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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD THAT HAS PASSED THE END DATE: 

Understand linear relationships and predicting linear trends using appropriate models 
SAQA US ID UNIT STANDARD TITLE
243835  Understand linear relationships and predicting linear trends using appropriate models 
ORIGINATOR
SGB Statistics 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY
-  
FIELD SUBFIELD
Field 10 - Physical, Mathematical, Computer and Life Sciences Mathematical Sciences 
ABET BAND UNIT STANDARD TYPE PRE-2009 NQF LEVEL NQF LEVEL CREDITS
Undefined  Regular-Fundamental  Level 4  NQF Level 04  5 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2018-07-01  2023-06-30  SAQA 06120/18 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2024-06-30   2027-06-30  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This unit standard does not replace any other unit standard and is not replaced by any other unit standard. 

PURPOSE OF THE UNIT STANDARD 
This unit standard is designed to model growth problems using financial formulae and population models in mathematical and contextual situations.

A person credited with this unit standard is able to:
  • Solve annuity problems involving changing circumstances.
  • Solve population increase and decrease problems using simple discrete population models.
  • Analyse and solve population increase and decrease problems using a discrete two species Lotka-Volterra predator-prey population model.

    In order to see this unit standard with its exact formulae, please use the link at the end of the Searchable Database home page. SAQA is in the process of adapting the National Learners' Records Database to accommodate such formulae. 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
    Mathematics at NQF Level 4: Specifically logarithms. 

    UNIT STANDARD RANGE 
    Growth problems refer to positive and negative growth, and simple and compound growth. 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Solve annuity problems involving changing circumstances. 
    OUTCOME RANGE 
    Changing circumstances include but are not limited to changes in time periods, repayments, withdrawals or interest rates. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The number of instalments is determined using logarithms on the calculator. 

    ASSESSMENT CRITERION 2 
    Timelines are formulated to support the conceptualisation of problems involving changing circumstances. 

    ASSESSMENT CRITERION 3 
    The number of payments and the final payment of a loan is calculated for fixed instalment loans. 

    ASSESSMENT CRITERION 4 
    Problems involving changing circumstances and time periods are solved by manipulating formulae or summing series. 

    SPECIFIC OUTCOME 2 
    Solve population increase and decrease problems using simple discrete population models. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Simple population increase or decrease is modelled using discrete Malthusian population models. 
    ASSESSMENT CRITERION RANGE 
    Models are of the form (as shown in the MS Word document).
     

    ASSESSMENT CRITERION 2 
    Simple population increase or decrease is modelled using discrete logistic population models. 
    ASSESSMENT CRITERION RANGE 
    Models are of the form (as shown in the MS Word document).
     

    ASSESSMENT CRITERION 3 
    A realistic population scenario is evaluated in order to select the most suitable model. 
    ASSESSMENT CRITERION RANGE 
    Models include Malthusian and logistic.
     

    ASSESSMENT CRITERION 4 
    The selected model is applied to the given scenario. 

    SPECIFIC OUTCOME 3 
    Analyse and solve population increase and decrease problems using a discrete two species Lotka-Volterra predator-prey population model. 
    OUTCOME RANGE 
    Lotka-Volterra predator-prey population models are of the form (See the formula shown in the MS Word document) and (See the formula shown in the MS Word document). 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Simple population increase or decrease problems are modelled using a discrete two species Lotka-Volterra predator-prey population model written in simple difference equation form. 

    ASSESSMENT CRITERION 2 
    Spiral graphs of Lotka-Volterra predator-prey population models are analysed to determine the equilibrium point. 

    ASSESSMENT CRITERION 3 
    Periodic graphs of Lotka-Volterra predator-prey population models are analysed to determine population of growth and decline cycles. 

    ASSESSMENT CRITERION 4 
    A realistic population scenario is evaluated in order to select the most suitable model. 
    ASSESSMENT CRITERION RANGE 
    Models include Malthusian, logistic and Lotka-Volterra.
     

