and draw conclusions work independently and follow their own line of enquiry 4 4b Assessment Objectives (AOs) The Assessment Objectives are common to both Foundation and Higher FSMQs and to the AQA Certificate in Use of Mathematics. The assessment units will assess the following objectives in the contexts of the content and skills set out in Section 3 (Subject Content). The assessment units will assess a candidate s ability to: AO1 AO2 AO3 recall, select and use mathematics appropriate to the situation, giving solutions to an appropriate degree of accuracy select and apply mathematical methods in a range of situations analyse problems and demonstrate strategies for solving them. Summarise and draw conclusions. 13

Weighting of Assessment Objectives for Foundation FSMQ in Money Management The table below shows the approximate weighting of each of the Assessment Objectives (AOs) in the Foundation FSMQ in Money Management. Assessment Objectives Overall weighting of AOs (%) AO1 55 65 AO2 15 25 AO3 10 20 Overall weighting (%) 100 Quality of Written Communication (QWC) This specification does not formally assess the quality of written communication. 4c Pre-release data sheets 4 Data sheets should be opened and issued to candidates between 1 and 3 weeks before the examination. Candidates will be able to work with their teachers in familiarising themselves with the contexts, clarifying any specialised vocabulary and considering the possible mathematics in the situations presented. Teachers will need to provide reasonable class time for this to happen. This should be at least one lesson, but there is no upper limit on the time candidates may spend considering the data sheets (provided they remain sealed until the date for release printed on the packet label). The pre-release data sheets may not be taken in to the examination room. A clean copy of the data sheet will be issued to all candidates at the start of the examination. This sheet will not be collected in and marked, so candidates should ensure that all working is presented in the question paper/answer book. 4d National criteria This specification complies with: the Arrangements for the Statutory Regulation of External Qualifications in England, Wales and Northern Ireland: Common Criteria the requirements for qualifications to provide access to Levels 1 and 2 of the National Qualification Framework. 4e Previous learning requirements There are no previous learning requirements for the Foundation FSMQ in Money Management. Any requirements set for entry to a course based on this specification are at your centre s discretion. 14

4f Access to assessment: diversity and inclusion Level 1 and 2 qualifications such as this FSMQ often need to assess a wide range of competences. This is because they are designed to prepare candidates for a wide range of occupations and further study. Assessments are reviewed to see whether any of the skills or knowledge needed present a possible difficulty to any candidates, whatever their ethnic background, religion, sex, age, disability or sexuality. If there are difficulties, the assessment is reviewed again to make sure that such tests of specific competences are only included if they are important to the subject. Arrangements are made for candidates with special needs to help them access the assessments as long as the competences being tested are not changed. Because of this, most candidates will be able to access any part of the assessment. More details are given in Section 5d. 4 15

5 Administration 5a Availability of assessment units and certification Examinations and certification for this specification are available as follows. June 2012 Foundation FSMQ Money Management 5b Entries Please check the current version of Entry Procedures and Codes for up-to-date entry procedures. You should use the following entry code for this qualification: Foundation FSMQ Money Management 4981 5c Private candidates This specification is available to private candidates. Private candidates should write to us for a copy of Supplementary Guidance for Private Candidates. 5 5d Access arrangements, reasonable adjustments and special consideration We have taken note of the equality and discrimination legislation and the interests of minority groups in developing and administering this specification. We follow the guidelines in the Joint Council for Qualifications (JCQ) document: Access Arrangements, Reasonable Adjustments and Special Consideration: General and Vocational Qualifications. This is published on the JCQ website (www.jcq.org.uk) or you can follow the link from our website (www.aqa.org.uk). Access arrangements We can arrange for candidates with special needs to access an assessment. These arrangements must be made before the examination. For example, we can produce a Braille paper for a candidate with sight problems. Reasonable adjustments An access arrangement which meets the needs of a particular disabled candidate would be a reasonable adjustment for that candidate. For example a Braille paper would be a reasonable adjustment for a Braille reader but not for a candidate who did not read Braille. The Disability Discrimination Act requires us to make reasonable adjustments to remove or lessen any disadvantage affecting a disabled candidate. Special consideration We can give special consideration to candidates who have had a temporary illness, injury or serious problem such as death of a relative, at the time of the examination. We can only do this after the examination. The Examinations Officer at the centre should apply online for access arrangements and special consideration by following the eaqa link from our website (www.aqa.org.uk). 16

