Field Sciences
Review of Mathematics and Statistics and Probability Level 1 achievement and unit standards
Unit standards
Subfield 
Domain 
ID 
Mathematics 
Algebra 
5223, 5226, 5238, 5239, 7568, 20659 
Geometry 
5229, 5231, 5237, 5252  
Mathematical Processes 
5233  
Mathematical Studies 
7559, 7561, 7570, 1231912322, 12328  
Measurement 
5228, 5241, 8492, 20662  
Number 
5224, 5225, 5227, 5234, 5235, 84898491, 20663, 23738, 23739  
Trigonometry 
5236  
Statistics and Probability 
Probability 
5232, 5242, 7571 
Statistics 
5230, 5240, 7565 
Achievement standards
Domain 
ID 
Subject reference 
Algebra 
90147, 90148, 90799, 90800 
Mathematics 1.1, 1.2, CAS Mathematics 1.1, 1.2 
Geometry 
90150, 90152, 90153 
Mathematics 1.4, 1.8, 1.9 
Measurement 
90149 
Mathematics 1.3 
Number 
90151 
Mathematics 1.7 
Probability 
90194 
Mathematics 1.6 
Statistics 
90193 
Mathematics 1.5 
This report was republished in April 2011 to change the expiry date of unit standards categorised as category C or D from December 2012 to December 2013. 
The Ministry of Education and NZQA National Qualifications Services (NQS) have completed the review of the unit standards and achievement standards listed above.
New registration date December 2010
Date new versions republished April 2011
Date new versions published December 2010
Planned review date December 2014
Summary of review and consultation process
In 2008 the Ministry of Education (MoE) and NZQA began to review achievement and unit standards in light of the revised New Zealand Curriculum (NZC). This Alignment of Standards (AoS) review also addressed duplication of outcomes, credit parity, fairness, consistency, and coherence. The AoS review was guided by the revised NZC itself and the Standards Review Guidelines. A copy of the NZC is available at
http://nzcurriculum.tki.org.nz/Curriculumdocuments/TheNewZealandCurriculum
Teacher subject associations were involved in the review, and draft achievement standards were the focus of wide consultation, especially with secondary schools and teachers. Extensive resources, including student exemplars, were also developed to support these standards, and are available on the MoE and/or the NZQA websites.
The review of unit standards included consultation with tertiary providers to assess continued relevance and likely future use of the standards. Unit standards that duplicate achievement standard outcomes and those without the likelihood of future use were recommended for expiry.
National consultation was undertaken in 2009, with the results analysed by Research New Zealand. The responses were generally positive.
The review of unit and achievement standards at Level 1 was completed in time for implementation in schools in 2011. Standards at Levels 2 and 3 will be implemented in 2012 and 2013 respectively.
Main changes resulting from the review
· All NZC Level 6 (NZQF Level 1) outcomes derived from the NZC are now assessed using achievement standards, and the three remaining unit standards are no longer linked to the NZC.
· Existing achievement standards were reviewed and new achievement standards were developed to align with the NZC. See table below.
· Grading criteria for achievement standards were reviewed in accordance with the Standards Review Guidelines.
· Unit standards that recognised similar outcomes as achievement standards were replaced or expired apart from unit standards 5223 and 5236; and unit standard 26567 which replaced unit standards 20662 and 20663. These three unit standards are required in the tertiary sector.
· The credit value of unit standards 5223 and 5236 was reduced from 2 to 1 to better reflect the required learning, practice, and assessment time.
In August 2010, unit standards 26623, 26626, and 26627 in the Numeracy domain were listed on the Directory of Assessment Standards (DAS). These unit standards are included in the Review Categories and changes to classification, title, level, and credits
table in italics as recommended alternatives for expiring standards.
Appendix 1 includes a detailed description of the review of, and the changes to, standards in the Mathematics and Statistics and Probability domains.
