This document is intended to aid centres to successfully plan, deliver and assess Application of Number.

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1 ESSENTIAL SKILLS WALES APPLICATION OF NUMBER General Guidance/Clarification This document is intended to aid centres to successfully plan, deliver and assess Application of Number. Whilst this guidance focuses on clarification and application of the first two columns of the standards You must provide evidence that you can & Evidence requirements it is emphasised that candidates must have covered sufficiently the skills included in the third column - In order to show that you are competent, you need to show how to: before attempting to produce a portfolio. This guidance/clarification should be read in conjunction with the following publications: Essential Skills Wales publication (WG, April 2010) Additional Clarification of Essential Skills Wales (WG, November 2011) WJEC Example Portfolios (Available on CD from WJEC) WJEC Handbook for Centres 2011/12 (Available from WJEC website) Please also refer to Appendix 1 - Clarification of Source/Presentation Types and Appendix 2 - Suggested Calculations at the end of this document Progression Throughout all levels progression is demonstrated by increasing levels of autonomy on the part of the candidate and increased complexity of planning, data sources, calculation, presentation and interpretation. Skills and Evidence Progression - Essential Skills Wales publication (p ) At all levels tasks should follow the whole process of: Understanding and tackling a problem collecting and interpreting data carrying out calculations checking results interpreting results presenting findings reflecting/reviewing the task (Guidance - Essential Skills Wales Publication (p.96) Each level should build upon the skills required at lower levels. Task Setting Whilst candidates can present evidence from a variety of different tasks, centres are encouraged to devise tasks which give candidates opportunities to cover all criteria using a single meaningful task. Centres are advised to look at levels above and below that aimed at. November

2 LEVEL 1 At level 1, tasks should follow the whole process of: Understanding and tackling a problem obtaining and interpreting data carrying out calculations checking results interpreting results presenting findings For tasks to be meaningful it is advised that candidates attempt to produce a portfolio based on a meaningful real life task that gives opportunities to meet all the criteria. Should candidates be unable to meet all the criteria of in the context of one task then they can produce stand-alone evidence for the missing criteria this evidence should also have a meaningful real-life purpose and in order to be realistic should include some evidence of interpretation. 2

3 N1.1 Understand numerical data N1.1.1 Understand and describe at least one given practical problem or task that involves a range of numerical data and information. N1.1.2 Agree with an appropriate person how you will tackle it. N1.1.3 Obtain relevant numerical data and information from at least two sources to meet the purpose of your task. Evidence requirements Clarification of Evidence Requirement Notes/Examples candidate has understood and described the given problem or task. Evidence must be in the form of notes produced by the candidate (by hand or electronically) candidate has contributed to deciding how the task will be tackled Evidence must be in the form of notes produced by the candidate (by hand or electronically) candidate is clear about how the data/information you obtain meets your purpose. All tasks should have a clear real-life purpose and all work should to be in the context of the task. i.e. why do we need to know this? Who needs to know this? The candidate needs to explain the task and its purpose in their own words. The task must have sufficient opportunities for the candidate to obtain relevant numerical data and use suitable methods. The task brief may be given to the candidates. This may be done at the beginning of each part of the task or as a whole at the beginning of the task. This requires the candidates to write the task brief in their own words and how they are going to tackle it. Careful planning for this criterion also provides coverage for: Planning could follow the structure shown in the Notes/Example column. The evidence may be located at various stages throughout the task. The candidates need to obtain data from at least two different sources and show how they have used these sources. Of these, at least one of the sources needs to be a chart / graph / diagram or table. For example - A person wants to buy a house in a certain area and wants to find out information about the average house in that area. A discussion with the tutor/teacher could follow the following pattern: What do I want to find out? Why do I want to find it? What data do I need to find it out? Where will I get this data? What calculations will I need to perform? How will I check that those calculations make sense? How will I present the findings effectively? How will I know if I've found out what I wanted to find? Then the candidate could outline the key points and the teacher/tutor could sign it to show agreement For example, in the house task: One source could be a table of records of 10 houses in a certain area. The second source could be a scale diagram of the floor plan of an average house in the area. 3

4 Your sources must include at least one of a table, a chart, a graph, or a diagram. Evidence must include data/information obtained from at least two different sources. At least one source must include a table, chart, graph or diagram. Evidence must include: copies of source material details of the site/s of observation/measurement records of data/information obtained Sources may include: information from the internet information from books/magazines direct measurements surveys/questionnaires maps/scale diagrams ALL SOURCES NEED TO BE SHOWN AND THEIR USE NEEDS TO BE EXPLICIT. I.E. The candidate needs to show how they have used each source. E.g. by marking on graphs. A map showing the location of the houses that are for sale. A graph showing house prices in the area. 4

