Access to HE
Mathematics
GCSE Equivalent Scheme
Handbook
2011-12
Contents:
Section
1
2
3
4
5
6
7
Appendix 1
Appendix 2
Title
Page
2
2
2
3
3
4
4
Context
GCSE Equivalent Status
LASER Endorsement of GCSE Equivalent Status
Summary of Units in the Scheme
Assessment Methodology
Retention of sample marked assignments and test scripts
Claiming the Access GCSE Equivalence Certificate for
Students
Units
5
9
Extract from Key Stage 4 Mathematics Requirements
Access GCSE Equivalent Maths Academic Year 2011-2012 © LASER 2011 v2
1
Access to HE Mathematics Equivalent Scheme
1. Context
This scheme has now replaced the previous AVA Mathematics GCSE Equivalent
schemes inherited by Laser Learning Awards (LASER) from the former AVAs of
OCNHIS and OCNKM.
LASER will endorse the scheme as being equivalent in standard to a GCSE grade C
pass for appropriate student matriculation into HE purposes.
From 2011-12 onwards, this scheme will be the only GCSE Maths equivalence scheme
endorsed by LASER. Older schemes will no longer be awarded a GCSE Equivalent
certificate. Where other qualifications are used to evidence GCSE equivalence, this
should be registered using APCL.
2. GCSE Equivalent Status
2.1 This scheme is only for use by students on LASER Access to HE Diplomas. The
GCSE equivalent scheme for Mathematics is intended to enable Access students to
meet the matriculation requirements for entry to a range of HE degree courses
where a GCSE pass A-C grade is required.
2.2 The scheme does NOT have any function beyond this and is not intended to be
used as a substitute for any statutory requirements placed on an individual in order
to be competent to practice, whether this is as a teacher, nurse, or midwife etc.
2.3 Access centres must make clear the status of any GCSE equivalent to student upon
commencement of the Access Diploma. Students obtaining a place on an HE course
using a LASER approved GCSE equivalent scheme, must be advised that they may
have to undertake additional statutory requirements (such as obtaining an actual
GCSE or taking another prescribed test) in order to be qualified to enter a specific
career.
3. LASER Endorsement of GCSE Equivalent Status
The status of GCSE Equivalence is conferred on the achievement of the units outlined
below only when achieved as part of an LASER AVA Access to HE Diploma.
The following conditions and rules apply:
a) All four units totalling 12 credits at Level Two must be achieved by a student.
b) The ‘Minimum Assessment Requirements’ (see below) have been met
c) The credit achievement may be included in, or be additional to, the Diploma rules of
combination where it is required for progression to HE.
d) Achievement of credit in other LASER-validated Mathematics units will not confer
GCSE equivalence, although centres may use the LASER APL process where
appropriate.
2
4. Summary of Units in the Scheme
Unit Title
Level Credits
Shape, Space and
Two
3
Measurement
Collecting, Recording
Two
3
and Analysing Data
Development of Ideas
Two
3
in Algebra
Number and Algebra
Two
3
Total Credits
12
Click on links to go to the unit details
National
Unit
Code
Code
RB42SE901 SER945
Status
RB72SE904 SER946
M
RB32SE903 SER947
M
RB32SE904 SER948
M
M1
5. Assessment Methodology
All learners must compile a portfolio of evidence comprising marked assignments which are
mapped to the relevant assessment criteria in the units for internal verification and LASER
external moderation.
5.1
Across the units, learners should be given the opportunity, and encouraged to:







5.2
use and apply Mathematics accurately in practical, real-life situations as well as
within the classroom
recognise the rich historical and cultural roots of mathematics
select mathematical tools that are appropriate to the problem
use methods that communicate mathematics effectively
understand the creative process in mathematics, combining understanding,
experiences, imagination and reasoning to construct new knowledge
develop convincing arguments, and pose appropriate questions to challenge
others’ arguments
use the abstract concepts of mathematics to model, interpret or represent
situations.
The AVA is committed to regional standardisation in assessing the Access to HE
GCSE equivalence Mathematics units. Therefore, for GCSE equivalence, the AVA
requires all centres to undertake a standard pattern of assessment outlined below.
a) Centre-devised marked assessments: There must be evidence of achievement
of all assessment criteria in all units. Mandatory assessment information is
provided below. Centres should devise their own assessments, within the
permitted assessment rules for each unit.