Impact on existing accreditations
Current Accreditation for 
Accreditation extended to  
Nature of accreditation 
Classification or ID 
Level 
Nature of accreditation 
ID 
Level 
Field 
Sciences 
Any 
Standards 
26623, 26626, 26627 
1 
Subfield 
Mathematics 
Any 
Standards 
26623, 26626, 26627 
1 
Domain 
Measurement 
Any 
Standard 
26627 
1 
Domain 
Measurement 
1 
Standard 
26567 
1 
Domain 
Number 
Any 
Standards 
26623, 26627 
1 
Standard 
5224 
1 
Standard 
26623 
1 
Standard 
5225 
1 
Standard 
26623 
1 
Standard 
5227 
1 
Standard 
26623 
1 
Standard 
5228 
1 
Standard 
26627 
1 
Standard 
5229 
1 
Standard 
26623 
1 
Standard 
5235 
1 
Standard 
91026 
1 
Standard 
5240 
1 
Standards 
91035, 91036 
1 
Standard 
5241 
1 
Standard 
91030 
1 
Standard 
5252 
1 
Standard 
91031 
1 
Standard 
8489 
1 
Standard 
26623 
1 
Standard 
8490 
1 
Standard 
26623 
1 
Standard 
8491 
1 
Standard 
26626 
1 
Standard 
8492 
1 
Standard 
26627 
1 
Standard 
20662 
1 
Standard 
26567 
1 
Standard 
23738 
1 
Standard 
26623 
1 
Standard 
23739 
1 
Standard 
26623 
1 
Impact on Accreditation and Moderation Action Plan (AMAP)
All new achievement standards have been registered on AMAP 0233.
All unit standards have been registered on AMAP 0071.
Impact on registered qualifications
Key to type of impact  
Affected 
The qualification lists a reviewed classification (domain or subfield) in an elective set The qualification lists a standard that has changes to level or credits The qualification lists a C or D category standard 
Not materially affected 
The qualification lists a standard that has a new title The qualification lists a standard that has a new classification 
The following NZQA National Qualifications Services qualification is Affected by the outcomes of this review and will be updated when it is reviewed in 2011.
Ref 
Qualification Title 
ID 
0231 
National Certificate in Employment Skills 
8489, 8490, 8491 
The following table identifies qualifications developed by other SSBs that are Affected by the outcomes of this review. The SSBs have been advised that the qualifications require revision.
Ref 
Qualification Title 
ID 
SSB Name 
0147 
National Certificate in Leather Garment Manufacture (Level 3) with specialist strands in Material Selection and Cutting, Sewing and Garment Assembly, and Garment Finishing and Inspection 
8489, 8492 
Apparel and Textile Industry Training Organisation 
0877 
National Certificate in Boatbuilding (Level 4) with strands in Marine Cabinetmaking, Composite Sparmaking, Alloy Boatbuilding, Marine Rigging, Marine Painting, Composite Boatbuilding, Steel Boatbuilding, Wooden Boatbuilding, Marine Systems Engineering, Metal Sparmaking, Composite Production Trailer Boats, and Alloy Production Trailer Boats 
5231 
Boating Industry Training Organisation 
0272 
National Certificate in Fibre Cement Linings (Level 4) with strands in Fixing, and Finishing 
8492 
Building and Construction Industry Training Organisation 
0273 
National Certificate in Fibrous Plaster (Installation) (Level 4) with an optional strand in Specialist Systems 
8492  
0274 
National Certificate in Fibrous Plaster (Manufacture) (Level 4) with optional strands in Panels and Tiles, and Specialist Models and Mould Making 
8492  
0275 
National Certificate in Plaster Board (Level 4) with strands in Fixing, and Finishing, and with an optional strand in Specialist 
8492  
0786 
National Certificate in Proprietary Plaster Cladding Systems (Level 4) with strands in Rebated Fibre Cement, Lightweight Fibre Cement, and External Insulation Finishing Systems (EIFS) 
8492  
1390 
National Certificate in Specialist Interiors (Installation) (Level 3) with strands in Suspended Ceilings, and Proprietary Partitions, and with an optional strand in Access Floors 
8492  
1450 
National Certificate in Basic Residential Property Maintenance (Level 2) with an optional strand in Basic Construction Project Work 
8492  
1452 
National Certificate in Concrete Core Skills (Level 2) 
8492  
0129 
National Certificate in Metal Casting (Technology) 
5223, 5226, 5228 
Competenz 
0342 
National Certificate in Food and Related Products Processing (Level 2) 
8489, 8491  
0568 
National Certificate in Hand Operated Fire Fighting Equipment (Level 3) 
8490, 8492  
0570 
National Certificate in Fixed Fire Protection Systems (Level 4) 
8490  
0765 
National Certificate in Architectural Aluminium Joinery (Entry Skills) (Level 2) 
8489  
0863 