5 N1.2 Carry out calculations N1.2.1 Use appropriate methods to get the results you need and describe the methods you have used. N1.2.2 Use the data and information you have obtained to carry out calculations relevant to your task to do with: amounts or sizes scales or proportion handling statistics candidate can identify and describe the methods and calculations that are suitable for getting the results you need. Evidence of describing methods must normally be in the form of notes produced by the candidate (by hand or electronically) candidate: has used data and information from N1.1 is clear about the purpose and relevance of your calculations Evidence for the second bullet may be in the form of either notes or a witness statement. Evidence must include calculations (at least one from each category) relating to: amounts or sizes scales or proportion handling statistics and show how the candidate has checked their methods and calculations. Evidence must show the results make sense in relation to the purpose of the task. This criterion could be met during the planning stage of the task or at the beginning of each part of the task. The candidate should identify and describe the methods they are using. Answering the questions: What do I want to find out? What calculations will I need to perform to find it out? should give evidence for this criterion. For example: I want to know the average house price in the area. To do this I will calculate the mean price of 10 ten houses by adding the prices up and dividing by 10. For each category (a, b, c) below there is a requirement of a minimum of one purposeful calculation accompanied by evidence of the methods used and checking the accuracy of the results. Candidates should not claim the same calculation for (a), (b) and (c). Proportional percentage calculations may be claimed for (a) or (b) but cannot be claimed for both simultaneously. Use of ICT for the purpose of calculation is acceptable. However, in order to claim the work for candidates must show evidence of more than merely inputting data into a spreadsheet. e.g. If the candidates produce their own spreadsheet they need to show evidence of the creation and evidence of the formulae used. a) Amounts or Sizes see appendix b) Scale or Proportion All calculations for scale diagrams must be shown and the scale must be included on the diagram. Appropriate scales for level 1 are such as: 1:2, 1:10, 1:100, 1:1000 If a pie chart is to be claimed for 1.2.2(b) then the calculations must be shown and the pie chart must be hand-drawn. For example: Calculation of floor space could include conversion of room measurements from cm to m. Calculation of the area of the floor (e.g. simple rectangles) They could be given a scale diagram of the floor plan of the average house and use it to calculate the actual dimensions. Pie chart showing the types of houses available for sale (e.g. detached, semi-detached, terraced). 5

6 This evidence must normally be in the form of notes produced by the candidate (by hand or electronically). c) Handling statistics Evidence needs to include calculation of mean and range of about 10 items of data Calculating the statistics for houses in a certain area to find the average house. Checking Candidate must show evidence of checking results of at least one calculation in each category (a, b, c). Checking areas by estimation. Using spreadsheet to calculate mean /range to check manually calculated values. Checking statistics are sensible. 6

7 N1.3 Interpret results and present findings N1.3.1 Present your findings using charts, graphs or diagrams. candidate can choose how to present your findings using two appropriate ways (i.e. chart and diagram or graph and diagram) present their findings correctly Whether or not ICT is used to produce graphics, evidence must show that the candidate has checked their accuracy and can explain them fully. Evidence of this understanding may be in the form of a witness statement. Candidates need to choose how to present their findings. They could do this verbally with the teacher/tutor who could provide a suitable witness statement. They do not need to illustrate the same data using several different methods unless there is a purpose in doing so. The candidates must have at least one type of presentation from each of the following categories: Category 1: Graph or chart Category 2: Diagram or table All presentations must be labelled correctly (suitable heading, correctly labelled axes, suitable scales on axes). Use of ICT to draw presentations is acceptable but they must be accurate and correctly labelled. For example: Category 1: GRAPH I am going to use pie chart to show the distribution of types of houses in each area. Category 2: TABLE I will present a table showing how far my chosen house is from local amenities (e.g. school, shops, leisure centre, internet café) N1.3.2 Describe what your results tell you and explain how they meet the purpose of your task. candidate can describe the results of your calculations explain how they relate to the purpose of the task Evidence must normally be in the form of written notes produced by the candidate (by hand or electronically). Any presentations/findings should be accompanied by an explanation of what it shows in relation to the task. Candidates need to show an understanding of their results in the context of the task. They should be answering: What do the results tell them? Have they found out what they want to find out? For example: Comments such as: I have found that the mean house price in the area is 124,000. The range of the house prices was 230,000. This shows that there is a big difference between house prices in the area. The floor space of the average house is 115m 2. The most common type of house is semi-detached half of the houses in my survey were semi-detached. 7

