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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD: 

Solve realistic and abstract numerical problems 
SAQA US ID UNIT STANDARD TITLE
13491  Solve realistic and abstract numerical problems 
ORIGINATOR
SGB Math. Literacy Mathematics and Math Sciences 
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
ABET Level 2  Regular-Fundamental  Below Level 1  Level TBA:Pre-2009 BelowL1  4 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2003-07-01  2006-06-30  SAQA 1043/02 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2007-06-30   2010-06-30  

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 for people who are able to apply basic mathematical principles and strategies to solve problems generally found in everyday contexts. People credited with this unit standard are able to solve problems involving whole numbers, decimals, fractions and percentages, and can demonstrate their ability to describe problems in mathematical language, develop their own strategies and validate solutions in terms of the context. 

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
'Demonstrate understanding of and use the number system';
'Solve simple realistic and abstract problems';
'Demonstrate and apply understanding of the number system'. 

UNIT STANDARD RANGE 
Problems are of an everyday nature and solvable through basic application of logic, mathematical principles, basic number concept and simple addition, subtraction, division and multiplication strategies. The problems include situations involving whole numbers up to 100 000, fractions with denominators of 2 to 10, three digit decimals and common percentages. 

Specific Outcomes and Assessment Criteria: 

SPECIFIC OUTCOME 1 
Solve problems involving addition, subtraction, multiplication and division of whole numbers. 
OUTCOME RANGE 
Problems include combining, separating, changing, comparing and equalising numbers. Sharing situations include equal and simple proportional sharing.
Problems are abstract or realistic and are given in the form of words and/or pictures and/or orally.
Mixed operations are limited to addition and subtraction.
Addition and subtraction for whole numbers up to at least 100 000.
Multiplication limited to whole numbers, at least the product of 2 digits by 1 digit and 2 digits by multiples of 10.
Division to involve situations of sharing and grouping of at least 3 digits by 1 or 2 digits, and 3 or 4 digits by multiples of 10, 100 or 1000. 

ASSESSMENT CRITERIA 

ASSESSMENT CRITERION 1 
1. The solution includes a description of the problem situation using words and/or symbols so that the description is consistent with the original problem. 

ASSESSMENT CRITERION 2 
2. The method used is consistent with the problem. 

ASSESSMENT CRITERION 3 
3. Mathematical symbols and symbols denoting quantity are used in terms of accepted conventions and non-standard symbols used are explained or used so that the meaning is clear. 

ASSESSMENT CRITERION 4 
4. Numbers are added, subtracted, multiplied and/or divided, or related operations are used and justified in accordance within the problem context. 

ASSESSMENT CRITERION 5 
5. The solution is verified in terms of the problem context. 

ASSESSMENT CRITERION 6 
6. Estimates of solutions and differences between exact and approximate solutions are justified in terms of methods used and the need for closeness of the estimate. 

ASSESSMENT CRITERION 7 
7. Simple equations involving addition, subtraction, multiplication and division are read and used in accordance with accepted conventions. 

ASSESSMENT CRITERION 8 
8. Simple equations involving addition, subtraction, multiplication and division are interpreted in realistic contexts. 

ASSESSMENT CRITERION 9 
9. The relationships between the various operations are established in terms of the equivalence of simple equations. 

SPECIFIC OUTCOME 2 
Use fractions, decimals and percentages to solve problems. 
OUTCOME RANGE 
Operations on fractions are limited to addition and subtraction of fractions with the same denominator.
Problems include fractional parts of shapes, lengths and quantities and establishing the equivalence of fractions.
Percentages include, but are not limited, to 5%, 10%, 20%, 25%, 40%, 50%, 60%, 75%, 80%, 100%.
Addition and subtraction of decimals up to at least 3 decimal places (digits).
Situations requiring multiplication of fractions are such that repeated addition is easily performed. 

ASSESSMENT CRITERIA 

ASSESSMENT CRITERION 1 
1. The solution includes a description of the problem situation using words and/or symbols so that the description is consistent with the original problem. 

ASSESSMENT CRITERION 2 
2. The method is consistent with the problem. 

ASSESSMENT CRITERION 3 
3. The solution is verified in terms of the problem context. 

ASSESSMENT CRITERION 4 
4. Simple equations involving addition and subtraction are used in accordance with accepted conventions and interpreted in realistic contexts. 

ASSESSMENT CRITERION 5 
5. The relationships between the various operations are established in terms of the equivalence of simple equations. 

ASSESSMENT CRITERION 6 
6. The size of fractional parts of shapes are close enough to exact sizes to make the fraction denoted clear, and the size of fractional parts of quantities or lengths are exactly correct. 

ASSESSMENT CRITERION 7 
7. Symbolic representations of fractions, decimals and percentages accord with recognised conventions and relate to one another. 
ASSESSMENT CRITERION RANGE 
Includes the following conventions:
  • ; 3/4; 0.75; 75%; 75/100
     
    		•

    ASSESSMENT CRITERION 8 
    8. Explanations of how to find fractions of shapes, lengths and quantities clarify the role of the denominator and numerator. 

    ASSESSMENT CRITERION 9 
    9. The language and names of fractions are used correctly. 
    ASSESSMENT CRITERION RANGE 
    Language includes half, third, quarter, halves, thirds, quarters, whole, equal parts, divide between, share.
     

    ASSESSMENT CRITERION 10 
    10. Descriptions of the uses of fractions, decimals and percentages are in line with everyday examples. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
    Evaluation of documentation and visit by SAQA or ETQA expert in the field of mathematics education.

    Moderation:
    According to system devised by the NSB. 

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
    Embedded knowledge is addressed as part of assessment criteria.
    Assessment of candidates must test the ability to do realistic and abstract problems. 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Solve problems. 

    UNIT STANDARD CCFO COMMUNICATING 
    Communicate effectively using visual, mathematical and language skills in the modes of oral and written presentations. 

    UNIT STANDARD CCFO DEMONSTRATING 
    Demonstrate an understanding of the world as a set of related systems. 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
    NONE 


    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.