Units: Collecting, Recording And Analysing Data, and Shape, Space and
Measurement
The assessment criteria for these units may be evidenced entirely or in part by
work produced for the other units on an Access Diploma course. Alternatively
centres may generate specific assignments or use a combination of specific
assignments and other work produced on the Access Diploma.
1
These units are mandatory for the achievement of a CGSE Equivalent but are not mandatory for the
achievement of an Access Diploma unless specifically required in the rules of combination (RoC) for a Diploma.
LASER strongly advises that these units are not entered as mandatory in the RoC for Access Diplomas.
3
b) Evidence from other parts of an Access Diploma: Where centres choose to
draw evidence for achievement from other elements of an Access to HE Diploma,
there must be a clear explanation of how the chosen evidence meets the
assessment criteria in the relevant GCSE equivalence unit. This is best
demonstrated by using a cover sheet for such pieces of evidence which clearly
identifies how the evidence meets the individual criteria.
c) Written tests: At least two tests, of at least 40 minutes duration, must be set
and marked internally and taken under examination conditions.
The centre must relate the contents of the tests to learning outcomes in the
units listed below. At least one learning outcome from each of the units must be
tested across the two tests.


Development of Ideas in Algebra
Number and Algebra
Centres could test all of the unit contents via appropriately set tests or
supplement the test evidence with additional course work as required.
Unit Title
Level
Shape, Space and Measurement
Two
Collecting, Recording and
Two
Analysing Data
Development of Ideas in Algebra
Two
Number and Algebra
Two
Total Credits
Credits
Mandatory
Test?
Course Work
Option?
3
3
3
3
12
Y
Y
Y
Y
Y
Y
6. Retention of sample marked assignments and test scripts
Centres should retain representative samples of marked student assignments relating
to each unit in the scheme. Further guidelines can be found in the current version of
the Access Quality & Moderation Guidelines but as a minimum centres should retain
the equivalent of one full student portfolio of evidence for the scheme per year. These
should be retained for a minimum of three years. An LASER Access external
moderator will sample the evidence produced by students and will produce an annual
report on each centre using the scheme.
7. Claiming the Access GCSE Equivalence Certificate for Students
The GCSE Mathematics Equivalence units must be included within the units available
for the Access Diplomas at the centre. Where a student has achieved the required
units, this should be recorded on the RAC in the usual way. The box claiming the
GCSE equivalent for Mathematics for each learner on the RAC must also be ticked.
At the point of certification the student will receive a certificate stating that s/he has
achieved an equivalent to GCSE Mathematics grade C and above and the units will
be listed on his/her credit transcript. LASER levies a charge to centres for each
GCSE equivalent certificate produced per student. Please see current Access
charges for further details.
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Appendix 1 - Units
UNIT TITLE:
Shape, Space and Measurement
LEVEL:
CREDIT VALUE:
UNIT CODE:
NATIONAL CODE:
Two
3
SER945
RB42SE901
(Access/A2)
This unit has 3 learning outcomes.
LEARNING OUTCOMES
ASSESSMENT CRITERIA
The learner will:
The learner can:
1. Understand and use properties of shape.
1.1 Distinguish between specific triangles,
quadrilaterals and polygons by their
properties.
1.2 Distinguish 3D shapes by their properties
and recognise their nets.
1.3 Measure angles in 2D shapes and deduce
their size using the following:
- angles in a straight line,
- angles around a point, and
- opposite, alternate and corresponding
angles.
2. Understand the basic trigonometry of a
right-angled triangle.
2.1 Calculate measurements using similar
right-angled triangles.
2.2 Use Pythagoras' theorem to calculate the
length of a side in a right-angled triangle.
3. Solve problems using measurements in
two and three dimensions.
3.1 Calculate, where appropriate, perimeters,
areas, surface areas and volumes of
simple regular shapes.
3.2 Interpret scale drawings.
3.3 Estimate measurements of everyday
items.
3.4 Convert measurements between units
(e.g. cm2 and m2) and make rough
conversions between imperial and metric
units.
3.5 Make calculations using compound
measure (e.g. speed, density) and use
appropriate units.