8 LEVEL 2 At level 2 tasks should follow the whole process of: Understanding and tackling a problem collecting and interpreting data carrying out calculations checking results interpreting results presenting findings reflecting and reviewing For tasks to be meaningful it is advised that candidates attempt to produce a portfolio based on a meaningful real life task that gives opportunities to meet all the criteria. One task must include evidence that covers the entire process of 2.1, 2.2 and 2.3. However, should candidates be unable to meet all the criteria of in the context of one task then they can produce a supplementary task for the missing criteria this evidence must also have a meaningful real-life purpose and must include evidence of either 2.1 or 2.3 8

9 N2.1 Understand numerical data Evidence requirements Clarification of Evidence Requirement Notes/Examples N2.1.1 Help to identify and describe at least one practical problem or task that involves a range of numerical data and information. candidate has played an active part in identifying and describing the problem or task about which you have been briefed or which you have chosen. Evidence must be in the form of notes produced by the candidate (by hand or electronically). All tasks must have a clear real-life purpose and all work needs to be in the context of the task. i.e. why do we need to know this? Who needs to know this i.e. who are the audience? The candidate needs to explain the task and its purpose in their own words and there must be evidence of some candidate input to the task. The problem must have sufficient opportunities for the candidate to select data and analysis methods suitable for the level. The task brief could be general but candidates should be encouraged to follow their own lines of enquiry. This must be done at the beginning of the task this cannot be completed retrospectively. For example - A person wants to buy a house costing between 120,000 and 150,000 and needs to choose between two different locations your brief is to compare the types of houses available in two different areas and their average price and present your findings to the house buyer. The task may be outlined in a class discussion but candidates need to plan how they are going to compare the houses - what data they are going to collect, how they are going to use that data and how they are going to present their findings. N2.1.2 Confirm with an appropriate person how you plan to tackle it. Evidence of planning must include: details of how you intend to obtain relevant data and information a clear sequence of tasks showing how you intend to use this information Evidence must be in the form of notes produced by the candidate (by hand or electronically). This requires the candidates to write a clear plan which needs to be individual. Careful planning for this criterion also provides coverage for: Planning could follow the structure shown in the Notes/Example column. Once the plan is complete it should be checked by a teacher/tutor/trainer that it is appropriate and should be signed by the tutor/trainer. What do I want to find out? Why do I want to find it? What data do I need to find it out? Where will I get this data? What calculations will I need to perform? Why perform those calculations? How will I check that those calculations make sense? How will I present the findings effectively? Why use that method to present? How will I know if I've found out what I wanted to find? 9

10 N2.1.3 Collect relevant numerical data and information from a range of sources to meet the purpose of your task. Your sources must include at least two of a table, a chart, a graph or a diagram. candidate is clear about how the data/information you obtain meets your purpose. Evidence must include: data/information collected from at least three sources at least one source must require the candidate to collect and record data/information copies of source material details of the site/s of observation/measurement records of data and information obtained The candidates need to make use of data from three different sources and show how they have used these sources. (These should have been identified in the planning stage.) Of these, at least two of the sources need to be different charts / graphs / diagrams or tables. Candidates are required to collect relevant data this could include: sampling from a larger data set survey/questionnaire gathering information from the internet/books direct measurement. maps & scale diagrams ALL SOURCES NEED TO BE SHOWN AND THEIR USE NEEDS TO BE EXPLICIT. I.E. The candidate needs to show how they have used each source. E.g. by marking on graphs. For example, in the house task: One source could be a table of records of houses in a certain area from which the candidate could sample appropriately. (This meets the requirement of collecting relevant data and a table source.) For the second source - the candidates could use the internet to gather information on houses in another area for comparison. (Again requiring the candidate to collect relevant information this is good practice since it gives the work individuality). A third source could be a graph showing house prices in different areas over a period of time. (This source could be provided for them.) Other sources that the candidate themselves may decide to consider could include, e.g. floor plans of houses, crime rates, council tax bands, commuting distances, amenities dependant on the initial purposes of the task. Again this will give the candidates' work individuality. 10