5e Examination language We will only provide units for this specification in English. 5f Qualification title The qualification based on this specification is: AQA Foundation FSMQ in Money Management 5g Awarding grades and reporting results All Foundation FSMQs will be graded on a five-grade scale: A, B, C, D and E. Candidates who fail to reach the minimum standard for grade E in any Foundation FSMQ will be recorded as U (unclassified) and will not receive the FSMQ certificate. We will publish the minimum raw mark for each grade for this FSMQ when we issue candidates results. Because a Foundation FSMQ may form part of the AQA Certificate in Use of Mathematics we will also report candidates FSMQ results to centres in terms of uniform marks and grades. For each Foundation FSMQ, the uniform mark corresponds to a grade as follows: Foundation FSMQ Maximum Uniform Mark = 69 Grade Uniform Mark Range A 60 69 B 50 59 C 40 49 D 30 39 E 20 29 U 0 19 We calculate a candidate s uniform mark for a unit using the grade boundaries set by the Awarding Committee. For example, a candidate who achieves the minimum raw mark required for grade C in the Foundation FSMQ in Money Management receives a uniform mark of 40. A uniform mark for this FSMQ may be combined with a uniform mark from one other FSMQ (together with a non-certificated Core unit) and may be used towards the AQA Certificate in Use of Mathematics. Information regarding allowed combinations can be found in the specification for the AQA Certificate in Use of Mathematics. 5 5h Re-sits and how long unit results remain available to count towards certification Candidates may re-sit any FSMQ as many times as they want to. Candidates grades are based on the work they submit for assessment. Foundation FSMQ results remain available to count towards certification of the AQA Certificate in Use of Mathematics within the shelf life of that specification, whether or not they have already been used. 17

Appendices A Spiritual, moral, ethical, social, legislative, sustainable development, economic and cultural issues, and health and safety considerations We have taken great care to make sure that any wider issues (for example, spiritual, moral, ethical, social, legal, sustainable development, economic and cultural issues), including those relevant to the education of students at Key Stage 4, have been taken into account when preparing this specification. They will only form part of the assessment requirements where they are relevant to the specific content of the specification and have been identified in Section 3: Content. European Dimension We have taken the 1988 Resolution of the Council of the European Community into account when preparing this specification and associated specimen units. Environmental Education We have taken the 1988 Resolution of the Council of the European Community and the Report Environmental Responsibility: An Agenda for Further and Higher Education 1993 into account when preparing this specification and associated specimen units. Avoiding bias We have taken great care to avoid bias of any kind when preparing this specification and specimen units. A 18

B Overlaps with other qualifications Summary of structural changes from legacy FSMQ Foundation and previous pilot specifications This specification Legacy FSMQ Pathways pilot assessment (1999 2011) specification (2008 2011) Foundation FSMQ Foundation FSMQ Foundation FSMQ Spans GCSE grades C to G Spanned GCSE grades D to G Spanned GCSE grades D to G No portfolio work 50% portfolio work 50% portfolio work Graded A to E Graded A to E Graded A to E Overlap with legacy Foundation FSMQ in Managing Money This specification Legacy FSMQ assessment on which it is based FSMQ: Money Management 6981 Timetables added Exchange Rates added B 19

C Wider Key Skills Teaching, developing and providing opportunities for generating evidence Introduction The Key Skills Qualification requires candidates to demonstrate levels of achievement in the Key Skills of Communication, Application of Number and Information and Communication Technology. The Wider Key Skills of Improving own Learning and Performance, Working with Others and Problem Solving are also available. The acquisition and demonstration of ability in these wider Key Skills is deemed highly desirable for all candidates. The units for each key skill comprise three sections: What you need to know What you must do Guidance. Candidates following a course of study based on this specification for Foundation FSMQ in Money Management can be offered opportunities to develop and generate evidence of attainment in aspects of the Key Skills of: Communication Application of Number Information and Communication Technology Working with Others Improving own Learning and Performance Problem Solving. Areas of study and learning that can be used to encourage the acquisition and use of Key Skills, and to provide opportunities to generate evidence for Part B of units, are provided in the Teachers Resource Bank for this specification. The above information is given in the context of the knowledge that Key Skills at levels 1 and 2 will be available until 2010 with last certification in 2012. Key Skills Qualifications of Communication, Application of Number and Information and Communication Technology will be phased out and replaced by Functional Skills qualifications in English, Mathematics and ICT from September 2010 onwards. For further information see the AQA website: http://web.aqa.org.uk/qual/keyskills/ com04.php C 20

Free-Standing Mathematics Qualification (FSMQ) Foundation Level Using Spatial Techniques 4982 This specification should be read in conjunction with: Specimen Papers and Mark Schemes 21

