Introduction

The purpose of this Guidance is to assist teachers and candidates in understanding the requirements of Application of Number. Whilst this Guidance focuses upon the assessment of Part B of the Standards, it is emphasised that candidates must be wholly familiar with Part A – You Must Know How To – to ensure mastery of the techniques and knowledge needed to successfully apply these skills.

This guidance should be read in conjunction with the following publication:

·  Key Skills Standards and Guidance – Application of Number, Communication and Information Communication Technology (DELLS, CCEA and QCA)

·  Current WJEC Key Skills Handbook for Centres

·  WJEC and regulator’s example portfolios

·  WJEC Candidate logbooks or centre-produced equivalents

The aim of the application of number standards is to encourage candidates to develop and demonstrate their skills in interpreting information involving numbers, carrying out calculations, interpreting results and presenting findings. The standards are essentially concerned with developing and recognising the ability of candidates to select and apply numerical, graphical and related mathematical skills in ways that are appropriate to their particular context. However, they can also be used to help individuals make connection with less familiar contexts and develop their ability to progress to higher levels of competence.

Techniques such as being able to measure and read scales, carry out specific calculations, or draw a particular type of diagram , are essential, but so too are the skills of application, such as interpreting information from tables, graphs or charts, selecting appropriate methods, describing what findings show, etc. Techniques and skills of application both contribute to understanding a task or problem and to deciding on the best course of action.

Application of number requires candidates to interpret information presented in different graphical forms and to produce these themselves in order to present their own findings. For the purpose of the key skill, it is not necessary to distinguish between “graph” and “chart”. The basic differences between these representations and a diagram are set out in the table below

Chart or Graph / A representation of the relationship between variables such as categories and frequency data, or x and y coordinates. / Pie or bar chart, histogram, pictogram, frequency polygon, frequency chart or diagram. Single or multiple line graph; scatter graph or without line of best fit.
Diagram / Any other graphical method of representation where scale is or is not a factor / Sale drawing, plan or workshop drawing, circuit drawing, 3D representation, flow chart, critical path or network diagram, organisation chart

Progression from levels 1-3

The key skills standards are designed to recognise candidates’ progression in terms of both techniques and skills of application.

Progression through the levels is demonstrated by increased ability to internalise the cycle of:

Collect Process Interpret

With these three element corresponding to the three sections of Part B of the standards.

At level 1 candidates are required to handle simple numerical and graphical information and techniques applied in the context of short activities. Calculation will usually involve only one or two steps. Much of the numerical content will be concerned with whole numbers and the use of decimals in everyday contexts (e.g. in using money or taking measurements) and the use of common units of measurement. At this level, candidates must cover each element of the Collect Process Interpret cycle, but are not required to combine them. Evidence for each element may be presented separately.

At level 2 candidates are required to set their use of application of number skills in the context of at least one activity that covers all of the assessment criteria. Such an activity will give them more scope to make decisions on how to find the information they need, what calculations to use and how best to present their findings. Calculations will involve two or more steps and a more demanding range of techniques and understanding. Candidates will be expected to know how to work with numbers of any size, including addition and subtraction of factions, calculations involving area and volumes, ratio, unit conversions, percentages and scaling, as well as the use of formulae and graphs. At this level, at least one piece of work must show evidence of the whole Collect Process Interpret cycle, with other work showing evidence of ‘collect and process’ or ‘process and interpret’.

At level 3 there is an increase in the complexity of activities and techniques needed. Candidates are required to be responsible for planning and carrying through their use of application of number in the context of one or more activities that cover all of the assessment criteria, including handling data from a large data set. Compared with level 2, calculations will involve several stages. Candidates need to justify their approaches and methods, in addition to presenting their findings. Calculations involve use of compound units and powers, as well as using formulae. At this level, all of the candidate’s work must show evidence of the whole data handing cycle.