    ASSESSMENT CRITERION 5 
    The selected model is applied to the given scenario. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
  • The assessment will be governed by the policies and guidelines of the relevant Education and Training Quality Assuror (ETQA) that has jurisdiction over this field of learning.
  • The assessor will be accredited, have the competence of this unit standard and be a subject matter expert in this learning area. 
    		•

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
    Solve population growth and decay problems using simple discrete population models such as:
  • A discrete Malthusian population model of the form (See the formula shown in the MS Word document).
  • A discrete Logistic population model of the form (See the formula shown in the MS Word document).
  • A discrete two species Lotka-Volterra predator-prey population model written in difference equation form (See the formula shown in the MS Word document) and (Using the formula shown in the MS Word document).

    Formulate and apply mathematical models and formulae to various contexts in order to solve problems that occur in various situations. 
    		•

    UNIT STANDARD DEVELOPMENTAL OUTCOME 
    N/A 

    UNIT STANDARD LINKAGES 
    N/A 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Identifying and solving problems in which responses display that responsible decisions using critical and creative thinking have been made when:
  • Solving a variety of mathematical problems requiring recursion. 
    		•

    UNIT STANDARD CCFO WORKING 
    Working effectively with others as a member of a team, group, organisation, and community during:
  • Class investigation, projects and group work. 
    		•

    UNIT STANDARD CCFO ORGANISING 
    Organising and managing oneself and one's activities responsibly and effectively when:
  • Doing investigations and projects. 
    		•

    UNIT STANDARD CCFO COLLECTING 
    Collecting, analysing, organising and critically evaluating information to better understand and explain:
  • Interpret information in order to develop a corresponding mathematical model of the context. 
    		•

    UNIT STANDARD CCFO COMMUNICATING 
    Communicating effectively using visual, mathematical and/or language skills in the modes of oral and/or written persuasion when:
  • Use everyday language and mathematical language and symbols to describe processes and in solving mathematical problems. 
    		•

    UNIT STANDARD CCFO SCIENCE 
    Using science and technology effectively and critically, showing responsibility towards the environment and health of others when:
  • Generating higher terms of a recursive sequence. 
    		•

    UNIT STANDARD CCFO DEMONSTRATING 
    Demonstrating an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation when:
  • Positive and negative growth and annuities.
  • Predator-prey modelling.
  • Recognising that mathematical argument, proof and problem-solving do not exist in isolation of the broader mathematical community and the applications of mathematical in a social world. 
    		•

    UNIT STANDARD ASSESSOR CRITERIA 
    N/A 

    REREGISTRATION HISTORY 
    As per the SAQA Board decision/s at that time, this unit standard was Reregistered in 2012; 2015. 

    UNIT STANDARD NOTES 
    Notes to Assessors:

    Assessors should keep the following general principles in mind when designing and conducting assessments against this unit standard:
  • Focus the assessment activities on gathering evidence in terms of the main outcome expressed in the title to ensure assessment is integrated rather than fragmented. The goal is to declare the learner competent in terms of the title. Where assessment at title level is unmanageable, focus assessment around each specific outcome, or groups of specific outcomes.
  • Make sure evidence is gathered across the range as expressed under the title. Specific range statements under individual outcomes or assessment criteria are examples, from which Learning Programme developers can select and modify.
  • Do not focus the assessment activities on each assessment criterion. Ensure that the assessment activities focus on outcomes and that sufficient evidence around all the assessment criteria is gathered.
  • The assessment criteria provide the specifications against which assessment judgements should be made. In most cases, knowledge can be inferred from the quality of the written solutions, but in other cases, knowledge and understanding will have to be tested through additional assessment techniques.
  • The task of the assessor is to gather sufficient evidence, of the prescribed type and quality , as specified in the unit standard, that the candidate can achieve the outcomes in a number of different contexts. Thus means that assessors will have to judge how many repeat performances are required before they believe fair and consistent assessment has take place.

    All assessments should be constructed in line with the following well documented principles of assessment: appropriateness, fairness, manageability, integration into work or learning. Assessment should be valid, direct, authentic, sufficient, systematic, open and consistent.
  • Use scientific calculators or computers in order to derive formulae and solve problems in various contexts. 
    		•

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Core  65649   National Certificate: Official Statistics  Level 5  Level TBA: Pre-2009 was L5  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  PSETA 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS UNIT STANDARD: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    NONE 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.