Contents 1 Introduction 24 1a Why choose AQA? 24 1b Why choose the Foundation FSMQ in Using Spatial Techniques? 25 1c How do I start using this specification? 25 1d How can I find out more? 26 2 Specification at a Glance 27 3 Subject Content 28 Using Spatial Techniques 4982 28 4 Scheme of Assessment 32 4a Aims and learning outcomes 32 4b Assessment Objectives 32 4c Pre-release data sheets 33 4d National criteria 33 4e Previous learning requirements 33 4f Access to assessment: diversity and inclusion 34 5 Administration 35 5a Availability of assessment units and certification 35 5b Entries 35 5c Private candidates 35 5d Access arrangements, reasonable adjustments and special consideration 35 5e Examination language 36 5f Qualification title 36 5g Awarding Grades and reporting results 36 5h Re-sits and how long unit results remain available to count towards certification 36 Appendices 37 A Spiritual, moral, ethical, social, legislative, sustainable development, economic and cultural issues and health and safety considerations 37 B Overlaps with other qualifications 38 C Wider Key Skills Teaching, developing and providing opportunities for generating evidence 39 23

1b Why choose the Foundation Free-Standing Mathematics Qualification (FSMQ) in Using Spatial Techniques? Each Free-Standing Mathematics Qualification (FSMQ) has been designed to encourage students to apply mathematical principles in their studies, work or interests. Foundation FSMQs provide a fresh start for students who have previously been less than successful in the mathematics classroom. FSMQs at all levels strive to be both practical and relevant to the real world, training students not only in mathematical skills but also in problem solving and modelling. The Foundation FSMQ in Using Spatial Techniques will allow students to become competent in the use and production of detailed plans and drawings, basic construction techniques, the solution of spatial problems and the understanding and use of geometrical and associated terminology. This qualification will appeal particularly to those involved with courses in various areas of technology, including many branches of engineering, and to those involved with courses in areas of art and design. All FSMQs feature pre-release data sheets, ensuring students are familiar with and understand contexts and vocabulary in advance of the examination. FSMQs have assessed mathematics in context since 1999. This FSMQ benefits from the experience gained through these established qualifications. This specification has evolved from the successful Mathematics Pathways project, where pilot FSMQs were used as components of the pilot GCSE Use of Mathematics. Following this pilot we have extended the range of both Higher FSMQs and Foundation FSMQs, providing parity of opportunity with GCSE tiers. Students can use this Foundation FSMQ as the first step towards achieving the AQA Certificate in Use of Mathematics, which requires two FSMQs plus a Core unit. The AQA Certificate in Use of Mathematics is equivalent in standard to GCSE Mathematics. 1 1c How do I start using this specification? You need to register at www.aqa.org.uk/ askaqa.php to ensure that you receive regular updates and have access to mark schemes, past question papers, a whole range of teacher support materials and receive details of teacher support meetings. Once you have decided to enter candidates you need to tell us so we can make sure that you get all the material you need for the examinations. This is very important as prerelease material is sent to you before the final entry deadline. You can let us know by filling in the appropriate Intention to Enter and Estimated Entry forms. If your centre is registered on e-aqa you will receive an email prompting you to submit entry information online. If you are not e-aqa registered we will send copies to your exams officer. Both forms can be downloaded from our website (www.aqa.org.uk/admin/p_entries.php). If your centre has not used AQA for any examinations in the past, please contact our centre approval team at centreapproval@ aqa.org.uk. 25

2 Specification at a Glance 60 GLH (guided learning hours) Free-Standing Mathematics Qualification Foundation Level Using Spatial Techniques One written paper with pre-release data sheet Externally assessed 1 hour 40 marks 2 Calculator allowed Level of demand All Foundation FSMQ units are graded A to E and are set at the level of demand of GCSE grades C to G. 27

3 Subject Content Foundation FSMQ: Using Spatial Techniques There are no specific requirements for this qualification in respect of prior learning. What you need to learn Using calculators and computers A basic calculator with a memory facility will be sufficient for you to use with this qualification. However, any calculator may be used in this qualification provided that it conforms with JCQ Regulations. You should learn to use your calculator effectively and efficiently. Whenever you use a calculator you should record your working as well as the result. It is important that you are also able to carry out simple calculations without using a calculator. 3 You are encouraged to use available computer software when developing some drawings and plans. Reading and recording You should learn to: This includes: measurements select the appropriate instrument to for lengths selecting from make measurements of lengths ruler and angles tape measure micrometer use a ruler, tape measure, micrometer protractor to make measurements to the nearest whole unit an appropriate level of accuracy use and understand metric and common imperial measurements of length angle use and understand metric measurements of area reading to the nearest whole unit selected as appropriate for example to the nearest centimetre if appropriate even if the scale allows you to measure in millimetres length mm cm m km inches feet yards miles angle degrees area mm 2 cm 2 m 2 28