AON Guidance 26/02/2008

APPLICATON OF NUMBER LEVEL1

All work submitted should be in the context. Standalone exercises are acceptable, but should be in a context.

N / Definition / Best Practice / Best Avoided
1.1 / Interpret information from 2 different sources at least one source must include a table, chart, graph or diagram. / One source MUST be graphical (a table, chart or diagram).
The other should be different, e.g. questionnaire / survey; direct measurement. / All sources are provided for candidates, with everyone using the same information.
The purpose of the task should be set out at the beginning of the work. / A series of standalone exercises lacking context.
The candidates must identify with some guidance which calculations to do for themselves and explain why they are doing those calculations e.g. “I am going to add these numbers to get the total”. / A worksheet that tells candidates exactly what to do and identifies the calculations needed.
No explanation of what they are doing is given.
1.2 / Carry out and check calculations / Sensible rounding must be done. Candidates need to be aware of sensible levels of accuracy and present results to a given level of accuracy / Inappropriate or no rounding e.g. money.
Candidates unaware of level of accuracy required.
Calculations should be checked.
Estimation should be encouraged, reverse calculation, common sense. / Reliance on reverse calculation for all checks.
No estimation or checking sense of calculation.
Perform a number of different types of calculation, with and without a calculator. / Repeating of same calculations.

Each of the following types of calculation MUST be performed

1.2.1(a) / Amounts or sizes / These cover:
·  Decimals
·  Fractions and Percentages
·  Simple areas and volumes
Good practise would be to include more than one of these where appropriate to the task. / Depending on one type of calculation e.g. only percentages.
1.2.1(b) / Scales or proportion / These cover:
·  Simple ratios
·  Use of scale diagrams
These should be in the context of a task and scale should be noted on the diagram. / Confusing presentation with calculation. Use of pie chart is presentation not good evidence of proportion.
1.2.1(c) / Handling Statistics / These cover:
·  Mean
·  Range
Interpretation should show understanding of the meaning of these.
Checking sense of mean as a mid-value is a good example of checking calculations. / No checking of sense of statistics and incorrect calculations leading to nonsensical mean / range.
1.3 / Interpret the results of your calculations and present your findings – in two different ways using charts or diagrams.
1.3.1 / Choose suitable ways to present your findings / Explain why they choose a specific type of chart, graph or diagram. This needn’t be a lengthy. / Presenting the same findings numerous times.
1.3.2 / Use more than one way of presenting your findings / They MUST present findings in TWO DIFFERENT ways using suitable charts or diagrams.
Diagrams needn’t be to scale. / Drawing graphs for their own sake. Showing the same results several times - candidates should choose the best way to present information.
1.3.3 / Present your findings clearly using a chart or diagram. / All graphs or diagrams must be labelled suitably. / Diagrams and graphs incorrectly labelled or not labelled at all.
1.3.4 / Describe what your results tell you. / Candidates must draw some conclusions from their results, graphs, diagrams, etc.
These should be related to the original purpose of the task. / Not interpreting graphs, etc, at all.
Incorrect interpreting.

APPLICATON OF NUMBER LEVEL 2

All work submitted MUST be relevant and in context. Standalone exercises are NOT acceptable.

The portfolio must contain at least one task.

One task MUST cover all criteria: Collect (N2.1), Process (N2.2 (a, b, c and d)) and Interpret (2.3)

Any subsequent tasks MUST cover either Collect (N2.1) AND Process (2.2) or Process (2.2) AND Interpret (2.3)

There MUST be two information sources one of which MUST be either a chart or graph.