5
UNIT TITLE:
Collecting, Recording and Analysing Data
LEVEL:
CREDIT VALUE:
UNIT CODE:
NATIONAL CODE:
Two
3
SER946
RB72SE904
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES
ASSESSMENT CRITERIA
The learner will:
The learner can:
1. Collect data for a purpose.
1.1 Design and use a questionnaire to
collect data comprised of open and
closed questions.
1.2 Use data collection sheets to record data
from a practical exercise (e.g.
measuring temperature change over
time).
1.3 Identify strengths and weaknesses of
different methods of data collection.
2.1 Using information from tables, lists, or
computer databases construct
frequency and grouped frequency
tables.
2.2 Using suitable examples distinguish
between discrete and continuous data.
3.1 Using suitable data construct bar charts,
pictograms, pie charts and line graphs.
3.2 Interpret critically statistical diagrams
and graphs, explaining the main
features of the data represented.
3.3 Construct and use histograms with equal
intervals from frequency distributions.
3.4 By drawing a scatter diagram and a line
of best fit by inspection, comment on the
correlation of the data.
4.1 Calculate mean, median and mode from
lists, ungrouped and grouped frequency
tables.
4.2 Calculate range and interquartile range.
4.3 Calculate the probability of a single event
within the context of the data collection.
2. Categorise and record data.
3. Represent and interpret data.
4. Analyse data.
6
UNIT TITLE:
Development of Ideas in Algebra
LEVEL:
CREDIT VALUE:
UNIT CODE:
NATIONAL CODE:
Two
3
SER947
RB32SE903
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES
ASSESSMENT CRITERIA
The learner will:
The learner can:
1. Manipulate algebraic expressions in
order to solve problems.
1.1 Change the subject of a formula where the
subject appears in one term only.
1.2 Simplify expressions using the rules of
indices.
1.3 Expand expressions involving brackets and
factorise simple expressions.
1.4 Solve simple linear equations up to those
including brackets, and where the unknown
appears on both sides.
2. Use graphical methods to represent
algebraic relationships.
2.1 Construct a table of values from linear
algebraic equations.
2.2 Plot the graph of a linear function from a
table of values.
2.3 Use the formula y = mx + c to calculate the
values of m and c from a graph or table of
data.
2.4 Recognise and sketch graphs of y = x2, y =
x3 and y = a/x.
3. Use graphical and non-graphical
methods to solve algebraic
problems.
3.1 Solve simultaneous equations containing two
variables graphically.
3.2 Plot the graph of a quadratic function.
3.3 Solve quadratic equations of the form
x2
+ ax + b = 0 using a graphical method.
3.4 Solve simple algebraic equations using a
'trial and improvement' method.
4. Perform an investigation, which leads
to an understanding of sequences.
4.1 Recognise and continue a pattern of
numbers to a specified term.
4.2 Recognise patterns of triangular numbers.
4.3 Find an algebraic expression for the nth term
of a linear sequence.
Access GCSE Equivalent Maths Academic Year 2011-2012 © LASER 2011 v2
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UNIT TITLE:
Number and Algebra
LEVEL:
CREDIT VALUE:
UNIT CODE:
NATIONAL CODE:
Two
3
SER948
RB32SE904
(Access/A2)
This unit has 4 learning outcomes.
LEARNING OUTCOMES
ASSESSMENT CRITERIA
The learner will:
The learner can:
1. Demonstrate an understanding of
mathematical language with respect
to number.
1.1 Use the following terms appropriately:
whole numbers, natural numbers, integers
(both positive and negative values), digits,
factors, prime numbers, fractions,
decimals, reciprocals, percentages,
indices, standard form.
1.2 Identify place value.
1.3 Convert percentages to decimals and
fractions and vice versa.
1.4 Recognise square numbers up to 15 x 15
and the cubes of 2,3,4,5 and 10.
2.1 Perform calculations using addition,
subtraction, multiplication, division and
simple applications of ratio using the types
of number and terms stated in 1.1.
2.2 Perform calculations involving brackets
and apply operators in the correct order.
2.3 Round numbers to a stated number of
significant figures or decimal places.
2.4 Estimate the results of calculations.
2.5 Choose and use appropriate levels of
accuracy to express an answer.
3.1 Substitute numerical values into given
formulae.
3.2 Perform addition, subtraction,
multiplication and division using algebraic
terms.
4.1 Draw axes with appropriate scales.
4.2 Plot points using Cartesian co-ordinates.
4.3 Interpret and sketch graphs from practical
situations (e.g. Hookes Law).