use of commonly used prefixes for units in the metric system for example centi-, milli-, kilo- volume use the most appropriate units for measurements record measurements on diagrams or in tables as appropriate volume mm 3 cm 3 m 3 use of correct notation giving both magnitude and units associated with measurements Carrying out You should learn to: This includes: calculations with measurements convert measurements within the metric system a system of measurement imperial system use of correct prefixes in the metric system conversion using scale factors 3 decide on the correct arithmetic (addition, subtraction, multiplication, division) to use with measurements in problems problems involving more than one stage carry out calculations with for lengths measurements you have found adding and subtracting lengths multiplying and dividing a length by a number for angles: adding and subtracting angles multiplying and dividing an angle by a number carry out calculations involving scaling from real to scaled situation (either drawing or model) from scaled (either drawing or model) to real situation with scaling represented in the forms 1: n 1 to n 1 n where n is 2, 5, 10, 50, 100, 500 or 1000 (or other common scaling used in your area of work) use measurements of length understanding circumference of a to calculate circle as perimeter perimeters finding circumferences of circles using areas the formula surface areas circumference = π diameter volume using the π button on your calculator giving values in correct units or the approximate value π = 3.14 (to 2 decimal places) 29

3 finding areas of rectangles triangles shapes formed by combinations of at most two rectangles or triangles or one of each using formula for area of rectangles: area = length width using formula for area of triangles area = (base perpendicular height) 1 2 finding the area enclosed by a circle using the formula area = π radius 2 finding surface areas and volumes of cuboids triangular prisms cylinders using formula for volume of cuboids, prisms, cylinders volume = area of cross-section length Working with You should learn to: This includes: drawings and plans use plans and elevations to visualise appreciation and use of simple scales, simple situations 1:n where n is 2, 5, 10, 50, 100, 500 or 1000 (or other common scaling used in your area of work) understanding that scaling alters lengths but not angles draw appreciation and use of simple scales, plans 1:n elevations where n is 2, 5, 10, 50, 100, 500 or of simple 2- and 3-dimensional 1000 (or other common scaling used situations in your area of work) understanding that scaling alters lengths but not angles Drawing with You should learn to: This includes: instruments use rulers, set squares, protractors rectangles (including squares) to draw plane shapes accurately triangles use a pair of compasses to draw circles accurately use a straight edge and a pair of compasses to construct accurately a line that is perpendicular to a given line, through a given point the mid-point of a line segment the perpendicular bisector of a line segment a regular hexagon inscribed in a circle 30

an equilateral triangle inscribed in a circle the bisector of an angle. Using geometrical You should learn to: This includes: terms and ideas use correctly the geometrical terms parallel perpendicular right angle bisect mid-point line segment line regular polygon pentagon hexagon octagon prism chord radius congruent 3 know and use the angle sums at a point at a point on a straight line of quadrilaterals of triangles recognise and classify plane symmetry recognise and classify plane shapes lines of symmetry rotational symmetry including the idea of centre and order quadrilaterals (including rectangle, square, parallelogram, rhombus, trapezium, kite) triangles (including obtuse-angled, acuteangled, right-angled) (including equilateral, isosceles, scalene) understanding of properties (limited to equal sides and angles) associated with regular polygons Accuracy, estimating You should learn to: This includes: and checking check your calculations using carrying out estimation calculations on estimation techniques paper check your calculations using inverse operations 31

4 Scheme of Assessment 4a Aims and learning outcomes 4 Free-Standing Mathematics Qualifications aim to promote: the development of a mathematics curriculum that is integrated with other areas of learners studies, work or interests the development of skills that enable learners to communicate, use and interpret their mathematics the development of learners confidence in, together with a positive attitude towards, using mathematics the recognition of mathematics as a useful tool in other areas of study, the world of work and society in general The Free-Standing Mathematics Qualification in Using Spatial Techniques should enable learners to: develop knowledge, skills and understanding of mathematical methods and concepts develop mathematical reasoning skills acquire the ability to solve open-ended problems develop and use mathematics as a model of reality and have an awareness of any limitations this may introduce into their analysis of a situation recognise when it is appropriate to use ICT, such as calculators and interactive geometry software, and when it is appropriate to use pencil and paper methods solve substantial and realistic problems encountered by adults communicate clearly, using logical reasoning and appropriate notation interpret what their mathematics tells them about the situation they are analysing or the problem they are solving, using this information to summarise and draw conclusions work independently and follow their own line of enquiry 4b Assessment Objectives (AOs) The Assessment Objectives are common to both Foundation and Higher FSMQs and to the AQA Certificate in Use of Mathematics. The assessment units will assess the following objectives in the contexts of the content and skills set out in Section 3 (Subject Content). The assessment units will assess a candidate s ability to: AO1 AO2 AO3 recall, select and use mathematics appropriate to the situation, giving solutions to an appropriate degree of accuracy select and apply mathematical methods in a range of situations analyse problems and demonstrate strategies for solving them. Summarise and draw conclusions. 32