N / Definition / Best Practice / Best Avoided
2.1 / Interpret information from a suitable source / One source MUST be a chart or graph
There should to be a data set containing at least 20 records.
There MUST be 2 sources / Use of a chart or graph that they draw does not constitute a source.
No record of source material.
A table is NOT a chart
The purpose of the task should be set out at the beginning of the work including an explanation of how they choose to get their information. / No explanation of why they have chosen to collect the information.
They can obtain relevant information from each source and explain why they need it for their task. / No explanation of how the information has been collected.
The candidates MUST identify which calculations to do for themselves and explain why they are doing those calculations. / A guided task that tells the candidates what to do and how to do it.
The task will identify the calculations needed.
No explanation of what they are doing is given.
2.2 / Carry out and check calculations / Sensible rounding must be done. Candidates need to be aware of sensible levels of accuracy and present results to an appropriate level of accuracy or within given limits without guidance. / Inappropriate or no rounding.
Calculations should be checked.
Estimation should be encouraged, reverse calculation, common sense.
Not all calculations need checking however a range of different checks should be shown. / Reliance on reverse calculation for all checks.
No estimation or checking sense of calculation.
Checking the same type of calculation several times.
Perform a number of different types of multi-step calculation, with and without a calculator.

Each of the following types of calculation MUST be performed

2.2.1(a) / Amounts or sizes / These cover:
·  Use of, and conversion between, fractions, decimals & percentages.
·  Conversion of measurement etc
·  Composite areas
·  Volume (multi-step)
These MUST involve multi-step calculations and be of a level greater than those exemplified at level 1. / Use of non multi-step calculations.
E.g.:
Area of simple rectangles,
Calculation of a fraction or percentage of a number, e.g. ¾ of 300, 25% of 140m
2.2.1(b) / Scales or proportion / These cover:
·  Ratios
·  Scale diagrams – calculation of length from scale diagram
·  Scale factor/enlargement
These should be in the context of a task.
This could involve the drawing of a scale diagram of suitable complexity (i.e. not a simple rectangle and a scale that isn’t 1:1) / Confusing presentation with calculation. Use of pie chart is presentation not good evidence of proportion.
A scale drawing is only acceptable in the context of a task and must therefore involve either some collection (N2.1) or interpretation (N2.3).
2.2.1(c) / Handling Statistics / These cover:
·  Comparison of two sets of data using mean, median, mode & percentages
·  Range
Interpretation should show understanding of the meaning of these.
Checking sense of statistics is a good example of checking calculations.
The data set should include at least 20 records. / No checking of sense of statistics and incorrect calculations leading to nonsensical statistics.
Not comparing two sets of data.
Calculation of statistics not followed by suitable interpretation.
2.2.1(d) / Using Formulae / Use of formulae:
·  In words
·  In symbols
The formula should be stated.
Needs to be used within context of the task. / Not stating the formula to be used.
Formula not an intrinsic part of the task.
2.3 / Interpret the results of your calculations and present your findings – in two different ways using charts or diagrams.
2.3.1 / Select effective ways to present your findings / Select the most appropriate method to display findings.
Explain their choice of methods / Presenting the same findings numerous times.
2.3.2 / Present your findings clearly using a chart, graph or diagram and describe your methods. / Choice of method should be justified.
All graphs or diagrams MUST be suitably labelled.
ICT can be used to present findings / The methods used should be the most appropriate method to display the information.
Inappropriate use of graphs and charts.
The drawing of a scale diagram without context.
Graphs produced using ICT must also be effective and suitably labelled.
Drawing graphs for their own sake. Showing the same results several times - candidates should choose the best way to present information.
2.3.3 / Use more than one way of presenting your findings / Findings must be presented using at least two of the following methods: chart or graph AND diagram
i.e. there must be evidence of a diagram. / Using only one method of presentation.
E.g. only using charts and graphs NO diagram.
2.3.4 / Describe what your results tell you. / Candidates must draw conclusions from their results, graphs, diagrams, etc.
These should be related to the original purpose of the task.
They should highlight their main findings.
They should either prove or disprove their original hypothesis. / Not interpreting graphs, etc, at all.
Incorrect interpreting.
Explaining all their results not selecting the most relevant ones.
Not relating finding to original purpose/hypothesis.

APPLICATION OF NUMBER LEVEL 3