11 N2.2 Carry out calculations N2.2.1 Use appropriate methods to get the results you need and explain the methods you have used. N2.2.2 Use the data and information you have obtained to carry out calculations relevant to your task to do with: a) amounts or sizes b) scales or proportion c) handling statistics d) using formulae candidate can: independently choose and use appropriate methods for getting the results you need explain why these methods are appropriate Evidence must be in the form of notes produced by the candidate (by hand or electronically). candidate: has used data and information from N2.2.1 is clear about the purpose and relevance of your calculations. Overall, evidence of calculations must include at least one example from each category: amounts or sizes scales or proportion handling statistics using formulae And must show how the candidate has checked your methods and calculations. Evidence must show methods and levels of accuracy, with justifications. This criterion could be met during the planning stage of the task. The candidate should identify the methods themselves and not be told which calculation to perform. However, they can seek advice. The candidate needs to explain the purpose of the calculation not merely describe how to perform it. Answering the questions: What calculations will I need to perform? Why perform those calculations? should give evidence for this criterion. For example: I want to know in which area the houses are least expensive. To do this I will compare the average price of houses in two areas by using mean, median and mode. For each category (a, b, c, and d) below there is a requirement of a minimum of one purposeful calculation accompanied by evidence of the methods used and checking the accuracy of the results. Candidates should not claim the same calculation for (a), (b) and (c). However, they can claim the use of a formula in (d) with any other category. Proportional percentage calculations may be claimed for (a) or (b) but cannot be claimed for both simultaneously. Use of ICT for the purpose of calculation is acceptable. However, in order to claim the work for candidates must show evidence of more than merely inputting data into a spreadsheet. e.g. If the candidates produce their own spreadsheet they need to show evidence of the creation and evidence of the formulae used. Suitable levels of accuracy should be used. E.g. Money to 2 decimal places. a) Amounts or Sizes All calculations at level 2 need to be more complex than those acceptable at level 1. Calculations should be multi-step, i.e. should involve more than one operation. See appendix For example: Calculation of floor space could include conversion of room measurements from Imperial to Metric (if necessary). Must be more complex than those expected at level 1. What percentage of houses in each area is terraced, semi-detached and detached? If candidates chose to compare locations in different countries they could convert between currencies in order to compare. 11

12 Evidence must include records of how the candidate has checked: your methods and calculations that the results make sense in relation to the purpose of the task Evidence must be in the form of written notes produced by the candidate (by hand or electronically). b) Scale or Proportion All calculations for scale diagrams must be shown and the scale and measurements must be of a suitable difficulty. See appendix c) Handling statistics Evidence needs to include calculation of mean, median, mode and range. Statistics need to be used for comparison of two sets of data. See appendix Draw a scale diagram of the average house in each area to compare the sizes of the houses. The candidates should use a suitable scale so that the diagram fits on the given piece of paper all calculations should be shown. What percentage of houses in each area is terraced, semi-detached and detached? What percentage of houses is in the price category that the house buyer can afford? Calculating the statistics for houses in two areas and using them to compare. d) Using formulae The formulae need not be shown as an algebraic formula but values need to be shown substituted into the formula. If spreadsheets are used for this criterion then the formulae must be input by the candidate and evidence of the formulae must be shown. Use of functions such as AVERAGE, MEDIAN, STDEV does not constitute suitable evidence. See appendix Use of formulae such as: Mean = total / number 12

13 Checking Candidate must show evidence of checking results of at least one calculation in each category (a, b, c). Checking of (d) will usually be covered within the checks of (a, b, c) Checking areas by estimation. Using spreadsheet to calculate mean/median/mode/range to check manually calculated values. Checking statistics are sensible. Reverse calculation of percentage calculations. 13