National Certificate in Fixed Fire Protection Systems (Level 3) with strands in Installation, and Testing 
8490  
0958 
National Certificate in Rail Transport (Level 2) 
8489  
1112 
National Certificate in Rail Infrastructure (Level 3) 
8489  
1262 
National Certificate in Mechanical Engineering (Level 4) with strands in Fitting and Machining, General Engineering, Machining, Maintenance Engineering, Toolmaking, and Electricity Supply 
5223, 5226, 5228  
1386 
National Certificate in Manufacturing (Metal and Related Products) (Level 2) 
8489, 8491  
1387 
National Certificate in Manufacturing (Metal and Related Products) (Level 3) 
8489  
1581 
National Certificate in Manufacturing (Core Skills) (Level 2) 
8489  
0432 
National Certificate in Surveying (Assistant) (Level 3) 
5236 
InfraTrain New Zealand 
1326 
National Certificate in Civil Construction Works with strands in Concrete Kerb and Channel; Concrete Work; Culverts and Drainage Systems; Interlocking Paving; Retaining Structures; Road Construction; Road Maintenance; Road Safety Barrier; Roadside Amenities; and Traffic Signage 
5225, 5228, 5235, 5241, 8491, 8492, 20662, 20663  
0955 
National Certificate in Meat Processing (Smallgoods) (Level 1) 
8489, 8491, 8492 
New Zealand Industry Training Organisation 
0956 
National Certificate in Meat Processing (Smallgoods) (Level 2) with strands in Raw Processing; Cooked Processing; and Slicing, Packaging and Dispatching; and with optional strands in Workplace Safety and Health; and Workplace Communications 
8489, 8491, 8492  
1078 
National Certificate in Amenity Turf Maintenance (Level 3) 
8492 
New Zealand Sports Turf Industry Training Organisation 
1340 
National Certificate in Industrial Textile Fabrication (Level 3) with strands in Canvas Fabrication; Sailmaking; and Vehicle Trimming and Upholstery 
8492 
NZ Motor Industry Training Organisation (Incorporated) 
0110 
National Certificate in Scaffolding (Level 4) with strands in Advanced Scaffolding, and Suspended Scaffolding 
5228, 8489 
Opportunity  The Training Organisation

0111 
National Certificate in Rigging with strands in Basic Rigging, Intermediate Rigging, and Advanced Rigging 
5228, 5236, 8489  
0118 
National Certificate in Cranes (Mobile Crane Supervision) (Level 5) 
5228, 5236  
0119 
National Certificate in Cranes (Mobile Crane Dispatch Supervision) (Level 3) 
5228, 5236  
0120 
National Certificate in Cranes (Tower Crane Supervision) (Level 5) 
5228, 5236  
1016 
National Certificate in Industrial Rope Access (Elementary Rope Skills) (Level 3) 
8489  
1352 
National Certificate in Scaffolding (Elementary) (Level 3) 
5228, 8489  
1520 
National Certificate in Cranes (Advanced Crane Operation) (Level 5) 
5228, 5236  
0566 
National Certificate in Cablemaking (Level 2) with strands in Wiredrawing, Conductor Assembly, Extrusion, Cable Assembly, and Cable Testing 
8489, 8490 
Plastics and Materials Processing Industry Training Organisation 
1233 
National Certificate in Pharmaceutical and Allied Products Manufacturing (Level 1) 
5228, 5240, 8490, 8491, 8492  
1235 
National Certificate in Engineering and Technology (Pharmaceutical and Allied Products) (Level 2) 
5223, 5226, 5228  
1361 
National Certificate in Plastics Processing Technology (Production) (Level 1) with strands in General, Injection Moulding, Extrusion, Blow Moulding, Thermoforming, Blown Film Extrusion, Film Conversion, Injection StretchBlow Moulding, Rotational Moulding 
8489, 8490  
0990 
National Certificate in Distribution (Level 2) 
8489, 8490 
Retail Institute 
0180 
National Certificate in Passenger Service (Small Passenger Vehicle) with an optional strand in Taxi Driving 
5234 
Tranzqual ITO

0189 
National Certificate in Commercial Road Transport (Introductory Skills) 
8489, 8490, 8492  
0190 
National Certificate in Passenger Service (Large Passenger Vehicle) with strands in School Bus; Urban and Local Route; and Long Distance 
8489, 8491  
1010 
National Certificate in Stevedoring and Ports Industry (Cargo Handling) (Level 3) 
8489  
1451 
National Certificate in Stevedoring and Ports Industry (Cargo Handling) (Level 2) 
8490  
1505 
National Certificate in Relocation Operations (Level 2) with strands in Domestic Relocation Operations, and International Relocation Operations 
8492 
Impact of changes on NCEA Exclusions List
For transition purposes, the following exclusions will apply for new achievement standards. This transition will apply until December 2011 only.