Weighting of Assessment Objectives for Foundation FSMQ in Using Spatial Techniques The table below shows the approximate weighting of each of the Assessment Objectives (AOs) in the Foundation FSMQ in Using Spatial Techniques. Assessment Objectives Overall weighting of AOs (%) AO1 55 65 AO2 15 25 AO3 10 20 Overall weighting (%) 100 Quality of Written Communication (QWC) This specification does not formally assess the quality of written communication. 4c Pre-release data sheets Data sheets should be opened and issued to candidates between 1 and 3 weeks before the examination. Candidates will be able to work with their teachers in familiarising themselves with the contexts, clarifying any specialised vocabulary and considering the possible mathematics in the situations presented. Teachers will need to provide reasonable class time for this to happen. This should be at least one lesson, but there is no upper limit on the time candidates may spend considering the data sheets (provided they remain sealed until the date for release printed on the packet label). The pre-release data sheets may not be taken in to the examination room. A clean copy of the data sheet will be issued to all candidates at the start of the examination. This sheet will not be collected in and marked, so candidates should ensure that all working is presented in the question paper/answer book. 4 4d National criteria This specification complies with: the Arrangements for the Statutory Regulation of External Qualifications in England, Wales and Northern Ireland: Common Criteria the requirements for qualifications to provide access to Levels 1 and 2 of the National Qualification Framework. 4e Previous learning requirements There are no previous learning requirements for the Foundation FSMQ in Using Spatial Techniques. Any requirements set for entry to a course based on this specification are at your centre s discretion. 33

5 Administration 5a Availability of assessment units and certification Examinations and certification for this specification are available as follows. June 2012 Foundation FSMQ Using Spatial Techniques 5b Entries Please check the current version of Entry Procedures and Codes for up-to-date entry procedures. You should use the following entry code for this qualification: Foundation FSMQ Using Spatial Techniques 4982 5c Private candidates This specification is available to private candidates. Private candidates should write to us for a copy of Supplementary Guidance for Private Candidates. 5d Access arrangements, reasonable adjustments and special consideration We have taken note of the equality and discrimination legislation and the interests of minority groups in developing and administering this specification. We follow the guidelines in the Joint Council for Qualifications (JCQ) document: Access Arrangements, Reasonable Adjustments and Special Consideration: General and Vocational Qualifications. This is published on the JCQ website (www.jcq.org.uk) or you can follow the link from our website (www.aqa.org.uk). Reasonable adjustments An access arrangement which meets the needs of a particular disabled candidate would be a reasonable adjustment for that candidate. For example a Braille paper would be a reasonable adjustment for a Braille reader but not for a candidate who did not read Braille. The Disability Discrimination Act requires us to make reasonable adjustments to remove or lessen any disadvantage affecting a disabled candidate. 5 Access arrangements We can arrange for candidates with special needs to access an assessment. These arrangements must be made before the examination. For example, we can produce a Braille paper for a candidate with sight problems. Special consideration We can give special consideration to candidates who have had a temporary illness, injury or serious problem such as death of a relative, at the time of the examination. We can only do this after the examination. The Examinations Officer at the centre should apply online for access arrangements and special consideration by following the eaqa link from our website (www.aqa.org.uk). 35

5e Examination language We will only provide units for this specification in English. 5f Qualification title The qualification based on this specification is: AQA Foundation FSMQ in Using Spatial Techniques 5g Awarding grades and reporting results 5 All Foundation FSMQs will be graded on a five-grade scale: A, B, C, D and E. Candidates who fail to reach the minimum standard for grade E in any Foundation FSMQ will be recorded as U (unclassified) and will not receive the FSMQ certificate. We will publish the minimum raw mark for each grade for this FSMQ when we issue candidates results. Because a Foundation FSMQ may form part of the AQA Certificate in Use of Mathematics we will also report candidates FSMQ results to centres in terms of uniform marks and grades. For each Foundation FSMQ, the uniform mark corresponds to a grade as follows: Foundation FSMQ Maximum Uniform Mark = 69 Grade Uniform Mark Range A 60 69 B 50 59 C 40 49 D 30 39 E 20 29 U 0 19 We calculate a candidate s uniform mark for a unit using the grade boundaries set by the Awarding Committee. For example, a candidate who achieves the minimum raw mark required for grade C in the Foundation FSMQ in Using Spatial Techniques receives a uniform mark of 40. A uniform mark for this FSMQ may be combined with a uniform mark from one other FSMQ (together with a non-certificated Core unit) and may be used towards the AQA Certificate in Use of Mathematics. Information regarding allowed combinations can be found in the specification for the AQA Certificate in Use of Mathematics. 5h Re-sits and how long unit results remain available to count towards certification Candidates may re-sit any FSMQ as many times as they want to. Candidates grades are based on the work they submit for assessment. Foundation FSMQ results remain available to count towards certification of the AQA Certificate in Use of Mathematics within the shelf life of that specification, whether or not they have already been used. 36