14 N2.3 Interpret results and present findings N2.3.1 Select two different candidate can ways to present your choose how to present your results, using charts or results, using two graphs, and tables or appropriate ways (i.e. charts diagrams appropriate and/or graphs, and tables to your audience. and/or diagrams) explain why these ways are appropriate to your audience Evidence must be in the form of written notes produced by the candidate (by hand or electronically). Candidates need to choose the most appropriate method to present their findings. All presentations must be accompanied by an explanation of why they are appropriate to the audience. This may be covered in the planning stage. They do not need to illustrate the same data using several different methods unless there is a purpose in doing so and this should then be explained. The presentations need to be of a level 2 standard, e.g. pie charts, line graphs, frequency polygon, scale drawing of suitable standard. The candidates must have at least one type of presentation from each of the following categories: Category 1: Graph or chart Category 2: Diagram or table For example: Category 1: GRAPH I am going to use pie chart to show the distribution of types of houses in each area. I am using a pie chart because it is appropriate for showing proportions and is easy to understand. Category 2: DIAGRAM I am going to draw a scale diagram of an average priced house in both areas in order to compare the sizes of the houses to see which gives more room. It is important that I use the same scale for both diagrams so that it is a fair comparison. N2.3.2 Present and explain your methods and findings and explain how they meet the purpose of your task and are appropriate to your audience. candidate can present your methods and findings effectively explain the methods you have used describe and explain what results of your calculations mean in relation to the problem/task you have tackled, emphasising the key points Good practise would be to consider which ONE graph/chart and which ONE table/diagram would be the best way to present the findings of their task to the target audience. As above candidates should choose the most appropriate method of presentation. Any presentations/findings should be accompanied by an explanation of what it shows in relation to the task. Candidates need to show an understanding of their results in the context of the task. They should be answering: What do the results tell them? Have they found out what they want to find out? For example: Correctly drawn presentations accompanied by explanations linked back to the original task as set out in Comments such as: I have found that the mean house price in Area A is more than in Area B. However, the mean house in Area A has a larger floor space than the mean house in Area B. 34% of houses in area A are in the price range whereas 46% of houses in area B are in the price range. 14

15 Evidence must be in the form of written notes produced by the candidate (by hand or electronically). Whether or not ICT is used to produce graphics, evidence must show that the candidate has checked their accuracy and can explain them fully. Evidence of this understanding may be in the form of a witness statement. All presentations must be labelled correctly (suitable heading, correctly labelled axes, suitable scales on axes). Use of ICT to draw presentations is acceptable but they must be accurate and correctly labelled. I would suggest buying a house in area B because they are cheaper and there is more choice. 15

16 LEVEL 3 At level 3 tasks should follow the whole process of: Understanding and tackling a problem collecting and interpreting data carrying out calculations checking results interpreting results presenting findings reflecting and reviewing For tasks to be meaningful it is advised that candidates attempt to produce a portfolio based on a meaningful real life task that gives opportunities to meet all the criteria. One task must include evidence that covers the entire process of 3.1, 3.2 and 3.3. However, should candidates be unable to meet all the criteria of in the context of one task then they can produce a supplementary task for the missing criteria this evidence must also have a meaningful real-life purpose and must include evidence of either 3.1 or

17 N3.1 Understand numerical data N3.1.1 Identify, analyse and accurately describe at least one practical problem or task that involves a range of numerical data and information. Evidence requirements Clarification of Evidence Requirement Notes/Examples candidate has independently identified, analysed and described the problem or task about which you have been briefed or which you have chosen. Evidence must be in the form of notes produced by the candidate (by hand or electronically). All tasks must have a clear real-life purpose and all work needs to be in the context of the task. i.e. why do we need to know this? Who needs to know this i.e. who are the audience? There must be evidence of significant candidate input to the task. The problem must have sufficient opportunities for the candidate to select data and analysis methods suitable for the level. Candidates' work needs to have an element of individuality and independence. This must be done at the beginning of the task this cannot be completed retrospectively. For example - A person wants to buy a house and needs to choose between two different locations your brief is to compare the houses in two different areas and present your findings to the house buyer. The class could be given the topic but candidates need to plan how they are going to compare the houses - what data they are going to collect, how they are going to use that data and how they are going to present their findings. N3.1.2 Plan how you will tackle it. N3.1.3 Collect relevant numerical data and information from a range of sources to meet the purpose of your task. Evidence of planning must include: details of how the candidate intends to obtain relevant data and information a clear sequence of tasks showing how you intend to use this information Evidence must be in the form of notes produced by the candidate (by hand or electronically). Evidence must include data/information collected from at least three sources, one of which must be an appropriate data set. candidate can: collect relevant data and information This requires the candidates to write a clear plan which needs to be individual. Careful planning for this criterion also provides coverage for: Planning could follow the structure shown in the Notes/Example column. The candidates need to make use of data from three different sources and show how they have used these sources. (These should have been identified in the planning stage.) Of these, at least two of the sources need to be different charts / graphs / diagrams or tables one of these needs to be 'complex' i.e. contains more data than is required for the task, e.g. a multiple line graph. 17 What do I want to find out? Why do I want to find it? What data do I need to find it out? Where will I get this data? What calculations will I need to perform? Why perform those calculations? How will I check that those calculations make sense? How will I present the findings effectively? Why use that method to present? How will I know if I've found out what I wanted to find? For example, in the house task: One source could be a table of one hundred records of houses in a certain area from which the candidate samples appropriately. (This meets the requirement of collecting relevant data, a table source and a large data set.)

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