4.4 Extract information from graphs (e.g.
conversion or distance/time graphs).
4.5 Extrapolate and interpolate graphical data
and draw a line of best fit.
2. Undertake and solve mathematical
problems.
3. Demonstrate an understanding of the
need for and use of symbolic
notation, and use correctly.
4. Use a Cartesian graph to represent
information.
Access GCSE Equivalent Maths Academic Year 2011-2012 © LASER 2011
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Appendix 2: Extract from Key Stage 4 Mathematics Requirements
Colleagues may find the extract from the National Curriculum Requirements for Key Stage 4
Mathematics, to be a useful guide for further support when devising assignments or assessing work
for an Access to HE GCSE equivalence course. Some of the links within the text below will take you
straight to the relevant web page.
http://curriculum.qca.org.uk/key-stages-3-and-4/subjects/key-stage-4/mathematics/index.aspx
2.1 Representing
Students should be able to:
1. identify the mathematical aspects of the situation or problem, including questions that can be
addressed using statistical methods
2. compare and evaluate representations of a situation before making a choice, including
moving between different representations in pure and applied contexts.
3. simplify the situation or problem in order to represent it mathematically using appropriate
variables, symbols, diagrams and models
4. select mathematical information, methods, tools and models to use.
2.2 Analysing
Use mathematical reasoning
Students should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
make connections within mathematics
use knowledge of related problems
visualise and work with dynamic images
identify and classify patterns
make and justify conjectures and generalisations, considering special cases and counterexamples
explore the effects of varying values and look for invariance and covariance
take account of feedback and learn from mistakes
work logically towards results and solutions, recognising the impact of constraints and
assumptions
identify a range of techniques that could be used to tackle a problem, appreciating that more
than one approach may be necessary.
Use appropriate mathematical procedures
Students should be able to:
1. make accurate mathematical diagrams, graphs and constructions on paper and on screen
2. calculate accurately, using mental methods or calculating devices as appropriate
3. manipulate numbers, algebraic expressions and equations and apply routine algorithms
4. use accurate notation, including correct syntax when using ICT
5. record methods, solutions and conclusions
6. estimate, approximate and check working.
2.3 Interpreting and evaluating
Students should be able to:
1. form convincing arguments to justify findings and general statements
Access GCSE Equivalent Maths Academic Year 2011-2012 © LASER 2011
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2. consider the assumptions made and the appropriateness and accuracy of results and
conclusions
3. appreciate the strength of empirical evidence and distinguish between evidence and proof
4. look at data to find patterns and exceptions
5. relate their findings to the original question or conjecture, and indicate reliability
6. make sense of someone else’s findings and judge their value in the light of the evidence they
present
7. critically examine strategies adopted.
2.4 Communicating and reflecting
Students should be able to:
1. use a range of forms to communicate findings to different audiences
2. engage in mathematical discussion of results
3. consider the elegance and efficiency of alternative solutions
4. look for equivalence in relation to both the different approaches to the problem and different
problems with similar structures
5. give examples of similar contexts they have previously encountered and identify how these
contexts differed from or were similar to the current situation and how and why the same, or
different, strategies were used.
Range and content of Mathematics key stage 4
The study of mathematics should enable students to apply their knowledge, skills and understanding
to relevant real-world situations. It should include:
3.1 Number and algebra
1. real numbers, their properties and their different representations
2. rules of arithmetic applied to calculations and manipulations with real numbers, including
standard index form and surds
3. proportional reasoning, direct and inverse proportion, proportional change and exponential
growth
4. upper and lower bounds
5. linear, quadratic and other expressions and equations
6. graphs of exponential and trigonometric functions
7. transformation of functions
8. graphs of simple loci
3.2 Geometry and measures
1. properties and mensuration of 2D and 3D shapes
2. circle theorems
3. trigonometrical relationships
4. properties and combinations of transformations
5. 3D coordinate systems
6. vectors in two dimensions
7. conversions between measures and compound measures
3.3 Statistics
1. the handling data cycle
2. presentation and analysis of large sets of grouped and ungrouped data, including box plots
and histograms, lines of best fit and their interpretation
3. measures of central tendency and spread
4. experimental and theoretical probabilities of single and combined events.
Access GCSE Equivalent Maths Academic Year 2011-2012 © LASER 2011
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