B Overlaps with other qualifications Summary of structural changes from legacy FSMQ Foundation and previous pilot specifications This specification Legacy FSMQ Pathways pilot assessment (1999 2011) specification (2008 2011) Foundation FSMQ Foundation FSMQ Foundation FSMQ Spans GCSE grades C to G Spanned GCSE grades D to G Spanned GCSE grades D to G No portfolio work 50% portfolio work 50% portfolio work Graded A to E Graded A to E Graded A to E Overlap with legacy Foundation FSMQ in Working in 2 and 3 Dimensions This specification Legacy FSMQ assessment on which it is based FSMQ: Using Spatial Techniques 6982 Measurement systems other than metric and imperial deleted Terms chord, radius and congruent added Added: Use a straight edge and a pair of compasses to construct accurately the bisector of an angle B 38

C Wider Key Skills Teaching, developing and providing opportunities for generating evidence Introduction The Key Skills Qualification requires candidates to demonstrate levels of achievement in the Key Skills of Communication, Application of Number and Information and Communication Technology. The Wider Key Skills of Improving own Learning and Performance, Working with Others and Problem Solving are also available. The acquisition and demonstration of ability in these wider Key Skills is deemed highly desirable for all candidates. The units for each key skill comprise three sections: What you need to know What you must do Guidance. Candidates following a course of study based on this specification for Foundation FSMQ in Using Spatial Techniques can be offered opportunities to develop and generate evidence of attainment in aspects of the Key Skills of: Communication Application of Number Information and Communication Technology Working with Others Improving own Learning and Performance Problem Solving. Areas of study and learning that can be used to encourage the acquisition and use of Key Skills, and to provide opportunities to generate evidence for Part B of units, are provided in the Teachers Resource Bank for this specification. The above information is given in the context of the knowledge that Key Skills at levels 1 and 2 will be available until 2010 with last certification in 2012. Key Skills Qualifications of Communication, Application of Number and Information and Communication Technology will be phased out and replaced by Functional Skills qualifications in English, Mathematics and ICT from September 2010 onwards. For further information see the AQA website: http://web.aqa.org.uk/qual/keyskills/ com04.php C 39

Free-Standing Mathematics Qualification (FSMQ) Foundation Level Using Data 4983 This specification should be read in conjunction with: Specimen Papers and Mark Schemes 41

Contents 1 Introduction 44 1a Why choose AQA? 44 1b Why choose the Foundation FSMQ in Using Data? 45 1c How do I start using this specification? 45 1d How can I find out more? 46 2 Specification at a Glance 47 3 Subject Content 48 Using Data 4983 48 4 Scheme of Assessment 52 4a Aims and learning outcomes 52 4b Assessment Objectives 52 4c Pre-release data sheets 53 4d National criteria 53 4e Previous learning requirements 53 4f Access to assessment: diversity and inclusion 54 5 Administration 55 5a Availability of assessment units and certification 55 5b Entries 55 5c Private candidates 55 5d Access arrangements, reasonable adjustments and special consideration 55 5e Examination language 56 5f Qualification title 56 5g Awarding Grades and reporting results 56 5h Re-sits and how long unit results remain available to count towards certification 56 Appendices 57 A Spiritual, moral, ethical, social, legislative, sustainable development, economic and cultural issues and health and safety considerations 57 B Overlaps with other qualifications 58 C Wider Key Skills Teaching, developing and providing opportunities for generating evidence 59 43

