KEY SKILLS
Guidance on Assessing Application of Number
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:
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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.
Diagram
Any other graphical method of
representation where scale is or is not a
factor
AON Guidance 26/02/2008
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.
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
1.1
1.2
Definition
Interpret information from 2
different sources at least
one source must include a
table, chart, graph or
diagram.
Carry out and check
calculations
Best Practice
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.
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, sense of result. Use of
spreadsheets/calculations.
Perform a number of different types of
calculation, with and without a calculator,
showing methods.
Each of the following types of calculation MUST be performed
AON Guidance 26/02/2008
Best Avoided
Reliance on reverse calculation for all checks.
No estimation or checking sense of calculation. “I have
used a calculator….”
Repeating of same calculations.
These cover:
 Decimals
Amounts or
1.2.1(a)
Depending on one type of calculation e.g. only
 Fractions and Percentages
sizes
percentages.
 Simple areas and volumes
Good practise would be to include more than one
of these where appropriate to the task.
These cover:
 Simple ratios
Confusing presentation with calculation. Use of pie
Scales or
1.2.1(b)
chart is presentation not good evidence of proportion.
 Use of scale diagrams
proportion
(Unless calculation of angles and use is shown)
These should be in the context of a task and
scale should be noted on the diagram.
These cover:
 Mean and
 Range*
Handling
No checking of sense of statistics and incorrect
*Use
of other statistics is acceptable.
1.2.1(c)
Statistics
calculations leading to nonsensical 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.
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, graphs
or diagrams. Diagrams need not 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
AON Guidance 26/02/2008
1.3.3
Present your
findings
clearly using
a chart or
diagram.
All graphs, charts or diagrams must be labelled
suitably.
Diagrams, charts 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.
AON Guidance 26/02/2008
APPLICATION 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
2.1
Definition
Interpret information from a
suitable source
AON Guidance 26/02/2008
Best Practice
Best Avoided
One source MUST be a chart or graph
There should to be a data set containing a
suitable number of records for comparison,
e.g. 20 records.
There MUST be 2 sources. Sources must
be clearly referenced e.g. www.
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.
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.
Calculations should be checked.
Estimation should be encouraged, reverse
calculation, sense of result. Use of
spreadsheets/calculations.
Not all calculations need checking however a
range of different checks should be shown.
Perform a number of different types of multistep calculation, with and without a
calculator, showing methods.
2.2
Each of the following types of calculation MUST be performed
These cover:
 Use of, and conversion between,
fractions, decimals & percentages.
 Conversion of measurement etc
2.2.1(a) Amounts or sizes
 Composite areas
 Volume (multi-step)
These MUST involve multi-step calculations
and be of a level greater than those
exemplified at level 1.
AON Guidance 26/02/2008
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.
Inappropriate or no rounding.
Reliance on reverse calculation for all checks.
No estimation or checking sense of calculation.
Checking the same type of calculation several times.
Reliance on one type of calculation to cover several criteria.
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)
2.2.1(c)
2.2.1(d)
Scales or proportion
Handling Statistics
Using Formulae
AON Guidance 26/02/2008
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)
These cover:
 Comparison of two sets of data
using mean, median, mode &
percentages
 Range*
*Use of other statistics is acceptable.
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.
Use of formulae:
 In words
 In symbols
The formula should be stated.
Needs to be used within context of the task.
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).
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.
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.
Select effective
Select the most appropriate method to
2.3.1
ways to present
display findings.
Presenting the same findings numerous times.
your findings
Explain their choice of methods
The methods used should be the most appropriate method to
display the information.
Present your
Inappropriate use of graphs and charts.
findings clearly
Choice of method should be justified.
The drawing of a scale diagram without context.
using a chart, graph All charts, graphs or diagrams MUST be
2.3.2
Graphs produced using ICT must also be effective and
or diagram and
suitably labelled.
suitably labelled.
describe your
ICT can be used to present findings
Drawing graphs for their own sake. Showing the same results
methods.
several times - candidates should choose the best way to
present information.
Use more than one
Findings must be presented using at least
two different methods including charts,
2.3.3
way of presenting
Using only one method of presentation e.g. only using a chart.
your findings
graphs or diagrams.
Candidates must draw conclusions from their
results, graphs, diagrams, etc.
Not interpreting graphs, etc, at all.
These should be related to the original
Incorrect interpreting.
Describe what your
2.3.4
purpose of the task.
Explaining all their results not selecting the most relevant
results tell you.
They should highlight their main findings.
ones.
They should either prove or disprove their
Not relating finding to original purpose/hypothesis.
original hypothesis.
AON Guidance 26/02/2008
APPLICATION OF NUMBER LEVEL 3
All work submitted MUST be in context. Standalone exercises are NOT acceptable. The portfolio must contain one or more activities.
ALL activities must cover ALL criteria: Collect (N3.1), Process (N3.2) AND Interpret (N3.3)
There must be two different types of information sources, one of which MUST be a large data set (i.e. over 50 records)
Multi-stage calculations differ from multi-step as follows:
Multi-step / stage: a multi-step / stage calculation could involve calculation of the total of a set of data and then dividing it by the number of data
items to calculate the mean.