New achievement standard 
Existing achievement standard 
91030 
90149 
91033 
90150 
91034 
90150 
91035 
90193 
91036 
90193 
For transition purposes where there is impact on qualifications, the following exclusions will apply for new achievement standards. This transition will apply until December 2013 only, when the unit standards will expire.
New achievement standard 
Existing unit standards 
91026 
5235 
91027 [Externally assessed] 
5239 
91028 [Externally assessed] 
5238 
91029 
5238 
91030 
5241 
91031 [Externally assessed] 
5252 
91032 
5236 
91033 
5231, 5237 
91034 
5237 
91035 
5240 
91036 
5240 
Review Categories and changes to classification, title, level, and credits
The following summary shows the changes made to the standards as a result of the review. All changes are in bold. Recommended alternatives for Category D unit standards are shown in italics.
Key to review category  
A 
Dates changed, but no other changes are made  the new version of the standard carries the same ID and a new version number 
B 
Changes made, but the overall outcome remains the same  the new version of the standard carries the same ID and a new version number 
C 
Major changes that necessitate the registration of a replacement standard with a new ID 
D 
Standard will expire and not be replaced 
Externally assessed achievement standards categorised as category C or D expire at the end of 
December 2010 
Internally assessed achievement standards categorised as category C or D expire at the end of 
December 2011 
Unit standards categorised as category C or D expire at the end of 
December 2013 
Sciences > Mathematics > Algebra
ID 
Title 
Level 
Credit 
Review Category 
5223 
Use formulae and equations to solve problems Use formula and equations to solve problems in the workplace 
1 
2 1 
B 
5226 
Construct and use tables and graphs 
1 
2 
D 
5238 91028
91029 
Draw and describe graphs involving two variables Investigate relationships between tables, equations and graphs [Externally assessed] Apply linear algebra in solving problems 
1 1
1 
4 4
3 
C 
5239
91027 
Describe patterns and solve problems and equations Apply algebraic procedures in solving problems [Externally assessed] 
1
1 
3
4 
C 
7568 
Use formulae to solve problems and describe rates from graphs 
1

2

D 
20659 
Demonstrate basic algebra skills 
1 
2 
D 
90147 
Use straightforward algebraic methods and solve equations 
1 
4 
D 
90148 
Sketch and interpret graphs 
1 
3 
D 
90799 
Demonstrate an understanding of straightforward algebraic methods 
1 
4 
D 
90800 
Demonstrate an understanding of the features of graphs 
1 
3 
D 
Sciences > Mathematics > Geometry
ID 
Title 
Level 
Credit 
Review Category 
5229 
Use geometry to describe situations and solve problems 
1 
2 
D 
5231
5237 90150
91033
91034 
Use constructions and make drawings for geometrical situations Describe situations using transformations and loci Use geometric techniques to produce a pattern or object Apply knowledge of geometric representations in solving problems Apply transformation geometry in solving problems 
1
1 1
1
1 
2
3 2
3
2 
C
C C 
5252
91031 
Derive angle properties of circles and use them to solve mathematical problems Apply geometric reasoning in solving problems [Externally assessed] 
1
1 
3
4 
C 
90152 91032 
Solve rightangled triangle problems Apply rightangled triangles in solving measurement problems 
1 1 
2 3 
C 
90153 
Use geometric reasoning to solve problems 
1 
2 
D 
Sciences > Mathematics > Mathematical Processes
ID 
Title 
Level 
Credit 
Review Category 
5233 
Use mathematical processes and skills in a variety of contexts 
1 
7 
D 
Sciences > Mathematics > Mathematical Studies
ID 
Title 
Level 
Credit 
Review Category 
7559 
Demonstrate knowledge of the mathematics of geometry patterns 
1 
2 
D 
7561 
Demonstrate knowledge of the mathematics of number patterns 
1 
2 
D 
7570 
Carry out and report on a given mathematical study 
1 
2 
D 
12319 
Find relationships between measurements 
1 
2 
D 
12320 
Demonstrate knowledge of finite arithmetic systems 
1 
2 
D 
12321 
Describe mathematical algorithms and use them to solve problems 
1 
2 
D 
12322 
Use mathematics in the design of a given object or process 
1 
2 
D 
12328 