1b Why choose the Foundation Free-Standing Mathematics Qualification (FSMQ) in Using Data? Each Free-Standing Mathematics Qualification (FSMQ) has been designed to encourage students to apply mathematical principles in their studies, work or interests. Foundation FSMQs provide a fresh start for students who have previously been less than successful in the mathematics classroom. FSMQs at all levels strive to be both practical and relevant to the real world, training students not only in mathematical skills but also in problem solving and modelling. The Foundation FSMQ in Using Data will provide students with a strong basis of numerical mathematical skills and enable them to develop some basic ideas of algebra. It will focus on the organisation of data and its representation using statistical diagrams and Cartesian graphs. This qualification will appeal particularly to those involved with courses in the areas of science, technology, business, leisure and tourism, geography, social sciences and health and social care. All FSMQs feature pre-release data sheets, ensuring students are familiar with and understand contexts and vocabulary in advance of the examination. FSMQs have assessed mathematics in context since 1999. This FSMQ benefits from the experience gained through these established qualifications. This specification has evolved from the successful Mathematics Pathways project, where pilot FSMQs were used as components of the pilot GCSE Use of Mathematics. Following this pilot we have extended the range of both Higher FSMQs and Foundation FSMQs, providing parity of opportunity with GCSE tiers. Students can use this Foundation FSMQ as the first step towards achieving the AQA Certificate in Use of Mathematics, which requires two FSMQs plus a Core unit. The AQA Certificate in Use of Mathematics is equivalent in standard to GCSE Mathematics. 1 1c How do I start using this specification? You need to register at www.aqa.org.uk/ askaqa.php to ensure that you receive regular updates and have access to mark schemes, past question papers, a whole range of teacher support materials and receive details of teacher support meetings. Once you have decided to enter candidates you need to tell us so we can make sure that you get all the material you need for the examinations. This is very important as prerelease material is sent to you before the final entry deadline. You can let us know by filling in the appropriate Intention to Enter and Estimated Entry forms. If your centre is registered on e-aqa you will receive an email prompting you to submit entry information online. If you are not e-aqa registered we will send copies to your exams officer. Both forms can be downloaded from our website (www.aqa.org.uk/admin/p_entries.php). If your centre has not used AQA for any examinations in the past, please contact our centre approval team at centreapproval@ aqa.org.uk. 45

2 Specification at a Glance 60 GLH (guided learning hours) Free-Standing Mathematics Qualification Foundation Level Using Data One written paper with pre-release data sheet Externally assessed 1 hour 40 marks 2 Calculator allowed Level of demand All Foundation FSMQ units are graded A to E and are set at the level of demand of GCSE grades C to G. 47

3 Subject Content Foundation FSMQ: Using Data There are no specific requirements for this qualification in respect of prior learning. What you need to learn Using calculators and computers A basic calculator with a memory facility will be sufficient for you to use with this qualification. However, any calculator may be used in this qualification provided that it conforms with JCQ Regulations. You should learn to use a calculator effectively and efficiently. Whenever you use a calculator you should record your working as well as the result. It is important that you are also able to carry out simple calculations without using a calculator. 3 You should learn how to use a spreadsheet. You should learn to use a This includes: calculator to: sum data calculate averages use of memory facility use of memory facility carry out basic calculations such as finding a fraction of quantity It is important that you are also able to carry out simple calculations without using a calculator, using both written methods and mental techniques (calculations in your head) where appropriate. You should learn to use a spreadsheet to: draw tables and record data draw charts and diagrams carry out calculations including finding averages This includes: formatting column widths so as to input headings and data formatting cells, when necessary, so that data is expressed correctly using a tally chart pie charts, bar charts, line (scatter) diagrams using spreadsheet formulae such as =A1+A2+A3 to sum values in cells =2*X where column A has been named X = SUM (A1:A10) =MEAN (A1:A10) = MEDIAN (A1:A10) = MODE (A1:A10) sort data into increasing and decreasing order (for example, when finding the range of data values) 48

Drawing up tables You should learn to: This includes: and recording data identify the data that is appropriate to your investigation select categories into which you will sort data draw up tables labelling headings accurately giving units for data when necessary use methods to check that your tables include all data Carrying out calculations and finding statistical measures You should learn to: This includes: calculate the sum (total) of data values using the memory facility on a calculator using spreadsheet formulae (including for example, =A1+A2+...A10 = SUM (A1:A10) 3 express one quantity as a proportion of another for example one data value as a proportion of the total express two quantities as a ratio as a fraction as a decimal as a percentage converting fractions to percentages using spreadsheet formulae, for example, =A1*100, =A1/A15 reducing to simplest form divide a quantity in a given ratio for example dividing 50 in the ratio 2:3 know common equivalencies for = 0.5 = 50% 2 simple fractions, decimals and 1 percentages = 0.25 = 25% 1 4 1 3 1 10 1 5 1 3 = 0.3 = 33 % = 0.1 = 10% = 0.2 = 20% and multiples of these calculate average values mean median mode calculate the range for a set of data using the memory facility on a calculator using spreadsheet formulae for mean, median, mode using a spreadsheet to sort data into increasing or decreasing order to find the median using a spreadsheet to sort data into increasing or decreasing order 49