Multi-stage: the mean is calculated and the result is then used in the calculation for standard deviation.
N
3.1
Definition
Plan an activity and get
relevant information from
relevant sources.
Best practise
The plan should include a clear description of the
activity and explain its purpose. Candidates
should decide for themselves the approach to
take when working on the activity.
Candidates need to explain how information is
obtained: questionnaire, measurement,
experimentation, and graphical or written
material.
A clear indication of the methods chosen by the
candidate justifying the choice of those methods.
Best avoided
A brief introduction that doesn't explain any clear purpose
for the activity. Activities whose plans are intrinsic and as a
result require no planning on the part of the candidate.
A set of data given to the candidate that includes no
reference to how or why it was collected
No reference to methods chosen or why they were chosen.
3.2
Carry out and check
multistage calculations
AON Guidance 26/02/2008
Answers should be rounded appropriately and
the level of accuracy noted.
Calculations MUST involve more than one stage
where results from one stage are used in a
subsequent stage. Multi-stage calculations are
required for each of 3.2.2 (a), (b), (c) and (d)
Candidates should show their method.
Inappropriate or no rounding and level of accuracy not
stated.
Calculations not of appropriate difficulty.
3.2.2 (a)
3.2.2 (b)
3.2.2 (c)
Check methods
Calculations should be checked using a range of
methods as at level 2. Candidates should identify
any errors in the work that are obvious and
subsequently correct them.
An obvious error in the work e.g. averages outside range of
the data, standard deviation not sensible for the data.
Amounts OR Sizes
These cover:
 Powers and roots.
 Trigonometry
 Complex volumes and areas
These must include multi-stage calculations that
involve a follow through and be of a greater
difficulty than those exemplified at Level 2.
Simple calculations of fractions, percentages and decimals
that are not multi-stage.
Geometry calculations that do not involve a greater level of
difficulty than those at level 2.
Scales OR proportions
These cover:
 Proportional change
 Use of scale, area and volume factors,
e.g. doubling the dimension of a pool
would increase its volume by 8 times.
A scale drawing must be within the context of the
task.
Scale diagrams whose complexity does not exceed those
described at level 2. Scale diagrams are often included for
their own sake and are not really necessary within the
context of the task.
Handling statistics
These cover:
 Mean & median of grouped data.
 Cumulative frequency – inter-quartile
range.
 Standard deviation
 Histograms, frequency polygons, scatter
graphs.
There must be comparison using statistical
methods, i.e. graphs, charts, etc or numerical
statistics.
Data MUST be grouped at this level and use
made of the grouping e.g. putting heights into
groups… 1.5 – 1.59....
Statistics not checked for plausibility. Nonsensical
measures of average and spread.
No comparison between sets of data.
No use of grouped data.
AON Guidance 26/02/2008
3.2.2 (d)
Using Formulae
AON Guidance 26/02/2008
These cover:
 Use of geometric formulae – area,
volume, density etc.
 Rearranging geometric formulae – e.g.
find height of cylinder given volume and
radius
 Creating formulae in spreadsheet
 Solving of simultaneous equations
 Standard deviation
The formulae should be stated algebraically.
Results from formulae should be checked for
plausibility.
Formulae should involve calculations of a level 3
nature as given in 3.2.2 (a), (b) & (c)
Formulas not of a complexity beyond level 2.
E.g. use of area of rectangle formula.
Results from formulae not checked for plausibility,
especially evident with standard deviation.
Interpret the results of your calculations, present your finding and justify your methods.
3.3.1
Select appropriate
methods of presentation
and justify your choice.
3.3.2
Present your findings
effectively
3.3.3
Describe what your
results tell you and
whether they meet your
purpose.
AON Guidance 26/02/2008
Choose the best graph to:
 compare distributions
 show trends
 make comparisons
and explain your choice – i.e. Why choose to
use that graph?
At least TWO DIFFERENT ways should be used
for presentation of findings.
 Charts AND Graphs
 Charts AND Diagrams
 Graphs AND Diagrams
or
 Graphs, Charts AND Diagrams
Correct use of graphs/charts and no redundancy.
All graphs should be labelled correctly.
ICT may be used but candidates must check the
accuracy of the presentation.
Candidates explain what results tell them and
refer these results back to their original plan.
Candidates discuss how possible errors affected
results.
Graphing the same data using a variety of different
methods for no apparent reason.
ONE way used to present findings
 Charts only
 Graphs only
 Diagrams only
Graphs/charts drawn and no reference made to what they
display or why they were chosen.
Graphs/charts labelled incorrectly or missing labels.
Diagrams drawn without any purpose.
Graphs drawn using ICT often are incorrectly labelled or do
not follow the correct conventions. E.g. Histograms labelled
as bar charts.
No analysis of findings.
Candidates merely state results rather than interpreting
them.
Not referring back to original purpose/hypothesis.