Demonstrate knowledge of the history of a mathematical topic or mathematician 
1 
2 
D 
Sciences > Mathematics > Measurement
ID 
Title 
Level 
Credit 
Review Category 
5228
8492 
Take measurements and use calculations to solve measurement problems Use standard units of measurement 
1
1 
3
3 
D
D 
26627 
Use measurement to solve problems 
1 
3 

5241 90149
91030 
Use strategies to solve measurement problems Solve problems involving measurement of everyday objects Apply measurement in solving problems 
1 1
1 
3 3
3 
C C 
Sciences > Mathematics > Number
ID 
Title 
Level 
Credit 
Review Category 
5224 5225
5227 8489
8490
23738
23739
26623 
Use decimals and percentages to solve problems Use fractions, ratio, and proportion to solve problems Solve problems involving money Solve problems which require calculation with whole numbers Solve problems using calculations with numbers expressed in different forms Use numeracy strategies to solve problems involving whole numbers Use numeracy strategies to solve number problems involving decimals, percentages and fractions Use number to solve problems 
1 1
1 1
1
1
1
1 
2 2
3 2
2
2
2
4 
D D
D D
D
D
D 
5234 
Use calculations in money situations 
1 
3 
D 
5235 91026 
Use strategies to solve number problems Apply numeric reasoning in solving problems 
1 1 
2 4 
C 
8491
26626 
Read and interpret information presented in tables and graphs Interpret statistical information for a purpose 
1
1 
2
3 
D 
90151 
Solve straightforward number problems in context 
1 
3 
D 
Sciences > Mathematics > Trigonometry
ID 
Title 
Level 
Credit 
Review Category 
5236 
Use Pythagoras' Theorem and trigonometry to find unknowns in rightangled triangles Use Pythagoras' theorem and trigonometry to solve problems related to rightangled triangles in the workplace 
1
1 
2
1 
B 
Sciences > Statistics and Probability > Probability
ID 
Title 
Level 
Credit 
Review Category 
5232 
Determine probabilities in practical situations 
1 
2 
D 
5242 
Determine probabilities 
1 
2 
D 
7571 
Use simulation techniques to determine probability and solve problems 
1 
2 
D 
90194 
Determine probabilities 
1 
2 
D 
91038 
Investigate a situation involving elements of chance 
1 
3 
New 
Sciences > Statistics and Probability > Statistics
ID 
Title 
Level 
Credit 
Review Category 
5230 
Carry out a statistical investigation and interpret data 
1 
3 
D 
5240 90193 91035
91036 
Explore data and evaluate reports Use statistical methods and information Investigate a given multivariate data set using the statistical enquiry cycle Investigate bivariate numerical data using the statistical enquiry cycle 
1 1 1
1 
3 3 4
3 
C C 
7565 
Carry out and report on a given statistical investigation 
1 
2 
D 
91037 
Demonstrate understanding of chance and data [Externally assessed] 
1 
4 
New 
Sciences > Mathematics
ID 
Domain 
Title 
Level 
Credit 
Review Category 
20662
20663
26567 
Measurement
Number
Number 
Make estimates of measurements with common units Use a strategy to estimate the solution to number problems Use a strategy to estimate the solutions to number problems and make estimates of measurements in the workplace 
1
1
1 
2
2
2 
C
C 
Appendix 1
Development of L1 Mathematics and Statistics Standards
Process of Aligning Standards with the New Zealand (NZC)
The reviewed standards are derived from the achievement objectives from the Mathematics and Statistics learning area in the NZC. Various ways of grouping the achievement objectives of the NZC into standards for assessment were considered. The decision was made by the writing group to stay with the current split into the traditional topic based standards. This has the advantage of the title of each standard succinctly conveying the content of the standard. The most NZC change has occurred in the statistics strand and the standards reflect this.
Addressing Duplication
All of the existing registered mathematics achievement standards are replaced by the aligned standards. In addition, some unit standards based on the old NZC at Levels 6, 7, or 8 duplicate new standards and are therefore recommended for expiry. Unit standards which do not duplicate achievement standards and have high usage in the tertiary sector have been reviewed and retained.