Drawing statistical You should be able to draw the This includes: diagrams and graphs following by hand and where of data pairs possible using a spreadsheet: pictograms bar charts 3 pie charts line graphs of data pairs calculating size of a sector using a fraction of 360 for example of a data set is 1 5 represented by 360 = 72 5 using 1% represented by 3.6 1 choosing axes for each set of data scaling axes (for data not necessarily starting at zero) plotting points accurately joining data pairs with line segments where appropriate showing a trend in data by drawing a straight line where appropriate using a spreadsheet (to draw a scatter diagram to obtain a line graph) Understanding situations involving direct proportion You should learn to: This includes: recognise when one set of data is directly proportional to another by considering step sizes in both sets of data recognise the graph of data that is directly proportional as giving a straight line passing through the origin give the equation that represents a situation involving direct proportion understanding that with data from real situations the step lengths may only be approximately equal understanding how a step of fixed size in one set of data always gives steps of a fixed size in the other as shown by such graphs from information given in words from a graph of the situation Interpreting statistical diagrams and graphs of data pairs You should learn to: This includes: be able to express in words what statistical diagrams tell you about the situation they represent pictograms bar charts pie charts be able to express in words what, in general, a line graph tells you about the situation it represents 50

make sense of what is happening in the real situation where the graph of data pairs cuts the axes make sense in general terms of the gradient of graphs of data pairs the idea of steep, shallow, horizontal and vertical gradients only, i.e. calculation of gradients is not included except in situations involving direct proportion be able to find the gradient of a graph of a situation involving direct proportion and understand what this represents be able to use and interpret timetables Reading and using timetables given in 24 and 12 hour clock finding the length of time of a journey Using probabilities You should learn to: This includes: understand that the probability that an event occurs lies between 0 and 1 understanding numerical values associated with events having low, equally likely, and high probabilities 3 understand that if the probability that an event, A, occurs is p(a), then the probability that it does not occur is 1 p(a) express probabilities as fractions decimals percentages estimate probabilities from real data Accuracy, estimating and checking You should learn to: This includes: understanding the idea of, and limitations of, probability as relative frequency for simple situations check your work using estimation techniques check your work using inverse operations carrying out estimation calculations on paper by hand, mentally, using a calculator, using a spreadsheet check mentally the approximate size of a calculated result 51

4 Scheme of Assessment 4a Aims and learning outcomes 4 Free-Standing Mathematics Qualifications aim to promote: the development of a mathematics curriculum that is integrated with other areas of learners studies, work or interests the development of skills that enable learners to communicate, use and interpret their mathematics the development of learners confidence in, together with a positive attitude towards, using mathematics the recognition of mathematics as a useful tool in other areas of study, the world of work and society in general The Free-Standing Mathematics Qualification in Using Data should enable learners to: develop knowledge, skills and understanding of mathematical methods and concepts develop mathematical reasoning skills acquire the ability to solve open-ended problems develop and use mathematics as a model of reality and have an awareness of any limitations this may introduce into their analysis of a situation recognise when it is appropriate to use ICT, such as calculators and computer spreadsheets, and when it is appropriate to use pencil and paper methods solve substantial and realistic problems encountered by adults communicate clearly, using logical reasoning and appropriate notation interpret what their mathematics tells them about the situation they are analysing or the problem they are solving, using this information to summarise and draw conclusions work independently and follow their own line of enquiry 4b Assessment Objectives (AOs) The Assessment Objectives are common to both Foundation and Higher FSMQs and to the AQA Certificate in Use of Mathematics. The assessment units will assess the following objectives in the contexts of the content and skills set out in Section 3 (Subject Content). The assessment units will assess a candidate s ability to: AO1 AO2 AO3 recall, select and use mathematics appropriate to the situation, giving solutions to an appropriate degree of accuracy select and apply mathematical methods in a range of situations analyse problems and demonstrate strategies for solving them. Summarise and draw conclusions. 52

Weighting of Assessment Objectives for Foundation FSMQ in Using Data The table below shows the approximate weighting of each of the Assessment Objectives (AOs) in the Foundation FSMQ in Using Data. Assessment Objectives Overall weighting of AOs (%) AO1 55 65 AO2 15 25 AO3 10 20 Overall weighting (%) 100 Quality of Written Communication (QWC) This specification does not formally assess the quality of written communication. 4c Pre-release data sheets Data sheets should be opened and issued to candidates between 1 and 3 weeks before the examination. Candidates will be able to work with their teachers in familiarising themselves with the contexts, clarifying any specialised vocabulary and considering the possible mathematics in the situations presented. Teachers will need to provide reasonable class time for this to happen. This should be at least one lesson, but there is no upper limit on the time candidates may spend considering the data sheets (provided they remain sealed until the date for release printed on the packet label). The pre-release data sheets may not be taken in to the examination room. A clean copy of the data sheet will be issued to all candidates at the start of the examination. This sheet will not be collected in and marked, so candidates should ensure that all working is presented in the question paper/answer book. 4 4d National criteria This specification complies with: the Arrangements for the Statutory Regulation of External Qualifications in England, Wales and Northern Ireland: Common Criteria the requirements for qualifications to provide access to Levels 1 and 2 of the National Qualification Framework. 4e Previous learning requirements There are no previous learning requirements for the Foundation FSMQ in Using Data. Any requirements set for entry to a course based on this specification are at your centre s discretion. 53