Addressing Credit Parity
The guideline of 10 hours of learning for each credit has been applied to the standards. It should be noted that this time includes time both in class and out of class for teaching, practice, study and assessment for a notional average student. It was assumed that about 5 hours of in class time could be associated with each credit which in most schools would mean more than one week per credit. In general, credit values are similar to the previous standards, with some increases where it was considered that the learning programme would need more time.
External and Internal Assessment:
The Principles for Standards Review recommend that there be a maximum of three externally assessed standards in a three hour examination. This is to provide students with a reasonable amount of time to provide their best evidence. The limit of three externally assessed standards was a big change from the previous six externally assessed standards at this level. After considerable discussion it was decided to develop one external standard derived from each of the three strands of the learning area. Various factors were considered in the discussions leading to this decision.
· Given strong feedback in the early consultation that technology restrictions should be placed on externals rather than internals, it was decided to choose standards for external assessment that were suitable for assessment under examination conditions where students are restricted to the use of a graphic calculator. For internally assessed standards there are more options for project work, assignments, and the use of Computer Algebra System (CAS) or computer technology, which would be particularly appropriate for practical work in geometry or statistics.
· The equity issues associated with technology particularly apply to the standards which are algebraic in nature, where a graphic or CAS calculator would give an unfair advantage. For this reason it was decided to make the algebra standard at Level 1 (AS 1.2) a technology free standard, which can be assessed by a Common Assessment Task (CAT), set externally, but marked and moderated as for an internal. This standard has now been designated external to acknowledge the external setting. The Level 2 and 3 algebra and calculus standards are recommended to be external and limited to graphic calculators.
· The new standard involving graphs (AS 1.3) has a new emphasis on linking graphs, tables and equations.
What has changed?
· All the standards assessing outcomes from the NZC are now achievement standards
· The format and design of the standards has changed (see below)
· There are sufficient achievement standards at each level to offer a choice of assessment tools for different learning programmes.
Format of the standards
The titles of these standards are identical to the achieved criterion in each standard because this is the level of performance which must be reached to gain credit. Each standard has a single outcome. This will enable a more holistic approach in assessment design and in making judgements against the standard.
The steps up to merit and excellence grades are described in terms of the quality of thinking (not in terms of content). Current practice, and the direction for teaching and learning described in the NZC, was taken into consideration when trying to describe the quality of thinking for each grade level. It was decided that a generic description across all mathematics standards was possible. The challenge was to find a short word or phrase which would describe each grade level. Some terminology has been borrowed from the Structure of Observed Learning Outcomes (SOLO) taxonomy. It was considered that "relational thinking" is a good summary of merit level thinking, and that "extended abstract thinking" could apply to excellence level thinking. These descriptions are written into the achievement criteria and explanatory note 2 in each standard. A similar generic distinction and label was arrived at for statistics, where "justification" is required for merit and "statistical insight" for excellence.
This terminology is included in the assessment resources, and exemplars of student work, developed for each of the standards.
Programmes of learning
It is not expected that schools will include all of the NZC objectives in a learning programme or course nor would schools use all of the standards to assess the outcomes of such a programme or course. Schools have a choice, and should offer pathways, including courses and assessments, appropriate for the needs and capabilities of their students. In several consultations about mathematics assessment in recent years there has been a consistent message that it is unrealistic to try to cover all curriculum outcomes in one course. The new mathematics and statistics learning area in the NZC has an increased emphasis on statistics but very little has been removed from the other parts of the NZC to make room for this. Teachers now have the option of choosing which aspects of the NZC are best suited to various groups of students. The matrix of aligned standards offers sufficient choice to provide for a variety of courses appropriate for a range of students.
Issues arising from national consultation included:
· credit allocation
· mode of assessment
· the lack of detail about mathematical content in the standards
· the need for examples of assessment tasks
· a perception that there is a lot to be assessed in a one year course.
Changes to all mathematics standards as a result of feedback from consultation included the following:
· The explanatory notes have been adjusted to clarify the distinction between the mathematical process and the communication elements of the description. Both the application and the communication are required.
· Explanatory note 2 may include the words "a range of" indicating that at least three different methods should be demonstrated.
· In the definition for relational thinking the words "selecting and" have been added to "carrying out a logical sequence of steps" to clarify that giving a list of steps for students to follow is not acceptable, and that at merit level students are expected to be selecting the sequence of steps.
· The stems to these definitions have been clarified by changing "could involve" to "must involve".
· The definition of "problem" has been modified so that it does not include the word "modelling" because modelling is not generally required by the criterion for Achieved.